From af8a3626e1c1178ef70f553af326d8469a68a0bf Mon Sep 17 00:00:00 2001
From: quantecon-services <services@quantecon.org>
Date: Tue, 30 May 2023 23:49:41 +0000
Subject: [PATCH] auto publishing updates to notebooks

---
 BCG_complete_mkts.ipynb           |  78 ++++-----
 BCG_incomplete_mkts.ipynb         | 104 ++++++------
 additive_functionals.ipynb        |  86 +++++-----
 amss.ipynb                        |  96 ++++++------
 amss2.ipynb                       | 106 ++++++-------
 amss3.ipynb                       | 128 +++++++--------
 arellano.ipynb                    |  88 +++++------
 arma.ipynb                        |  98 ++++++------
 asset_pricing_lph.ipynb           | 108 ++++++-------
 black_litterman.ipynb             |  62 ++++----
 calvo.ipynb                       | 116 +++++++-------
 cattle_cycles.ipynb               |  54 +++----
 chang_credible.ipynb              |  58 +++----
 chang_ramsey.ipynb                |  76 ++++-----
 classical_filtering.ipynb         |  70 ++++-----
 coase.ipynb                       |  82 +++++-----
 cons_news.ipynb                   |  78 ++++-----
 discrete_dp.ipynb                 | 206 ++++++++++++------------
 dyn_stack.ipynb                   | 252 ++++++++++++++++++------------
 entropy.ipynb                     |  38 ++---
 estspec.ipynb                     |  54 +++----
 five_preferences.ipynb            | 142 ++++++++---------
 growth_in_dles.ipynb              | 100 ++++++------
 hs_invertibility_example.ipynb    |  38 ++---
 hs_recursive_models.ipynb         | 104 ++++++------
 intro.ipynb                       |  24 +--
 irfs_in_hall_model.ipynb          |  54 +++----
 knowing_forecasts_of_others.ipynb | 146 ++++++++---------
 lqramsey.ipynb                    |  78 ++++-----
 lu_tricks.ipynb                   |  60 +++----
 lucas_asset_pricing_dles.ipynb    |  58 +++----
 lucas_model.ipynb                 |  66 ++++----
 markov_jump_lq.ipynb              | 122 +++++++--------
 matsuyama.ipynb                   |  54 +++----
 muth_kalman.ipynb                 |  54 +++----
 opt_tax_recur.ipynb               | 100 ++++++------
 orth_proj.ipynb                   |  90 +++++------
 permanent_income_dles.ipynb       |  30 ++--
 rob_markov_perf.ipynb             |  76 ++++-----
 robustness.ipynb                  |  64 ++++----
 rosen_schooling_model.ipynb       |  46 +++---
 smoothing.ipynb                   |  58 +++----
 smoothing_tax.ipynb               |  94 +++++------
 stationary_densities.ipynb        |  86 +++++-----
 status.ipynb                      | 106 ++++++-------
 tax_smoothing_1.ipynb             |  56 +++----
 tax_smoothing_2.ipynb             |  48 +++---
 tax_smoothing_3.ipynb             |  34 ++--
 troubleshooting.ipynb             |  14 +-
 un_insure.ipynb                   |  78 ++++-----
 zreferences.ipynb                 |   6 +-
 51 files changed, 2084 insertions(+), 2040 deletions(-)

diff --git a/BCG_complete_mkts.ipynb b/BCG_complete_mkts.ipynb
index 13a2cde..01108c2 100644
--- a/BCG_complete_mkts.ipynb
+++ b/BCG_complete_mkts.ipynb
@@ -2,7 +2,7 @@
  "cells": [
   {
    "cell_type": "markdown",
-   "id": "c8f45e6c",
+   "id": "96e9cc56",
    "metadata": {},
    "source": [
     "\n",
@@ -11,7 +11,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1083a206",
+   "id": "6d7f531e",
    "metadata": {},
    "source": [
     "# Irrelevance of Capital Structures with Complete Markets"
@@ -19,7 +19,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "65a38935",
+   "id": "43176217",
    "metadata": {},
    "source": [
     "## Contents\n",
@@ -32,7 +32,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "086c6212",
+   "id": "a5c5f040",
    "metadata": {},
    "source": [
     "In addition to what’s in Anaconda, this lecture will need the following libraries:"
@@ -41,7 +41,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "42c30913",
+   "id": "755b4403",
    "metadata": {
     "hide-output": false
    },
@@ -54,7 +54,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4032602f",
+   "id": "52e80252",
    "metadata": {},
    "source": [
     "## Introduction\n",
@@ -87,7 +87,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "162a9778",
+   "id": "e5addf3f",
    "metadata": {},
    "source": [
     "### Setup\n",
@@ -120,7 +120,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "2bf3f17f",
+   "id": "23bddf02",
    "metadata": {},
    "source": [
     "### Endowments\n",
@@ -145,7 +145,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3fd7714d",
+   "id": "12d913ed",
    "metadata": {},
    "source": [
     "### Technology:\n",
@@ -162,7 +162,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "09471949",
+   "id": "a6e54082",
    "metadata": {},
    "source": [
     "### Preferences:\n",
@@ -187,7 +187,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "371c9fa0",
+   "id": "01c4a1d8",
    "metadata": {},
    "source": [
     "### Parameterizations\n",
@@ -210,7 +210,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "06d226fa",
+   "id": "fcc1958b",
    "metadata": {},
    "source": [
     "### Pareto criterion and planning problem\n",
@@ -268,7 +268,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "2a36b95e",
+   "id": "1d80f034",
    "metadata": {},
    "source": [
     "### Helpful observations and bookkeeping\n",
@@ -349,7 +349,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "92a74505",
+   "id": "3d050ce8",
    "metadata": {},
    "source": [
     "#### Remarks\n",
@@ -368,7 +368,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b7ecc904",
+   "id": "4e73b4ef",
    "metadata": {},
    "source": [
     "## Competitive equilibrium\n",
@@ -387,7 +387,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7647dd50",
+   "id": "1ffc774a",
    "metadata": {},
    "source": [
     "### Measures of agents and firms\n",
@@ -439,7 +439,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "8569ee0d",
+   "id": "65f9cd11",
    "metadata": {},
    "source": [
     "#### Ownership\n",
@@ -479,7 +479,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7a297e57",
+   "id": "d7ff1d8c",
    "metadata": {},
    "source": [
     "#### Asset markets\n",
@@ -498,7 +498,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f59d1012",
+   "id": "11fd5dda",
    "metadata": {},
    "source": [
     "### Objects appearing in a competitive equilibrium\n",
@@ -527,7 +527,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7a55e935",
+   "id": "5401a369",
    "metadata": {},
    "source": [
     "### A representative firm’s problem\n",
@@ -574,7 +574,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d078980f",
+   "id": "94e74df6",
    "metadata": {},
    "source": [
     "### A consumer’s problem\n",
@@ -747,7 +747,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "0571b20d",
+   "id": "d7745e87",
    "metadata": {},
    "source": [
     "### Computing competitive equilibrium prices and quantities\n",
@@ -842,7 +842,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d5d8b029",
+   "id": "bda6a46f",
    "metadata": {},
    "source": [
     "### Modigliani-Miller theorem\n",
@@ -924,7 +924,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1050e6b7",
+   "id": "b757a100",
    "metadata": {},
    "source": [
     "## Code\n",
@@ -998,7 +998,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "2513d112",
+   "id": "b992013b",
    "metadata": {
     "hide-output": false
    },
@@ -1016,7 +1016,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "4deeda7c",
+   "id": "9752af83",
    "metadata": {
     "hide-output": false
    },
@@ -1211,7 +1211,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "dee2e65d",
+   "id": "a5965762",
    "metadata": {},
    "source": [
     "### Examples\n",
@@ -1221,7 +1221,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "692f41a3",
+   "id": "0bd8691c",
    "metadata": {},
    "source": [
     "#### 1st example\n",
@@ -1240,7 +1240,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "8b3a055f",
+   "id": "4c0f152b",
    "metadata": {
     "hide-output": false
    },
@@ -1253,7 +1253,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3272a03c",
+   "id": "4aff44e1",
    "metadata": {},
    "source": [
     "Let’s plot the agents’ time-1 endowments with respect to shocks to see\n",
@@ -1263,7 +1263,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "a5668c83",
+   "id": "8876d17a",
    "metadata": {
     "hide-output": false
    },
@@ -1300,7 +1300,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "52e482c1",
+   "id": "aae8b648",
    "metadata": {},
    "source": [
     "Let’s also compare the optimal capital stock, $ k $, and optimal\n",
@@ -1310,7 +1310,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "df0b62e5",
+   "id": "78413cc2",
    "metadata": {
     "hide-output": false
    },
@@ -1333,7 +1333,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5bebe1fb",
+   "id": "5aeb5dfd",
    "metadata": {},
    "source": [
     "#### 2nd example\n",
@@ -1348,7 +1348,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "6b654fa7",
+   "id": "3b12e2f8",
    "metadata": {
     "hide-output": false
    },
@@ -1380,7 +1380,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "4da55ccc",
+   "id": "b17f6cdf",
    "metadata": {
     "hide-output": false
    },
@@ -1393,7 +1393,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "13a3e561",
+   "id": "3d0550d2",
    "metadata": {
     "hide-output": false
    },
@@ -1407,7 +1407,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "5b4bc1a4",
+   "id": "d0c118ef",
    "metadata": {
     "hide-output": false
    },
@@ -1438,7 +1438,7 @@
   }
  ],
  "metadata": {
-  "date": 1680677523.0149946,
+  "date": 1685490450.0954695,
   "filename": "BCG_complete_mkts.md",
   "kernelspec": {
    "display_name": "Python",
diff --git a/BCG_incomplete_mkts.ipynb b/BCG_incomplete_mkts.ipynb
index 1f3464a..904cd2a 100644
--- a/BCG_incomplete_mkts.ipynb
+++ b/BCG_incomplete_mkts.ipynb
@@ -2,7 +2,7 @@
  "cells": [
   {
    "cell_type": "markdown",
-   "id": "6cbf990a",
+   "id": "c7b29cca",
    "metadata": {},
    "source": [
     "\n",
@@ -11,7 +11,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "30b7128c",
+   "id": "4bc31f30",
    "metadata": {},
    "source": [
     "# Equilibrium Capital Structures with Incomplete Markets"
@@ -19,7 +19,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "68cbb00c",
+   "id": "6976cdc4",
    "metadata": {},
    "source": [
     "## Contents\n",
@@ -36,7 +36,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "564a07a6",
+   "id": "9dfefadd",
    "metadata": {},
    "source": [
     "In addition to what’s in Anaconda, this lecture will need the following libraries:"
@@ -45,7 +45,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "66417401",
+   "id": "5b34e5b6",
    "metadata": {
     "hide-output": false
    },
@@ -58,7 +58,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "64a6627b",
+   "id": "248de70e",
    "metadata": {},
    "source": [
     "## Introduction\n",
@@ -109,7 +109,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "57b94157",
+   "id": "a307283f",
    "metadata": {},
    "source": [
     "### Setup\n",
@@ -133,7 +133,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3edca186",
+   "id": "46b48e6c",
    "metadata": {},
    "source": [
     "### Ownership\n",
@@ -148,7 +148,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "eb99fc80",
+   "id": "24dbcf88",
    "metadata": {},
    "source": [
     "### Measures of agents and firms\n",
@@ -225,7 +225,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e3ac6dca",
+   "id": "69e4f455",
    "metadata": {},
    "source": [
     "### Endowments\n",
@@ -242,7 +242,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "45593c21",
+   "id": "2934638a",
    "metadata": {},
    "source": [
     "### Feasibility:\n",
@@ -261,7 +261,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "50a568fb",
+   "id": "6ba859a3",
    "metadata": {},
    "source": [
     "### Parameterizations\n",
@@ -284,7 +284,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "04cc77ea",
+   "id": "a97ca9fe",
    "metadata": {},
    "source": [
     "### Preferences:\n",
@@ -309,7 +309,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "43b08fcd",
+   "id": "de52fe58",
    "metadata": {},
    "source": [
     "### Risk-sharing motives\n",
@@ -329,7 +329,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f8d10c43",
+   "id": "de82f252",
    "metadata": {},
    "source": [
     "## Asset Markets\n",
@@ -385,7 +385,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "61510a56",
+   "id": "442455a2",
    "metadata": {},
    "source": [
     "### Consumers\n",
@@ -476,7 +476,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "22029450",
+   "id": "4ecdfdae",
    "metadata": {},
    "source": [
     "### Pricing functions\n",
@@ -515,7 +515,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5451e262",
+   "id": "e516fbd6",
    "metadata": {},
    "source": [
     "### Firms\n",
@@ -572,7 +572,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c3dd91cf",
+   "id": "cc653188",
    "metadata": {},
    "source": [
     "#### Firm’s optimization problem\n",
@@ -645,7 +645,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7431acec",
+   "id": "4f9f0ae6",
    "metadata": {},
    "source": [
     "## Equilibrium verification\n",
@@ -672,7 +672,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "406ffaf5",
+   "id": "1779f5f1",
    "metadata": {},
    "source": [
     "## Pseudo Code\n",
@@ -770,7 +770,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "2dbfe3f1",
+   "id": "a93d401b",
    "metadata": {},
    "source": [
     "## Code\n",
@@ -817,7 +817,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "532b1330",
+   "id": "7c8ff17c",
    "metadata": {
     "hide-output": false
    },
@@ -836,7 +836,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "b6492f1f",
+   "id": "1b00f97a",
    "metadata": {
     "hide-output": false
    },
@@ -1329,7 +1329,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "2a426622",
+   "id": "ebbed204",
    "metadata": {},
    "source": [
     "## Examples\n",
@@ -1339,7 +1339,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "97dfc9e2",
+   "id": "9de713f2",
    "metadata": {},
    "source": [
     "### First example\n",
@@ -1351,7 +1351,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "db54c073",
+   "id": "b13fb60f",
    "metadata": {
     "hide-output": false
    },
@@ -1364,7 +1364,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "b81e84a0",
+   "id": "c24d2afe",
    "metadata": {
     "hide-output": false
    },
@@ -1377,7 +1377,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "0f9215f4",
+   "id": "2b8bd3a7",
    "metadata": {},
    "source": [
     "Python reports to us that the equilibrium firm value is $ V=0.101 $,\n",
@@ -1394,7 +1394,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "fcaf1a49",
+   "id": "02a1e25a",
    "metadata": {
     "hide-output": false
    },
@@ -1408,7 +1408,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "697df849",
+   "id": "5532bc6b",
    "metadata": {},
    "source": [
     "Up to the approximation involved in using a discrete grid, these numbers\n",
@@ -1425,7 +1425,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "431d4a04",
+   "id": "79246efc",
    "metadata": {
     "hide-output": false
    },
@@ -1466,7 +1466,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "36cae3a8",
+   "id": "f703a8ff",
    "metadata": {},
    "source": [
     "#### A Modigliani-Miller theorem?\n",
@@ -1561,7 +1561,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "b79cb454",
+   "id": "0dfc7d36",
    "metadata": {
     "hide-output": false
    },
@@ -1785,7 +1785,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "69d174b1",
+   "id": "1649c9ca",
    "metadata": {},
    "source": [
     "Here is our strategy for checking *stability* of an equilibrium.\n",
@@ -1811,7 +1811,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "d2ba3182",
+   "id": "9ddde123",
    "metadata": {
     "hide-output": false
    },
@@ -1859,7 +1859,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "edfb338c",
+   "id": "5623e018",
    "metadata": {},
    "source": [
     "In the above 3D surface of prospective firm valuations, the perturbed\n",
@@ -1877,7 +1877,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "e58cf65f",
+   "id": "1ee06248",
    "metadata": {
     "hide-output": false
    },
@@ -1924,7 +1924,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "418ba551",
+   "id": "773eb9b8",
    "metadata": {},
    "source": [
     "In contrast to $ (k^*,b^* - e) $, the 3D surface for\n",
@@ -1944,7 +1944,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "76c9ffce",
+   "id": "a27d5165",
    "metadata": {
     "hide-output": false
    },
@@ -1955,7 +1955,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "db0d518b",
+   "id": "6d4cbf46",
    "metadata": {},
    "source": [
     "Our two *stability experiments* suggest that the equilibrium capital\n",
@@ -1969,7 +1969,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "23699433",
+   "id": "e3a87712",
    "metadata": {},
    "source": [
     "#### Equilibrium equity and bond price functions\n",
@@ -1982,7 +1982,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "57c581c7",
+   "id": "3b9e332a",
    "metadata": {
     "hide-output": false
    },
@@ -2020,7 +2020,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "91c99424",
+   "id": "78146637",
    "metadata": {
     "hide-output": false
    },
@@ -2057,7 +2057,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6386139e",
+   "id": "540ff0fe",
    "metadata": {},
    "source": [
     "### Comments on equilibrium pricing functions\n",
@@ -2073,7 +2073,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "da972492",
+   "id": "9019e726",
    "metadata": {},
    "source": [
     "### Another example economy\n",
@@ -2099,7 +2099,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "c9673884",
+   "id": "03b9a905",
    "metadata": {
     "hide-output": false
    },
@@ -2154,7 +2154,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "df8046cb",
+   "id": "75e89b35",
    "metadata": {
     "hide-output": false
    },
@@ -2193,7 +2193,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "de9cf3c5",
+   "id": "fbcdd130",
    "metadata": {},
    "source": [
     "## A picture worth a thousand words\n",
@@ -2213,7 +2213,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "251bde7a",
+   "id": "2bfeb3b6",
    "metadata": {
     "hide-output": false
    },
@@ -2245,7 +2245,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c0366383",
+   "id": "83646a14",
    "metadata": {},
    "source": [
     "It is rewarding to stare at the above plots too.\n",
@@ -2261,7 +2261,7 @@
   }
  ],
  "metadata": {
-  "date": 1680677523.1082954,
+  "date": 1685490450.1857154,
   "filename": "BCG_incomplete_mkts.md",
   "kernelspec": {
    "display_name": "Python",
diff --git a/additive_functionals.ipynb b/additive_functionals.ipynb
index c448a42..0f11653 100644
--- a/additive_functionals.ipynb
+++ b/additive_functionals.ipynb
@@ -2,7 +2,7 @@
  "cells": [
   {
    "cell_type": "markdown",
-   "id": "d0d5f37d",
+   "id": "b77d1432",
    "metadata": {},
    "source": [
     "\n",
@@ -11,7 +11,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "97d368d9",
+   "id": "da982747",
    "metadata": {},
    "source": [
     "# Additive and Multiplicative Functionals\n",
@@ -22,7 +22,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ffd3ad8a",
+   "id": "47f55475",
    "metadata": {},
    "source": [
     "## Contents\n",
@@ -37,7 +37,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f3accf71",
+   "id": "0e695a83",
    "metadata": {},
    "source": [
     "In addition to what’s in Anaconda, this lecture will need the following libraries:"
@@ -46,7 +46,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "1a16f571",
+   "id": "890e8e35",
    "metadata": {
     "hide-output": false
    },
@@ -57,7 +57,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "068390e3",
+   "id": "78561324",
    "metadata": {},
    "source": [
     "## Overview\n",
@@ -68,11 +68,9 @@
     "\n",
     "Asymptotic stationarity and ergodicity are key assumptions needed to make it possible to learn by applying statistical methods.\n",
     "\n",
-    "Are there ways to model time series that have persistent growth that still enable statistical learning based on a law of large numbers for an asymptotically stationary and ergodic process?\n",
+    "But  there are good ways to model time series that have persistent growth that still enable statistical learning based on a law of large numbers for an asymptotically stationary and ergodic process.\n",
     "\n",
-    "The answer provided by Hansen  [[Han12](https://python-advanced.quantecon.org/zreferences.html#id240)] is yes.\n",
-    "\n",
-    "He described  two classes of time series models that accommodate growth.\n",
+    "Thus, [[Han12](https://python-advanced.quantecon.org/zreferences.html#id240)]  described  two classes of time series models that accommodate growth.\n",
     "\n",
     "They are\n",
     "\n",
@@ -104,7 +102,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "f227aa5c",
+   "id": "41544fd5",
    "metadata": {
     "hide-output": false
    },
@@ -121,7 +119,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "af1e2879",
+   "id": "7be39c0f",
    "metadata": {},
    "source": [
     "## A Particular Additive Functional\n",
@@ -175,7 +173,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "82d56821",
+   "id": "338b4793",
    "metadata": {},
    "source": [
     "### Linear State-Space Representation\n",
@@ -246,7 +244,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "8756b2cd",
+   "id": "e57b02bc",
    "metadata": {},
    "source": [
     "## Dynamics\n",
@@ -295,7 +293,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e4ed5427",
+   "id": "b8ff0152",
    "metadata": {},
    "source": [
     "### Simulation\n",
@@ -313,7 +311,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "c23bcf59",
+   "id": "97896573",
    "metadata": {
     "hide-output": false
    },
@@ -473,7 +471,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "74f4d9ce",
+   "id": "8d2274e9",
    "metadata": {},
    "source": [
     "#### Plotting\n",
@@ -484,7 +482,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "e38e3f7e",
+   "id": "c1fcfc04",
    "metadata": {
     "hide-output": false
    },
@@ -767,7 +765,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "25d3a22c",
+   "id": "96012a1b",
    "metadata": {},
    "source": [
     "For now, we just plot $ y_t $ and $ x_t $, postponing until later a description of exactly how we compute them.\n",
@@ -779,7 +777,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "eeb2f069",
+   "id": "2890320e",
    "metadata": {
     "hide-output": false
    },
@@ -818,7 +816,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "0c60d5bc",
+   "id": "2575a2fa",
    "metadata": {},
    "source": [
     "Notice the irregular but persistent growth in $ y_t $."
@@ -826,7 +824,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "cb8941d3",
+   "id": "0ffb5e1d",
    "metadata": {},
    "source": [
     "### Decomposition\n",
@@ -962,7 +960,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "62bf1381",
+   "id": "86f2ca73",
    "metadata": {},
    "source": [
     "## Code\n",
@@ -985,7 +983,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "40a40473",
+   "id": "96b9a271",
    "metadata": {
     "hide-output": false
    },
@@ -997,7 +995,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "2e8c0f35",
+   "id": "11838bf3",
    "metadata": {},
    "source": [
     "When we plot multiple realizations of a component in the 2nd, 3rd, and 4th panels, we also plot the population 95% probability coverage sets computed using the LinearStateSpace class.\n",
@@ -1014,7 +1012,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4bfb9a5b",
+   "id": "e1903510",
    "metadata": {},
    "source": [
     "### Associated Multiplicative Functional\n",
@@ -1061,7 +1059,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "f94b92df",
+   "id": "a6fe0784",
    "metadata": {
     "hide-output": false
    },
@@ -1073,7 +1071,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "fab0629f",
+   "id": "10eb935e",
    "metadata": {},
    "source": [
     "As before, when we plotted multiple realizations of a component in the 2nd, 3rd, and 4th panels, we also plotted population 95% confidence bands computed using the LinearStateSpace class.\n",
@@ -1091,7 +1089,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d0f8658a",
+   "id": "26ee32f7",
    "metadata": {},
    "source": [
     "### Peculiar Large Sample Property\n",
@@ -1116,7 +1114,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "cede538a",
+   "id": "d505dd35",
    "metadata": {
     "hide-output": false
    },
@@ -1129,7 +1127,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b391f98f",
+   "id": "4bde63e6",
    "metadata": {},
    "source": [
     "The dotted line in the above graph is the mean $ E \\tilde M_t = 1 $ of the martingale.\n",
@@ -1141,7 +1139,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b2a4cc79",
+   "id": "107332c6",
    "metadata": {},
    "source": [
     "## More About the Multiplicative Martingale\n",
@@ -1162,7 +1160,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "dbd4beb0",
+   "id": "7833bf89",
    "metadata": {},
    "source": [
     "### Simulating a Multiplicative Martingale Again\n",
@@ -1179,7 +1177,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "8c71acc0",
+   "id": "a1aaf79c",
    "metadata": {},
    "source": [
     "### Sample Paths\n",
@@ -1192,7 +1190,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "d647d328",
+   "id": "6355c47b",
    "metadata": {
     "hide-output": false
    },
@@ -1304,7 +1302,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f395d1e4",
+   "id": "519d3fe3",
    "metadata": {},
    "source": [
     "The heavy lifting is done inside the `AMF_LSS_VAR` class.\n",
@@ -1315,7 +1313,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "0672fa93",
+   "id": "085ae708",
    "metadata": {
     "hide-output": false
    },
@@ -1365,7 +1363,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ecebf779",
+   "id": "1a43750d",
    "metadata": {},
    "source": [
     "Now that we have these functions in our toolkit, let’s apply them to run some\n",
@@ -1375,7 +1373,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "3df93f6e",
+   "id": "1a6bf5db",
    "metadata": {
     "hide-output": false
    },
@@ -1418,7 +1416,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4179851d",
+   "id": "81b576ff",
    "metadata": {},
    "source": [
     "Let’s plot the probability density functions for $ \\log {\\widetilde M}_t $ for\n",
@@ -1445,7 +1443,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "545d9e9b",
+   "id": "f8737f92",
    "metadata": {
     "hide-output": false
    },
@@ -1500,7 +1498,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "61674988",
+   "id": "8a370b06",
    "metadata": {},
    "source": [
     "These probability density functions help us understand mechanics underlying the  **peculiar property** of our multiplicative martingale\n",
@@ -1515,7 +1513,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "17e65361",
+   "id": "cdfa5edf",
    "metadata": {},
    "source": [
     "### Multiplicative Martingale as Likelihood Ratio Process\n",
@@ -1531,7 +1529,7 @@
   }
  ],
  "metadata": {
-  "date": 1680677523.1599522,
+  "date": 1685490450.2383587,
   "filename": "additive_functionals.md",
   "kernelspec": {
    "display_name": "Python",
diff --git a/amss.ipynb b/amss.ipynb
index c4493cd..cc020ce 100644
--- a/amss.ipynb
+++ b/amss.ipynb
@@ -2,7 +2,7 @@
  "cells": [
   {
    "cell_type": "markdown",
-   "id": "fd13a8d7",
+   "id": "2c445c5e",
    "metadata": {},
    "source": [
     "\n",
@@ -11,7 +11,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "dde89be0",
+   "id": "61eda6ad",
    "metadata": {},
    "source": [
     "# Optimal Taxation without State-Contingent Debt"
@@ -19,7 +19,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "22af500f",
+   "id": "b6c379fa",
    "metadata": {},
    "source": [
     "## Contents\n",
@@ -33,7 +33,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "fbb36d50",
+   "id": "a2162af0",
    "metadata": {},
    "source": [
     "In addition to what’s in Anaconda, this lecture will need the following libraries:"
@@ -42,7 +42,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "f0c6ff2e",
+   "id": "260bfa16",
    "metadata": {
     "hide-output": false
    },
@@ -54,7 +54,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1d038810",
+   "id": "d86de9e5",
    "metadata": {},
    "source": [
     "## Overview\n",
@@ -65,7 +65,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "eabbcebe",
+   "id": "80e4a037",
    "metadata": {
     "hide-output": false
    },
@@ -84,7 +84,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "cc378590",
+   "id": "29a77631",
    "metadata": {},
    "source": [
     "In [an earlier lecture](https://python-advanced.quantecon.org/opt_tax_recur.html), we described a model of\n",
@@ -108,7 +108,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "344ef417",
+   "id": "a3434ee5",
    "metadata": {},
    "source": [
     "## Competitive Equilibrium with Distorting Taxes\n",
@@ -172,7 +172,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9f97f913",
+   "id": "590c99ad",
    "metadata": {},
    "source": [
     "### Risk-free One-Period Debt Only\n",
@@ -306,7 +306,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "25770fcf",
+   "id": "39630f00",
    "metadata": {},
    "source": [
     "### Comparison with Lucas-Stokey Economy\n",
@@ -322,7 +322,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b2a1aa41",
+   "id": "bd71e726",
    "metadata": {},
    "source": [
     "### Ramsey Problem Without State-contingent Debt\n",
@@ -360,7 +360,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4f2824d0",
+   "id": "2322f095",
    "metadata": {},
    "source": [
     "#### Lagrangian Formulation\n",
@@ -396,7 +396,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "2637c08c",
+   "id": "8087dbee",
    "metadata": {},
    "source": [
     "### Some Calculations\n",
@@ -486,7 +486,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "8c80ed75",
+   "id": "382cba44",
    "metadata": {
     "hide-output": false
    },
@@ -694,7 +694,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d6b6ab75",
+   "id": "9b6b0006",
    "metadata": {},
    "source": [
     "To analyze the AMSS model, we find it useful to adopt a recursive formulation\n",
@@ -703,7 +703,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9fa0c346",
+   "id": "2eadb70d",
    "metadata": {},
    "source": [
     "## Recursive Version of AMSS Model\n",
@@ -726,7 +726,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b3b97878",
+   "id": "46aea9f8",
    "metadata": {},
    "source": [
     "### Recasting State Variables\n",
@@ -795,7 +795,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "bdcf36af",
+   "id": "ed0aab89",
    "metadata": {},
    "source": [
     "### Measurability Constraints\n",
@@ -824,7 +824,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d5cd1475",
+   "id": "1ec609c7",
    "metadata": {},
    "source": [
     "### Two Bellman Equations\n",
@@ -888,7 +888,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "71b1fb61",
+   "id": "c1b29793",
    "metadata": {},
    "source": [
     "### Martingale Supercedes State-Variable Degeneracy\n",
@@ -937,7 +937,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "2b4d6662",
+   "id": "2bcbbf24",
    "metadata": {},
    "source": [
     "### Exercise 43.1\n",
@@ -949,7 +949,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "989c7085",
+   "id": "722b9d69",
    "metadata": {},
    "source": [
     "### Absence of State Variable Degeneracy\n",
@@ -978,7 +978,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "fd3af1bc",
+   "id": "e5dd26fa",
    "metadata": {},
    "source": [
     "### Digression on Non-negative Transfers\n",
@@ -1015,7 +1015,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "246e04fa",
+   "id": "436577de",
    "metadata": {},
    "source": [
     "### Code\n",
@@ -1026,7 +1026,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "6fcad146",
+   "id": "98016258",
    "metadata": {
     "hide-output": false
    },
@@ -1248,7 +1248,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "dcf2ac9f",
+   "id": "aa934255",
    "metadata": {},
    "source": [
     "## Examples\n",
@@ -1258,7 +1258,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "87312fde",
+   "id": "f6d800df",
    "metadata": {},
    "source": [
     "### Anticipated One-Period War\n",
@@ -1324,7 +1324,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "712f77b5",
+   "id": "e7217651",
    "metadata": {
     "hide-output": false
    },
@@ -1380,7 +1380,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "71d07e41",
+   "id": "e85b0bc9",
    "metadata": {},
    "source": [
     "The following figure plots  Ramsey plans under complete and incomplete\n",
@@ -1396,7 +1396,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "0a44ef20",
+   "id": "b1daabe7",
    "metadata": {
     "hide-output": false
    },
@@ -1432,7 +1432,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "4f51c460",
+   "id": "294c34e2",
    "metadata": {
     "hide-output": false
    },
@@ -1454,7 +1454,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "2638173c",
+   "id": "108bfa84",
    "metadata": {
     "hide-output": false
    },
@@ -1468,7 +1468,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "42545a12",
+   "id": "2479aa03",
    "metadata": {
     "hide-output": false
    },
@@ -1481,7 +1481,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "d2722d59",
+   "id": "949416b5",
    "metadata": {
     "hide-output": false
    },
@@ -1515,7 +1515,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "03aff1e8",
+   "id": "db4d7e24",
    "metadata": {},
    "source": [
     "How a Ramsey planner responds to  war depends on the structure of the asset market.\n",
@@ -1559,7 +1559,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f2045fab",
+   "id": "1b42166f",
    "metadata": {},
    "source": [
     "#### Perpetual War Alert\n",
@@ -1584,7 +1584,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "a03b43ce",
+   "id": "bf948aa1",
    "metadata": {
     "hide-output": false
    },
@@ -1630,7 +1630,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "117ea915",
+   "id": "3d5e0b14",
    "metadata": {},
    "source": [
     "With these preferences, Ramsey tax rates will vary even in the Lucas-Stokey\n",
@@ -1644,7 +1644,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "496789f2",
+   "id": "3a38a9a1",
    "metadata": {
     "hide-output": false
    },
@@ -1681,7 +1681,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "d45463e0",
+   "id": "653ee697",
    "metadata": {
     "hide-output": false
    },
@@ -1696,7 +1696,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "946cdfb8",
+   "id": "374f12db",
    "metadata": {
     "hide-output": false
    },
@@ -1708,7 +1708,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "1bfbcbc5",
+   "id": "9068e7cd",
    "metadata": {
     "hide-output": false
    },
@@ -1740,7 +1740,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "921466cd",
+   "id": "c245b271",
    "metadata": {},
    "source": [
     "When the government experiences a prolonged period of peace, it is able to reduce\n",
@@ -1762,7 +1762,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "2f6e2ada",
+   "id": "8caf01c6",
    "metadata": {
     "hide-output": false
    },
@@ -1778,7 +1778,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "bacf7efa",
+   "id": "5742d454",
    "metadata": {
     "hide-output": false
    },
@@ -1806,7 +1806,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "cb204a8d",
+   "id": "106c5a73",
    "metadata": {},
    "source": [
     "<p><a id=fn-a href=#fn-a-link><strong>[1]</strong></a> In an allocation that solves the Ramsey problem and that levies distorting\n",
@@ -1826,7 +1826,7 @@
   }
  ],
  "metadata": {
-  "date": 1680677523.2296166,
+  "date": 1685490450.3090146,
   "filename": "amss.md",
   "kernelspec": {
    "display_name": "Python",
diff --git a/amss2.ipynb b/amss2.ipynb
index 1b75af3..69e1688 100644
--- a/amss2.ipynb
+++ b/amss2.ipynb
@@ -2,7 +2,7 @@
  "cells": [
   {
    "cell_type": "markdown",
-   "id": "a4af84de",
+   "id": "67187299",
    "metadata": {},
    "source": [
     "\n",
@@ -11,7 +11,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7c334839",
+   "id": "fcf54a75",
    "metadata": {},
    "source": [
     "# Fluctuating Interest Rates Deliver Fiscal Insurance"
@@ -19,7 +19,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3933b36f",
+   "id": "ce058d5c",
    "metadata": {},
    "source": [
     "## Contents\n",
@@ -38,7 +38,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c368d3c6",
+   "id": "32391475",
    "metadata": {},
    "source": [
     "In addition to what’s in Anaconda, this lecture will need the following libraries:"
@@ -47,7 +47,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "47d6de40",
+   "id": "f7768436",
    "metadata": {
     "hide-output": false
    },
@@ -58,7 +58,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f0db6835",
+   "id": "0f5f881e",
    "metadata": {},
    "source": [
     "## Overview\n",
@@ -120,7 +120,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "d6575a8f",
+   "id": "dad3b15d",
    "metadata": {
     "hide-output": false
    },
@@ -133,7 +133,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "05bf8cf7",
+   "id": "a49779ba",
    "metadata": {},
    "source": [
     "## Forces at Work\n",
@@ -163,7 +163,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f2fc6a64",
+   "id": "b071ecfc",
    "metadata": {},
    "source": [
     "## Logical Flow of Lecture\n",
@@ -183,7 +183,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3a03b468",
+   "id": "8c2e61dd",
    "metadata": {},
    "source": [
     "### Equations from Lucas-Stokey (1983) Model\n",
@@ -252,7 +252,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c0608f44",
+   "id": "d85e16e8",
    "metadata": {},
    "source": [
     "### Specification with CRRA Utility\n",
@@ -310,7 +310,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "553eab23",
+   "id": "6b375d74",
    "metadata": {
     "hide-output": false
    },
@@ -358,7 +358,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "689a6963",
+   "id": "50113d5a",
    "metadata": {},
    "source": [
     "## Example Economy\n",
@@ -392,7 +392,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "5e15bc91",
+   "id": "4370f199",
    "metadata": {
     "hide-output": false
    },
@@ -561,7 +561,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "fbf1d171",
+   "id": "4fbb3aa5",
    "metadata": {
     "hide-output": false
    },
@@ -870,7 +870,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "9822a018",
+   "id": "67d5ff11",
    "metadata": {
     "hide-output": false
    },
@@ -949,7 +949,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e0ff55c8",
+   "id": "3a97c8c9",
    "metadata": {},
    "source": [
     "## Reverse Engineering Strategy\n",
@@ -1000,7 +1000,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b3c72ae7",
+   "id": "93ec54f9",
    "metadata": {},
    "source": [
     "## Code for Reverse Engineering\n",
@@ -1011,7 +1011,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "df99f914",
+   "id": "7905ac3d",
    "metadata": {
     "hide-output": false
    },
@@ -1057,7 +1057,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f02cdca4",
+   "id": "efe3672b",
    "metadata": {},
    "source": [
     "To recover and print out $ \\bar b $"
@@ -1066,7 +1066,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "03e0e335",
+   "id": "841d6af2",
    "metadata": {
     "hide-output": false
    },
@@ -1078,7 +1078,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b636ef4c",
+   "id": "4a254fb1",
    "metadata": {},
    "source": [
     "To complete the reverse engineering exercise by jointly determining $ c_0, b_0 $,  we\n",
@@ -1088,7 +1088,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "363c4fcb",
+   "id": "c5578bf6",
    "metadata": {
     "hide-output": false
    },
@@ -1115,7 +1115,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "46b77a85",
+   "id": "33ef2a73",
    "metadata": {},
    "source": [
     "To solve the equations for $ c_0, b_0 $, we use SciPy’s fsolve function"
@@ -1124,7 +1124,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "6e7d6a9c",
+   "id": "850fcbd9",
    "metadata": {
     "hide-output": false
    },
@@ -1137,7 +1137,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "914fcfa0",
+   "id": "75e59653",
    "metadata": {},
    "source": [
     "Thus, we have reverse engineered an initial $ b0 = -1.038698407551764 $ that ought to render the AMSS measurability constraints slack."
@@ -1145,7 +1145,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c589918b",
+   "id": "0ad6bc3c",
    "metadata": {},
    "source": [
     "## Short Simulation for Reverse-engineered: Initial Debt\n",
@@ -1159,7 +1159,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "d8ba8712",
+   "id": "80068dac",
    "metadata": {
     "hide-output": false
    },
@@ -1207,7 +1207,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ae2c6ecb",
+   "id": "178ab562",
    "metadata": {},
    "source": [
     "The Ramsey allocations and Ramsey outcomes are **identical** for the Lucas-Stokey and AMSS economies.\n",
@@ -1221,7 +1221,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "66bb70f3",
+   "id": "d85580bd",
    "metadata": {},
    "source": [
     "## Long Simulation\n",
@@ -1256,7 +1256,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "9e53946d",
+   "id": "8a31c6ab",
    "metadata": {
     "hide-output": false
    },
@@ -1284,7 +1284,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a5568ae4",
+   "id": "bcdab763",
    "metadata": {},
    "source": [
     "### Remarks about Long Simulation\n",
@@ -1305,7 +1305,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6c650de0",
+   "id": "a5b4360a",
    "metadata": {},
    "source": [
     "## BEGS Approximations of Limiting Debt and Convergence Rate\n",
@@ -1348,7 +1348,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1d2fc8c6",
+   "id": "0019793c",
    "metadata": {},
    "source": [
     "### Asymptotic Mean\n",
@@ -1388,7 +1388,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "cc9e1555",
+   "id": "983a7776",
    "metadata": {},
    "source": [
     "### Rate of Convergence\n",
@@ -1406,7 +1406,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "49cb6474",
+   "id": "08ee9bc4",
    "metadata": {},
    "source": [
     "### Formulas and Code Details\n",
@@ -1454,7 +1454,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "797b8d3d",
+   "id": "e7d0db78",
    "metadata": {
     "hide-output": false
    },
@@ -1476,7 +1476,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6dbadd23",
+   "id": "43a16d03",
    "metadata": {},
    "source": [
     "Now let’s form the two random variables $ {\\mathcal R}, {\\mathcal X} $ appearing in the BEGS approximating formulas"
@@ -1485,7 +1485,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "c0e67d6a",
+   "id": "84a4b2f6",
    "metadata": {
     "hide-output": false
    },
@@ -1511,7 +1511,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ea615989",
+   "id": "d8199290",
    "metadata": {},
    "source": [
     "Now let’s compute the ingredient of the approximating limit and the approximating rate of convergence"
@@ -1520,7 +1520,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "eef031b8",
+   "id": "4f349b3c",
    "metadata": {
     "hide-output": false
    },
@@ -1534,7 +1534,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "743a3a2e",
+   "id": "d9e6699a",
    "metadata": {},
    "source": [
     "Print out $ \\hat b $ and $ \\bar b $"
@@ -1543,7 +1543,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "dbfb8bc9",
+   "id": "18bf8df1",
    "metadata": {
     "hide-output": false
    },
@@ -1554,7 +1554,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "0b43ab4d",
+   "id": "696a0ffd",
    "metadata": {},
    "source": [
     "So we have"
@@ -1563,7 +1563,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "dcb46bf9",
+   "id": "926c55b2",
    "metadata": {
     "hide-output": false
    },
@@ -1574,7 +1574,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "0c1b4dda",
+   "id": "38fc2ef7",
    "metadata": {},
    "source": [
     "These outcomes show that $ \\hat b $ does a remarkably good job of approximating $ \\bar b $.\n",
@@ -1585,7 +1585,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "562d17eb",
+   "id": "fb8a65cb",
    "metadata": {
     "hide-output": false
    },
@@ -1597,7 +1597,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "464b0ccc",
+   "id": "101a4229",
    "metadata": {},
    "source": [
     "This is *machine zero*, a verification that $ \\hat b $ succeeds in minimizing the nonnegative fiscal cost criterion $ J ( {\\mathcal B}^*) $ defined in\n",
@@ -1609,7 +1609,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "afe2c8d7",
+   "id": "98ccfce6",
    "metadata": {
     "hide-output": false
    },
@@ -1622,7 +1622,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "14602ab3",
+   "id": "ac1ce1ed",
    "metadata": {},
    "source": [
     "Now let’s compute the implied meantime to get to within 0.01 of the limit"
@@ -1631,7 +1631,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "36951e86",
+   "id": "7cf4a9cb",
    "metadata": {
     "hide-output": false
    },
@@ -1643,7 +1643,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "cf4e58ed",
+   "id": "17693f71",
    "metadata": {},
    "source": [
     "The slow rate of convergence and the implied time of getting within one percent of the limiting value do a good job of approximating\n",
@@ -1654,7 +1654,7 @@
   }
  ],
  "metadata": {
-  "date": 1680677523.4979053,
+  "date": 1685490450.5272586,
   "filename": "amss2.md",
   "kernelspec": {
    "display_name": "Python",
diff --git a/amss3.ipynb b/amss3.ipynb
index 846bfb6..86ec562 100644
--- a/amss3.ipynb
+++ b/amss3.ipynb
@@ -2,7 +2,7 @@
  "cells": [
   {
    "cell_type": "markdown",
-   "id": "f06094d4",
+   "id": "6e462098",
    "metadata": {},
    "source": [
     "\n",
@@ -11,7 +11,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "cc21e715",
+   "id": "7f82d3b6",
    "metadata": {},
    "source": [
     "# Fiscal Risk and Government Debt"
@@ -19,7 +19,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "583b6f3f",
+   "id": "3b6788db",
    "metadata": {},
    "source": [
     "## Contents\n",
@@ -33,7 +33,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a4171932",
+   "id": "e67d90c7",
    "metadata": {},
    "source": [
     "In addition to what’s in Anaconda, this lecture will need the following libraries:"
@@ -42,7 +42,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "0894ffbe",
+   "id": "1a6cb217",
    "metadata": {
     "hide-output": false
    },
@@ -53,7 +53,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "cafef4a4",
+   "id": "b8f7a0fe",
    "metadata": {},
    "source": [
     "## Overview\n",
@@ -101,7 +101,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "06e0119c",
+   "id": "d9bf6b5c",
    "metadata": {
     "hide-output": false
    },
@@ -114,7 +114,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b3ff7f27",
+   "id": "4caa3cc6",
    "metadata": {},
    "source": [
     "## The Economy\n",
@@ -159,7 +159,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "2b39ef01",
+   "id": "4e104dcf",
    "metadata": {
     "hide-output": false
    },
@@ -207,7 +207,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d8d5d98a",
+   "id": "8a584054",
    "metadata": {},
    "source": [
     "### First and Second Moments\n",
@@ -220,7 +220,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "abccdd41",
+   "id": "fbd5e831",
    "metadata": {
     "hide-output": false
    },
@@ -242,7 +242,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7baaa0f7",
+   "id": "565c126a",
    "metadata": {},
    "source": [
     "## Long Simulation\n",
@@ -257,7 +257,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "edc42dd1",
+   "id": "9c078838",
    "metadata": {
     "hide-output": false
    },
@@ -426,7 +426,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "ef50c7da",
+   "id": "7de43c4e",
    "metadata": {
     "hide-output": false
    },
@@ -735,7 +735,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "7c1b8fbe",
+   "id": "9e47f3f5",
    "metadata": {
     "hide-output": false
    },
@@ -814,7 +814,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "95fb2f85",
+   "id": "863f5c05",
    "metadata": {},
    "source": [
     "Next, we show the code that we use to generate a very long simulation starting from initial\n",
@@ -826,7 +826,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "d4b74ddb",
+   "id": "e0b51f90",
    "metadata": {
     "hide-output": false
    },
@@ -867,7 +867,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "817a8f87",
+   "id": "bf6400eb",
    "metadata": {},
    "source": [
     "![https://python-advanced.quantecon.org/_static/lecture_specific/amss3/amss3_g1.png](https://python-advanced.quantecon.org/_static/lecture_specific/amss3/amss3_g1.png)\n",
@@ -899,7 +899,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "9baeca00",
+   "id": "df84a467",
    "metadata": {
     "hide-output": false
    },
@@ -927,7 +927,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "46993023",
+   "id": "319d8e50",
    "metadata": {},
    "source": [
     "![https://python-advanced.quantecon.org/_static/lecture_specific/amss3/amss3_g2.png](https://python-advanced.quantecon.org/_static/lecture_specific/amss3/amss3_g2.png)\n",
@@ -943,7 +943,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7a921f50",
+   "id": "34820333",
    "metadata": {},
    "source": [
     "## Asymptotic Mean and Rate of Convergence\n",
@@ -997,7 +997,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e42c91e5",
+   "id": "28f01030",
    "metadata": {},
    "source": [
     "### Asymptotic Mean\n",
@@ -1040,7 +1040,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f400dc48",
+   "id": "ade3f8c7",
    "metadata": {},
    "source": [
     "### Rate of Convergence\n",
@@ -1059,7 +1059,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "bbf6993f",
+   "id": "d7b6d739",
    "metadata": {},
    "source": [
     "### More Advanced Topic\n",
@@ -1071,7 +1071,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3430ae58",
+   "id": "e3a435e1",
    "metadata": {},
    "source": [
     "### Chicken and Egg\n",
@@ -1096,7 +1096,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3fcdeb49",
+   "id": "6e0c9744",
    "metadata": {},
    "source": [
     "### Approximating the Ergodic Mean\n",
@@ -1118,7 +1118,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "43aba7a5",
+   "id": "47bc111e",
    "metadata": {},
    "source": [
     "### Step by Step\n",
@@ -1261,7 +1261,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c1344f51",
+   "id": "bd87bfd7",
    "metadata": {},
    "source": [
     "### Execution\n",
@@ -1271,7 +1271,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9efab1b1",
+   "id": "0d596378",
    "metadata": {},
    "source": [
     "#### Step 1"
@@ -1280,7 +1280,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "b9ca5644",
+   "id": "b470ab2b",
    "metadata": {
     "hide-output": false
    },
@@ -1304,7 +1304,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "01eb235a",
+   "id": "907284ef",
    "metadata": {
     "hide-output": false
    },
@@ -1315,7 +1315,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5c712549",
+   "id": "593408a7",
    "metadata": {},
    "source": [
     "#### Step 2"
@@ -1324,7 +1324,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "112c26de",
+   "id": "bebdbc48",
    "metadata": {
     "hide-output": false
    },
@@ -1335,7 +1335,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "88570ba0",
+   "id": "272a48a9",
    "metadata": {},
    "source": [
     "### Note about Code\n",
@@ -1352,7 +1352,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "bf98a10c",
+   "id": "c7e05e07",
    "metadata": {},
    "source": [
     "### Running the code\n",
@@ -1366,7 +1366,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "317fbf3d",
+   "id": "f8d08057",
    "metadata": {
     "hide-output": false
    },
@@ -1385,7 +1385,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "eab1c198",
+   "id": "de5e4c30",
    "metadata": {
     "hide-output": false
    },
@@ -1397,7 +1397,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "ba874847",
+   "id": "f44b3a46",
    "metadata": {
     "hide-output": false
    },
@@ -1408,7 +1408,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "caf07dc0",
+   "id": "056c6587",
    "metadata": {},
    "source": [
     "We only want unconditional expectations because we are in an IID case.\n",
@@ -1420,7 +1420,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "67edabae",
+   "id": "05f3864c",
    "metadata": {
     "hide-output": false
    },
@@ -1433,7 +1433,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e6402677",
+   "id": "3905ed6c",
    "metadata": {},
    "source": [
     "Let’s look at the random variables $ {\\mathcal R}, {\\mathcal X} $"
@@ -1442,7 +1442,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "dcc74d8d",
+   "id": "cc82ddc2",
    "metadata": {
     "hide-output": false
    },
@@ -1454,7 +1454,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "b0505d92",
+   "id": "b0a5fc4d",
    "metadata": {
     "hide-output": false
    },
@@ -1466,7 +1466,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "c0fb693b",
+   "id": "2b6a0960",
    "metadata": {
     "hide-output": false
    },
@@ -1478,7 +1478,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "1e375884",
+   "id": "c3a9ecbe",
    "metadata": {
     "hide-output": false
    },
@@ -1490,7 +1490,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "6b1c356a",
+   "id": "d9e95c1c",
    "metadata": {
     "hide-output": false
    },
@@ -1501,7 +1501,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "924dade6",
+   "id": "b7854925",
    "metadata": {},
    "source": [
     "#### Step 3"
@@ -1510,7 +1510,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "7f86cf37",
+   "id": "ec75dafc",
    "metadata": {
     "hide-output": false
    },
@@ -1523,7 +1523,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "fead0be8",
+   "id": "40118924",
    "metadata": {},
    "source": [
     "Note that $ B $ is a scalar.\n",
@@ -1534,7 +1534,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "47a5315a",
+   "id": "71d3bebb",
    "metadata": {
     "hide-output": false
    },
@@ -1549,7 +1549,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "655c6d7c",
+   "id": "f09f69d6",
    "metadata": {},
    "source": [
     "In the above cell, B is fixed at 1 and $ \\tau $ is to be computed as\n",
@@ -1561,7 +1561,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ea5b9820",
+   "id": "bedc8eb7",
    "metadata": {},
    "source": [
     "#### Step 4"
@@ -1570,7 +1570,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "7ee5e72e",
+   "id": "9b06890f",
    "metadata": {
     "hide-output": false
    },
@@ -1586,7 +1586,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "1307c825",
+   "id": "a9779e33",
    "metadata": {
     "hide-output": false
    },
@@ -1597,7 +1597,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "8773baac",
+   "id": "26e5ceb0",
    "metadata": {},
    "source": [
     "#### Step 6"
@@ -1606,7 +1606,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "77a1e7c1",
+   "id": "c432de82",
    "metadata": {
     "hide-output": false
    },
@@ -1619,7 +1619,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "5725d814",
+   "id": "cafbfbc5",
    "metadata": {
     "hide-output": false
    },
@@ -1631,7 +1631,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "6112718c",
+   "id": "7accbfcf",
    "metadata": {
     "hide-output": false
    },
@@ -1645,7 +1645,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "b6e44226",
+   "id": "512f4d69",
    "metadata": {
     "hide-output": false
    },
@@ -1658,7 +1658,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "3d6f33ce",
+   "id": "0b41fbfa",
    "metadata": {
     "hide-output": false
    },
@@ -1671,7 +1671,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "a4305c5b",
+   "id": "ffc15e6d",
    "metadata": {
     "hide-output": false
    },
@@ -1684,7 +1684,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "f5cc4fe5",
+   "id": "13cde38c",
    "metadata": {
     "hide-output": false
    },
@@ -1697,7 +1697,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "048a5a8c",
+   "id": "e6ee5c7d",
    "metadata": {
     "hide-output": false
    },
@@ -1708,7 +1708,7 @@
   }
  ],
  "metadata": {
-  "date": 1680677523.5757244,
+  "date": 1685490450.6040769,
   "filename": "amss3.md",
   "kernelspec": {
    "display_name": "Python",
diff --git a/arellano.ipynb b/arellano.ipynb
index 5bb7ef4..e7977d1 100644
--- a/arellano.ipynb
+++ b/arellano.ipynb
@@ -2,7 +2,7 @@
  "cells": [
   {
    "cell_type": "markdown",
-   "id": "83e95c06",
+   "id": "0232faa2",
    "metadata": {},
    "source": [
     "\n",
@@ -11,7 +11,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e3b45eb2",
+   "id": "66ac0555",
    "metadata": {},
    "source": [
     "# Default Risk and Income Fluctuations"
@@ -19,7 +19,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "29fb371a",
+   "id": "92deca77",
    "metadata": {},
    "source": [
     "## Contents\n",
@@ -35,7 +35,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d41624bf",
+   "id": "23df5c82",
    "metadata": {},
    "source": [
     "In addition to what’s in Anaconda, this lecture will need the following libraries:"
@@ -44,7 +44,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "849d0713",
+   "id": "1f5a0bf1",
    "metadata": {
     "hide-output": false
    },
@@ -55,7 +55,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "72bc2e1b",
+   "id": "1241c95d",
    "metadata": {},
    "source": [
     "## Overview\n",
@@ -107,7 +107,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "be6944d2",
+   "id": "f2886730",
    "metadata": {
     "hide-output": false
    },
@@ -125,7 +125,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "37551328",
+   "id": "1bedd9b3",
    "metadata": {},
    "source": [
     "## Structure\n",
@@ -135,7 +135,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d666774c",
+   "id": "c638ea38",
    "metadata": {},
    "source": [
     "### Output, Consumption and Debt\n",
@@ -177,7 +177,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a328bba1",
+   "id": "34473ac5",
    "metadata": {},
    "source": [
     "### Asset Markets\n",
@@ -219,7 +219,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "51c030fa",
+   "id": "204bfadb",
    "metadata": {},
    "source": [
     "### Financial Markets\n",
@@ -251,7 +251,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4b5ef006",
+   "id": "918db776",
    "metadata": {},
    "source": [
     "### Government’s Decisions\n",
@@ -277,7 +277,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4c20cbb9",
+   "id": "9bb9f859",
    "metadata": {},
    "source": [
     "### Reentering International Credit Market\n",
@@ -288,7 +288,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c84f1e69",
+   "id": "6dbd9732",
    "metadata": {},
    "source": [
     "## Equilibrium\n",
@@ -380,7 +380,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b15fea7b",
+   "id": "4d5a9665",
    "metadata": {},
    "source": [
     "### Definition of Equilibrium\n",
@@ -405,7 +405,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "583120f5",
+   "id": "adfeace7",
    "metadata": {},
    "source": [
     "## Computation\n",
@@ -451,7 +451,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "2cc086c2",
+   "id": "2ab36d03",
    "metadata": {
     "hide-output": false
    },
@@ -498,7 +498,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d4c44aba",
+   "id": "10a2c323",
    "metadata": {},
    "source": [
     "Notice how the class returns the data it stores as simple numerical values and\n",
@@ -514,7 +514,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "ff48fd3e",
+   "id": "f8091f9d",
    "metadata": {
     "hide-output": false
    },
@@ -527,7 +527,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "58dec527",
+   "id": "bdf6bc0c",
    "metadata": {},
    "source": [
     "Here is a function to compute the bond price at each state, given $ v_c $ and\n",
@@ -537,7 +537,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "bc556c4e",
+   "id": "924cd056",
    "metadata": {
     "hide-output": false
    },
@@ -565,7 +565,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "da5c01b8",
+   "id": "bd94f6dc",
    "metadata": {},
    "source": [
     "Next we introduce Bellman operators that updated $ v_d $ and $ v_c $."
@@ -574,7 +574,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "f386b59b",
+   "id": "0afa9668",
    "metadata": {
     "hide-output": false
    },
@@ -626,7 +626,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "bb0d01d4",
+   "id": "8459219d",
    "metadata": {},
    "source": [
     "Here is a fast function that calls these operators in the right sequence."
@@ -635,7 +635,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "2550dc2a",
+   "id": "132da180",
    "metadata": {
     "hide-output": false
    },
@@ -672,7 +672,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6f767949",
+   "id": "4a7434d2",
    "metadata": {},
    "source": [
     "We can now write a function that will use the `Arellano_Economy` class and the\n",
@@ -689,7 +689,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "bc9eaea4",
+   "id": "e6a886ca",
    "metadata": {
     "hide-output": false
    },
@@ -733,7 +733,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1612f822",
+   "id": "03303f96",
    "metadata": {},
    "source": [
     "Finally, we write a function that will allow us to simulate the economy once\n",
@@ -743,7 +743,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "ed5dda6f",
+   "id": "16bc7bf4",
    "metadata": {
     "hide-output": false
    },
@@ -813,7 +813,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "eee44f0b",
+   "id": "d9bfbed3",
    "metadata": {},
    "source": [
     "## Results\n",
@@ -884,7 +884,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7937969a",
+   "id": "097ed6c6",
    "metadata": {},
    "source": [
     "## Exercises\n",
@@ -895,7 +895,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ea8f8483",
+   "id": "9c5510d3",
    "metadata": {},
    "source": [
     "## Exercise 13.1\n",
@@ -908,7 +908,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "8b312cfb",
+   "id": "f9528911",
    "metadata": {},
    "source": [
     "## Solution to[ Exercise 13.1](https://python-advanced.quantecon.org/#arella_ex1)\n",
@@ -919,7 +919,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "1863ab53",
+   "id": "85e7557f",
    "metadata": {
     "hide-output": false
    },
@@ -931,7 +931,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "9a2d7681",
+   "id": "f0e4234e",
    "metadata": {
     "hide-output": false
    },
@@ -942,7 +942,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "2af5d6f0",
+   "id": "a38768cb",
    "metadata": {},
    "source": [
     "Compute the bond price schedule as seen in figure 3 of Arellano (2008)"
@@ -951,7 +951,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "0ce648e0",
+   "id": "b5307241",
    "metadata": {
     "hide-output": false
    },
@@ -987,7 +987,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "787ccf04",
+   "id": "717d6eff",
    "metadata": {},
    "source": [
     "Draw a plot of the value functions"
@@ -996,7 +996,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "1d6d5f83",
+   "id": "3d648585",
    "metadata": {
     "hide-output": false
    },
@@ -1016,7 +1016,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e0e2721c",
+   "id": "91d5b913",
    "metadata": {},
    "source": [
     "Draw a heat map for default probability"
@@ -1025,7 +1025,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "ccfe662e",
+   "id": "b26cf40b",
    "metadata": {
     "hide-output": false
    },
@@ -1051,7 +1051,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "58675af6",
+   "id": "8ba5e356",
    "metadata": {},
    "source": [
     "Plot a time series of major variables simulated from the model"
@@ -1060,7 +1060,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "8002ab51",
+   "id": "e4c071bb",
    "metadata": {
     "hide-output": false
    },
@@ -1109,7 +1109,7 @@
   }
  ],
  "metadata": {
-  "date": 1680677523.6228049,
+  "date": 1685490450.649887,
   "filename": "arellano.md",
   "kernelspec": {
    "display_name": "Python",
diff --git a/arma.ipynb b/arma.ipynb
index 5e2a66c..7efa937 100644
--- a/arma.ipynb
+++ b/arma.ipynb
@@ -2,7 +2,7 @@
  "cells": [
   {
    "cell_type": "markdown",
-   "id": "0388081a",
+   "id": "1ed3b281",
    "metadata": {},
    "source": [
     "\n",
@@ -11,7 +11,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "70c7c36d",
+   "id": "6c308ac9",
    "metadata": {},
    "source": [
     "# Covariance Stationary Processes"
@@ -19,7 +19,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "92e6088b",
+   "id": "acbc3a43",
    "metadata": {},
    "source": [
     "## Contents\n",
@@ -33,7 +33,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "eb20f9fe",
+   "id": "fa412016",
    "metadata": {},
    "source": [
     "In addition to what’s in Anaconda, this lecture will need the following libraries:"
@@ -42,7 +42,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "48f04af9",
+   "id": "2a15173c",
    "metadata": {
     "hide-output": false
    },
@@ -53,7 +53,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "77af9b8c",
+   "id": "1a71d82c",
    "metadata": {},
    "source": [
     "## Overview\n",
@@ -72,7 +72,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6d71fcb8",
+   "id": "7f436f7a",
    "metadata": {},
    "source": [
     "### ARMA Processes\n",
@@ -88,7 +88,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7337d23e",
+   "id": "722ae560",
    "metadata": {},
    "source": [
     "### Spectral Analysis\n",
@@ -109,7 +109,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "2604f333",
+   "id": "bea0a38a",
    "metadata": {},
    "source": [
     "### Other Reading\n",
@@ -122,7 +122,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "68a27406",
+   "id": "84ed4fd3",
    "metadata": {
     "hide-output": false
    },
@@ -136,7 +136,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "bc750cf6",
+   "id": "9b5ab822",
    "metadata": {},
    "source": [
     "## Introduction\n",
@@ -158,7 +158,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "094c94e0",
+   "id": "22e3042d",
    "metadata": {},
    "source": [
     "### Definitions\n",
@@ -180,7 +180,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6ff2a714",
+   "id": "bfb68850",
    "metadata": {},
    "source": [
     "### Example 1: White Noise\n",
@@ -203,7 +203,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4d87669c",
+   "id": "0e027b60",
    "metadata": {},
    "source": [
     "### Example 2: General Linear Processes\n",
@@ -242,7 +242,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7a5f5d3b",
+   "id": "fa69e4bc",
    "metadata": {},
    "source": [
     "### Wold Representation\n",
@@ -270,7 +270,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4faed259",
+   "id": "e513d7ab",
    "metadata": {},
    "source": [
     "### AR and MA\n",
@@ -313,7 +313,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "613cf449",
+   "id": "7951a370",
    "metadata": {
     "hide-output": false
    },
@@ -337,7 +337,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c3aa3a09",
+   "id": "79590671",
    "metadata": {},
    "source": [
     "Another very simple process is the MA(1) process (here MA means “moving average”)\n",
@@ -363,7 +363,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "686b11c1",
+   "id": "bf85ddbf",
    "metadata": {},
    "source": [
     "### ARMA Processes\n",
@@ -432,7 +432,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7203326e",
+   "id": "85604c0e",
    "metadata": {},
    "source": [
     "## Spectral Analysis\n",
@@ -450,7 +450,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a90608d8",
+   "id": "81ba9c61",
    "metadata": {},
    "source": [
     "### Complex Numbers\n",
@@ -491,7 +491,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "39ee3e0d",
+   "id": "42ba2ee3",
    "metadata": {},
    "source": [
     "### Spectral Densities\n",
@@ -533,7 +533,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "aa984b95",
+   "id": "60094d4b",
    "metadata": {},
    "source": [
     "### Example 1: White Noise\n",
@@ -549,7 +549,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f21c3d41",
+   "id": "d117fd6d",
    "metadata": {},
    "source": [
     "### Example 2: AR and MA and ARMA\n",
@@ -597,7 +597,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "143059d5",
+   "id": "e31844d9",
    "metadata": {},
    "source": [
     "### Interpreting the Spectral Density\n",
@@ -610,7 +610,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "bda65a35",
+   "id": "c9d08ff2",
    "metadata": {
     "hide-output": false
    },
@@ -637,7 +637,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f4588055",
+   "id": "38a75975",
    "metadata": {},
    "source": [
     "These spectral densities correspond to the autocovariance functions for the\n",
@@ -671,7 +671,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "b311983d",
+   "id": "8b9d3699",
    "metadata": {
     "hide-output": false
    },
@@ -714,7 +714,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "80943ff7",
+   "id": "3dcecf95",
    "metadata": {},
    "source": [
     "On the other hand, if we evaluate $ f(\\omega) $ at $ \\omega = \\pi / 3 $, then the cycles are\n",
@@ -725,7 +725,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "27a1eacd",
+   "id": "a19fa24b",
    "metadata": {
     "hide-output": false
    },
@@ -768,7 +768,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "07e861a8",
+   "id": "f1f83037",
    "metadata": {},
    "source": [
     "In summary, the spectral density is large at frequencies $ \\omega $ where the autocovariance function exhibits damped cycles."
@@ -776,7 +776,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f49f34cc",
+   "id": "80149ac0",
    "metadata": {},
    "source": [
     "### Inverting the Transformation\n",
@@ -802,7 +802,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "0460427d",
+   "id": "0994b7bc",
    "metadata": {},
    "source": [
     "### Mathematical Theory\n",
@@ -891,7 +891,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "dca9ef64",
+   "id": "1675d5ac",
    "metadata": {},
    "source": [
     "## Implementation\n",
@@ -912,7 +912,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "768a2db0",
+   "id": "6f79a79c",
    "metadata": {},
    "source": [
     "### Application\n",
@@ -925,7 +925,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "9d46573d",
+   "id": "06f809a5",
    "metadata": {
     "hide-output": false
    },
@@ -986,7 +986,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7627245d",
+   "id": "995b3f0a",
    "metadata": {},
    "source": [
     "Now let’s call these functions to generate plots.\n",
@@ -997,7 +997,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "00291568",
+   "id": "d0e7c136",
    "metadata": {
     "hide-output": false
    },
@@ -1011,7 +1011,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "cf8f52d0",
+   "id": "cc0e73c3",
    "metadata": {},
    "source": [
     "If we look carefully, things look good: the spectrum is the flat line at $ 10^0 $ at the very top of the spectrum graphs,\n",
@@ -1033,7 +1033,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "90aaf05b",
+   "id": "5e14769b",
    "metadata": {
     "hide-output": false
    },
@@ -1047,7 +1047,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e6f023b5",
+   "id": "d87daaef",
    "metadata": {},
    "source": [
     "Ljungqvist and Sargent’s second model is $ X_t = .9 X_{t-1} + \\epsilon_t $"
@@ -1056,7 +1056,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "405dd178",
+   "id": "bd6fb853",
    "metadata": {
     "hide-output": false
    },
@@ -1070,7 +1070,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "835b6dcb",
+   "id": "da579295",
    "metadata": {},
    "source": [
     "Ljungqvist and Sargent’s third  model is  $ X_t = .8 X_{t-4} + \\epsilon_t $"
@@ -1079,7 +1079,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "b8e4c490",
+   "id": "50af53c4",
    "metadata": {
     "hide-output": false
    },
@@ -1093,7 +1093,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c12deccd",
+   "id": "ff38b552",
    "metadata": {},
    "source": [
     "Ljungqvist and Sargent’s fourth  model is  $ X_t = .98 X_{t-1}  + \\epsilon_t -.7 \\epsilon_{t-1} $"
@@ -1102,7 +1102,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "042bcfc8",
+   "id": "86929c34",
    "metadata": {
     "hide-output": false
    },
@@ -1116,7 +1116,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "63d7a2cb",
+   "id": "f980b740",
    "metadata": {},
    "source": [
     "### Explanation\n",
@@ -1174,7 +1174,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ce1e7a8f",
+   "id": "405f4423",
    "metadata": {},
    "source": [
     "### Computing the Autocovariance Function\n",
@@ -1219,7 +1219,7 @@
   }
  ],
  "metadata": {
-  "date": 1680677523.6954412,
+  "date": 1685490450.7223623,
   "filename": "arma.md",
   "kernelspec": {
    "display_name": "Python",
diff --git a/asset_pricing_lph.ipynb b/asset_pricing_lph.ipynb
index 366cca3..ca6db7d 100644
--- a/asset_pricing_lph.ipynb
+++ b/asset_pricing_lph.ipynb
@@ -2,7 +2,7 @@
  "cells": [
   {
    "cell_type": "markdown",
-   "id": "546df03d",
+   "id": "3d643f5e",
    "metadata": {},
    "source": [
     "# Elementary Asset Pricing Theory\n",
@@ -13,7 +13,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a11671a4",
+   "id": "ef34987b",
    "metadata": {},
    "source": [
     "## Contents\n",
@@ -33,7 +33,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d6efac49",
+   "id": "8ed72055",
    "metadata": {},
    "source": [
     "## Overview\n",
@@ -78,7 +78,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5f82ea5a",
+   "id": "731126b8",
    "metadata": {},
    "source": [
     "## Key Equation\n",
@@ -122,7 +122,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "2ec4aa44",
+   "id": "9abf47de",
    "metadata": {},
    "source": [
     "## Implications of Key Equation\n",
@@ -198,7 +198,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "222f2b15",
+   "id": "8a9c68d6",
    "metadata": {},
    "source": [
     "## Expected Return - Beta Representation\n",
@@ -317,7 +317,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5b0b2a25",
+   "id": "c6679c75",
    "metadata": {},
    "source": [
     "## Mean-Variance Frontier\n",
@@ -391,7 +391,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "f6f143d3",
+   "id": "11085220",
    "metadata": {
     "hide-output": false
    },
@@ -440,7 +440,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "2318629a",
+   "id": "9eb8dbf3",
    "metadata": {},
    "source": [
     "The figure shows two straight lines, the blue upper one being the locus of $ ( \\sigma(R^i), E(R^i) $ pairs that are on\n",
@@ -475,7 +475,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7608fbb7",
+   "id": "11283146",
    "metadata": {},
    "source": [
     "## Sharpe Ratios and the Price of Risk\n",
@@ -500,7 +500,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "16be7b9b",
+   "id": "59b43c5a",
    "metadata": {},
    "source": [
     "## Mathematical Structure of Frontier\n",
@@ -532,7 +532,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "50b6f5a1",
+   "id": "44888c10",
    "metadata": {},
    "source": [
     "## Multi-factor Models\n",
@@ -570,7 +570,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "005fd6e5",
+   "id": "355b5504",
    "metadata": {},
    "source": [
     "## Empirical Implementations\n",
@@ -634,7 +634,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4666502f",
+   "id": "beb8fb6c",
    "metadata": {},
    "source": [
     "## Exercises\n",
@@ -645,7 +645,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "12744aff",
+   "id": "d1cdd7d7",
    "metadata": {
     "hide-output": false
    },
@@ -661,7 +661,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "668e2d1a",
+   "id": "aeb5d2b7",
    "metadata": {},
    "source": [
     "Lots of our calculations will involve computing population and sample OLS regressions.\n",
@@ -672,7 +672,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "59ad3333",
+   "id": "94fe242a",
    "metadata": {
     "hide-output": false
    },
@@ -694,7 +694,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d74e57a3",
+   "id": "c810acfc",
    "metadata": {},
    "source": [
     "## Exercise 35.1\n",
@@ -710,7 +710,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "18e29f6e",
+   "id": "fb30006f",
    "metadata": {},
    "source": [
     "## Solution to[ Exercise 35.1](https://python-advanced.quantecon.org/#apl_ex1)\n",
@@ -736,7 +736,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c0c8d86a",
+   "id": "75365c39",
    "metadata": {},
    "source": [
     "## Exercise 35.2\n",
@@ -746,7 +746,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "de36b1c1",
+   "id": "13c87bfc",
    "metadata": {},
    "source": [
     "## Solution to[ Exercise 35.2](https://python-advanced.quantecon.org/#apl_ex2)\n",
@@ -760,7 +760,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4ee75306",
+   "id": "e77b66e5",
    "metadata": {},
    "source": [
     "## Exercise 35.3\n",
@@ -815,7 +815,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4b1de0d5",
+   "id": "9b83c229",
    "metadata": {},
    "source": [
     "## Solution to[ Exercise 35.3](https://python-advanced.quantecon.org/#apl_ex3)\n",
@@ -826,7 +826,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "ae6c9f6a",
+   "id": "50e5ca26",
    "metadata": {
     "hide-output": false
    },
@@ -846,7 +846,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "47a803ce",
+   "id": "1b3ca746",
    "metadata": {
     "hide-output": false
    },
@@ -861,7 +861,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "9ce91f7d",
+   "id": "8a7e13b9",
    "metadata": {
     "hide-output": false
    },
@@ -876,7 +876,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "c4002d21",
+   "id": "9e6aee55",
    "metadata": {
     "hide-output": false
    },
@@ -897,7 +897,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "87a5fa25",
+   "id": "94f54cd2",
    "metadata": {},
    "source": [
     "Now that we have a panel of data, we’d like to solve the inverse problem by assuming the theory specified above and estimating the coefficients given above."
@@ -906,7 +906,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "eda0c35d",
+   "id": "3cfddc8d",
    "metadata": {
     "hide-output": false
    },
@@ -917,7 +917,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "08021d29",
+   "id": "d146b913",
    "metadata": {},
    "source": [
     "**Inverse Problem:**\n",
@@ -930,7 +930,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "8d45d827",
+   "id": "039e1d42",
    "metadata": {
     "hide-output": false
    },
@@ -942,7 +942,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "58769e38",
+   "id": "e705c692",
    "metadata": {
     "hide-output": false
    },
@@ -953,7 +953,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "467251ae",
+   "id": "152f9434",
    "metadata": {},
    "source": [
     "Let’s  compare these with the *true* population parameter values."
@@ -962,7 +962,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "c8486c9c",
+   "id": "f2ce8244",
    "metadata": {
     "hide-output": false
    },
@@ -973,7 +973,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "42fd5ef9",
+   "id": "e3adcb1d",
    "metadata": {},
    "source": [
     "1. $ \\xi $ and $ \\lambda $  "
@@ -982,7 +982,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "2e4666ce",
+   "id": "0c405424",
    "metadata": {
     "hide-output": false
    },
@@ -994,7 +994,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "e55f7af1",
+   "id": "d45ceeb8",
    "metadata": {
     "hide-output": false
    },
@@ -1006,7 +1006,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "96b6eafa",
+   "id": "62df88c4",
    "metadata": {
     "hide-output": false
    },
@@ -1017,7 +1017,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c692e97f",
+   "id": "575bcc4c",
    "metadata": {},
    "source": [
     "1. $ \\beta_{i, R^m} $ and $ \\sigma_i $  "
@@ -1026,7 +1026,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "1b1f80aa",
+   "id": "8d205eaa",
    "metadata": {
     "hide-output": false
    },
@@ -1042,7 +1042,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "28d9e314",
+   "id": "b4090775",
    "metadata": {
     "hide-output": false
    },
@@ -1054,7 +1054,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "935c4f77",
+   "id": "9a325d07",
    "metadata": {
     "hide-output": false
    },
@@ -1065,7 +1065,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "55ce6872",
+   "id": "e20119af",
    "metadata": {},
    "source": [
     "Q: How close did your estimates come to the parameters we specified?"
@@ -1073,7 +1073,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1f9402ba",
+   "id": "afc91dc3",
    "metadata": {},
    "source": [
     "## Exercise 35.4\n",
@@ -1087,7 +1087,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a898a9af",
+   "id": "342717ae",
    "metadata": {},
    "source": [
     "## Solution to[ Exercise 35.4](https://python-advanced.quantecon.org/#apl_ex4)\n",
@@ -1105,7 +1105,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "9e42eda1",
+   "id": "34929465",
    "metadata": {
     "hide-output": false
    },
@@ -1128,7 +1128,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "001ef942",
+   "id": "5361cf2c",
    "metadata": {},
    "source": [
     "Let’s try to solve $ a $ and $ b $ using the actual model parameters."
@@ -1137,7 +1137,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "a95f74fe",
+   "id": "5d51c20a",
    "metadata": {
     "hide-output": false
    },
@@ -1149,7 +1149,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "71848ba9",
+   "id": "9b63edb5",
    "metadata": {
     "hide-output": false
    },
@@ -1160,7 +1160,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "19879c3d",
+   "id": "f6ffbe41",
    "metadata": {},
    "source": [
     "## Exercise 35.5\n",
@@ -1170,7 +1170,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "aa47a2c4",
+   "id": "686bcf64",
    "metadata": {},
    "source": [
     "## Solution to[ Exercise 35.5](https://python-advanced.quantecon.org/#apl_ex5)\n",
@@ -1181,7 +1181,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "b950dfac",
+   "id": "b260c5ec",
    "metadata": {
     "hide-output": false
    },
@@ -1193,7 +1193,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "f896a923",
+   "id": "81836c0e",
    "metadata": {
     "hide-output": false
    },
@@ -1204,7 +1204,7 @@
   }
  ],
  "metadata": {
-  "date": 1680677523.7622435,
+  "date": 1685490450.7898748,
   "filename": "asset_pricing_lph.md",
   "kernelspec": {
    "display_name": "Python",
diff --git a/black_litterman.ipynb b/black_litterman.ipynb
index c5c6938..0c1acdc 100644
--- a/black_litterman.ipynb
+++ b/black_litterman.ipynb
@@ -2,7 +2,7 @@
  "cells": [
   {
    "cell_type": "markdown",
-   "id": "e35057b3",
+   "id": "385f0969",
    "metadata": {},
    "source": [
     "\n",
@@ -13,7 +13,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "82c1a2ad",
+   "id": "37f74e22",
    "metadata": {},
    "source": [
     "# Two Modifications of Mean-Variance Portfolio Theory"
@@ -21,7 +21,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d35ce060",
+   "id": "b105a619",
    "metadata": {},
    "source": [
     "## Contents\n",
@@ -46,7 +46,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f5b923f0",
+   "id": "2ea5fd71",
    "metadata": {},
    "source": [
     "## Overview\n",
@@ -106,7 +106,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "c08f8f07",
+   "id": "886c4ba0",
    "metadata": {
     "hide-output": false
    },
@@ -122,7 +122,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "59061c91",
+   "id": "79868deb",
    "metadata": {},
    "source": [
     "## Mean-Variance Portfolio Choice\n",
@@ -185,7 +185,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "56f75a15",
+   "id": "66890846",
    "metadata": {},
    "source": [
     "## Estimating  Mean and Variance\n",
@@ -205,7 +205,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d7a40f62",
+   "id": "d35b44e4",
    "metadata": {},
    "source": [
     "## Black-Litterman Starting Point\n",
@@ -223,7 +223,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "236a09f8",
+   "id": "f1eac687",
    "metadata": {
     "hide-output": false
    },
@@ -276,7 +276,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6608f12b",
+   "id": "e6b053a7",
    "metadata": {},
    "source": [
     "Black and Litterman’s responded to this situation in the following way:\n",
@@ -304,7 +304,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "158e40e2",
+   "id": "f3ef8f5e",
    "metadata": {},
    "source": [
     "## Details\n",
@@ -376,7 +376,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "398962ac",
+   "id": "0a872402",
    "metadata": {
     "hide-output": false
    },
@@ -411,7 +411,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3eb440ab",
+   "id": "c033d4f6",
    "metadata": {},
    "source": [
     "## Adding Views\n",
@@ -474,7 +474,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "737fd5dd",
+   "id": "63ac1653",
    "metadata": {
     "hide-output": false
    },
@@ -538,7 +538,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e221c994",
+   "id": "ffe4b373",
    "metadata": {},
    "source": [
     "## Bayesian Interpretation\n",
@@ -588,7 +588,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "861bf601",
+   "id": "12fc553a",
    "metadata": {},
    "source": [
     "## Curve Decolletage\n",
@@ -718,7 +718,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "ac094d0a",
+   "id": "f6404904",
    "metadata": {
     "hide-output": false
    },
@@ -796,7 +796,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "dc215344",
+   "id": "90cf7d6f",
    "metadata": {},
    "source": [
     "Note that the line that connects the two points\n",
@@ -817,7 +817,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "d37e33e9",
+   "id": "0765f90d",
    "metadata": {
     "hide-output": false
    },
@@ -867,7 +867,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "2addce5d",
+   "id": "4ae94103",
    "metadata": {},
    "source": [
     "## Black-Litterman Recommendation as Regularization\n",
@@ -1023,7 +1023,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c0269209",
+   "id": "76dce325",
    "metadata": {},
    "source": [
     "## A Robust Control Operator\n",
@@ -1163,7 +1163,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "510c397d",
+   "id": "e7340952",
    "metadata": {},
    "source": [
     "## A Robust Mean-Variance Portfolio Model\n",
@@ -1234,7 +1234,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b896688f",
+   "id": "e4d3415c",
    "metadata": {},
    "source": [
     "## Appendix\n",
@@ -1310,7 +1310,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "56db4922",
+   "id": "7185307d",
    "metadata": {},
    "source": [
     "## Special Case – IID Sample\n",
@@ -1353,7 +1353,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9353a4b3",
+   "id": "094dc26a",
    "metadata": {},
    "source": [
     "## Dependence and Sampling Frequency\n",
@@ -1418,7 +1418,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "79cb2388",
+   "id": "f21e80d6",
    "metadata": {
     "hide-output": false
    },
@@ -1449,7 +1449,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "27afbc27",
+   "id": "2ee5d755",
    "metadata": {},
    "source": [
     "## Frequency and the Mean Estimator\n",
@@ -1531,7 +1531,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "e268e534",
+   "id": "3ea371a1",
    "metadata": {
     "hide-output": false
    },
@@ -1559,7 +1559,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "6e210ef2",
+   "id": "0d916246",
    "metadata": {
     "hide-output": false
    },
@@ -1605,7 +1605,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "075d6f7a",
+   "id": "00946a8b",
    "metadata": {},
    "source": [
     "The above figure illustrates the relationship between the asymptotic\n",
@@ -1623,7 +1623,7 @@
   }
  ],
  "metadata": {
-  "date": 1680677524.0314505,
+  "date": 1685490450.8584445,
   "filename": "black_litterman.md",
   "kernelspec": {
    "display_name": "Python",
diff --git a/calvo.ipynb b/calvo.ipynb
index d9df109..b9f0c00 100644
--- a/calvo.ipynb
+++ b/calvo.ipynb
@@ -2,7 +2,7 @@
  "cells": [
   {
    "cell_type": "markdown",
-   "id": "9be97fb2",
+   "id": "cddd368b",
    "metadata": {},
    "source": [
     "\n",
@@ -11,7 +11,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7953459f",
+   "id": "6fd5accc",
    "metadata": {},
    "source": [
     "# Ramsey Plans, Time Inconsistency, Sustainable Plans\n",
@@ -22,7 +22,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "139fc8ea",
+   "id": "9a1afa18",
    "metadata": {},
    "source": [
     "## Contents\n",
@@ -46,7 +46,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "2e5e418e",
+   "id": "67c9f50d",
    "metadata": {},
    "source": [
     "In addition to what’s in Anaconda, this lecture will need the following libraries:"
@@ -55,7 +55,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "d250ef6e",
+   "id": "fe1fb658",
    "metadata": {
     "hide-output": false
    },
@@ -66,7 +66,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e3556983",
+   "id": "86f8b4ce",
    "metadata": {},
    "source": [
     "## Overview\n",
@@ -116,7 +116,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "244b1fef",
+   "id": "71456c9a",
    "metadata": {
     "hide-output": false
    },
@@ -130,7 +130,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a00325ee",
+   "id": "b444874e",
    "metadata": {},
    "source": [
     "## The Model\n",
@@ -181,11 +181,11 @@
     "\n",
     "Because $ \\alpha > 0 $,  $ 0 < \\frac{\\alpha}{1+\\alpha} < 1 $.\n",
     "\n",
-    "**Definition:** For a scalar $ x_t $, let $ L^2 $ be the space of sequences\n",
-    "$ \\{x_t\\}_{t=0}^\\infty $ satisfying\n",
+    "**Definition:** For a scalar $ b_t $, let $ L^2 $ be the space of sequences\n",
+    "$ \\{b_t\\}_{t=0}^\\infty $ satisfying\n",
     "\n",
     "$$\n",
-    "\\sum_{t=0}^\\infty  x_t^2 < +\\infty\n",
+    "\\sum_{t=0}^\\infty  b_t^2 < +\\infty\n",
     "$$\n",
     "\n",
     "We say that a sequence that belongs to $ L^2 $   is **square summable**.\n",
@@ -312,7 +312,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7c5c5aae",
+   "id": "321f1f64",
    "metadata": {},
    "source": [
     "## Structure\n",
@@ -347,7 +347,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6fdccead",
+   "id": "823e3bf2",
    "metadata": {},
    "source": [
     "## Intertemporal Structure\n",
@@ -372,7 +372,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "36207cc9",
+   "id": "eceafdd3",
    "metadata": {},
    "source": [
     "## Four Models of Government Policy\n",
@@ -427,7 +427,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9ea5d1bc",
+   "id": "35eebc3f",
    "metadata": {},
    "source": [
     "## A Ramsey Planner\n",
@@ -454,7 +454,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9b73b187",
+   "id": "a60fc44c",
    "metadata": {},
    "source": [
     "### Subproblem 1\n",
@@ -505,7 +505,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "0412aa61",
+   "id": "749acd42",
    "metadata": {},
    "source": [
     "### Subproblem 2\n",
@@ -539,7 +539,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1e58da40",
+   "id": "ad6d8326",
    "metadata": {},
    "source": [
     "### Representation of Ramsey Plan\n",
@@ -578,7 +578,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5f85166d",
+   "id": "2d415afa",
    "metadata": {},
    "source": [
     "### Multiple roles of $ \\theta_t $\n",
@@ -600,7 +600,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "26676f63",
+   "id": "ed4dfe37",
    "metadata": {},
    "source": [
     "### Time Inconsistency\n",
@@ -618,7 +618,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "61b06221",
+   "id": "7481f6a1",
    "metadata": {},
    "source": [
     "## A Constrained-to-a-Constant-Growth-Rate Ramsey Government\n",
@@ -654,7 +654,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3afec3c1",
+   "id": "084559d6",
    "metadata": {},
    "source": [
     "## Markov Perfect Governments\n",
@@ -721,7 +721,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6add7480",
+   "id": "46d41641",
    "metadata": {},
    "source": [
     "## Outcomes under Three Timing Protocols\n",
@@ -743,7 +743,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "0098a878",
+   "id": "9ca09fb1",
    "metadata": {
     "hide-output": false
    },
@@ -850,7 +850,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "cc8d78b2",
+   "id": "c5fff618",
    "metadata": {},
    "source": [
     "We will create an instance of ChangLQ with the following parameters"
@@ -859,7 +859,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "4d280404",
+   "id": "1788236b",
    "metadata": {
     "hide-output": false
    },
@@ -871,7 +871,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "40c893f1",
+   "id": "5188cf28",
    "metadata": {},
    "source": [
     "The following code generates a figure that plots the value function from the Ramsey Planner’s\n",
@@ -883,7 +883,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "39a33d71",
+   "id": "0cf0d65b",
    "metadata": {
     "hide-output": false
    },
@@ -928,7 +928,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "402e1079",
+   "id": "202d6510",
    "metadata": {},
    "source": [
     "The next code generates a figure that plots the value function from the Ramsey Planner’s\n",
@@ -939,7 +939,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "396f47b9",
+   "id": "bd53b865",
    "metadata": {
     "hide-output": false
    },
@@ -985,7 +985,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "918dbc76",
+   "id": "12d8de32",
    "metadata": {},
    "source": [
     "The next code generates  figures that plot the policy functions for a continuation Ramsey\n",
@@ -1001,7 +1001,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "38859a12",
+   "id": "87825a90",
    "metadata": {
     "hide-output": false
    },
@@ -1062,7 +1062,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "074fc2ca",
+   "id": "83768c45",
    "metadata": {},
    "source": [
     "The following code generates a figure that plots sequences of $ \\mu $ and $ \\theta $\n",
@@ -1074,7 +1074,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "466a3825",
+   "id": "d8c9ae46",
    "metadata": {
     "hide-output": false
    },
@@ -1110,7 +1110,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3cd3d0f6",
+   "id": "e01d5e75",
    "metadata": {},
    "source": [
     "### Time Inconsistency of Ramsey Plan\n",
@@ -1135,7 +1135,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "8985ef85",
+   "id": "b20060c4",
    "metadata": {},
    "source": [
     "### Meaning of Time Inconsistency\n",
@@ -1159,7 +1159,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "892bdaf0",
+   "id": "17a5c186",
    "metadata": {},
    "source": [
     "### Ramsey Plans Strike Back\n",
@@ -1176,7 +1176,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9451d01d",
+   "id": "64dc9582",
    "metadata": {},
    "source": [
     "## A Fourth Model of Government Decision Making\n",
@@ -1198,7 +1198,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5e8a5569",
+   "id": "8beae558",
    "metadata": {},
    "source": [
     "### A Theory of Government Decision Making\n",
@@ -1234,7 +1234,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "69c856b4",
+   "id": "1c319124",
    "metadata": {},
    "source": [
     "### Temptation to Deviate from Plan\n",
@@ -1266,7 +1266,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "46d08c02",
+   "id": "a9ce3bba",
    "metadata": {},
    "source": [
     "## Sustainable or Credible Plan\n",
@@ -1309,7 +1309,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3b4be6b9",
+   "id": "ca5aefac",
    "metadata": {},
    "source": [
     "### Abreu’s Self-Enforcing Plan\n",
@@ -1381,7 +1381,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "cf6e4572",
+   "id": "7b34eff2",
    "metadata": {},
    "source": [
     "### Abreu Carrot-Stick Plan\n",
@@ -1423,7 +1423,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d70775bc",
+   "id": "43bd2b53",
    "metadata": {},
    "source": [
     "### Example of Self-Enforcing Plan\n",
@@ -1452,7 +1452,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "b979acbb",
+   "id": "3f6fb9e2",
    "metadata": {
     "hide-output": false
    },
@@ -1509,7 +1509,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "00f0a063",
+   "id": "c0cf464f",
    "metadata": {},
    "source": [
     "To confirm that the plan $ \\vec \\mu^A $ is **self-enforcing**,  we\n",
@@ -1532,7 +1532,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "34ed43ac",
+   "id": "0546b2c7",
    "metadata": {
     "hide-output": false
    },
@@ -1543,7 +1543,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f5c9a142",
+   "id": "04e99dd3",
    "metadata": {},
    "source": [
     "Given that plan $ \\vec \\mu^A $ is self-enforcing, we can check that\n",
@@ -1557,7 +1557,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "f066a30d",
+   "id": "848932c9",
    "metadata": {
     "hide-output": false
    },
@@ -1578,7 +1578,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ab84323c",
+   "id": "f851ac77",
    "metadata": {},
    "source": [
     "### Recursive Representation of a Sustainable Plan\n",
@@ -1615,7 +1615,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "cc69ce92",
+   "id": "55722179",
    "metadata": {},
    "source": [
     "## Whose Credible Plan is it?\n",
@@ -1638,7 +1638,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "da7760f6",
+   "id": "3910163c",
    "metadata": {},
    "source": [
     "## Comparison of Equilibrium Values\n",
@@ -1663,7 +1663,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "075b3e9b",
+   "id": "ca60845d",
    "metadata": {
     "hide-output": false
    },
@@ -1675,7 +1675,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "1dc55f72",
+   "id": "d0a38ecf",
    "metadata": {
     "hide-output": false
    },
@@ -1687,7 +1687,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "83e1b190",
+   "id": "3148d0fb",
    "metadata": {
     "hide-output": false
    },
@@ -1698,7 +1698,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1b4f8c68",
+   "id": "fd415b24",
    "metadata": {},
    "source": [
     "We have also computed **credible plans** for a government or sequence\n",
@@ -1713,7 +1713,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1de07cff",
+   "id": "6f6030c5",
    "metadata": {},
    "source": [
     "## Note on Dynamic Programming Squared\n",
@@ -1735,7 +1735,7 @@
   }
  ],
  "metadata": {
-  "date": 1680677524.1368499,
+  "date": 1685490451.1258068,
   "filename": "calvo.md",
   "kernelspec": {
    "display_name": "Python",
diff --git a/cattle_cycles.ipynb b/cattle_cycles.ipynb
index 232b8c5..769b5c7 100644
--- a/cattle_cycles.ipynb
+++ b/cattle_cycles.ipynb
@@ -2,7 +2,7 @@
  "cells": [
   {
    "cell_type": "markdown",
-   "id": "efcb2a46",
+   "id": "2f2e8748",
    "metadata": {},
    "source": [
     "\n",
@@ -13,7 +13,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e4eeef3f",
+   "id": "2bec4a7e",
    "metadata": {},
    "source": [
     "# Cattle Cycles"
@@ -21,7 +21,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "8e93f3c0",
+   "id": "e16a43c3",
    "metadata": {},
    "source": [
     "## Contents\n",
@@ -33,7 +33,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4b07071c",
+   "id": "3a65f24f",
    "metadata": {},
    "source": [
     "This is another member of a suite of lectures that use the quantecon DLE class to instantiate models within the\n",
@@ -45,7 +45,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "61e497a6",
+   "id": "a218abc2",
    "metadata": {
     "hide-output": false
    },
@@ -56,7 +56,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "bfdef01a",
+   "id": "3b4ddfc3",
    "metadata": {},
    "source": [
     "This lecture uses the DLE class to construct instances of  the “Cattle Cycles” model\n",
@@ -71,7 +71,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "9b83a067",
+   "id": "580b231f",
    "metadata": {
     "hide-output": false
    },
@@ -88,7 +88,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c254f1f0",
+   "id": "92687121",
    "metadata": {},
    "source": [
     "## The Model\n",
@@ -150,7 +150,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1ff0888b",
+   "id": "e3047b8d",
    "metadata": {},
    "source": [
     "## Mapping into HS2013 Framework"
@@ -158,7 +158,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d1387e6c",
+   "id": "7afe05ab",
    "metadata": {},
    "source": [
     "### Preferences\n",
@@ -173,7 +173,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3031323b",
+   "id": "1cda90eb",
    "metadata": {},
    "source": [
     "### Technology\n",
@@ -223,7 +223,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9c996c79",
+   "id": "e2858367",
    "metadata": {},
    "source": [
     "### Information\n",
@@ -262,7 +262,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "764867af",
+   "id": "7612f189",
    "metadata": {
     "hide-output": false
    },
@@ -278,7 +278,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6b61996a",
+   "id": "61054bbf",
    "metadata": {},
    "source": [
     "We set parameters to those used by [[RMS94](https://python-advanced.quantecon.org/zreferences.html#id70)]"
@@ -287,7 +287,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "7e8e116c",
+   "id": "fa916352",
    "metadata": {
     "hide-output": false
    },
@@ -361,7 +361,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "efa44727",
+   "id": "f39a6f98",
    "metadata": {},
    "source": [
     "Notice that we have set $ \\rho_1 = \\rho_2 = 0 $, so $ h_t $ and\n",
@@ -378,7 +378,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "a1907261",
+   "id": "c5231265",
    "metadata": {
     "hide-output": false
    },
@@ -411,7 +411,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "8ea5b5ba",
+   "id": "0e57b0ca",
    "metadata": {
     "hide-output": false
    },
@@ -430,7 +430,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "94d5cd23",
+   "id": "190ea7a7",
    "metadata": {
     "hide-output": false
    },
@@ -441,7 +441,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f9978496",
+   "id": "d32c4131",
    "metadata": {},
    "source": [
     "[[RMS94](https://python-advanced.quantecon.org/zreferences.html#id70)] use the model to understand the\n",
@@ -454,7 +454,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "a27784e0",
+   "id": "5febc460",
    "metadata": {
     "hide-output": false
    },
@@ -471,7 +471,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "378f2f38",
+   "id": "2b000a06",
    "metadata": {},
    "source": [
     "In their Figure 3, [[RMS94](https://python-advanced.quantecon.org/zreferences.html#id70)] plot the impulse response functions\n",
@@ -484,7 +484,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "2e4c1f90",
+   "id": "98faf3e7",
    "metadata": {
     "hide-output": false
    },
@@ -513,7 +513,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "cb7e0ee5",
+   "id": "b75df70e",
    "metadata": {},
    "source": [
     "The above figures show how consumption patterns differ markedly,\n",
@@ -536,7 +536,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "7c97bbe1",
+   "id": "cc3685e8",
    "metadata": {
     "hide-output": false
    },
@@ -558,7 +558,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "afb0164d",
+   "id": "09567f32",
    "metadata": {},
    "source": [
     "The fact that $ y_t $ is a weighted moving average of $ x_t $\n",
@@ -569,7 +569,7 @@
   }
  ],
  "metadata": {
-  "date": 1680677524.1644647,
+  "date": 1685490451.1539695,
   "filename": "cattle_cycles.md",
   "kernelspec": {
    "display_name": "Python",
diff --git a/chang_credible.ipynb b/chang_credible.ipynb
index cecf1de..383e043 100644
--- a/chang_credible.ipynb
+++ b/chang_credible.ipynb
@@ -2,7 +2,7 @@
  "cells": [
   {
    "cell_type": "markdown",
-   "id": "2316a8fe",
+   "id": "90531a2d",
    "metadata": {},
    "source": [
     "\n",
@@ -11,7 +11,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "cf90adf0",
+   "id": "fa4aa109",
    "metadata": {},
    "source": [
     "# Credible Government Policies in a Model of Chang"
@@ -19,7 +19,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "af26a123",
+   "id": "7fbf2757",
    "metadata": {},
    "source": [
     "## Contents\n",
@@ -32,7 +32,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "bc1149d1",
+   "id": "241a791b",
    "metadata": {},
    "source": [
     "In addition to what’s in Anaconda, this lecture will need the following libraries:"
@@ -41,7 +41,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "994182fd",
+   "id": "75791d42",
    "metadata": {
     "hide-output": false
    },
@@ -52,7 +52,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "2f1107b5",
+   "id": "a91197c0",
    "metadata": {},
    "source": [
     "## Overview\n",
@@ -111,7 +111,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "9ff880e6",
+   "id": "576a3d3c",
    "metadata": {
     "hide-output": false
    },
@@ -126,7 +126,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9e8a83fc",
+   "id": "daeb6a4b",
    "metadata": {},
    "source": [
     "## The Setting\n",
@@ -181,7 +181,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ed9b60cb",
+   "id": "43b36636",
    "metadata": {},
    "source": [
     "### The Household’s Problem\n",
@@ -242,7 +242,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7d9b69ce",
+   "id": "bf5ebfb3",
    "metadata": {},
    "source": [
     "### Government\n",
@@ -301,7 +301,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6d7da1f7",
+   "id": "71852d87",
    "metadata": {},
    "source": [
     "### Within-period Timing Protocol\n",
@@ -331,7 +331,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "8e1667bb",
+   "id": "a4fb3b32",
    "metadata": {},
    "source": [
     "### Household’s Problem\n",
@@ -398,7 +398,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "cb5530f5",
+   "id": "372dff0a",
    "metadata": {},
    "source": [
     "### Competitive Equilibrium\n",
@@ -424,7 +424,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d39ae8fa",
+   "id": "87c35a02",
    "metadata": {},
    "source": [
     "### A Credible Government Policy\n",
@@ -507,7 +507,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "11d420b5",
+   "id": "a3e3370f",
    "metadata": {},
    "source": [
     "### Sustainable Plans\n",
@@ -684,7 +684,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "32f7ee76",
+   "id": "88d3cacd",
    "metadata": {},
    "source": [
     "## Calculating the Set of Sustainable Promise-Value Pairs\n",
@@ -900,7 +900,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "9f335d5e",
+   "id": "8b2d9678",
    "metadata": {
     "hide-output": false
    },
@@ -1408,7 +1408,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "61bf3c17",
+   "id": "8c959e9f",
    "metadata": {},
    "source": [
     "### Comparison of Sets\n",
@@ -1423,7 +1423,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "da8eb921",
+   "id": "42b0562d",
    "metadata": {
     "hide-output": false
    },
@@ -1435,7 +1435,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "6946afa5",
+   "id": "3b25bc7f",
    "metadata": {
     "hide-output": false
    },
@@ -1446,7 +1446,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9e124b8e",
+   "id": "53097b74",
    "metadata": {},
    "source": [
     "The following plot shows both the set of $ w,\\theta $ pairs associated with competitive equilibria (in red)\n",
@@ -1456,7 +1456,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "f45ad2e5",
+   "id": "eecaebb4",
    "metadata": {
     "hide-output": false
    },
@@ -1498,7 +1498,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3589e8a9",
+   "id": "acc1ef86",
    "metadata": {},
    "source": [
     "Evidently, the Ramsey plan, denoted by the $ R $, is not sustainable.\n",
@@ -1509,7 +1509,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "e586100b",
+   "id": "95a623cb",
    "metadata": {
     "hide-output": false
    },
@@ -1522,7 +1522,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "af15a272",
+   "id": "1ad1210e",
    "metadata": {
     "hide-output": false
    },
@@ -1533,7 +1533,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "520e5503",
+   "id": "e4f12369",
    "metadata": {},
    "source": [
     "Let’s plot both sets"
@@ -1542,7 +1542,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "d85ba50b",
+   "id": "fab78dc2",
    "metadata": {
     "hide-output": false
    },
@@ -1553,7 +1553,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "8234d147",
+   "id": "50ce7803",
    "metadata": {},
    "source": [
     "Evidently, the Ramsey plan is now sustainable."
@@ -1561,7 +1561,7 @@
   }
  ],
  "metadata": {
-  "date": 1680677524.22787,
+  "date": 1685490451.2194736,
   "filename": "chang_credible.md",
   "kernelspec": {
    "display_name": "Python",
diff --git a/chang_ramsey.ipynb b/chang_ramsey.ipynb
index 2265b14..82f10d2 100644
--- a/chang_ramsey.ipynb
+++ b/chang_ramsey.ipynb
@@ -2,7 +2,7 @@
  "cells": [
   {
    "cell_type": "markdown",
-   "id": "792cd219",
+   "id": "c637b47d",
    "metadata": {},
    "source": [
     "\n",
@@ -11,7 +11,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a111da10",
+   "id": "448b3ffc",
    "metadata": {},
    "source": [
     "# Competitive Equilibria of a Model of Chang"
@@ -19,7 +19,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4ff4af78",
+   "id": "5a2d2f70",
    "metadata": {},
    "source": [
     "## Contents\n",
@@ -36,7 +36,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f19138a5",
+   "id": "ebf224f3",
    "metadata": {},
    "source": [
     "In addition to what’s in Anaconda, this lecture will need the following libraries:"
@@ -45,7 +45,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "ccd27e1d",
+   "id": "c9f8cbfa",
    "metadata": {
     "hide-output": false
    },
@@ -56,7 +56,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1c516bfd",
+   "id": "1e4a1a34",
    "metadata": {},
    "source": [
     "## Overview\n",
@@ -104,7 +104,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "e56ec5f6",
+   "id": "4d2cc741",
    "metadata": {
     "hide-output": false
    },
@@ -119,7 +119,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f931f500",
+   "id": "7b5493d1",
    "metadata": {},
    "source": [
     "### The Setting\n",
@@ -177,7 +177,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3e9d06eb",
+   "id": "3a1a4535",
    "metadata": {},
    "source": [
     "## Setting"
@@ -185,7 +185,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "33002c3a",
+   "id": "cd0acad7",
    "metadata": {},
    "source": [
     "### The Household’s Problem\n",
@@ -246,7 +246,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "bb739c2f",
+   "id": "b7ce87a0",
    "metadata": {},
    "source": [
     "### Government\n",
@@ -338,7 +338,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7dfc5301",
+   "id": "5fc6bc80",
    "metadata": {},
    "source": [
     "### Household’s Problem\n",
@@ -410,7 +410,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "2321e225",
+   "id": "e5f4cc21",
    "metadata": {},
    "source": [
     "## Competitive Equilibrium\n",
@@ -436,7 +436,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "32433359",
+   "id": "0c247e15",
    "metadata": {},
    "source": [
     "## Inventory of Objects in Play\n",
@@ -495,7 +495,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4d1eaa93",
+   "id": "679f7715",
    "metadata": {},
    "source": [
     "## Analysis\n",
@@ -669,7 +669,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f23949c9",
+   "id": "6f9181b3",
    "metadata": {},
    "source": [
     "### Some Useful Notation\n",
@@ -736,7 +736,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "36ba2cba",
+   "id": "0d892ad8",
    "metadata": {},
    "source": [
     "### Another Operator\n",
@@ -838,7 +838,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c016c1b5",
+   "id": "c6d70401",
    "metadata": {},
    "source": [
     "## Calculating all Promise-Value Pairs in CE\n",
@@ -991,7 +991,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "ad89930a",
+   "id": "3a862904",
    "metadata": {
     "hide-output": false
    },
@@ -1500,7 +1500,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "ec101f87",
+   "id": "0673e558",
    "metadata": {
     "hide-output": false
    },
@@ -1513,7 +1513,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "60b6542c",
+   "id": "1f7b6335",
    "metadata": {
     "hide-output": false
    },
@@ -1554,7 +1554,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "ea719b89",
+   "id": "110f1b15",
    "metadata": {
     "hide-output": false
    },
@@ -1568,7 +1568,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "b8fa9721",
+   "id": "c80109f4",
    "metadata": {
     "hide-output": false
    },
@@ -1579,7 +1579,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5d8d2132",
+   "id": "6cc65e37",
    "metadata": {},
    "source": [
     "## Solving a Continuation Ramsey Planner’s Bellman Equation\n",
@@ -1640,7 +1640,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "f0b3ce8b",
+   "id": "a6ced0c7",
    "metadata": {
     "hide-output": false
    },
@@ -1655,7 +1655,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "b44bcfa0",
+   "id": "720bf017",
    "metadata": {
     "hide-output": false
    },
@@ -1667,7 +1667,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "22a347d6",
+   "id": "f6be9744",
    "metadata": {},
    "source": [
     "First, a quick check that our approximations of the value functions are\n",
@@ -1679,7 +1679,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "d2fe693d",
+   "id": "abe5993d",
    "metadata": {
     "hide-output": false
    },
@@ -1690,7 +1690,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "96226e7c",
+   "id": "78ae241d",
    "metadata": {},
    "source": [
     "The value functions plotted below trace out the right edges of the sets\n",
@@ -1700,7 +1700,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "fd022afd",
+   "id": "b06389ce",
    "metadata": {
     "hide-output": false
    },
@@ -1719,7 +1719,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d3f4bea8",
+   "id": "18536c4e",
    "metadata": {},
    "source": [
     "The next figure plots the optimal policy functions; values of\n",
@@ -1729,7 +1729,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "63f314e4",
+   "id": "838a7f5d",
    "metadata": {
     "hide-output": false
    },
@@ -1754,7 +1754,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5f28af12",
+   "id": "de833d91",
    "metadata": {},
    "source": [
     "With the first set of parameter values,  the value of $ \\theta' $ chosen by the Ramsey\n",
@@ -1775,7 +1775,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "479b0f34",
+   "id": "c5613b2b",
    "metadata": {
     "hide-output": false
    },
@@ -1794,7 +1794,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3cce09a7",
+   "id": "4e970ea5",
    "metadata": {},
    "source": [
     "Subproblem 2 is equivalent to the planner choosing the initial value of\n",
@@ -1810,7 +1810,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "8d96e53f",
+   "id": "c1b7f2da",
    "metadata": {
     "hide-output": false
    },
@@ -1833,7 +1833,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1703c3e5",
+   "id": "6d2fd339",
    "metadata": {},
    "source": [
     "### Next Steps\n",
@@ -1849,7 +1849,7 @@
   }
  ],
  "metadata": {
-  "date": 1680677524.3144863,
+  "date": 1685490451.3060262,
   "filename": "chang_ramsey.md",
   "kernelspec": {
    "display_name": "Python",
diff --git a/classical_filtering.ipynb b/classical_filtering.ipynb
index bcca85a..ed07b2c 100644
--- a/classical_filtering.ipynb
+++ b/classical_filtering.ipynb
@@ -2,7 +2,7 @@
  "cells": [
   {
    "cell_type": "markdown",
-   "id": "eb8b41f4",
+   "id": "a19345bd",
    "metadata": {},
    "source": [
     "\n",
@@ -11,7 +11,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "fde30b06",
+   "id": "f919c9c3",
    "metadata": {},
    "source": [
     "# Classical Prediction and Filtering With Linear Algebra"
@@ -19,7 +19,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9adb48cb",
+   "id": "7e60d61c",
    "metadata": {},
    "source": [
     "## Contents\n",
@@ -34,7 +34,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "547fa1db",
+   "id": "01ca56f6",
    "metadata": {},
    "source": [
     "## Overview\n",
@@ -87,7 +87,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "d9197e1f",
+   "id": "2c03bb06",
    "metadata": {
     "hide-output": false
    },
@@ -98,7 +98,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b29752ba",
+   "id": "1c36e6e2",
    "metadata": {},
    "source": [
     "### References\n",
@@ -108,7 +108,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "af12fcef",
+   "id": "8e86fa27",
    "metadata": {},
    "source": [
     "## Finite Dimensional Prediction\n",
@@ -260,7 +260,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "76eeddc9",
+   "id": "bc89ab56",
    "metadata": {},
    "source": [
     "### Implementation\n",
@@ -271,7 +271,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "203e5d07",
+   "id": "0e7837f4",
    "metadata": {
     "hide-output": false
    },
@@ -587,7 +587,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "bf200a20",
+   "id": "b39ecf17",
    "metadata": {},
    "source": [
     "Let’s use this code to tackle two interesting examples."
@@ -595,7 +595,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3e750646",
+   "id": "585cf286",
    "metadata": {},
    "source": [
     "### Example 1\n",
@@ -618,7 +618,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "83cc393d",
+   "id": "0558bd1a",
    "metadata": {
     "hide-output": false
    },
@@ -634,7 +634,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "371ea6e6",
+   "id": "45862974",
    "metadata": {},
    "source": [
     "The Wold representation is computed by `example.coeffs_of_c()`.\n",
@@ -645,7 +645,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "bbf52187",
+   "id": "3eb357cc",
    "metadata": {
     "hide-output": false
    },
@@ -657,7 +657,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "8b256f79",
+   "id": "7f60b34c",
    "metadata": {
     "hide-output": false
    },
@@ -668,7 +668,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5c75500d",
+   "id": "d7b5a9ac",
    "metadata": {},
    "source": [
     "Now let’s form the covariance matrix of a time series vector of length $ N $\n",
@@ -681,7 +681,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "ab3277bb",
+   "id": "502e2ed6",
    "metadata": {
     "hide-output": false
    },
@@ -693,7 +693,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4e373c21",
+   "id": "1c89ceb4",
    "metadata": {},
    "source": [
     "Notice how the lower rows of the “moving average representations” are converging to the appropriate infinite history Wold representation\n",
@@ -703,7 +703,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "39ef1abc",
+   "id": "a571d60b",
    "metadata": {
     "hide-output": false
    },
@@ -715,7 +715,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "02b059f0",
+   "id": "ad388524",
    "metadata": {},
    "source": [
     "Notice how the lower rows of the “autoregressive representations” are converging to the appropriate infinite-history\n",
@@ -725,7 +725,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "7999e4e4",
+   "id": "ec300abe",
    "metadata": {
     "hide-output": false
    },
@@ -737,7 +737,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e9ecb0ae",
+   "id": "a3b98313",
    "metadata": {},
    "source": [
     "### Example 2\n",
@@ -764,7 +764,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "8c371256",
+   "id": "d0110d79",
    "metadata": {
     "hide-output": false
    },
@@ -782,7 +782,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "0c4401a8",
+   "id": "35c53ccd",
    "metadata": {
     "hide-output": false
    },
@@ -794,7 +794,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "d48632df",
+   "id": "634fe24d",
    "metadata": {
     "hide-output": false
    },
@@ -807,7 +807,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "dc93af90",
+   "id": "b36a9485",
    "metadata": {
     "hide-output": false
    },
@@ -820,7 +820,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "4757671e",
+   "id": "2cffa0be",
    "metadata": {
     "hide-output": false
    },
@@ -832,7 +832,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f5798b1e",
+   "id": "4f49c18f",
    "metadata": {},
    "source": [
     "### Prediction\n",
@@ -914,7 +914,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a386b15f",
+   "id": "b0332d6e",
    "metadata": {},
    "source": [
     "## Combined Finite Dimensional Control and Prediction\n",
@@ -1002,7 +1002,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "0c3e275b",
+   "id": "8686fc12",
    "metadata": {},
    "source": [
     "## Infinite Horizon Prediction and Filtering Problems\n",
@@ -1068,7 +1068,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "421fe385",
+   "id": "3b70ce7e",
    "metadata": {},
    "source": [
     "### Problem Formulation\n",
@@ -1448,7 +1448,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f4dff48c",
+   "id": "79b03efa",
    "metadata": {},
    "source": [
     "## Exercises"
@@ -1456,7 +1456,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4996d988",
+   "id": "ab7fa290",
    "metadata": {},
    "source": [
     "## Exercise 32.1\n",
@@ -1491,7 +1491,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "16b38e80",
+   "id": "a99c6b35",
    "metadata": {},
    "source": [
     "## Exercise 32.2\n",
@@ -1571,7 +1571,7 @@
   }
  ],
  "metadata": {
-  "date": 1680677524.3873453,
+  "date": 1685490451.3799813,
   "filename": "classical_filtering.md",
   "kernelspec": {
    "display_name": "Python",
diff --git a/coase.ipynb b/coase.ipynb
index 7ab0c5f..9cfec24 100644
--- a/coase.ipynb
+++ b/coase.ipynb
@@ -2,7 +2,7 @@
  "cells": [
   {
    "cell_type": "markdown",
-   "id": "06430654",
+   "id": "521486eb",
    "metadata": {},
    "source": [
     "\n",
@@ -11,7 +11,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5f04c55d",
+   "id": "9270a698",
    "metadata": {},
    "source": [
     "# Coase’s Theory of the Firm"
@@ -19,7 +19,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "df4038c9",
+   "id": "f640c0b4",
    "metadata": {},
    "source": [
     "## Contents\n",
@@ -35,7 +35,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "8cab7335",
+   "id": "cdfbdde1",
    "metadata": {},
    "source": [
     "In addition to what’s in Anaconda, this lecture will need the following libraries:"
@@ -44,7 +44,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "f662a2b8",
+   "id": "61653ff7",
    "metadata": {
     "hide-output": false
    },
@@ -55,7 +55,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5c8a5bb9",
+   "id": "6a899475",
    "metadata": {},
    "source": [
     "## Overview\n",
@@ -86,7 +86,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "691359dd",
+   "id": "683ea44d",
    "metadata": {
     "hide-output": false
    },
@@ -101,7 +101,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "069da296",
+   "id": "850266ce",
    "metadata": {},
    "source": [
     "### Why Firms Exist\n",
@@ -134,7 +134,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "cabe5aab",
+   "id": "c1994dd4",
    "metadata": {},
    "source": [
     "### A Trade-Off\n",
@@ -171,7 +171,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "43f24908",
+   "id": "54fa3897",
    "metadata": {},
    "source": [
     "### Summary\n",
@@ -185,7 +185,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a3f86e7d",
+   "id": "e3fba190",
    "metadata": {},
    "source": [
     "### A Quantitative Interpretation\n",
@@ -203,7 +203,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "bb436677",
+   "id": "3e87e3d4",
    "metadata": {},
    "source": [
     "## The Model\n",
@@ -219,7 +219,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f2f7218d",
+   "id": "8ba4eabe",
    "metadata": {},
    "source": [
     "### Subcontracting\n",
@@ -262,7 +262,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4d293fe9",
+   "id": "508c3fbe",
    "metadata": {},
    "source": [
     "### Costs\n",
@@ -292,7 +292,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "63f15c7e",
+   "id": "9dc833a6",
    "metadata": {},
    "source": [
     "## Equilibrium\n",
@@ -315,7 +315,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c5dd6906",
+   "id": "e6108741",
    "metadata": {},
    "source": [
     "### Informal Definition of Equilibrium\n",
@@ -329,7 +329,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9090fb84",
+   "id": "434f26f2",
    "metadata": {},
    "source": [
     "### Formal Definition of Equilibrium\n",
@@ -387,7 +387,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "efc50ef8",
+   "id": "812f9b05",
    "metadata": {},
    "source": [
     "## Existence, Uniqueness and Computation of Equilibria\n",
@@ -397,7 +397,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "068affb4",
+   "id": "d599fdd1",
    "metadata": {},
    "source": [
     "### A Fixed Point Method\n",
@@ -498,7 +498,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1b9698f6",
+   "id": "03ea9470",
    "metadata": {},
    "source": [
     "### Marginal Conditions\n",
@@ -552,7 +552,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "012e5410",
+   "id": "ecde43b3",
    "metadata": {},
    "source": [
     "## Implementation\n",
@@ -577,7 +577,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "fcfeb4ba",
+   "id": "e78ec140",
    "metadata": {
     "hide-output": false
    },
@@ -596,7 +596,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "82d718e5",
+   "id": "cf8eebaa",
    "metadata": {},
    "source": [
     "Now let’s implement and iterate with $ T $ until convergence.\n",
@@ -608,7 +608,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "e49cdb99",
+   "id": "2b92d778",
    "metadata": {
     "hide-output": false
    },
@@ -647,7 +647,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d76ab843",
+   "id": "cd44aa5e",
    "metadata": {},
    "source": [
     "The next function computes optimal choice of upstream boundary and range of\n",
@@ -657,7 +657,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "1a8c14f0",
+   "id": "f5226363",
    "metadata": {
     "hide-output": false
    },
@@ -684,7 +684,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1b83bb67",
+   "id": "b2cbea1c",
    "metadata": {},
    "source": [
     "The allocation of firms can be computed by recursively stepping through firms’ choices of\n",
@@ -696,7 +696,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "f8488a7f",
+   "id": "27f75dac",
    "metadata": {
     "hide-output": false
    },
@@ -713,7 +713,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "31788601",
+   "id": "ee6aa211",
    "metadata": {},
    "source": [
     "Let’s try this at the default parameters.\n",
@@ -725,7 +725,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "c47cd315",
+   "id": "42925147",
    "metadata": {
     "hide-output": false
    },
@@ -748,7 +748,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "53fbaf3f",
+   "id": "1a063ce5",
    "metadata": {},
    "source": [
     "Here’s the function $ \\ell^* $, which shows how large a firm with\n",
@@ -758,7 +758,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "93116a69",
+   "id": "9ce3882f",
    "metadata": {
     "hide-output": false
    },
@@ -777,7 +777,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ae1c7030",
+   "id": "70425f63",
    "metadata": {},
    "source": [
     "Note that downstream firms choose to be larger, a point we return to below."
@@ -785,7 +785,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "60eba7b3",
+   "id": "361d8648",
    "metadata": {},
    "source": [
     "## Exercises\n",
@@ -796,7 +796,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c33539e1",
+   "id": "b5cde36a",
    "metadata": {},
    "source": [
     "## Exercise 15.1\n",
@@ -810,7 +810,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3e8ffacd",
+   "id": "43cb9600",
    "metadata": {},
    "source": [
     "## Solution to[ Exercise 15.1](https://python-advanced.quantecon.org/#coa_ex1)\n",
@@ -821,7 +821,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "3020cfaf",
+   "id": "65faefbc",
    "metadata": {
     "hide-output": false
    },
@@ -838,7 +838,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1ebabe80",
+   "id": "7599518b",
    "metadata": {},
    "source": [
     "## Exercise 15.2\n",
@@ -854,7 +854,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "727bb2aa",
+   "id": "d9fc26dd",
    "metadata": {},
    "source": [
     "## Solution to[ Exercise 15.2](https://python-advanced.quantecon.org/#coa_ex2)\n",
@@ -877,7 +877,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "9940bcad",
+   "id": "277bc311",
    "metadata": {
     "hide-output": false
    },
@@ -901,7 +901,7 @@
   }
  ],
  "metadata": {
-  "date": 1680677524.641318,
+  "date": 1685490451.4266462,
   "filename": "coase.md",
   "kernelspec": {
    "display_name": "Python",
diff --git a/cons_news.ipynb b/cons_news.ipynb
index c8ffe4a..4468ae8 100644
--- a/cons_news.ipynb
+++ b/cons_news.ipynb
@@ -2,7 +2,7 @@
  "cells": [
   {
    "cell_type": "markdown",
-   "id": "0fa2560a",
+   "id": "ed7e4a51",
    "metadata": {},
    "source": [
     "\n",
@@ -11,7 +11,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "0e5e186f",
+   "id": "e029c301",
    "metadata": {},
    "source": [
     "# Information and Consumption Smoothing"
@@ -19,7 +19,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "be29e05d",
+   "id": "3f7a6c5e",
    "metadata": {},
    "source": [
     "## Contents\n",
@@ -41,7 +41,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "364a4fb1",
+   "id": "a9f07d4f",
    "metadata": {},
    "source": [
     "In addition to what’s in Anaconda, this lecture employs the following libraries:"
@@ -50,7 +50,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "ec845999",
+   "id": "6f616004",
    "metadata": {
     "hide-output": false
    },
@@ -61,7 +61,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "92ae8676",
+   "id": "731e2515",
    "metadata": {},
    "source": [
     "## Overview\n",
@@ -87,7 +87,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "687d8574",
+   "id": "04845219",
    "metadata": {},
    "source": [
     "### Same non-financial incomes, different information\n",
@@ -148,7 +148,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5461bbcd",
+   "id": "4a64a0f6",
    "metadata": {},
    "source": [
     "## Two Representations of  One Nonfinancial Income Process\n",
@@ -279,7 +279,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "60a9f1f7",
+   "id": "734beec1",
    "metadata": {},
    "source": [
     "## Application of Kalman filter\n",
@@ -327,7 +327,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d33630b8",
+   "id": "b217153a",
    "metadata": {},
    "source": [
     "## News Shocks and Less Informative Shocks\n",
@@ -426,7 +426,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "662d1cd6",
+   "id": "c0c096ab",
    "metadata": {},
    "source": [
     "## Representation of $ \\epsilon_t $ Shock in Terms of Future $ y_t $\n",
@@ -458,7 +458,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4a121221",
+   "id": "c53c7ea2",
    "metadata": {},
    "source": [
     "## Representation in Terms of $ a_t $ Shocks\n",
@@ -487,7 +487,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e11c36d0",
+   "id": "1445ff41",
    "metadata": {},
    "source": [
     "## Permanent Income Consumption-Smoothing Model\n",
@@ -543,7 +543,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "217cde9f",
+   "id": "91fbc26f",
    "metadata": {},
    "source": [
     "## State Space Representations\n",
@@ -585,7 +585,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f928964c",
+   "id": "0ba16f4a",
    "metadata": {},
    "source": [
     "## Computations\n",
@@ -706,7 +706,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "8e6742a0",
+   "id": "c68b0e7e",
    "metadata": {
     "hide-output": false
    },
@@ -721,7 +721,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "b88e1ab9",
+   "id": "6f7d4f12",
    "metadata": {
     "hide-output": false
    },
@@ -743,7 +743,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "1bd74142",
+   "id": "f9f3868e",
    "metadata": {
     "hide-output": false
    },
@@ -764,7 +764,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "92565541",
+   "id": "eea6d47d",
    "metadata": {
     "hide-output": false
    },
@@ -776,7 +776,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "18183521",
+   "id": "a204a390",
    "metadata": {},
    "source": [
     "Evidently, optimal consumption and debt decision rules for the consumer\n",
@@ -795,7 +795,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "d576d6e7",
+   "id": "1fd04c01",
    "metadata": {
     "hide-output": false
    },
@@ -815,7 +815,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "efbf4c93",
+   "id": "ec9a10e6",
    "metadata": {
     "hide-output": false
    },
@@ -826,7 +826,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "bf47605b",
+   "id": "ec7f03a9",
    "metadata": {},
    "source": [
     "For a consumer having access only to the information associated with the\n",
@@ -879,7 +879,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "e39adb23",
+   "id": "6869f287",
    "metadata": {
     "hide-output": false
    },
@@ -899,7 +899,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "dff2e121",
+   "id": "6f0434c4",
    "metadata": {},
    "source": [
     "The following code computes impulse response functions of\n",
@@ -909,7 +909,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "3177355f",
+   "id": "f83dcabb",
    "metadata": {
     "hide-output": false
    },
@@ -929,7 +929,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "9bc0ccf8",
+   "id": "537688d7",
    "metadata": {
     "hide-output": false
    },
@@ -941,7 +941,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "bd08aa7b",
+   "id": "0e337ab2",
    "metadata": {
     "hide-output": false
    },
@@ -955,7 +955,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "0dce3fbe",
+   "id": "d78c0711",
    "metadata": {},
    "source": [
     "The above two impulse response functions show that when the consumer has\n",
@@ -971,7 +971,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "f73a3fbd",
+   "id": "b3e999f9",
    "metadata": {
     "hide-output": false
    },
@@ -983,7 +983,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "f9fe4908",
+   "id": "5a321d1b",
    "metadata": {
     "hide-output": false
    },
@@ -998,7 +998,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ab7e1a8a",
+   "id": "1c8fda5a",
    "metadata": {},
    "source": [
     "The above impulse responses show that when the consumer has only the\n",
@@ -1022,7 +1022,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "89cba0aa",
+   "id": "eb03de54",
    "metadata": {
     "hide-output": false
    },
@@ -1035,7 +1035,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "8e62dd7f",
+   "id": "450eed60",
    "metadata": {
     "hide-output": false
    },
@@ -1052,7 +1052,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "0fa044a9",
+   "id": "17150bea",
    "metadata": {
     "hide-output": false
    },
@@ -1068,7 +1068,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f1444a94",
+   "id": "8307df15",
    "metadata": {},
    "source": [
     "## Simulating  Income Process and Two Associated Shock Processes\n",
@@ -1107,7 +1107,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "24bffa3b",
+   "id": "51316c93",
    "metadata": {},
    "source": [
     "## Calculating Innovations in Another Way\n",
@@ -1135,7 +1135,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "39cf95cd",
+   "id": "cebfe6bf",
    "metadata": {},
    "source": [
     "## Another Invertibility Issue\n",
@@ -1149,7 +1149,7 @@
   }
  ],
  "metadata": {
-  "date": 1680677524.7046556,
+  "date": 1685490451.6691341,
   "filename": "cons_news.md",
   "kernelspec": {
    "display_name": "Python",
diff --git a/discrete_dp.ipynb b/discrete_dp.ipynb
index 9fa3dc4..5bb722c 100644
--- a/discrete_dp.ipynb
+++ b/discrete_dp.ipynb
@@ -2,7 +2,7 @@
  "cells": [
   {
    "cell_type": "markdown",
-   "id": "bd86db13",
+   "id": "006a938b",
    "metadata": {},
    "source": [
     "\n",
@@ -11,7 +11,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "df75ba7d",
+   "id": "98f777c3",
    "metadata": {},
    "source": [
     "# Discrete State Dynamic Programming"
@@ -19,7 +19,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "992feaa2",
+   "id": "611a4e20",
    "metadata": {},
    "source": [
     "## Contents\n",
@@ -36,7 +36,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "041c11e3",
+   "id": "e79b250a",
    "metadata": {},
    "source": [
     "In addition to what’s in Anaconda, this lecture will need the following libraries:"
@@ -45,7 +45,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "ecfcbb1d",
+   "id": "cf27f9c2",
    "metadata": {
     "hide-output": false
    },
@@ -56,7 +56,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7097e091",
+   "id": "57e908b8",
    "metadata": {},
    "source": [
     "## Overview\n",
@@ -96,7 +96,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "f46aac84",
+   "id": "344ff064",
    "metadata": {
     "hide-output": false
    },
@@ -113,7 +113,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "744f2fdb",
+   "id": "87444033",
    "metadata": {},
    "source": [
     "### How to Read this Lecture\n",
@@ -129,7 +129,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "161ffe8d",
+   "id": "772c466e",
    "metadata": {},
    "source": [
     "### Code\n",
@@ -148,7 +148,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d1a73aca",
+   "id": "aaa98f18",
    "metadata": {},
    "source": [
     "### References\n",
@@ -170,7 +170,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b185f569",
+   "id": "44ab312f",
    "metadata": {},
    "source": [
     "## Discrete DPs\n",
@@ -209,7 +209,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "2d37e062",
+   "id": "134d7826",
    "metadata": {},
    "source": [
     "### Policies\n",
@@ -240,7 +240,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ea3e887d",
+   "id": "ca81a694",
    "metadata": {},
    "source": [
     "### Formal Definition\n",
@@ -303,7 +303,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3f235818",
+   "id": "2100e08b",
    "metadata": {},
    "source": [
     "### Value and Optimality\n",
@@ -348,7 +348,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "db693437",
+   "id": "4b10c2bb",
    "metadata": {},
    "source": [
     "### Two Operators\n",
@@ -400,7 +400,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a5a3dfff",
+   "id": "b6b3c02e",
    "metadata": {},
    "source": [
     "### The Bellman Equation and the Principle of Optimality\n",
@@ -436,7 +436,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c6186716",
+   "id": "418b7a97",
    "metadata": {},
    "source": [
     "## Solving Discrete DPs\n",
@@ -457,7 +457,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "8aa98054",
+   "id": "27cacff3",
    "metadata": {},
    "source": [
     "### Value Function Iteration\n",
@@ -473,7 +473,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "920c7091",
+   "id": "b0e01981",
    "metadata": {},
    "source": [
     "### Policy Function Iteration\n",
@@ -496,7 +496,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "67ed4911",
+   "id": "ec74361e",
    "metadata": {},
    "source": [
     "### Modified Policy Function Iteration\n",
@@ -515,7 +515,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3b8a5782",
+   "id": "8f00e64d",
    "metadata": {},
    "source": [
     "## Example: A Growth Model\n",
@@ -547,7 +547,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c3ae3497",
+   "id": "0344b219",
    "metadata": {},
    "source": [
     "### Discrete DP Representation\n",
@@ -580,7 +580,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "73f851b8",
+   "id": "3afc51ba",
    "metadata": {},
    "source": [
     "### Defining a DiscreteDP Instance\n",
@@ -609,7 +609,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "4a019cf0",
+   "id": "42bad1d8",
    "metadata": {
     "hide-output": false
    },
@@ -660,7 +660,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a963ba81",
+   "id": "d11dc571",
    "metadata": {},
    "source": [
     "Let’s run this code and create an instance of `SimpleOG`."
@@ -669,7 +669,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "8184f663",
+   "id": "0d9a08e9",
    "metadata": {
     "hide-output": false
    },
@@ -680,7 +680,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e624d140",
+   "id": "08dc111d",
    "metadata": {},
    "source": [
     "Instances of `DiscreteDP` are created using the signature `DiscreteDP(R, Q, β)`.\n",
@@ -691,7 +691,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "6849dd17",
+   "id": "9b1f8d96",
    "metadata": {
     "hide-output": false
    },
@@ -702,7 +702,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6a00a5d2",
+   "id": "c676844a",
    "metadata": {},
    "source": [
     "Now that we have an instance `ddp` of `DiscreteDP` we can solve it as follows"
@@ -711,7 +711,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "1c4815bf",
+   "id": "4158b402",
    "metadata": {
     "hide-output": false
    },
@@ -722,7 +722,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ee1d3faf",
+   "id": "94cd2029",
    "metadata": {},
    "source": [
     "Let’s see what we’ve got here"
@@ -731,7 +731,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "ecfddaf2",
+   "id": "2b5ca6d3",
    "metadata": {
     "hide-output": false
    },
@@ -742,7 +742,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "8953edf7",
+   "id": "00784c5a",
    "metadata": {},
    "source": [
     "(In IPython version 4.0 and above you can also type `results.` and hit the tab key)\n",
@@ -753,7 +753,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "6d2ab426",
+   "id": "3d9c7e43",
    "metadata": {
     "hide-output": false
    },
@@ -765,7 +765,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "d68249db",
+   "id": "5cb36e1c",
    "metadata": {
     "hide-output": false
    },
@@ -776,7 +776,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5815e967",
+   "id": "ebb5ceb3",
    "metadata": {},
    "source": [
     "Since we’ve used policy iteration, these results will be exact unless we hit the iteration bound `max_iter`.\n",
@@ -787,7 +787,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "76925df9",
+   "id": "1c299fe0",
    "metadata": {
     "hide-output": false
    },
@@ -799,7 +799,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "fa1b5bfc",
+   "id": "499c3321",
    "metadata": {
     "hide-output": false
    },
@@ -810,7 +810,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7ce24cbb",
+   "id": "735428e0",
    "metadata": {},
    "source": [
     "Another interesting object is `results.mc`, which is the controlled chain defined by $ Q_{\\sigma^*} $, where $ \\sigma^* $ is the optimal policy.\n",
@@ -824,7 +824,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "06d7d13f",
+   "id": "acacd57c",
    "metadata": {
     "hide-output": false
    },
@@ -835,7 +835,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "2a24d2a6",
+   "id": "f26ba5ce",
    "metadata": {},
    "source": [
     "Here’s the same information in a bar graph\n",
@@ -849,7 +849,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "0b4e9d51",
+   "id": "f43fa59e",
    "metadata": {
     "hide-output": false
    },
@@ -862,7 +862,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "00d7355d",
+   "id": "17648230",
    "metadata": {},
    "source": [
     "If we look at the bar graph we can see the rightward shift in probability mass\n",
@@ -872,7 +872,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "84cad36e",
+   "id": "7677e8d7",
    "metadata": {},
    "source": [
     "### State-Action Pair Formulation\n",
@@ -896,7 +896,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "11a7e6b9",
+   "id": "325fd438",
    "metadata": {
     "hide-output": false
    },
@@ -929,7 +929,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e002d5fa",
+   "id": "eba6d9ba",
    "metadata": {},
    "source": [
     "For larger problems, you might need to write this code more efficiently by vectorizing or using Numba."
@@ -937,7 +937,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5909bd84",
+   "id": "cf67a3f2",
    "metadata": {},
    "source": [
     "## Exercises\n",
@@ -949,7 +949,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "74446860",
+   "id": "208f504a",
    "metadata": {},
    "source": [
     "## Solutions"
@@ -957,7 +957,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "025db164",
+   "id": "962adce1",
    "metadata": {},
    "source": [
     "### Setup\n",
@@ -971,7 +971,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "9ea62af6",
+   "id": "60570bde",
    "metadata": {
     "hide-output": false
    },
@@ -985,7 +985,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "00be9a58",
+   "id": "37a0cbaa",
    "metadata": {},
    "source": [
     "Here we want to solve a finite state version of the continuous state model above.\n",
@@ -996,7 +996,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "30ee87d3",
+   "id": "2d5b8eb1",
    "metadata": {
     "hide-output": false
    },
@@ -1009,7 +1009,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "badd9a2e",
+   "id": "1370623f",
    "metadata": {},
    "source": [
     "We choose the action to be the amount of capital to save for the next\n",
@@ -1038,7 +1038,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "1b428f09",
+   "id": "7c3b00eb",
    "metadata": {
     "hide-output": false
    },
@@ -1060,7 +1060,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "69e90492",
+   "id": "76b19962",
    "metadata": {},
    "source": [
     "Reward vector `R` (of length `L`):"
@@ -1069,7 +1069,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "5a7676ac",
+   "id": "198fd001",
    "metadata": {
     "hide-output": false
    },
@@ -1080,7 +1080,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "85c5c9d0",
+   "id": "3f2e5180",
    "metadata": {},
    "source": [
     "(Degenerate) transition probability matrix `Q` (of shape `(L, grid_size)`), where we choose the [scipy.sparse.lil_matrix](http://docs.scipy.org/doc/scipy/reference/generated/scipy.sparse.lil_matrix.html) format, while any format will do (internally it will be converted to the csr format):"
@@ -1089,7 +1089,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "ca753f6c",
+   "id": "b7b5ebf3",
    "metadata": {
     "hide-output": false
    },
@@ -1101,7 +1101,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7e290c03",
+   "id": "ab46e714",
    "metadata": {},
    "source": [
     "(If you are familiar with the data structure of [scipy.sparse.csr_matrix](http://docs.scipy.org/doc/scipy/reference/generated/scipy.sparse.csr_matrix.html), the following is the most efficient way to create the `Q` matrix in\n",
@@ -1111,7 +1111,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "6d7fa525",
+   "id": "31e93f26",
    "metadata": {
     "hide-output": false
    },
@@ -1124,7 +1124,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f6bdc351",
+   "id": "ad268f96",
    "metadata": {},
    "source": [
     "Discrete growth model:"
@@ -1133,7 +1133,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "623cc5fd",
+   "id": "f43c1d08",
    "metadata": {
     "hide-output": false
    },
@@ -1144,7 +1144,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a93ef971",
+   "id": "886aecaa",
    "metadata": {},
    "source": [
     "**Notes**\n",
@@ -1156,7 +1156,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "21fe435d",
+   "id": "3bec432a",
    "metadata": {},
    "source": [
     "### Solving the Model\n",
@@ -1167,7 +1167,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "ff5ede70",
+   "id": "456035f3",
    "metadata": {
     "hide-output": false
    },
@@ -1180,7 +1180,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "23a9e835",
+   "id": "20c9bba5",
    "metadata": {},
    "source": [
     "Note that `sigma` contains the *indices* of the optimal *capital\n",
@@ -1191,7 +1191,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "022a949f",
+   "id": "934349e1",
    "metadata": {
     "hide-output": false
    },
@@ -1214,7 +1214,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "daa68d84",
+   "id": "a7100d9b",
    "metadata": {},
    "source": [
     "Let us compare the solution of the discrete model with that of the\n",
@@ -1224,7 +1224,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "d0a666a2",
+   "id": "8d733ee7",
    "metadata": {
     "hide-output": false
    },
@@ -1253,7 +1253,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "8cef2341",
+   "id": "7546d532",
    "metadata": {},
    "source": [
     "The outcomes appear very close to those of the continuous version.\n",
@@ -1264,7 +1264,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "53b0621b",
+   "id": "122f674d",
    "metadata": {
     "hide-output": false
    },
@@ -1276,7 +1276,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "3fb3764f",
+   "id": "30d7f438",
    "metadata": {
     "hide-output": false
    },
@@ -1287,7 +1287,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "02ff845f",
+   "id": "eb7761e6",
    "metadata": {},
    "source": [
     "The optimal consumption functions are close as well:"
@@ -1296,7 +1296,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "74a921bb",
+   "id": "8e52f084",
    "metadata": {
     "hide-output": false
    },
@@ -1307,7 +1307,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ad5b9e19",
+   "id": "9ec2e711",
    "metadata": {},
    "source": [
     "In fact, the optimal consumption obtained in the discrete version is not\n",
@@ -1317,7 +1317,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "b6029edf",
+   "id": "8bb0e52b",
    "metadata": {
     "hide-output": false
    },
@@ -1330,7 +1330,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "6d054fc6",
+   "id": "80ab9e6a",
    "metadata": {
     "hide-output": false
    },
@@ -1343,7 +1343,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "f6f41ea0",
+   "id": "92675670",
    "metadata": {
     "hide-output": false
    },
@@ -1354,7 +1354,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "8c248576",
+   "id": "21ca03d6",
    "metadata": {},
    "source": [
     "The value function is monotone:"
@@ -1363,7 +1363,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "3e7a088a",
+   "id": "7b521d1d",
    "metadata": {
     "hide-output": false
    },
@@ -1374,7 +1374,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "fa2ebbdd",
+   "id": "b982a748",
    "metadata": {},
    "source": [
     "### Comparison of the Solution Methods\n",
@@ -1384,7 +1384,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "996ad702",
+   "id": "c4b56897",
    "metadata": {},
    "source": [
     "#### Value Iteration"
@@ -1393,7 +1393,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "d09837cd",
+   "id": "7ebb67b3",
    "metadata": {
     "hide-output": false
    },
@@ -1408,7 +1408,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "e50bbc23",
+   "id": "f46e3cd4",
    "metadata": {
     "hide-output": false
    },
@@ -1419,7 +1419,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "859d1c96",
+   "id": "9472e42c",
    "metadata": {},
    "source": [
     "#### Modified Policy Iteration"
@@ -1428,7 +1428,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "46f34f9c",
+   "id": "1526c163",
    "metadata": {
     "hide-output": false
    },
@@ -1441,7 +1441,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "3e055e9a",
+   "id": "1343b9b7",
    "metadata": {
     "hide-output": false
    },
@@ -1452,7 +1452,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ddaffb3d",
+   "id": "ebdcbb2c",
    "metadata": {},
    "source": [
     "#### Speed Comparison"
@@ -1461,7 +1461,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "9a5028fe",
+   "id": "64c426fd",
    "metadata": {
     "hide-output": false
    },
@@ -1474,7 +1474,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c55b7197",
+   "id": "5c5c56cd",
    "metadata": {},
    "source": [
     "As is often the case, policy iteration and modified policy iteration are\n",
@@ -1483,7 +1483,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "68336c11",
+   "id": "661d0eed",
    "metadata": {},
    "source": [
     "### Replication of the Figures\n",
@@ -1493,7 +1493,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "36f0988e",
+   "id": "15188091",
    "metadata": {},
    "source": [
     "#### Convergence of Value Iteration\n",
@@ -1506,7 +1506,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "ada282a6",
+   "id": "80f6cdbe",
    "metadata": {
     "hide-output": false
    },
@@ -1531,7 +1531,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f0ac695e",
+   "id": "50fd49d3",
    "metadata": {},
    "source": [
     "We next plot the consumption policies along with the value iteration"
@@ -1540,7 +1540,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "711c7794",
+   "id": "9748a8bf",
    "metadata": {
     "hide-output": false
    },
@@ -1573,7 +1573,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "745f354e",
+   "id": "3f36b189",
    "metadata": {},
    "source": [
     "#### Dynamics of the Capital Stock\n",
@@ -1588,7 +1588,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "7f56b000",
+   "id": "ece646fc",
    "metadata": {
     "hide-output": false
    },
@@ -1623,7 +1623,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "055fc0b4",
+   "id": "24895af9",
    "metadata": {},
    "source": [
     "\n",
@@ -1632,7 +1632,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "12b441e1",
+   "id": "464515fa",
    "metadata": {},
    "source": [
     "## Appendix: Algorithms\n",
@@ -1647,7 +1647,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ef0bc3aa",
+   "id": "34f659cc",
    "metadata": {},
    "source": [
     "### Value Iteration\n",
@@ -1674,7 +1674,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4fa6590d",
+   "id": "5a75c822",
    "metadata": {},
    "source": [
     "### Policy Iteration\n",
@@ -1700,7 +1700,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c2b14057",
+   "id": "3bfb0ac2",
    "metadata": {},
    "source": [
     "### Modified Policy Iteration\n",
@@ -1726,7 +1726,7 @@
   }
  ],
  "metadata": {
-  "date": 1680677524.7917743,
+  "date": 1685490451.7548275,
   "filename": "discrete_dp.md",
   "kernelspec": {
    "display_name": "Python",
diff --git a/dyn_stack.ipynb b/dyn_stack.ipynb
index 10188c5..61599dd 100644
--- a/dyn_stack.ipynb
+++ b/dyn_stack.ipynb
@@ -2,7 +2,7 @@
  "cells": [
   {
    "cell_type": "markdown",
-   "id": "3432f1c5",
+   "id": "27257cd4",
    "metadata": {},
    "source": [
     "\n",
@@ -11,7 +11,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "fd64e3c6",
+   "id": "71eaeb53",
    "metadata": {},
    "source": [
     "# Stackelberg Plans"
@@ -19,7 +19,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "87f8acb9",
+   "id": "cc713f02",
    "metadata": {},
    "source": [
     "## Contents\n",
@@ -29,7 +29,7 @@
     "  - [Duopoly](#Duopoly)  \n",
     "  - [Stackelberg Problem](#Stackelberg-Problem)  \n",
     "  - [Two Bellman Equations](#Two-Bellman-Equations)  \n",
-    "  - [Stackelberg Plan](#Stackelberg-Plan)  \n",
+    "  - [Stackelberg Plan for Duopoly](#Stackelberg-Plan-for-Duopoly)  \n",
     "  - [Recursive Representation of Stackelberg Plan](#Recursive-Representation-of-Stackelberg-Plan)  \n",
     "  - [Dynamic Programming and Time Consistency of Follower’s Problem](#Dynamic-Programming-and-Time-Consistency-of-Follower’s-Problem)  \n",
     "  - [Computing  Stackelberg Plan](#Computing--Stackelberg-Plan)  \n",
@@ -42,7 +42,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e6fa2805",
+   "id": "d319e9db",
    "metadata": {},
    "source": [
     "In addition to what’s in Anaconda, this lecture will need the following libraries:"
@@ -51,7 +51,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "57e5eddb",
+   "id": "ac6956c7",
    "metadata": {
     "hide-output": false
    },
@@ -62,7 +62,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "2cfdf6e2",
+   "id": "e9b10d87",
    "metadata": {},
    "source": [
     "## Overview\n",
@@ -87,7 +87,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "7b42f9c0",
+   "id": "12b85034",
    "metadata": {
     "hide-output": false
    },
@@ -103,7 +103,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7f50ad13",
+   "id": "0924cdb3",
    "metadata": {},
    "source": [
     "## Duopoly\n",
@@ -153,7 +153,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c7b45cec",
+   "id": "4d99c396",
    "metadata": {},
    "source": [
     "### Stackelberg Leader and Follower\n",
@@ -179,7 +179,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "74226b18",
+   "id": "12ad6002",
    "metadata": {},
    "source": [
     "### Statement of  Leader’s and Follower’s Problems\n",
@@ -231,7 +231,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c4b148b5",
+   "id": "62e64474",
    "metadata": {},
    "source": [
     "### Firms’ Problems\n",
@@ -287,7 +287,7 @@
     "\n",
     "<a id='equation-sstack1'></a>\n",
     "$$\n",
-    "q_{1t} + (1+\\beta + c_1) q_{1t+1} - \\beta q_{1t+2} = c_0 - c_2 q_{2t+1} \\tag{40.1}\n",
+    "- q_{1t} + (1+\\beta + c_1) q_{1t+1} - \\beta q_{1t+2} = c_0 - c_2 q_{2t+1} \\tag{40.1}\n",
     "$$\n",
     "\n",
     "Equation [(40.1)](#equation-sstack1) is a second-order difference equation in the sequence\n",
@@ -372,23 +372,23 @@
     "**Remarks:** We have formulated the Stackelberg problem in a space of\n",
     "sequences.\n",
     "\n",
-    "The max-min problem associated with Lagrangian\n",
+    "The max-min problem associated with firm 2’s Lagrangian\n",
     "[(40.4)](#equation-sstack4) is unpleasant because the time $ t $\n",
-    "component of firm $ 1 $’s payoff function depends on the entire\n",
-    "future of its choices of $ \\{q_{1t+j}\\}_{j=0}^\\infty $.\n",
+    "component of firm $ 2 $’s payoff function depends on the entire\n",
+    "future of its choices of $ \\{q_{2t+j}\\}_{j=0}^\\infty $.\n",
     "\n",
-    "This renders a direct attack on the problem cumbersome.\n",
+    "This renders a direct attack on the problem in the space of sequences cumbersome.\n",
     "\n",
-    "Therefore, below we will formulate the Stackelberg leader’s problem\n",
+    "Therefore, below we will  formulate the Stackelberg leader’s problem\n",
     "recursively.\n",
     "\n",
-    "We’ll put our little duopoly model into a broader class of models with\n",
-    "the same  structure."
+    "We’ll proceed by putting  our  duopoly model into a broader class of models with\n",
+    "the same  general structure."
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "7af80acd",
+   "id": "182d0182",
    "metadata": {},
    "source": [
     "## Stackelberg Problem\n",
@@ -475,7 +475,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "59aaa26f",
+   "id": "ed29db75",
    "metadata": {},
    "source": [
     "### Interpretation of  Second Block of Equations\n",
@@ -510,7 +510,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7495ba77",
+   "id": "6822a700",
    "metadata": {},
    "source": [
     "### More Mechanical Details\n",
@@ -524,20 +524,20 @@
     "\\Omega(y_0) = \\left\\{ (\\vec y_1, \\vec u_0) :  y_{t+1} = A y_t + B u_t, \\forall t \\geq 0 \\right\\}\n",
     "$$\n",
     "\n",
-    "Please remember that the follower’s Euler equation is embedded in the\n",
+    "Please remember that the follower’s system of  Euler equations is embedded in the\n",
     "system of dynamic equations $ y_{t+1} = A y_t + B u_t $.\n",
     "\n",
-    "Note that in the definition of $ \\Omega(y_0) $, $ y_0 $\n",
-    "is taken as given.\n",
+    "Note that  the definition of $ \\Omega(y_0) $ treats  $ y_0 $\n",
+    "as given.\n",
     "\n",
     "Although it is taken as given in $ \\Omega(y_0) $,\n",
-    "eventually, the $ x_0 $ component of $ y_0 $ will be chosen by the\n",
+    "eventually, the $ x_0 $ component of $ y_0 $ is to  be chosen by the\n",
     "Stackelberg leader."
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "bcd88b9e",
+   "id": "359c1573",
    "metadata": {},
    "source": [
     "### Two Subproblems\n",
@@ -581,13 +581,12 @@
     "Subproblem 2 optimizes over $ x_0 $.\n",
     "\n",
     "The value function $ w(z_0) $ tells the value of the Stackelberg plan\n",
-    "as a function of the vector of natural state variables at time $ 0 $,\n",
-    "$ z_0 $."
+    "as a function of the vector of natural state variables $ z_0 $ at time $ 0 $."
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "30a47a19",
+   "id": "b550a63b",
    "metadata": {},
    "source": [
     "## Two Bellman Equations\n",
@@ -649,33 +648,61 @@
     "\n",
     "which implies that\n",
     "\n",
+    "\n",
+    "<a id='equation-eq-subprob2x0'></a>\n",
     "$$\n",
-    "x_0 = - P_{22}^{-1} P_{21} z_0\n",
+    "x_0 = - P_{22}^{-1} P_{21} z_0 \\tag{40.10}\n",
     "$$"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "16ae2aab",
+   "id": "aa20cdc7",
    "metadata": {},
    "source": [
-    "## Stackelberg Plan\n",
+    "## Stackelberg Plan for Duopoly\n",
     "\n",
     "Now let’s map our duopoly model into the above setup.\n",
     "\n",
-    "We will formulate a state space system\n",
+    "We  formulate a state vector\n",
     "\n",
     "$$\n",
     "y_t = \\begin{bmatrix} z_t \\cr x_t \\end{bmatrix}\n",
     "$$\n",
     "\n",
-    "where in this instance $ x_t = v_{1t} $, the time $ t $ decision\n",
-    "of the follower firm 1."
+    "where for our duopoly model\n",
+    "\n",
+    "$$\n",
+    "z_t = \\begin{bmatrix} 1 \\cr q_{2t} \\cr q_{1t} \\end{bmatrix} , \\quad x_t = v_{1t},\n",
+    "$$\n",
+    "\n",
+    "where  $ x_t = v_{1t} $ is  the time $ t $ decision\n",
+    "of the follower firm 1, $ u_t $ is the time $ t $ decision of the leader firm 2 and\n",
+    "\n",
+    "$$\n",
+    "v_{1t} = q_{1t+1} - q_{1t}, \\quad u_t = q_{2t+1} - q_{2t} .\n",
+    "$$\n",
+    "\n",
+    "For our duopoly model, initial conditions for the natural state variables in $ z_t $ are\n",
+    "\n",
+    "$$\n",
+    "z_0 =  \\begin{bmatrix} 1 \\cr q_{20} \\cr q_{10} \\end{bmatrix}\n",
+    "$$\n",
+    "\n",
+    "while $ x_0 = v_{10} = q_{11} - q_{10} $  is a choice variable for the Stackelberg leader firm 2, one that will ultimately be chosen according an optimal rule prescribed by  [(40.10)](#equation-eq-subprob2x0)\n",
+    "for subproblem 2 above.\n",
+    "\n",
+    "That the Stackelberg leader firm 2 chooses $ x_0 = v_{10} $ is subtle.\n",
+    "\n",
+    "Of course,  $ x_0 = v_{10} $ emerges from the feedback-feedforward solution [(40.3)](#equation-sstack3) of firm 1’s system of Euler equations, so that it is actually\n",
+    "firm 1 that sets $ x_0 $.\n",
+    "\n",
+    "But firm 2 manipulates firm 1’s  choice through firm 2’s choice of the sequence $ \\vec q_{2,1} = \\{q_{2t+1}\\}_{t=0}^\\infty $."
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "fe8fbea0",
+   "id": "e2663267",
    "metadata": {},
    "source": [
     "### Calculations to Prepare Duopoly Model\n",
@@ -693,7 +720,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "dee17734",
+   "id": "3d5eb84b",
    "metadata": {},
    "source": [
     "### Firm 1’s Problem\n",
@@ -791,7 +818,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "fe93f77a",
+   "id": "287689e2",
    "metadata": {},
    "source": [
     "## Recursive Representation of Stackelberg Plan\n",
@@ -845,7 +872,7 @@
     "imply that for $ t \\geq 1 $\n",
     "\n",
     "$$\n",
-    "x_t = \\sum_{j=1}^t H_j^t \\check z_{t-j}\n",
+    "\\check x_t = \\sum_{j=1}^t H_j^t \\check z_{t-j}\n",
     "$$\n",
     "\n",
     "where\n",
@@ -870,10 +897,10 @@
     "\n",
     "<a id='equation-finalrule'></a>\n",
     "$$\n",
-    "u_t  = - F_z \\check z_t - F_x \\sum_{j=1}^t H^t_j z_{t-j} = \\sigma_t(\\check z^t) \\tag{40.10}\n",
+    "u_t  = - F_z \\check z_t - F_x \\sum_{j=1}^t H^t_j z_{t-j} = \\sigma_t(\\check z^t) \\tag{40.11}\n",
     "$$\n",
     "\n",
-    "Representation [(40.10)](#equation-finalrule) confirms that whenever\n",
+    "Representation [(40.11)](#equation-finalrule) confirms that whenever\n",
     "$ F_x \\neq 0 $, the typical situation, the time $ t $ component\n",
     "$ \\sigma_t $ of a Stackelberg plan is **history-dependent**, meaning\n",
     "that the Stackelberg leader’s choice $ u_t $ depends not just on\n",
@@ -882,7 +909,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "77bfbdd1",
+   "id": "b899fce8",
    "metadata": {},
    "source": [
     "### Comments and Interpretations\n",
@@ -895,14 +922,14 @@
     "The answer is that if we want to present to the Stackelberg **follower**\n",
     "a history-dependent representation of the Stackelberg **leader’s**\n",
     "sequence $ \\vec q_2 $, we must use representation\n",
-    "[(40.10)](#equation-finalrule) cast in terms of the history\n",
+    "[(40.11)](#equation-finalrule) cast in terms of the history\n",
     "$ \\check z^t $ and **not** a corresponding representation cast in\n",
     "terms of $ z^t $."
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "5a175dd0",
+   "id": "0cc9422d",
    "metadata": {},
    "source": [
     "## Dynamic Programming and Time Consistency of Follower’s Problem\n",
@@ -921,7 +948,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "321954ff",
+   "id": "5a3400f3",
    "metadata": {},
    "source": [
     "### Recursive Formulation of a Follower’s Problem\n",
@@ -986,7 +1013,7 @@
     "\\begin{bmatrix} \\tilde y_{t+1} \\\\\n",
     "q_{1t+1} \\end{bmatrix} = \\begin{bmatrix} A - BF & 0 \\\\\n",
     "0  & 1 \\end{bmatrix}  \\begin{bmatrix} \\tilde y_{t} \\\\\n",
-    "q_{1t} \\end{bmatrix} + \\begin{bmatrix} 0 \\cr 1 \\end{bmatrix} x_t \\tag{40.11}\n",
+    "q_{1t} \\end{bmatrix} + \\begin{bmatrix} 0 \\cr 1 \\end{bmatrix} x_t \\tag{40.12}\n",
     "$$\n",
     "\n",
     "This specification assures that from the point of the view of  firm 1,\n",
@@ -1044,17 +1071,17 @@
   },
   {
    "cell_type": "markdown",
-   "id": "51987c9f",
+   "id": "4016d2d7",
    "metadata": {},
    "source": [
     "### Time Consistency of Follower’s Plan\n",
     "\n",
     "The follower can solve its problem using dynamic programming  because its\n",
-    "problem is recursive in  **natural state variables**,\n",
+    "problem is recursive in what for it are the  **natural state variables**,\n",
     "namely\n",
     "\n",
     "$$\n",
-    "\\begin{bmatrix} 1 \\cr q_{2t} \\cr \\tilde q_{10} \\cr \\tilde x_0   \\end{bmatrix}\n",
+    "\\begin{bmatrix} 1 \\cr q_{2t} \\cr \\tilde q_{1t} \\cr \\tilde x_t   \\end{bmatrix}\n",
     "$$\n",
     "\n",
     "It follows that the follower’s plan is time consistent."
@@ -1062,19 +1089,21 @@
   },
   {
    "cell_type": "markdown",
-   "id": "fb3ed664",
+   "id": "13a49827",
    "metadata": {},
    "source": [
     "## Computing  Stackelberg Plan\n",
     "\n",
     "Here is our code to compute a Stackelberg plan via the linear-quadratic\n",
-    "dynamic program describe above"
+    "dynamic program describe above.\n",
+    "\n",
+    "Let’s use it to compute the Stackelberg plan."
    ]
   },
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "be12316f",
+   "id": "6a5b35f5",
    "metadata": {
     "hide-output": false
    },
@@ -1098,7 +1127,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "b52d89a8",
+   "id": "5b26e363",
    "metadata": {
     "hide-output": false
    },
@@ -1152,24 +1181,26 @@
     "    π_leader[t] = -(yt[:, t].T @ π_matrix @ yt[:, t])\n",
     "\n",
     "# Display policies\n",
-    "print(\"Computed policy for Stackelberg leader\\n\")\n",
+    "print(\"Computed policy for Continuation Stackelberg leader\\n\")\n",
     "print(f\"F = {F}\")"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "2e59cc02",
+   "id": "b6558404",
    "metadata": {},
    "source": [
     "## Time Series for Price and Quantities\n",
     "\n",
-    "The following code plots the price and quantities produced by the Stackelberg leader and follower."
+    "Now let’s use the code to compute and display outcomes as a Stackelberg plan unfolds.\n",
+    "\n",
+    "The following code plots  quantities chosen by the Stackelberg leader and follower, together with the equilibrium output price."
    ]
   },
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "bc36323d",
+   "id": "bcc8cb79",
    "metadata": {
     "hide-output": false
    },
@@ -1192,12 +1223,12 @@
   },
   {
    "cell_type": "markdown",
-   "id": "532743c1",
+   "id": "90b26d0e",
    "metadata": {},
    "source": [
     "### Value of Stackelberg Leader\n",
     "\n",
-    "We’ll compute the present value earned by the Stackelberg leader.\n",
+    "We’ll compute the  value $ w(x_0) $ attained  by the Stackelberg leader, where $ x_0 $ is given by the maximizer [(40.10)](#equation-eq-subprob2x0) of subproblem 2.\n",
     "\n",
     "We’ll compute it two ways and get the same answer.\n",
     "\n",
@@ -1207,7 +1238,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "b3ec0f50",
+   "id": "a19e88ce",
    "metadata": {
     "hide-output": false
    },
@@ -1225,7 +1256,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "3163a385",
+   "id": "f39fe896",
    "metadata": {
     "hide-output": false
    },
@@ -1239,7 +1270,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "1e6065e0",
+   "id": "6306a8bb",
    "metadata": {
     "hide-output": false
    },
@@ -1254,17 +1285,17 @@
   },
   {
    "cell_type": "markdown",
-   "id": "0a6d579e",
+   "id": "3dd76c38",
    "metadata": {},
    "source": [
     "## Time Inconsistency of Stackelberg Plan\n",
     "\n",
     "In the code below we compare two values\n",
     "\n",
-    "- the continuation value $ - y_t P y_t $ earned by a continuation\n",
-    "  Stackelberg leader who inherits state $ y_t $ at $ t $  \n",
-    "- the value of a **reborn Stackelberg leader** who inherits state\n",
-    "  $ z_t $ at $ t $ and sets $ x_t = - P_{22}^{-1} P_{21} $  \n",
+    "- the continuation value $ v(y_t) = - y_t' P y_t $ earned by a **continuation\n",
+    "  Stackelberg leader** who inherits state $ y_t $ at $ t $  \n",
+    "- the value $ w(\\hat x_t) $ of a **reborn Stackelberg leader** who, at date $ t $ along the Stackelberg plan, inherits state\n",
+    "  $ z_t $ at $ t $ but who discards $ x_t $ from the time $ t $ continuation of the original Stackelberg plan  and  **resets** it to $ \\hat x_t = - P_{22}^{-1} P_{21} z_t $  \n",
     "\n",
     "\n",
     "The difference between these two values is a tell-tale sign of the time\n",
@@ -1274,7 +1305,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "a82753b1",
+   "id": "eff34d9a",
    "metadata": {
     "hide-output": false
    },
@@ -1295,7 +1326,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "37cb6e4f",
+   "id": "35ac014c",
    "metadata": {
     "hide-output": false
    },
@@ -1306,17 +1337,17 @@
     "axes[0].plot(range(n+1), (- F @ yt).flatten(), 'bo',\n",
     "    label='Stackelberg leader', ms=2)\n",
     "axes[0].plot(range(n+1), (- F @ yt_reset).flatten(), 'ro',\n",
-    "    label='continuation leader at t', ms=2)\n",
-    "axes[0].set(title=r'Leader control variable $u_{t}$', xlabel='t')\n",
+    "    label='reborn  at t Stackelberg leader', ms=2)\n",
+    "axes[0].set(title=r' $u_{t} = q_{2t+1} - q_t$', xlabel='t')\n",
     "axes[0].legend()\n",
     "\n",
     "axes[1].plot(range(n+1), yt[3, :], 'bo', ms=2)\n",
     "axes[1].plot(range(n+1), yt_reset[3, :], 'ro', ms=2)\n",
-    "axes[1].set(title=r'Follower control variable $x_{t}$', xlabel='t')\n",
+    "axes[1].set(title=r' $x_{t} = q_{1t+1} - q_{1t}$', xlabel='t')\n",
     "\n",
     "axes[2].plot(range(n), vt_leader, 'bo', ms=2)\n",
     "axes[2].plot(range(n), vt_reset_leader, 'ro', ms=2)\n",
-    "axes[2].set(title=r'Leader value $v(y_{t})$', xlabel='t')\n",
+    "axes[2].set(title=r'$v(y_{t})$ and $w(\\hat x_t)$', xlabel='t')\n",
     "\n",
     "plt.tight_layout()\n",
     "plt.show()"
@@ -1324,7 +1355,22 @@
   },
   {
    "cell_type": "markdown",
-   "id": "89bb564c",
+   "id": "51f3c995",
+   "metadata": {},
+   "source": [
+    "The figure above shows\n",
+    "\n",
+    "- in the third panel that for $ t \\geq 1 $  the **reborn at $ t $** Stackelberg leader’s’s value $ w(\\hat x_0) $  exceeds the continuation value $ v(y_t) $ of the time $ 0 $ Stackelberg leader  \n",
+    "- in the first panel that for $ t \\geq 1 $  the **reborn at $ t $** Stackelberg leader wants to reduce his output below that prescribed by the time $ 0 $ Stackelberg leader  \n",
+    "- in the second panel that for $ t \\geq 1 $  the **reborn at $ t $** Stackelberg leader wants to increase the output of the follower firm 2 below that prescribed by the time $ 0 $ Stackelberg leader  \n",
+    "\n",
+    "\n",
+    "Taken together, these outcomes express the time inconsistency of the original time $ 0 $ Stackelberg leaders’s plan."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "31db2b15",
    "metadata": {},
    "source": [
     "## Recursive Formulation of Follower’s Problem\n",
@@ -1339,7 +1385,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "f8e3db15",
+   "id": "e23ada14",
    "metadata": {
     "hide-output": false
    },
@@ -1367,7 +1413,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "bd487882",
+   "id": "3627f949",
    "metadata": {
     "hide-output": false
    },
@@ -1384,7 +1430,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6a121477",
+   "id": "829c5496",
    "metadata": {},
    "source": [
     "Note: Variables with `_tilde` are obtained from solving the follower’s\n",
@@ -1394,7 +1440,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "d73c6d01",
+   "id": "968a9921",
    "metadata": {
     "hide-output": false
    },
@@ -1408,7 +1454,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "bcbdd51d",
+   "id": "5a128df5",
    "metadata": {
     "hide-output": false
    },
@@ -1420,7 +1466,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "38335a11",
+   "id": "6e11161e",
    "metadata": {},
    "source": [
     "### Explanation of Alignment\n",
@@ -1438,7 +1484,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "f82ba84a",
+   "id": "17fa0237",
    "metadata": {
     "hide-output": false
    },
@@ -1451,7 +1497,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "2e13e8be",
+   "id": "477bff65",
    "metadata": {
     "hide-output": false
    },
@@ -1464,7 +1510,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "58e1fb4f",
+   "id": "8a58fe77",
    "metadata": {
     "hide-output": false
    },
@@ -1477,7 +1523,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "ee1c2488",
+   "id": "904c36fb",
    "metadata": {
     "hide-output": false
    },
@@ -1490,7 +1536,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "4bef7d34",
+   "id": "f9124ec6",
    "metadata": {
     "hide-output": false
    },
@@ -1509,7 +1555,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "2b936654",
+   "id": "9d3d4a1b",
    "metadata": {
     "hide-output": false
    },
@@ -1522,7 +1568,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "b3c21cb9",
+   "id": "88753b58",
    "metadata": {
     "hide-output": false
    },
@@ -1535,7 +1581,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "391cd78f",
+   "id": "d32c8af2",
    "metadata": {
     "hide-output": false
    },
@@ -1578,7 +1624,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "3aa641ea",
+   "id": "1e9e9992",
    "metadata": {
     "hide-output": false
    },
@@ -1604,7 +1650,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "2e96324e",
+   "id": "a0186e50",
    "metadata": {
     "hide-output": false
    },
@@ -1616,7 +1662,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "638254b1",
+   "id": "e9c69414",
    "metadata": {},
    "source": [
     "## Markov Perfect Equilibrium\n",
@@ -1656,7 +1702,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "c389c006",
+   "id": "3291b459",
    "metadata": {
     "hide-output": false
    },
@@ -1699,7 +1745,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "a9a4fc5e",
+   "id": "9db6ffef",
    "metadata": {
     "hide-output": false
    },
@@ -1722,7 +1768,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "42306365",
+   "id": "05b25b49",
    "metadata": {
     "hide-output": false
    },
@@ -1735,7 +1781,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "8ea52585",
+   "id": "3757bcef",
    "metadata": {
     "hide-output": false
    },
@@ -1763,7 +1809,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "00d8f5fb",
+   "id": "9f106646",
    "metadata": {
     "hide-output": false
    },
@@ -1781,7 +1827,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c61697f9",
+   "id": "a91cec67",
    "metadata": {},
    "source": [
     "## Comparing Markov Perfect Equilibrium and  Stackelberg Outcome\n",
@@ -1799,7 +1845,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "c6a5d4c2",
+   "id": "a0da9901",
    "metadata": {
     "hide-output": false
    },
@@ -1825,7 +1871,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "2eab678e",
+   "id": "1bac3e29",
    "metadata": {
     "hide-output": false
    },
@@ -1841,7 +1887,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "5c6d3c45",
+   "id": "c3eda7c4",
    "metadata": {
     "hide-output": false
    },
@@ -1853,7 +1899,7 @@
   }
  ],
  "metadata": {
-  "date": 1680677524.868336,
+  "date": 1685490451.8366625,
   "filename": "dyn_stack.md",
   "kernelspec": {
    "display_name": "Python",
diff --git a/entropy.ipynb b/entropy.ipynb
index 86f3608..595f485 100644
--- a/entropy.ipynb
+++ b/entropy.ipynb
@@ -2,7 +2,7 @@
  "cells": [
   {
    "cell_type": "markdown",
-   "id": "0c42aefc",
+   "id": "6740351d",
    "metadata": {},
    "source": [
     "# Etymology of Entropy\n",
@@ -26,7 +26,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "17a64e86",
+   "id": "28f7bbb2",
    "metadata": {},
    "source": [
     "## Information Theory\n",
@@ -65,7 +65,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "fc516a4c",
+   "id": "4121b01d",
    "metadata": {},
    "source": [
     "## A Measure of Unpredictability\n",
@@ -85,7 +85,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a11d9a54",
+   "id": "e6e89f91",
    "metadata": {},
    "source": [
     "### Example\n",
@@ -119,7 +119,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "8db7f28b",
+   "id": "83d00dee",
    "metadata": {},
    "source": [
     "### Example\n",
@@ -142,7 +142,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c753b51b",
+   "id": "a7a053df",
    "metadata": {},
    "source": [
     "## Mathematical Properties of Entropy\n",
@@ -160,7 +160,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "673a9ec9",
+   "id": "0f27cd5c",
    "metadata": {},
    "source": [
     "## Conditional Entropy\n",
@@ -182,7 +182,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "515a801a",
+   "id": "0d067555",
    "metadata": {},
    "source": [
     "## Independence as Maximum Conditional Entropy\n",
@@ -212,7 +212,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d2f368c9",
+   "id": "e360d5f0",
    "metadata": {},
    "source": [
     "## Thermodynamics\n",
@@ -235,7 +235,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ada9df62",
+   "id": "5529af46",
    "metadata": {},
    "source": [
     "## Statistical  Divergence\n",
@@ -270,7 +270,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "60ae4cf2",
+   "id": "e02fd806",
    "metadata": {},
    "source": [
     "## Continuous distributions\n",
@@ -284,7 +284,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6795405d",
+   "id": "f6664621",
    "metadata": {},
    "source": [
     "## Relative entropy and Gaussian distributions\n",
@@ -375,7 +375,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "860615c1",
+   "id": "e7b533bd",
    "metadata": {},
    "source": [
     "## Von Neumann Entropy\n",
@@ -401,7 +401,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "313e713f",
+   "id": "b5275607",
    "metadata": {},
    "source": [
     "## Backus-Chernov-Zin Entropy\n",
@@ -453,7 +453,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a395ad49",
+   "id": "857601ed",
    "metadata": {},
    "source": [
     "## Wiener-Kolmogorov Prediction Error Formula as Entropy\n",
@@ -500,7 +500,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "34191ade",
+   "id": "f23baeb8",
    "metadata": {},
    "source": [
     "## Multivariate Processes\n",
@@ -537,7 +537,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4815cbd4",
+   "id": "fb25a180",
    "metadata": {},
    "source": [
     "## Frequency Domain Robust Control\n",
@@ -570,7 +570,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b4c68ceb",
+   "id": "8e1782e7",
    "metadata": {},
    "source": [
     "## Relative Entropy for a Continuous Random Variable\n",
@@ -610,7 +610,7 @@
   }
  ],
  "metadata": {
-  "date": 1680677525.1504977,
+  "date": 1685490452.078611,
   "filename": "entropy.md",
   "kernelspec": {
    "display_name": "Python",
diff --git a/estspec.ipynb b/estspec.ipynb
index 3897e1f..1d99da4 100644
--- a/estspec.ipynb
+++ b/estspec.ipynb
@@ -2,7 +2,7 @@
  "cells": [
   {
    "cell_type": "markdown",
-   "id": "88cca633",
+   "id": "099f6198",
    "metadata": {},
    "source": [
     "\n",
@@ -11,7 +11,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b1af8463",
+   "id": "030e13c2",
    "metadata": {},
    "source": [
     "# Estimation of Spectra\n",
@@ -22,7 +22,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ff1e4fb7",
+   "id": "42a0532c",
    "metadata": {},
    "source": [
     "## Contents\n",
@@ -36,7 +36,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f6f72eb4",
+   "id": "69686122",
    "metadata": {},
    "source": [
     "In addition to what’s in Anaconda, this lecture will need the following libraries:"
@@ -45,7 +45,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "fd6b5600",
+   "id": "013e9984",
    "metadata": {
     "hide-output": false
    },
@@ -56,7 +56,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f6c84fe3",
+   "id": "cd5af652",
    "metadata": {},
    "source": [
     "## Overview\n",
@@ -82,7 +82,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "a1ced6a8",
+   "id": "5fe07755",
    "metadata": {
     "hide-output": false
    },
@@ -96,7 +96,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c339a8af",
+   "id": "cc68b2fb",
    "metadata": {},
    "source": [
     "\n",
@@ -105,7 +105,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4a44d03c",
+   "id": "a0cd541e",
    "metadata": {},
    "source": [
     "## Periodograms\n",
@@ -158,7 +158,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "0a09df9b",
+   "id": "a390ad6e",
    "metadata": {},
    "source": [
     "### Interpretation\n",
@@ -225,7 +225,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "18e1e2e8",
+   "id": "2b342c9b",
    "metadata": {},
    "source": [
     "### Calculation\n",
@@ -283,7 +283,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "cf04dd14",
+   "id": "8bd9626a",
    "metadata": {
     "hide-output": false
    },
@@ -305,7 +305,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "099f8bfd",
+   "id": "d43778a7",
    "metadata": {},
    "source": [
     "This estimate looks rather disappointing, but the data size is only 40, so\n",
@@ -323,7 +323,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e3a89dd9",
+   "id": "50f16896",
    "metadata": {},
    "source": [
     "## Smoothing\n",
@@ -376,7 +376,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "434674e5",
+   "id": "0fac24b7",
    "metadata": {
     "hide-output": false
    },
@@ -398,7 +398,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ef8e95ad",
+   "id": "828630a4",
    "metadata": {},
    "source": [
     "### Estimation with Smoothing\n",
@@ -444,7 +444,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "94deed92",
+   "id": "f01ea3e2",
    "metadata": {},
    "source": [
     "### Pre-Filtering and Smoothing\n",
@@ -494,7 +494,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1d13dc89",
+   "id": "c270c318",
    "metadata": {},
    "source": [
     "### The AR(1) Setting\n",
@@ -570,7 +570,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "19f67091",
+   "id": "319d0842",
    "metadata": {},
    "source": [
     "## Exercises\n",
@@ -581,7 +581,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e161929a",
+   "id": "3da4bd3b",
    "metadata": {},
    "source": [
     "## Exercise 29.1\n",
@@ -595,7 +595,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6431b9fd",
+   "id": "c9d1fa99",
    "metadata": {},
    "source": [
     "## Solution to[ Exercise 29.1](https://python-advanced.quantecon.org/#est_ex1)"
@@ -604,7 +604,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "dc01d4d9",
+   "id": "1dbcec6e",
    "metadata": {
     "hide-output": false
    },
@@ -637,7 +637,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b26178ba",
+   "id": "fed02665",
    "metadata": {},
    "source": [
     "\n",
@@ -646,7 +646,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9c454112",
+   "id": "331bf63b",
    "metadata": {},
    "source": [
     "## Exercise 29.2\n",
@@ -661,7 +661,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4a88b8e6",
+   "id": "aec47807",
    "metadata": {},
    "source": [
     "## Solution to[ Exercise 29.2](https://python-advanced.quantecon.org/#est_ex2)"
@@ -670,7 +670,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "fd16f40f",
+   "id": "b04ba510",
    "metadata": {
     "hide-output": false
    },
@@ -704,7 +704,7 @@
   }
  ],
  "metadata": {
-  "date": 1680677525.1859257,
+  "date": 1685490452.115035,
   "filename": "estspec.md",
   "kernelspec": {
    "display_name": "Python",
diff --git a/five_preferences.ipynb b/five_preferences.ipynb
index 4f102e6..c9db2b1 100644
--- a/five_preferences.ipynb
+++ b/five_preferences.ipynb
@@ -2,7 +2,7 @@
  "cells": [
   {
    "cell_type": "markdown",
-   "id": "0f64f514",
+   "id": "a1900f13",
    "metadata": {},
    "source": [
     "# Risk and Model Uncertainty"
@@ -10,7 +10,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c7a8df78",
+   "id": "c7c44a35",
    "metadata": {},
    "source": [
     "## Overview\n",
@@ -56,7 +56,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "74ce7d69",
+   "id": "04e5fa2e",
    "metadata": {
     "hide-output": false
    },
@@ -79,7 +79,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "25851880",
+   "id": "b23c5325",
    "metadata": {
     "hide-output": false
    },
@@ -108,7 +108,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "31ce09c5",
+   "id": "e91f4d77",
    "metadata": {
     "hide-output": false
    },
@@ -166,7 +166,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "027a8813",
+   "id": "e370a5d3",
    "metadata": {},
    "source": [
     "## Basic objects\n",
@@ -231,7 +231,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "4bce4c12",
+   "id": "556d3664",
    "metadata": {
     "hide-output": false
    },
@@ -263,7 +263,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "8a83cf41",
+   "id": "8bab41a5",
    "metadata": {
     "hide-output": false
    },
@@ -278,7 +278,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d849ef61",
+   "id": "bb1ba4d6",
    "metadata": {},
    "source": [
     "The heat maps in  the next two  figures vary both $ \\hat{\\pi}_1 $ and $ \\pi_1 $.\n",
@@ -289,7 +289,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "8a55f938",
+   "id": "4d1f514a",
    "metadata": {
     "hide-output": false
    },
@@ -318,7 +318,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "26e04cc7",
+   "id": "4eac57cd",
    "metadata": {
     "hide-output": false
    },
@@ -336,7 +336,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "79182ed7",
+   "id": "cc2b5256",
    "metadata": {},
    "source": [
     "The next figure plots  the logarithm of entropy."
@@ -345,7 +345,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "63f4bab3",
+   "id": "2a61fdfd",
    "metadata": {
     "hide-output": false
    },
@@ -360,7 +360,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "b067a5e3",
+   "id": "69c0d43e",
    "metadata": {
     "hide-output": false
    },
@@ -377,7 +377,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "95601179",
+   "id": "eab46434",
    "metadata": {},
    "source": [
     "## Five preference specifications\n",
@@ -402,7 +402,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e42ca232",
+   "id": "e26cdaff",
    "metadata": {},
    "source": [
     "## Expected utility\n",
@@ -424,7 +424,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e4c5c7ba",
+   "id": "0df69aa5",
    "metadata": {},
    "source": [
     "## Constraint preferences\n",
@@ -549,7 +549,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "718147ef",
+   "id": "97acf2fd",
    "metadata": {},
    "source": [
     "## Multiplier preferences\n",
@@ -612,7 +612,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d8ec9c4a",
+   "id": "0716df8d",
    "metadata": {},
    "source": [
     "## Risk-sensitive preferences\n",
@@ -641,7 +641,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "de8c6569",
+   "id": "6ec78799",
    "metadata": {
     "hide-output": false
    },
@@ -673,7 +673,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "924701dc",
+   "id": "d7d4906e",
    "metadata": {
     "hide-output": false
    },
@@ -689,7 +689,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e88926dd",
+   "id": "690ed81c",
    "metadata": {},
    "source": [
     "For large values of $ \\theta $, $ {\\sf T} u(c) $ is approximately linear in the probability $ \\pi_1 $, but for lower values of $ \\theta $, $ {\\sf T} u(c) $ has considerable    curvature as a function of $ \\pi_1 $.\n",
@@ -704,7 +704,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "d1c538df",
+   "id": "0d3fe69c",
    "metadata": {
     "hide-output": false
    },
@@ -747,7 +747,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "d7d814eb",
+   "id": "0dbf4947",
    "metadata": {
     "hide-output": false
    },
@@ -790,7 +790,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "92045baf",
+   "id": "a3d2498b",
    "metadata": {},
    "source": [
     "The panel on the right portrays how the transformation $ \\exp\\left(\\frac{-u\\left(c\\right)}{\\theta}\\right) $ sends $ u\\left(c\\right) $ to a new function by  (i)  flipping the  sign,  and (ii) increasing curvature in proportion to $ \\theta $.\n",
@@ -811,7 +811,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b784166c",
+   "id": "3c4de2ac",
    "metadata": {},
    "source": [
     "### Digression on moment generating functions\n",
@@ -863,7 +863,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b0f8e088",
+   "id": "cbdca20f",
    "metadata": {},
    "source": [
     "## Ex post Bayesian preferences\n",
@@ -883,7 +883,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7c50b95c",
+   "id": "40b6c238",
    "metadata": {},
    "source": [
     "## Comparing preferences\n",
@@ -908,7 +908,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "c7f75a6f",
+   "id": "491f209e",
    "metadata": {
     "hide-output": false
    },
@@ -938,7 +938,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "3901f6ec",
+   "id": "2c2b05b3",
    "metadata": {
     "hide-output": false
    },
@@ -957,7 +957,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5369cf9d",
+   "id": "8ed0d2a7",
    "metadata": {},
    "source": [
     "The next  figure shows the function $ \\sum_{i=1}^I \\pi_i m_i [  u(c_i) + \\theta \\log m_i ] $ that is to be\n",
@@ -969,7 +969,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "f9ba8c7a",
+   "id": "9f3fba75",
    "metadata": {
     "hide-output": false
    },
@@ -997,7 +997,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "140f4c91",
+   "id": "be9676e7",
    "metadata": {
     "hide-output": false
    },
@@ -1035,7 +1035,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a98fe33d",
+   "id": "ed1f71c2",
    "metadata": {},
    "source": [
     "Evidently, from this figure and also from formula [(24.12)](#equation-tom12), lower values of $ \\theta $ lead to lower,\n",
@@ -1063,7 +1063,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e7d084fd",
+   "id": "4d50f889",
    "metadata": {},
    "source": [
     "## Risk aversion and misspecification aversion\n",
@@ -1114,7 +1114,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "cbb1767c",
+   "id": "716d1027",
    "metadata": {},
    "source": [
     "## Indifference curves\n",
@@ -1158,7 +1158,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "cd44c428",
+   "id": "76ef7d46",
    "metadata": {
     "hide-output": false
    },
@@ -1279,7 +1279,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "ff3be45a",
+   "id": "88946318",
    "metadata": {
     "hide-output": false
    },
@@ -1327,7 +1327,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "0de7550c",
+   "id": "13e8d891",
    "metadata": {
     "hide-output": false
    },
@@ -1355,7 +1355,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a563f1ef",
+   "id": "60cbaf2b",
    "metadata": {},
    "source": [
     "**Kink at 45 degree line**\n",
@@ -1425,7 +1425,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "fb742e3e",
+   "id": "728f055b",
    "metadata": {
     "hide-output": false
    },
@@ -1474,7 +1474,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "65d7991f",
+   "id": "5e681089",
    "metadata": {
     "hide-output": false
    },
@@ -1502,7 +1502,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3533b2ab",
+   "id": "2bb4f6c4",
    "metadata": {},
    "source": [
     "Note that all three lines of the left graph intersect at (1, 3). While the intersection at (3, 1) is hard-coded, the intersection at (1,3) arises from the computation,  which confirms that the code seems to be\n",
@@ -1539,7 +1539,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5169d118",
+   "id": "303534e7",
    "metadata": {},
    "source": [
     "## State price deflators\n",
@@ -1579,7 +1579,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "ea86b34e",
+   "id": "d87870d0",
    "metadata": {
     "hide-output": false
    },
@@ -1609,7 +1609,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "6fc4e8e4",
+   "id": "881f06c9",
    "metadata": {
     "hide-output": false
    },
@@ -1632,7 +1632,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e479b803",
+   "id": "7d5f3472",
    "metadata": {},
    "source": [
     "Because budget constraints are linear, asset prices are identical under\n",
@@ -1650,7 +1650,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "433e188f",
+   "id": "dbd53527",
    "metadata": {},
    "source": [
     "### Consumption-equivalent measures of uncertainty aversion\n",
@@ -1665,7 +1665,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "27c924d1",
+   "id": "e86c14ff",
    "metadata": {
     "hide-output": false
    },
@@ -1697,7 +1697,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "62f56946",
+   "id": "d8884ca7",
    "metadata": {
     "hide-output": false
    },
@@ -1734,7 +1734,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "55ca164a",
+   "id": "a2f80044",
    "metadata": {},
    "source": [
     "The figure indicates that the certainty equivalent\n",
@@ -1762,7 +1762,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3647225f",
+   "id": "e3935d14",
    "metadata": {},
    "source": [
     "## Iso-utility and iso-entropy curves and expansion paths\n",
@@ -1796,7 +1796,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "cb7473fd",
+   "id": "54d0ca2a",
    "metadata": {
     "hide-output": false
    },
@@ -1845,7 +1845,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "2a00e7d1",
+   "id": "97ef5f5a",
    "metadata": {
     "hide-output": false
    },
@@ -1920,7 +1920,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "d8a07f61",
+   "id": "786e04c5",
    "metadata": {
     "hide-output": false
    },
@@ -1934,7 +1934,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "45ee3273",
+   "id": "340b448a",
    "metadata": {
     "hide-output": false
    },
@@ -1947,7 +1947,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "97e94377",
+   "id": "a8975520",
    "metadata": {},
    "source": [
     "## Bounds on expected utility\n",
@@ -2010,7 +2010,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "3f138af4",
+   "id": "18ba7cff",
    "metadata": {
     "hide-output": false
    },
@@ -2076,7 +2076,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "db37abbc",
+   "id": "17f7cc40",
    "metadata": {
     "hide-output": false
    },
@@ -2103,7 +2103,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "4637a8dc",
+   "id": "26a4e4c5",
    "metadata": {
     "hide-output": false
    },
@@ -2119,7 +2119,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "ab0e373a",
+   "id": "593bded3",
    "metadata": {
     "hide-output": false
    },
@@ -2136,7 +2136,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7bd805ed",
+   "id": "27cb829b",
    "metadata": {},
    "source": [
     "In this figure, expected utility is on the co-ordinate axis\n",
@@ -2186,7 +2186,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "34ac38d8",
+   "id": "6fbe977d",
    "metadata": {},
    "source": [
     "## Why entropy?\n",
@@ -2204,7 +2204,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a53030c9",
+   "id": "2a8ad601",
    "metadata": {},
    "source": [
     "### Entropy and statistical detection\n",
@@ -2252,7 +2252,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "21e62d7e",
+   "id": "cf62f273",
    "metadata": {
     "hide-output": false
    },
@@ -2270,7 +2270,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "530590bd",
+   "id": "34b0eb83",
    "metadata": {
     "hide-output": false
    },
@@ -2298,7 +2298,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "9fe95269",
+   "id": "8d751e30",
    "metadata": {
     "hide-output": false
    },
@@ -2321,7 +2321,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "03fb6f94",
+   "id": "1401c0de",
    "metadata": {
     "hide-output": false
    },
@@ -2332,7 +2332,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "727e2922",
+   "id": "41218b9d",
    "metadata": {},
    "source": [
     "The density for the approximating model is\n",
@@ -2352,7 +2352,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b593e411",
+   "id": "aac197af",
    "metadata": {},
    "source": [
     "### Axiomatic justifications\n",
@@ -2368,7 +2368,7 @@
   }
  ],
  "metadata": {
-  "date": 1680677525.2940261,
+  "date": 1685490452.222244,
   "filename": "five_preferences.md",
   "kernelspec": {
    "display_name": "Python",
diff --git a/growth_in_dles.ipynb b/growth_in_dles.ipynb
index d881ee2..0feef1f 100644
--- a/growth_in_dles.ipynb
+++ b/growth_in_dles.ipynb
@@ -2,7 +2,7 @@
  "cells": [
   {
    "cell_type": "markdown",
-   "id": "a7451b77",
+   "id": "bc18d6ec",
    "metadata": {},
    "source": [
     "\n",
@@ -13,7 +13,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "57b2dfa9",
+   "id": "f9ae2aca",
    "metadata": {},
    "source": [
     "# Growth in Dynamic Linear Economies"
@@ -21,7 +21,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b22aa010",
+   "id": "3328c06e",
    "metadata": {},
    "source": [
     "## Contents\n",
@@ -34,7 +34,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4a561f2d",
+   "id": "a90e306a",
    "metadata": {},
    "source": [
     "This is another member of a suite of lectures that use the quantecon DLE class to instantiate models within the\n",
@@ -46,7 +46,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "a956759a",
+   "id": "232eff0e",
    "metadata": {
     "hide-output": false
    },
@@ -57,7 +57,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4a2597d2",
+   "id": "2de9e629",
    "metadata": {},
    "source": [
     "This lecture describes several complete market economies having a\n",
@@ -74,7 +74,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "4bf88eb8",
+   "id": "9a707e2d",
    "metadata": {
     "hide-output": false
    },
@@ -88,7 +88,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e3894c37",
+   "id": "3b832131",
    "metadata": {},
    "source": [
     "## Common Structure\n",
@@ -152,7 +152,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "01353784",
+   "id": "8fa220cc",
    "metadata": {},
    "source": [
     "## A Planning Problem\n",
@@ -235,7 +235,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e94f9505",
+   "id": "60a312f4",
    "metadata": {},
    "source": [
     "## Example Economies\n",
@@ -320,7 +320,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9fd16112",
+   "id": "42403cee",
    "metadata": {},
    "source": [
     "### Example 1: Hall (1978)\n",
@@ -353,7 +353,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "d9cb3215",
+   "id": "6799122f",
    "metadata": {
     "hide-output": false
    },
@@ -396,7 +396,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9a9cc3a5",
+   "id": "1d667409",
    "metadata": {},
    "source": [
     "These parameter values are used to define an economy of the DLE class."
@@ -405,7 +405,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "6d025786",
+   "id": "f4545baa",
    "metadata": {
     "hide-output": false
    },
@@ -416,7 +416,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a8e3390d",
+   "id": "3fab3f98",
    "metadata": {},
    "source": [
     "We can then simulate the economy for a chosen length of time, from our\n",
@@ -426,7 +426,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "64b1258d",
+   "id": "8fa825a0",
    "metadata": {
     "hide-output": false
    },
@@ -437,7 +437,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "08ebae9c",
+   "id": "c4a68e91",
    "metadata": {},
    "source": [
     "The economy stores the simulated values for each variable. Below we plot\n",
@@ -447,7 +447,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "c7c6e1a9",
+   "id": "5c3af0be",
    "metadata": {
     "hide-output": false
    },
@@ -462,7 +462,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d3230535",
+   "id": "8ec1e147",
    "metadata": {},
    "source": [
     "Inspection of the plot shows that the sample paths of consumption and\n",
@@ -475,7 +475,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "1cf00d4d",
+   "id": "df154fb3",
    "metadata": {
     "hide-output": false
    },
@@ -486,7 +486,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f4d9005d",
+   "id": "0356d636",
    "metadata": {},
    "source": [
     "The endogenous eigenvalue that appears to be unity reflects the random\n",
@@ -499,7 +499,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "65744c75",
+   "id": "0859d018",
    "metadata": {
     "hide-output": false
    },
@@ -510,7 +510,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6a6af4f3",
+   "id": "ce990e66",
    "metadata": {},
    "source": [
     "The fact that the largest endogenous eigenvalue is strictly less than\n",
@@ -521,7 +521,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "55b15af1",
+   "id": "9acf7fc4",
    "metadata": {
     "hide-output": false
    },
@@ -534,7 +534,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7b01caec",
+   "id": "8cb2ad48",
    "metadata": {},
    "source": [
     "However, the near-unity endogenous eigenvalue means that these steady\n",
@@ -543,7 +543,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "fc58b286",
+   "id": "1dd35a15",
    "metadata": {},
    "source": [
     "### Example 2: Altered Growth Condition\n",
@@ -577,7 +577,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "69bb9179",
+   "id": "88addd52",
    "metadata": {
     "hide-output": false
    },
@@ -596,7 +596,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "141dd3c5",
+   "id": "4ab355c3",
    "metadata": {},
    "source": [
     "Creating the DLE class and then simulating gives the following plot for\n",
@@ -606,7 +606,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "df4a1b6a",
+   "id": "43ba55db",
    "metadata": {
     "hide-output": false
    },
@@ -624,7 +624,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b965b513",
+   "id": "406f0b83",
    "metadata": {},
    "source": [
     "Simulating our new economy shows that consumption grows quickly in the\n",
@@ -637,7 +637,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "3b97faa7",
+   "id": "5659a624",
    "metadata": {
     "hide-output": false
    },
@@ -649,7 +649,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e7f656f3",
+   "id": "fafaa8c8",
    "metadata": {},
    "source": [
     "The economy converges faster to this level than in Example 1 because the\n",
@@ -660,7 +660,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "715f0666",
+   "id": "11fc0122",
    "metadata": {
     "hide-output": false
    },
@@ -671,7 +671,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "edf94274",
+   "id": "2c8bdc31",
    "metadata": {},
    "source": [
     "### Example 3: A Jones-Manuelli (1990) Economy\n",
@@ -719,7 +719,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "e6a33853",
+   "id": "e523983a",
    "metadata": {
     "hide-output": false
    },
@@ -732,7 +732,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "30f9af47",
+   "id": "a6164eca",
    "metadata": {
     "hide-output": false
    },
@@ -743,7 +743,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "0bc8173b",
+   "id": "8d28d31c",
    "metadata": {},
    "source": [
     "We simulate this economy from the original state vector"
@@ -752,7 +752,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "6a649224",
+   "id": "0b7d927f",
    "metadata": {
     "hide-output": false
    },
@@ -769,7 +769,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "88dd62d3",
+   "id": "b0668323",
    "metadata": {},
    "source": [
     "Thus, adding habit persistence to the Hall model of Example 1 is enough\n",
@@ -782,7 +782,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "8706fb38",
+   "id": "a0e6b3df",
    "metadata": {
     "hide-output": false
    },
@@ -793,7 +793,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "31b77028",
+   "id": "b92de787",
    "metadata": {},
    "source": [
     "We now have two unit endogenous eigenvalues. One stems from satisfying\n",
@@ -807,7 +807,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "61906792",
+   "id": "8c8d05cd",
    "metadata": {},
    "source": [
     "### Example 3.1: Varying Sensitivity\n",
@@ -818,7 +818,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "771837b9",
+   "id": "5449d687",
    "metadata": {
     "hide-output": false
    },
@@ -839,7 +839,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "94a811f2",
+   "id": "ec4759a4",
    "metadata": {},
    "source": [
     "We no longer achieve sustained growth if $ \\lambda $ is raised from -1 to -0.7.\n",
@@ -851,7 +851,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "fcb36797",
+   "id": "fa02fa57",
    "metadata": {
     "hide-output": false
    },
@@ -862,7 +862,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e99f77a6",
+   "id": "45682701",
    "metadata": {},
    "source": [
     "### Example 3.2: More Impatience\n",
@@ -873,7 +873,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "890c823b",
+   "id": "d0b44956",
    "metadata": {
     "hide-output": false
    },
@@ -894,7 +894,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "8fa22448",
+   "id": "03e2761f",
    "metadata": {},
    "source": [
     "Growth also fails if we lower $ \\beta $, since we now have\n",
@@ -911,7 +911,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "cb1dac22",
+   "id": "2f05e3e7",
    "metadata": {
     "hide-output": false
    },
@@ -922,7 +922,7 @@
   }
  ],
  "metadata": {
-  "date": 1680677525.3327065,
+  "date": 1685490452.2615921,
   "filename": "growth_in_dles.md",
   "kernelspec": {
    "display_name": "Python",
diff --git a/hs_invertibility_example.ipynb b/hs_invertibility_example.ipynb
index 332b333..af3636e 100644
--- a/hs_invertibility_example.ipynb
+++ b/hs_invertibility_example.ipynb
@@ -2,7 +2,7 @@
  "cells": [
   {
    "cell_type": "markdown",
-   "id": "81b0d786",
+   "id": "e9226c5f",
    "metadata": {},
    "source": [
     "\n",
@@ -13,7 +13,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6e9452e9",
+   "id": "68293d84",
    "metadata": {},
    "source": [
     "# Shock Non Invertibility"
@@ -21,7 +21,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c6dcd238",
+   "id": "c77f6622",
    "metadata": {},
    "source": [
     "## Contents\n",
@@ -34,7 +34,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "42386cbd",
+   "id": "23cd2c7a",
    "metadata": {},
    "source": [
     "## Overview\n",
@@ -48,7 +48,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "dfa296cd",
+   "id": "09037cea",
    "metadata": {
     "hide-output": false
    },
@@ -59,7 +59,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "0b410ece",
+   "id": "cddcc522",
    "metadata": {},
    "source": [
     "We’ll make these imports:"
@@ -68,7 +68,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "0b7ced57",
+   "id": "4d246aee",
    "metadata": {
     "hide-output": false
    },
@@ -85,7 +85,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4c6ca13c",
+   "id": "4ce68373",
    "metadata": {},
    "source": [
     "This lecture describes  an early contribution to what is now often called\n",
@@ -111,7 +111,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7928da22",
+   "id": "4b84c0f5",
    "metadata": {},
    "source": [
     "## Model\n",
@@ -206,7 +206,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "2b40dc1c",
+   "id": "8f5a9d18",
    "metadata": {
     "hide-output": false
    },
@@ -244,7 +244,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "948be568",
+   "id": "04ff2077",
    "metadata": {},
    "source": [
     "We define the household’s net of interest deficit as $ c_t - d_t $.\n",
@@ -315,7 +315,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "dd71c168",
+   "id": "82509cd4",
    "metadata": {},
    "source": [
     "## Code\n",
@@ -327,7 +327,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "18810797",
+   "id": "c2cdbd18",
    "metadata": {
     "hide-output": false
    },
@@ -355,7 +355,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "8cb06b5c",
+   "id": "a4f2e2c4",
    "metadata": {},
    "source": [
     "The above figure displays the impulse response of consumption and the\n",
@@ -375,7 +375,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "4021d8c0",
+   "id": "a241fa24",
    "metadata": {
     "hide-output": false
    },
@@ -425,7 +425,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4a76281b",
+   "id": "d585f2c1",
    "metadata": {},
    "source": [
     "The above figure displays the impulse response of consumption and the\n",
@@ -445,7 +445,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "6d5c207f",
+   "id": "dbe2865c",
    "metadata": {
     "hide-output": false
    },
@@ -482,7 +482,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3ec53f2d",
+   "id": "30fe25ce",
    "metadata": {},
    "source": [
     "The above figure displays the impulse responses of $ u_t $ to\n",
@@ -503,7 +503,7 @@
   }
  ],
  "metadata": {
-  "date": 1680677525.3556733,
+  "date": 1685490452.2856295,
   "filename": "hs_invertibility_example.md",
   "kernelspec": {
    "display_name": "Python",
diff --git a/hs_recursive_models.ipynb b/hs_recursive_models.ipynb
index 2adf48c..4f98dbb 100644
--- a/hs_recursive_models.ipynb
+++ b/hs_recursive_models.ipynb
@@ -2,7 +2,7 @@
  "cells": [
   {
    "cell_type": "markdown",
-   "id": "39bd937f",
+   "id": "16f81822",
    "metadata": {},
    "source": [
     "\n",
@@ -13,7 +13,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1fbbe63a",
+   "id": "c2939d7c",
    "metadata": {},
    "source": [
     "# Recursive Models of Dynamic Linear Economies"
@@ -21,7 +21,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "8479f6d0",
+   "id": "c10106fc",
    "metadata": {},
    "source": [
     "## Contents\n",
@@ -43,7 +43,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a748b1ba",
+   "id": "9cc44a80",
    "metadata": {},
    "source": [
     "> “Mathematics is the art of giving the same name to different things” – Henri Poincare\n",
@@ -57,7 +57,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "bd50e671",
+   "id": "f62659a5",
    "metadata": {},
    "source": [
     "## A Suite of Models\n",
@@ -80,7 +80,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1dd8a6b0",
+   "id": "c9bc4b23",
    "metadata": {},
    "source": [
     "### Overview of the Models\n",
@@ -151,7 +151,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c2991fe6",
+   "id": "b49e38b1",
    "metadata": {},
    "source": [
     "### Forecasting?\n",
@@ -168,7 +168,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9b0a1f0f",
+   "id": "9e2556bd",
    "metadata": {},
    "source": [
     "### Theory and Econometrics\n",
@@ -193,7 +193,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "05c03084",
+   "id": "7948796a",
    "metadata": {},
    "source": [
     "### More Details\n",
@@ -276,7 +276,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "28d97459",
+   "id": "65678208",
    "metadata": {},
    "source": [
     "### Stochastic Model of Information Flows and Outcomes\n",
@@ -318,7 +318,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "0ef4c2b3",
+   "id": "ebbeaf04",
    "metadata": {},
    "source": [
     "### Information Sets\n",
@@ -332,7 +332,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ad737c29",
+   "id": "74576631",
    "metadata": {},
    "source": [
     "### Prediction Theory\n",
@@ -408,7 +408,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4a7ce3a1",
+   "id": "2ee03fa2",
    "metadata": {},
    "source": [
     "### Orthogonal Decomposition\n",
@@ -441,7 +441,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "808ad4f9",
+   "id": "2c18cb42",
    "metadata": {},
    "source": [
     "### Taste and Technology Shocks\n",
@@ -482,7 +482,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "cf2c162f",
+   "id": "827b3a47",
    "metadata": {},
    "source": [
     "### Production Technology\n",
@@ -507,7 +507,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "34fbfd18",
+   "id": "5a37ec78",
    "metadata": {},
    "source": [
     "### Household Technology\n",
@@ -534,7 +534,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9df5ddf3",
+   "id": "7d49103e",
    "metadata": {},
    "source": [
     "### Preferences\n",
@@ -564,7 +564,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "686e074b",
+   "id": "f50a5cdc",
    "metadata": {},
    "source": [
     "### Endowment Economy\n",
@@ -612,7 +612,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d9773f28",
+   "id": "7260daa7",
    "metadata": {},
    "source": [
     "### Single-Period Adjustment Costs\n",
@@ -926,7 +926,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1d02b5bc",
+   "id": "0223265c",
    "metadata": {},
    "source": [
     "### Optimal Resource Allocation\n",
@@ -979,7 +979,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d65afc27",
+   "id": "a31386d9",
    "metadata": {},
    "source": [
     "### Lagrangian Formulation\n",
@@ -1098,7 +1098,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "cf998d78",
+   "id": "9c5c2cee",
    "metadata": {},
    "source": [
     "### Dynamic Programming\n",
@@ -1314,7 +1314,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1a67eea5",
+   "id": "c38313d0",
    "metadata": {},
    "source": [
     "### Other mathematical infrastructure\n",
@@ -1343,7 +1343,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9b7c1737",
+   "id": "86715c00",
    "metadata": {},
    "source": [
     "### Representative Household\n",
@@ -1380,7 +1380,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ae365f9c",
+   "id": "69e765ac",
    "metadata": {},
    "source": [
     "### Type I Firm\n",
@@ -1410,7 +1410,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b84719bf",
+   "id": "c5f02b48",
    "metadata": {},
    "source": [
     "### Type II Firm\n",
@@ -1438,7 +1438,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "53aaae84",
+   "id": "13566fe2",
    "metadata": {},
    "source": [
     "### Competitive Equilibrium:  Definition\n",
@@ -1501,7 +1501,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "33c11928",
+   "id": "a69e6b05",
    "metadata": {},
    "source": [
     "### Asset pricing\n",
@@ -1549,7 +1549,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f42836ef",
+   "id": "519c8026",
    "metadata": {},
    "source": [
     "### Re-Opening Markets\n",
@@ -1595,7 +1595,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "15a8f601",
+   "id": "c99872bb",
    "metadata": {},
    "source": [
     "## Econometrics\n",
@@ -1708,7 +1708,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c95b281d",
+   "id": "6a8b8d2b",
    "metadata": {},
    "source": [
     "### Factorization of Likelihood Function\n",
@@ -1735,7 +1735,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d693a80d",
+   "id": "b2304a9d",
    "metadata": {},
    "source": [
     "### Covariance Generating Functions\n",
@@ -1748,7 +1748,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b42d2bc1",
+   "id": "76d64ba4",
    "metadata": {},
    "source": [
     "### Spectral Factorization Identity\n",
@@ -1792,7 +1792,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "20a6cc09",
+   "id": "281e5176",
    "metadata": {},
    "source": [
     "### Wold and Vector Autoregressive Representations\n",
@@ -1834,7 +1834,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3f33a42d",
+   "id": "c6301633",
    "metadata": {},
    "source": [
     "## Dynamic Demand Curves and Canonical Household Technologies"
@@ -1842,7 +1842,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "43de82bb",
+   "id": "9db5aa6f",
    "metadata": {},
    "source": [
     "### Canonical Household Technologies\n",
@@ -1890,7 +1890,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "869bc500",
+   "id": "ddd4396e",
    "metadata": {},
    "source": [
     "### Dynamic Demand Functions\n",
@@ -1943,7 +1943,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "0d95037b",
+   "id": "c402cd86",
    "metadata": {},
    "source": [
     "## Gorman Aggregation and Engel Curves\n",
@@ -1973,7 +1973,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d85c9a84",
+   "id": "c5c2db91",
    "metadata": {},
    "source": [
     "### Re-Opened Markets\n",
@@ -2017,7 +2017,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d576e7ef",
+   "id": "d3f7b8a1",
    "metadata": {},
    "source": [
     "### Dynamic Demand\n",
@@ -2045,7 +2045,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "290e02d8",
+   "id": "b8c6db0a",
    "metadata": {},
    "source": [
     "### Attaining a Canonical Household Technology\n",
@@ -2071,7 +2071,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "643047e5",
+   "id": "118416e2",
    "metadata": {},
    "source": [
     "## Partial Equilibrium\n",
@@ -2141,7 +2141,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "83de9c0d",
+   "id": "43739d8b",
    "metadata": {},
    "source": [
     "## Equilibrium Investment Under Uncertainty\n",
@@ -2178,7 +2178,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6235c8ed",
+   "id": "fa7960ad",
    "metadata": {},
    "source": [
     "## A Rosen-Topel Housing Model\n",
@@ -2227,7 +2227,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f7fd9738",
+   "id": "1f51ad2b",
    "metadata": {},
    "source": [
     "## Cattle Cycles\n",
@@ -2297,7 +2297,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f854f2de",
+   "id": "ce05f6bc",
    "metadata": {},
    "source": [
     "## Models of Occupational Choice and Pay\n",
@@ -2310,7 +2310,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "07152256",
+   "id": "0ad6ce3d",
    "metadata": {},
    "source": [
     "### Market for Engineers\n",
@@ -2387,7 +2387,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a1030b43",
+   "id": "d9ba7c09",
    "metadata": {},
    "source": [
     "### Skilled and Unskilled Workers\n",
@@ -2450,7 +2450,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f0799211",
+   "id": "8276b4d9",
    "metadata": {},
    "source": [
     "## Permanent Income Models\n",
@@ -2528,7 +2528,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "663e6b4d",
+   "id": "33805228",
    "metadata": {},
    "source": [
     "## Gorman Heterogeneous Households\n",
@@ -2628,7 +2628,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "17d64129",
+   "id": "7d230dd0",
    "metadata": {},
    "source": [
     "## Non-Gorman Heterogeneous Households\n",
@@ -2812,7 +2812,7 @@
   }
  ],
  "metadata": {
-  "date": 1680677525.466812,
+  "date": 1685490452.397977,
   "filename": "hs_recursive_models.md",
   "kernelspec": {
    "display_name": "Python",
diff --git a/intro.ipynb b/intro.ipynb
index ead805c..c8960f0 100644
--- a/intro.ipynb
+++ b/intro.ipynb
@@ -2,7 +2,7 @@
  "cells": [
   {
    "cell_type": "markdown",
-   "id": "2049eace",
+   "id": "2aa86dbd",
    "metadata": {},
    "source": [
     "# Advanced Quantitative Economics with Python\n",
@@ -15,7 +15,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5d735099",
+   "id": "ef43fb1a",
    "metadata": {},
    "source": [
     "# Tools and Techniques\n",
@@ -28,7 +28,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9744e869",
+   "id": "379772e3",
    "metadata": {},
    "source": [
     "# LQ Control\n",
@@ -45,7 +45,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d178328d",
+   "id": "3de6de39",
    "metadata": {},
    "source": [
     "# Multiple Agent Models\n",
@@ -57,7 +57,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f908b742",
+   "id": "914263ab",
    "metadata": {},
    "source": [
     "# Dynamic Linear Economies\n",
@@ -74,7 +74,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c2b31b24",
+   "id": "a08a24d5",
    "metadata": {},
    "source": [
     "# Risk, Model Uncertainty, and Robustness\n",
@@ -87,7 +87,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1b8aac43",
+   "id": "19a967c5",
    "metadata": {},
    "source": [
     "# Time Series Models\n",
@@ -102,7 +102,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "affef18a",
+   "id": "394735b5",
    "metadata": {},
    "source": [
     "# Asset Pricing and Finance\n",
@@ -116,7 +116,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ac262d75",
+   "id": "3b3fccc2",
    "metadata": {},
    "source": [
     "# Dynamic Programming Squared\n",
@@ -134,7 +134,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b80ca527",
+   "id": "a0dbfca6",
    "metadata": {},
    "source": [
     "# Other\n",
@@ -146,7 +146,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "fa396af7",
+   "id": "e4814e65",
    "metadata": {},
    "source": [
     "# Previous website\n",
@@ -156,7 +156,7 @@
   }
  ],
  "metadata": {
-  "date": 1680677525.7289388,
+  "date": 1685490452.4409819,
   "filename": "intro.md",
   "kernelspec": {
    "display_name": "Python",
diff --git a/irfs_in_hall_model.ipynb b/irfs_in_hall_model.ipynb
index c53c7f6..02d1fb4 100644
--- a/irfs_in_hall_model.ipynb
+++ b/irfs_in_hall_model.ipynb
@@ -2,7 +2,7 @@
  "cells": [
   {
    "cell_type": "markdown",
-   "id": "52f4f8ff",
+   "id": "e7ed43a3",
    "metadata": {},
    "source": [
     "\n",
@@ -13,7 +13,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "2a49de94",
+   "id": "a97343c2",
    "metadata": {},
    "source": [
     "# IRFs in Hall Models"
@@ -21,7 +21,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "26dd969d",
+   "id": "71da9dee",
    "metadata": {},
    "source": [
     "## Contents\n",
@@ -34,7 +34,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "87228059",
+   "id": "f73e6f56",
    "metadata": {},
    "source": [
     "This is another member of a suite of lectures that use the quantecon DLE class to instantiate models within the\n",
@@ -46,7 +46,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "e1c08aa2",
+   "id": "1fe4b423",
    "metadata": {
     "hide-output": false
    },
@@ -57,7 +57,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6b6ee7d5",
+   "id": "9ce62269",
    "metadata": {},
    "source": [
     "We’ll make these imports:"
@@ -66,7 +66,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "3cbec7e2",
+   "id": "ad69cdc9",
    "metadata": {
     "hide-output": false
    },
@@ -81,7 +81,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6bf813cf",
+   "id": "4b61450e",
    "metadata": {},
    "source": [
     "This lecture shows how the DLE class can be used to create impulse\n",
@@ -95,7 +95,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "2bd250d5",
+   "id": "aed0ae4e",
    "metadata": {},
    "source": [
     "## Example 1: Hall (1978)\n",
@@ -131,7 +131,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "eeabbee6",
+   "id": "d0798dbf",
    "metadata": {
     "hide-output": false
    },
@@ -168,7 +168,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "29bdc00f",
+   "id": "7f89e942",
    "metadata": {},
    "source": [
     "These parameter values are used to define an economy of the DLE class.\n",
@@ -183,7 +183,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "39047dba",
+   "id": "7799c94f",
    "metadata": {
     "hide-output": false
    },
@@ -201,7 +201,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d1c5d2a2",
+   "id": "b55634b6",
    "metadata": {},
    "source": [
     "The DLE class can be used to create impulse response functions for each\n",
@@ -218,7 +218,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "43ec7f78",
+   "id": "1babd37f",
    "metadata": {
     "hide-output": false
    },
@@ -234,7 +234,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b8c75891",
+   "id": "6cdbcf7c",
    "metadata": {},
    "source": [
     "It can be seen that the endowment shock has permanent effects on the\n",
@@ -247,7 +247,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d058e28a",
+   "id": "b0e86a30",
    "metadata": {},
    "source": [
     "## Example 2: Higher Adjustment Costs\n",
@@ -263,7 +263,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "c9425308",
+   "id": "d7aeac94",
    "metadata": {
     "hide-output": false
    },
@@ -286,7 +286,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "57083ba7",
+   "id": "251c44b3",
    "metadata": {
     "hide-output": false
    },
@@ -303,7 +303,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "fdaa019d",
+   "id": "509d2185",
    "metadata": {
     "hide-output": false
    },
@@ -315,7 +315,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "5b0fbf91",
+   "id": "3a9b56a8",
    "metadata": {
     "hide-output": false
    },
@@ -327,7 +327,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4d8c8bb4",
+   "id": "6d3c07a6",
    "metadata": {},
    "source": [
     "The first graph shows that there seems to be a downward trend in both\n",
@@ -350,7 +350,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1204295a",
+   "id": "0607da14",
    "metadata": {},
    "source": [
     "## Example 3: Durable Consumption Goods\n",
@@ -391,7 +391,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "4e8c2ad3",
+   "id": "e3f0368f",
    "metadata": {
     "hide-output": false
    },
@@ -423,7 +423,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "65b47c26",
+   "id": "ecf0283f",
    "metadata": {},
    "source": [
     "In contrast to Hall’s original model of Example 1, it is now investment\n",
@@ -436,7 +436,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "2dd368f7",
+   "id": "1739c0ee",
    "metadata": {
     "hide-output": false
    },
@@ -452,7 +452,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6230b742",
+   "id": "4975d198",
    "metadata": {},
    "source": [
     "The impulse response functions confirm that consumption is now much more\n",
@@ -465,7 +465,7 @@
   }
  ],
  "metadata": {
-  "date": 1680677525.7492938,
+  "date": 1685490452.4590886,
   "filename": "irfs_in_hall_model.md",
   "kernelspec": {
    "display_name": "Python",
diff --git a/knowing_forecasts_of_others.ipynb b/knowing_forecasts_of_others.ipynb
index c2280f1..4c7e307 100644
--- a/knowing_forecasts_of_others.ipynb
+++ b/knowing_forecasts_of_others.ipynb
@@ -2,7 +2,7 @@
  "cells": [
   {
    "cell_type": "markdown",
-   "id": "98940788",
+   "id": "20394933",
    "metadata": {},
    "source": [
     "\n",
@@ -11,7 +11,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1130ce10",
+   "id": "1424ce1f",
    "metadata": {},
    "source": [
     "# Knowing the Forecasts of Others"
@@ -19,7 +19,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b24460ac",
+   "id": "6f4b87d0",
    "metadata": {},
    "source": [
     "## Contents\n",
@@ -41,7 +41,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "bc7e94a3",
+   "id": "1f9d0e0d",
    "metadata": {},
    "source": [
     "In addition to what’s in Anaconda, this lecture will need the following libraries:"
@@ -50,7 +50,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "4ecb0850",
+   "id": "259b5656",
    "metadata": {
     "hide-output": false
    },
@@ -62,7 +62,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b6c0aea2",
+   "id": "64587d36",
    "metadata": {},
    "source": [
     "## Introduction\n",
@@ -130,7 +130,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "fff05a99",
+   "id": "83518c5e",
    "metadata": {},
    "source": [
     "### A Sequence of Models\n",
@@ -163,7 +163,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a960d84f",
+   "id": "9bc046e1",
    "metadata": {},
    "source": [
     "## The Setting\n",
@@ -250,7 +250,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d7175111",
+   "id": "d976099c",
    "metadata": {},
    "source": [
     "## Tactics\n",
@@ -350,7 +350,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "445d588a",
+   "id": "f191f533",
    "metadata": {},
    "source": [
     "## Equilibrium Conditions\n",
@@ -445,7 +445,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7e34f916",
+   "id": "8f8fa5c1",
    "metadata": {},
    "source": [
     "### Equilibrium under perfect foresight\n",
@@ -525,7 +525,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9f5e8e17",
+   "id": "17745926",
    "metadata": {},
    "source": [
     "## Equilibrium with $ \\theta_t $ stochastic but observed at $ t $\n",
@@ -590,7 +590,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "011d6ce5",
+   "id": "464b7963",
    "metadata": {},
    "source": [
     "### Filtering"
@@ -598,7 +598,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7ef670a0",
+   "id": "a8fccd05",
    "metadata": {},
    "source": [
     "#### One noisy signal\n",
@@ -670,7 +670,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d13bb0ba",
+   "id": "40c62be7",
    "metadata": {},
    "source": [
     "#### State-reconstruction error\n",
@@ -749,7 +749,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "33d89ff4",
+   "id": "0ae1c337",
    "metadata": {},
    "source": [
     "### A new state variable\n",
@@ -788,7 +788,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e65544e5",
+   "id": "c53802f4",
    "metadata": {},
    "source": [
     "### Two Noisy Signals\n",
@@ -881,7 +881,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e8b728b8",
+   "id": "af35969b",
    "metadata": {},
    "source": [
     "## Guess-and-Verify Tactic\n",
@@ -912,7 +912,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c4edd778",
+   "id": "86cdc192",
    "metadata": {},
    "source": [
     "## Equilibrium with One Noisy Signal on $ \\theta_t $"
@@ -920,7 +920,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5efc247e",
+   "id": "0032f199",
    "metadata": {},
    "source": [
     "### Step 1: Solve for $ \\tilde{\\lambda} $ and $ \\lambda $\n",
@@ -939,7 +939,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "91e0cb87",
+   "id": "64de5b95",
    "metadata": {},
    "source": [
     "### Step 2: Solve for $ p $\n",
@@ -972,7 +972,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9a4aef6a",
+   "id": "c7673e33",
    "metadata": {},
    "source": [
     "### Step 3: Represent the system using `quantecon.LinearStateSpace`\n",
@@ -1054,7 +1054,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "8a536b6b",
+   "id": "604aa1be",
    "metadata": {
     "hide-output": false
    },
@@ -1075,7 +1075,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "e8d1100f",
+   "id": "5ed2c693",
    "metadata": {
     "hide-output": false
    },
@@ -1091,7 +1091,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "c73f26b0",
+   "id": "741ea819",
    "metadata": {
     "hide-output": false
    },
@@ -1107,7 +1107,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "660fdee4",
+   "id": "4cec76d5",
    "metadata": {
     "hide-output": false
    },
@@ -1121,7 +1121,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "397c39bd",
+   "id": "42ea6389",
    "metadata": {
     "hide-output": false
    },
@@ -1140,7 +1140,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "8bdc6b4a",
+   "id": "0055ae81",
    "metadata": {
     "hide-output": false
    },
@@ -1154,7 +1154,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "cf96b14d",
+   "id": "66069181",
    "metadata": {
     "hide-output": false
    },
@@ -1187,7 +1187,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "1738d291",
+   "id": "4e557f24",
    "metadata": {
     "hide-output": false
    },
@@ -1201,7 +1201,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "902b4a91",
+   "id": "f56b9191",
    "metadata": {
     "hide-output": false
    },
@@ -1214,7 +1214,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "cbd28052",
+   "id": "e5a42eac",
    "metadata": {
     "hide-output": false
    },
@@ -1226,7 +1226,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "2eadd981",
+   "id": "e8ef77bc",
    "metadata": {},
    "source": [
     "### Step 4: Compute impulse response functions\n",
@@ -1238,7 +1238,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "e07e8d64",
+   "id": "56d01cdb",
    "metadata": {
     "hide-output": false
    },
@@ -1261,7 +1261,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "70d4f43e",
+   "id": "84edd865",
    "metadata": {},
    "source": [
     "### Step 5: Compute stationary covariance matrices and population regressions\n",
@@ -1295,7 +1295,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "15e6669d",
+   "id": "74c9adcd",
    "metadata": {
     "hide-output": false
    },
@@ -1320,7 +1320,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "98c7f1e4",
+   "id": "c3eacd12",
    "metadata": {
     "hide-output": false
    },
@@ -1334,7 +1334,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "297d5f62",
+   "id": "df856fb7",
    "metadata": {
     "hide-output": false
    },
@@ -1349,7 +1349,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "5bd2ed8d",
+   "id": "efb1cfe9",
    "metadata": {
     "hide-output": false
    },
@@ -1362,7 +1362,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "bd51168e",
+   "id": "65bc6546",
    "metadata": {
     "hide-output": false
    },
@@ -1376,7 +1376,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5935a8ab",
+   "id": "e0ff4c64",
    "metadata": {},
    "source": [
     "## Equilibrium with Two Noisy Signals on $ \\theta_t $\n",
@@ -1480,7 +1480,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "6325e4e1",
+   "id": "10300e15",
    "metadata": {
     "hide-output": false
    },
@@ -1499,7 +1499,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "36a08cf6",
+   "id": "f6984f8f",
    "metadata": {
     "hide-output": false
    },
@@ -1513,7 +1513,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "6a630be0",
+   "id": "c5731754",
    "metadata": {
     "hide-output": false
    },
@@ -1553,7 +1553,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "b11ce96c",
+   "id": "857897cf",
    "metadata": {
     "hide-output": false
    },
@@ -1567,7 +1567,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "147e3447",
+   "id": "698d1a38",
    "metadata": {
     "hide-output": false
    },
@@ -1580,7 +1580,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "4631e3c1",
+   "id": "8d751d74",
    "metadata": {
     "hide-output": false
    },
@@ -1592,7 +1592,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "85f32fed",
+   "id": "b1752de9",
    "metadata": {
     "hide-output": false
    },
@@ -1616,7 +1616,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "f579f1ef",
+   "id": "11fd3e73",
    "metadata": {
     "hide-output": false
    },
@@ -1641,7 +1641,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "08830b18",
+   "id": "21f81265",
    "metadata": {
     "hide-output": false
    },
@@ -1655,7 +1655,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "b68fc56f",
+   "id": "56c2f256",
    "metadata": {
     "hide-output": false
    },
@@ -1670,7 +1670,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "36e56c75",
+   "id": "d6ba53bb",
    "metadata": {
     "hide-output": false
    },
@@ -1683,7 +1683,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "d4feb1ef",
+   "id": "2e05276c",
    "metadata": {
     "hide-output": false
    },
@@ -1709,7 +1709,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "85619352",
+   "id": "c5f46472",
    "metadata": {
     "hide-output": false
    },
@@ -1722,7 +1722,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4648daa1",
+   "id": "6f18412f",
    "metadata": {},
    "source": [
     "## Key Step\n",
@@ -1740,7 +1740,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "7da8175a",
+   "id": "c6049124",
    "metadata": {
     "hide-output": false
    },
@@ -1759,7 +1759,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "132acf6d",
+   "id": "33fda223",
    "metadata": {
     "hide-output": false
    },
@@ -1770,7 +1770,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4213b414",
+   "id": "89125d80",
    "metadata": {},
    "source": [
     "The $ R^2 $ in this regression equals $ 1 $.\n",
@@ -1783,7 +1783,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "04d4e6bb",
+   "id": "f7c6cde9",
    "metadata": {},
    "source": [
     "## An observed common shock benchmark\n",
@@ -1846,7 +1846,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "0bb70042",
+   "id": "401d758e",
    "metadata": {
     "hide-output": false
    },
@@ -1863,7 +1863,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "01ff252d",
+   "id": "23796dbc",
    "metadata": {
     "hide-output": false
    },
@@ -1876,7 +1876,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "09b79948",
+   "id": "df44024a",
    "metadata": {},
    "source": [
     "Now let’s form and plot an  impulse response function of $ k_t^i $ to shocks $ v_t $ to $ \\theta_{t+1} $"
@@ -1885,7 +1885,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "96017c69",
+   "id": "2366afe5",
    "metadata": {
     "hide-output": false
    },
@@ -1907,7 +1907,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "8bebdaaf",
+   "id": "e809a7ce",
    "metadata": {},
    "source": [
     "## Comparison of  All Signal Structures\n",
@@ -1922,7 +1922,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "dbd9d9ba",
+   "id": "3ceeeaf4",
    "metadata": {
     "hide-output": false
    },
@@ -1946,7 +1946,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1652d2c7",
+   "id": "d8765646",
    "metadata": {},
    "source": [
     "The three panels in the graph above show that\n",
@@ -1973,7 +1973,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "4bb512bc",
+   "id": "76f84f0c",
    "metadata": {
     "hide-output": false
    },
@@ -1986,7 +1986,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "635383e3",
+   "id": "0b3e0762",
    "metadata": {},
    "source": [
     "Kalman gains  for the two\n",
@@ -1996,7 +1996,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "04bc2b78",
+   "id": "c8ffbc3a",
    "metadata": {
     "hide-output": false
    },
@@ -2009,7 +2009,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "417f3a22",
+   "id": "57bfdfa1",
    "metadata": {},
    "source": [
     "Another  lesson that comes from the preceding three-panel graph is that the presence of iid noise\n",
@@ -2018,7 +2018,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6fdf9251",
+   "id": "4938d950",
    "metadata": {},
    "source": [
     "## Notes on History of the Problem\n",
@@ -2078,7 +2078,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "8641b86b",
+   "id": "6e8a9a2e",
    "metadata": {},
    "source": [
     "### Further historical remarks\n",
@@ -2146,7 +2146,7 @@
   }
  ],
  "metadata": {
-  "date": 1680677525.869328,
+  "date": 1685490452.7577474,
   "filename": "knowing_forecasts_of_others.md",
   "kernelspec": {
    "display_name": "Python",
diff --git a/lqramsey.ipynb b/lqramsey.ipynb
index 0a3499b..997c0a5 100644
--- a/lqramsey.ipynb
+++ b/lqramsey.ipynb
@@ -2,7 +2,7 @@
  "cells": [
   {
    "cell_type": "markdown",
-   "id": "ec1003e2",
+   "id": "5220738b",
    "metadata": {},
    "source": [
     "\n",
@@ -11,7 +11,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ef517dc2",
+   "id": "3d2ca9e8",
    "metadata": {},
    "source": [
     "# Optimal Taxation in an LQ Economy\n",
@@ -22,7 +22,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7ae9d07a",
+   "id": "e7dc2471",
    "metadata": {},
    "source": [
     "## Contents\n",
@@ -37,7 +37,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b3b0f236",
+   "id": "6a448cb7",
    "metadata": {},
    "source": [
     "In addition to what’s in Anaconda, this lecture will need the following libraries:"
@@ -46,7 +46,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "dcd27d46",
+   "id": "ea9d842a",
    "metadata": {
     "hide-output": false
    },
@@ -57,7 +57,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3e608b3b",
+   "id": "a39e8e84",
    "metadata": {},
    "source": [
     "## Overview\n",
@@ -95,7 +95,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "5a0157fe",
+   "id": "d29f82d6",
    "metadata": {
     "hide-output": false
    },
@@ -114,7 +114,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "85b7ee45",
+   "id": "3023b0fa",
    "metadata": {},
    "source": [
     "### Model Features\n",
@@ -127,7 +127,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "0107c57a",
+   "id": "5e9f9f18",
    "metadata": {},
    "source": [
     "## The Ramsey Problem\n",
@@ -137,7 +137,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "307228f1",
+   "id": "9be3cdde",
    "metadata": {},
    "source": [
     "### Technology\n",
@@ -153,7 +153,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d7c643bb",
+   "id": "9a060f92",
    "metadata": {},
    "source": [
     "### Households\n",
@@ -209,7 +209,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "13fcdee9",
+   "id": "db9aa0ac",
    "metadata": {},
    "source": [
     "### Government\n",
@@ -225,7 +225,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "657e10a7",
+   "id": "627187e8",
    "metadata": {},
    "source": [
     "### Exogenous Variables\n",
@@ -252,7 +252,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ff976a54",
+   "id": "bbf8719f",
    "metadata": {},
    "source": [
     "### Feasibility\n",
@@ -270,7 +270,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a83b0c2e",
+   "id": "14caccba",
    "metadata": {},
    "source": [
     "### Government Budget Constraint\n",
@@ -287,7 +287,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3aae5db5",
+   "id": "0fd6900e",
    "metadata": {},
    "source": [
     "### Equilibrium\n",
@@ -321,7 +321,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4462e82f",
+   "id": "2867e6fe",
    "metadata": {},
    "source": [
     "### Solution\n",
@@ -442,7 +442,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "269f0aaa",
+   "id": "b0f367fd",
    "metadata": {},
    "source": [
     "### Computing the Quadratic Term\n",
@@ -515,7 +515,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1b646198",
+   "id": "f4c8c2e8",
    "metadata": {},
    "source": [
     "### Finite State Markov Case\n",
@@ -557,7 +557,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9a0801c9",
+   "id": "4dce5a59",
    "metadata": {},
    "source": [
     "### Other Variables\n",
@@ -631,7 +631,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "28503d09",
+   "id": "6051ac69",
    "metadata": {},
    "source": [
     "### A Martingale\n",
@@ -695,7 +695,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5685984d",
+   "id": "7f3ec3fa",
    "metadata": {},
    "source": [
     "## Implementation\n",
@@ -712,7 +712,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "69ef26b7",
+   "id": "bacd58d4",
    "metadata": {
     "hide-output": false
    },
@@ -980,7 +980,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "2c40aee2",
+   "id": "781bf479",
    "metadata": {},
    "source": [
     "### Comments on the Code\n",
@@ -1008,7 +1008,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "54c9db31",
+   "id": "8f85443b",
    "metadata": {},
    "source": [
     "## Examples\n",
@@ -1021,7 +1021,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "78fc5bbb",
+   "id": "1a8476d8",
    "metadata": {},
    "source": [
     "### The Continuous Case\n",
@@ -1048,7 +1048,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "a6fecd7f",
+   "id": "86c69322",
    "metadata": {
     "hide-output": false
    },
@@ -1076,7 +1076,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6b87f875",
+   "id": "de459c87",
    "metadata": {},
    "source": [
     "The legends on the figures indicate the variables being tracked.\n",
@@ -1088,7 +1088,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "289a0314",
+   "id": "3079f221",
    "metadata": {
     "hide-output": false
    },
@@ -1099,7 +1099,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "05524f69",
+   "id": "6b6daf18",
    "metadata": {},
    "source": [
     "### The Discrete Case\n",
@@ -1110,7 +1110,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "39231398",
+   "id": "69968790",
    "metadata": {
     "hide-output": false
    },
@@ -1145,7 +1145,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b000d8be",
+   "id": "95b9ba1b",
    "metadata": {},
    "source": [
     "The call `gen_fig_2(path)` generates"
@@ -1154,7 +1154,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "39b16501",
+   "id": "78088e2f",
    "metadata": {
     "hide-output": false
    },
@@ -1165,7 +1165,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "43e4f935",
+   "id": "f23d5f7b",
    "metadata": {},
    "source": [
     "## Exercises\n",
@@ -1176,7 +1176,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "da2141d1",
+   "id": "747523e6",
    "metadata": {},
    "source": [
     "## Exercise 12.1\n",
@@ -1194,7 +1194,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "8d3f156b",
+   "id": "da18ea22",
    "metadata": {},
    "source": [
     "## Solution to[ Exercise 12.1](https://python-advanced.quantecon.org/#lq_ex1)"
@@ -1203,7 +1203,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "faa37dfa",
+   "id": "4d3e66a6",
    "metadata": {
     "hide-output": false
    },
@@ -1237,7 +1237,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "3af0925a",
+   "id": "886736cd",
    "metadata": {
     "hide-output": false
    },
@@ -1248,7 +1248,7 @@
   }
  ],
  "metadata": {
-  "date": 1680677525.9247503,
+  "date": 1685490452.8124762,
   "filename": "lqramsey.md",
   "kernelspec": {
    "display_name": "Python",
diff --git a/lu_tricks.ipynb b/lu_tricks.ipynb
index e6445bf..3d1a22c 100644
--- a/lu_tricks.ipynb
+++ b/lu_tricks.ipynb
@@ -2,7 +2,7 @@
  "cells": [
   {
    "cell_type": "markdown",
-   "id": "b422ef39",
+   "id": "de760754",
    "metadata": {},
    "source": [
     "\n",
@@ -11,7 +11,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "038d3c41",
+   "id": "f11b7982",
    "metadata": {},
    "source": [
     "# Classical Control with Linear Algebra"
@@ -19,7 +19,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "588b9a35",
+   "id": "c63d4a1c",
    "metadata": {},
    "source": [
     "## Contents\n",
@@ -36,7 +36,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7ba4e89e",
+   "id": "3eb7f7f1",
    "metadata": {},
    "source": [
     "## Overview\n",
@@ -77,7 +77,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "ca743bd0",
+   "id": "27756c27",
    "metadata": {
     "hide-output": false
    },
@@ -90,7 +90,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b674872f",
+   "id": "3da221a2",
    "metadata": {},
    "source": [
     "### References\n",
@@ -100,7 +100,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "0ab311e4",
+   "id": "d2f8cfe8",
    "metadata": {},
    "source": [
     "## A Control Problem\n",
@@ -141,7 +141,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d94b0288",
+   "id": "32165b23",
    "metadata": {},
    "source": [
     "### Example\n",
@@ -183,7 +183,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "8d56c413",
+   "id": "301d1204",
    "metadata": {},
    "source": [
     "## Finite Horizon Theory\n",
@@ -313,7 +313,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "83fff53e",
+   "id": "ba898197",
    "metadata": {},
    "source": [
     "### Matrix Methods\n",
@@ -323,7 +323,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5143c8f9",
+   "id": "4e6b6417",
    "metadata": {},
    "source": [
     "#### A Single Lag Term\n",
@@ -422,7 +422,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "bfca5140",
+   "id": "0fb51592",
    "metadata": {},
    "source": [
     "#### An Alternative Representation\n",
@@ -515,7 +515,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5959b546",
+   "id": "3c58387a",
    "metadata": {},
    "source": [
     "#### Additional Lag Terms\n",
@@ -634,7 +634,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a2f64196",
+   "id": "1cafae90",
    "metadata": {},
    "source": [
     "## Infinite Horizon Limit\n",
@@ -864,7 +864,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "fb738270",
+   "id": "b5000b20",
    "metadata": {},
    "source": [
     "## Undiscounted Problems\n",
@@ -906,7 +906,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5abe4f19",
+   "id": "a743f2d2",
    "metadata": {},
    "source": [
     "### Transforming Discounted to Undiscounted Problem\n",
@@ -991,7 +991,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "87356e9b",
+   "id": "2a2d683b",
    "metadata": {},
    "source": [
     "## Implementation\n",
@@ -1003,7 +1003,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "faff8606",
+   "id": "1370f33a",
    "metadata": {
     "hide-output": false
    },
@@ -1319,7 +1319,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "12920ebb",
+   "id": "6e101365",
    "metadata": {},
    "source": [
     "### Example\n",
@@ -1352,7 +1352,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "9964d5d0",
+   "id": "bcce2d4a",
    "metadata": {
     "hide-output": false
    },
@@ -1392,7 +1392,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5a69b3cf",
+   "id": "8d10cb0c",
    "metadata": {},
    "source": [
     "Here’s what happens when we change $ \\gamma $ to 5.0"
@@ -1401,7 +1401,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "85a96173",
+   "id": "2383e0ae",
    "metadata": {
     "hide-output": false
    },
@@ -1412,7 +1412,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "529b9d6b",
+   "id": "16b21906",
    "metadata": {},
    "source": [
     "And here’s $ \\gamma = 10 $"
@@ -1421,7 +1421,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "22cb7eda",
+   "id": "928b9819",
    "metadata": {
     "hide-output": false
    },
@@ -1432,7 +1432,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "decf3976",
+   "id": "1b582ef7",
    "metadata": {},
    "source": [
     "## Exercises"
@@ -1440,7 +1440,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "31860b5f",
+   "id": "956c5ccb",
    "metadata": {},
    "source": [
     "## Exercise 31.1\n",
@@ -1486,7 +1486,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d9d94df0",
+   "id": "8d5af520",
    "metadata": {},
    "source": [
     "## Exercise 31.2\n",
@@ -1510,7 +1510,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "940a7845",
+   "id": "90cfd77d",
    "metadata": {},
    "source": [
     "## Exercise 31.3\n",
@@ -1531,7 +1531,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "0b33ac00",
+   "id": "a7e1bd9d",
    "metadata": {},
    "source": [
     "## Exercise 31.4\n",
@@ -1551,7 +1551,7 @@
   }
  ],
  "metadata": {
-  "date": 1680677525.9943342,
+  "date": 1685490452.8831491,
   "filename": "lu_tricks.md",
   "kernelspec": {
    "display_name": "Python",
diff --git a/lucas_asset_pricing_dles.ipynb b/lucas_asset_pricing_dles.ipynb
index df1c01a..a36b06a 100644
--- a/lucas_asset_pricing_dles.ipynb
+++ b/lucas_asset_pricing_dles.ipynb
@@ -2,7 +2,7 @@
  "cells": [
   {
    "cell_type": "markdown",
-   "id": "de023d09",
+   "id": "e5823dfa",
    "metadata": {},
    "source": [
     "\n",
@@ -13,7 +13,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3ff2ddc3",
+   "id": "46b7fdd9",
    "metadata": {},
    "source": [
     "# Lucas Asset Pricing Using DLE"
@@ -21,7 +21,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "213b655a",
+   "id": "88c7bedf",
    "metadata": {},
    "source": [
     "## Contents\n",
@@ -33,7 +33,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a4959eb9",
+   "id": "92bf8329",
    "metadata": {},
    "source": [
     "This is one of a suite of lectures that use the quantecon DLE class to instantiate models within the\n",
@@ -45,7 +45,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "3cf13b53",
+   "id": "1bf0cd08",
    "metadata": {
     "hide-output": false
    },
@@ -56,7 +56,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "52faedac",
+   "id": "ba5a9112",
    "metadata": {},
    "source": [
     "This lecture uses  the DLE class to price payout\n",
@@ -76,7 +76,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "dd14c860",
+   "id": "26a59a4e",
    "metadata": {
     "hide-output": false
    },
@@ -91,7 +91,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ceff0d08",
+   "id": "e356d3e0",
    "metadata": {},
    "source": [
     "We use a linear-quadratic version of an economy that Lucas (1978) [[Luc78](https://python-advanced.quantecon.org/zreferences.html#id174)] used\n",
@@ -175,7 +175,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "837f6b2c",
+   "id": "03806a64",
    "metadata": {},
    "source": [
     "## Asset Pricing Equations\n",
@@ -209,7 +209,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "17a7c8c4",
+   "id": "2c46c881",
    "metadata": {},
    "source": [
     "## Asset Pricing Simulations"
@@ -218,7 +218,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "c599a9df",
+   "id": "f9455cf9",
    "metadata": {
     "hide-output": false
    },
@@ -255,7 +255,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "71181c11",
+   "id": "79782a94",
    "metadata": {
     "hide-output": false
    },
@@ -266,7 +266,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "86b2e776",
+   "id": "5cfbacec",
    "metadata": {},
    "source": [
     "After specifying a “Pay” matrix, we simulate the economy.\n",
@@ -278,7 +278,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "e9c369ff",
+   "id": "5f16b685",
    "metadata": {
     "hide-output": false
    },
@@ -289,7 +289,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ce5e86ca",
+   "id": "bc775de7",
    "metadata": {},
    "source": [
     "The graph below plots the price of this claim over time:"
@@ -298,7 +298,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "e607c595",
+   "id": "3804f57f",
    "metadata": {
     "hide-output": false
    },
@@ -312,7 +312,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "0e88000f",
+   "id": "d395eaf4",
    "metadata": {},
    "source": [
     "The next plot displays the realized gross rate of return on this “Lucas\n",
@@ -322,7 +322,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "f2d9c396",
+   "id": "8b19e590",
    "metadata": {
     "hide-output": false
    },
@@ -338,7 +338,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "23fdae20",
+   "id": "5cd4125a",
    "metadata": {
     "hide-output": false
    },
@@ -349,7 +349,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "efe2af31",
+   "id": "1642a564",
    "metadata": {},
    "source": [
     "Above we have also calculated the correlation coefficient between these\n",
@@ -363,7 +363,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "2e01b5a6",
+   "id": "383ee639",
    "metadata": {
     "hide-output": false
    },
@@ -378,7 +378,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "8af035f4",
+   "id": "7e81d604",
    "metadata": {},
    "source": [
     "From the above plot, we can see the tendency of the term structure to\n",
@@ -396,7 +396,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "0cefb98e",
+   "id": "1c266241",
    "metadata": {
     "hide-output": false
    },
@@ -414,7 +414,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "7809ed32",
+   "id": "4164c5d9",
    "metadata": {
     "hide-output": false
    },
@@ -430,7 +430,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "b08000f4",
+   "id": "d32c57b8",
    "metadata": {
     "hide-output": false
    },
@@ -441,7 +441,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "babe1b6e",
+   "id": "cf13a206",
    "metadata": {},
    "source": [
     "The correlation between these two gross rates is now more negative.\n",
@@ -453,7 +453,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "945dd1ff",
+   "id": "407a9ce9",
    "metadata": {
     "hide-output": false
    },
@@ -468,7 +468,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a250127d",
+   "id": "0b8e1c95",
    "metadata": {},
    "source": [
     "We can see the tendency of the term structure to slope up when rates are\n",
@@ -478,7 +478,7 @@
   }
  ],
  "metadata": {
-  "date": 1680677526.0152297,
+  "date": 1685490452.9043407,
   "filename": "lucas_asset_pricing_dles.md",
   "kernelspec": {
    "display_name": "Python",
diff --git a/lucas_model.ipynb b/lucas_model.ipynb
index 8aa433e..29c0061 100644
--- a/lucas_model.ipynb
+++ b/lucas_model.ipynb
@@ -2,7 +2,7 @@
  "cells": [
   {
    "cell_type": "markdown",
-   "id": "c6e51d8a",
+   "id": "f4c32243",
    "metadata": {},
    "source": [
     "\n",
@@ -11,7 +11,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "dba8dbab",
+   "id": "c72f118f",
    "metadata": {},
    "source": [
     "# Asset Pricing II: The Lucas Asset Pricing Model\n",
@@ -22,7 +22,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c8e76076",
+   "id": "d632da6b",
    "metadata": {},
    "source": [
     "## Contents\n",
@@ -35,7 +35,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5ab80a2b",
+   "id": "98e54c40",
    "metadata": {},
    "source": [
     "In addition to what’s in Anaconda, this lecture will need the following libraries:"
@@ -44,7 +44,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "5417890d",
+   "id": "eab3f7fd",
    "metadata": {
     "hide-output": false
    },
@@ -55,7 +55,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "fe561a0e",
+   "id": "f5c20070",
    "metadata": {},
    "source": [
     "## Overview\n",
@@ -78,7 +78,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "94cf55bf",
+   "id": "70d09788",
    "metadata": {
     "hide-output": false
    },
@@ -94,7 +94,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "53411cb1",
+   "id": "bb191884",
    "metadata": {},
    "source": [
     "## The Lucas Model\n",
@@ -116,7 +116,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "2ee74f7d",
+   "id": "ec8dabfd",
    "metadata": {},
    "source": [
     "### Basic Setup\n",
@@ -126,7 +126,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "225bf499",
+   "id": "9df0fce8",
    "metadata": {},
    "source": [
     "#### Assets\n",
@@ -156,7 +156,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "40ac54ea",
+   "id": "2038910a",
    "metadata": {},
    "source": [
     "#### Consumers\n",
@@ -180,7 +180,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1418983f",
+   "id": "661d75e6",
    "metadata": {},
    "source": [
     "### Pricing a Lucas Tree\n",
@@ -219,7 +219,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a757bce2",
+   "id": "cab9f740",
    "metadata": {},
    "source": [
     "#### The Dynamic Program\n",
@@ -277,7 +277,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "97595a22",
+   "id": "a8ffbd86",
    "metadata": {},
    "source": [
     "#### Next Steps\n",
@@ -296,7 +296,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6e2018cb",
+   "id": "35ced0b2",
    "metadata": {},
    "source": [
     "#### Equilibrium Constraints\n",
@@ -315,7 +315,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "22be1f02",
+   "id": "ec84d970",
    "metadata": {},
    "source": [
     "#### The Equilibrium Price Function\n",
@@ -361,7 +361,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "80322422",
+   "id": "f302b46e",
    "metadata": {},
    "source": [
     "### Solving the Model\n",
@@ -377,7 +377,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "8af4cab0",
+   "id": "1ab29a19",
    "metadata": {},
    "source": [
     "#### Setting up the Problem\n",
@@ -427,7 +427,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b98ba357",
+   "id": "bc1e9af9",
    "metadata": {},
    "source": [
     "#### A Little Fixed Point Theory\n",
@@ -489,7 +489,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "bacbb02c",
+   "id": "bff5498a",
    "metadata": {},
    "source": [
     "### Computation – An Example\n",
@@ -510,7 +510,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "5a4996d1",
+   "id": "17ac73ff",
    "metadata": {
     "hide-output": false
    },
@@ -549,7 +549,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d17d369d",
+   "id": "f7a66743",
    "metadata": {},
    "source": [
     "The following function takes an instance of the `LucasTree` and generates a\n",
@@ -559,7 +559,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "f65da46e",
+   "id": "05696621",
    "metadata": {
     "hide-output": false
    },
@@ -601,7 +601,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "2b9c3af9",
+   "id": "66dc7f20",
    "metadata": {},
    "source": [
     "To solve the model, we write a function that iterates using the Lucas operator\n",
@@ -611,7 +611,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "109ce6a5",
+   "id": "3b279caf",
    "metadata": {
     "hide-output": false
    },
@@ -647,7 +647,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "12fcdb0f",
+   "id": "f5b3f433",
    "metadata": {},
    "source": [
     "Solving the model and plotting the resulting price function"
@@ -656,7 +656,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "190bfed0",
+   "id": "e998d99c",
    "metadata": {
     "hide-output": false
    },
@@ -675,7 +675,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e5c09a35",
+   "id": "97b0c343",
    "metadata": {},
    "source": [
     "We see that the price is increasing, even if we remove all serial correlation from the endowment process.\n",
@@ -701,7 +701,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "70a350f3",
+   "id": "1d4af700",
    "metadata": {},
    "source": [
     "## Exercises\n",
@@ -712,7 +712,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e5276d63",
+   "id": "99491586",
    "metadata": {},
    "source": [
     "## Exercise 34.1\n",
@@ -722,7 +722,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "2b64f02a",
+   "id": "5ee85c90",
    "metadata": {},
    "source": [
     "## Solution to[ Exercise 34.1](https://python-advanced.quantecon.org/#lucas_ex1)"
@@ -731,7 +731,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "1b81666b",
+   "id": "33dcada0",
    "metadata": {
     "hide-output": false
    },
@@ -753,7 +753,7 @@
   }
  ],
  "metadata": {
-  "date": 1680677526.0478728,
+  "date": 1685490452.9368224,
   "filename": "lucas_model.md",
   "kernelspec": {
    "display_name": "Python",
diff --git a/markov_jump_lq.ipynb b/markov_jump_lq.ipynb
index d5a5b6f..0375c93 100644
--- a/markov_jump_lq.ipynb
+++ b/markov_jump_lq.ipynb
@@ -2,7 +2,7 @@
  "cells": [
   {
    "cell_type": "markdown",
-   "id": "99d80b8e",
+   "id": "0598f894",
    "metadata": {},
    "source": [
     "\n",
@@ -13,7 +13,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3cebd43a",
+   "id": "f4b4b578",
    "metadata": {},
    "source": [
     "# Markov Jump Linear Quadratic Dynamic Programming"
@@ -21,7 +21,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "32be6e75",
+   "id": "5f523100",
    "metadata": {},
    "source": [
     "## Contents\n",
@@ -38,7 +38,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e3730b2b",
+   "id": "716505d7",
    "metadata": {},
    "source": [
     "In addition to what’s in Anaconda, this lecture will need the following libraries:"
@@ -47,7 +47,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "9405089b",
+   "id": "f228591b",
    "metadata": {
     "hide-output": false
    },
@@ -58,7 +58,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "dc8aec7f",
+   "id": "e00aca06",
    "metadata": {},
    "source": [
     "## Overview\n",
@@ -98,7 +98,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "680caf98",
+   "id": "94fe059a",
    "metadata": {},
    "source": [
     "## Review of useful LQ dynamic programming formulas\n",
@@ -172,7 +172,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "81c1e85f",
+   "id": "faccf7fa",
    "metadata": {},
    "source": [
     "## Linked Riccati equations for Markov LQ dynamic programming\n",
@@ -285,7 +285,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1849826c",
+   "id": "68f6ed0f",
    "metadata": {},
    "source": [
     "## Applications\n",
@@ -298,7 +298,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "89976d5d",
+   "id": "195ee1a6",
    "metadata": {
     "hide-output": false
    },
@@ -315,7 +315,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "f1e0e5eb",
+   "id": "d7dae34b",
    "metadata": {
     "hide-output": false
    },
@@ -327,7 +327,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9ad1253f",
+   "id": "35eced2a",
    "metadata": {},
    "source": [
     "## Example 1\n",
@@ -397,7 +397,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "63a6ea64",
+   "id": "9db2a706",
    "metadata": {
     "hide-output": false
    },
@@ -442,7 +442,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c92cf198",
+   "id": "287b134a",
    "metadata": {},
    "source": [
     "The continuous part of the state $ x_t $ consists of two variables,\n",
@@ -452,7 +452,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "d08342c2",
+   "id": "d8f639e4",
    "metadata": {
     "hide-output": false
    },
@@ -463,7 +463,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "cec40828",
+   "id": "023b334d",
    "metadata": {},
    "source": [
     "We start with a Markov transition matrix that makes the Markov state be\n",
@@ -503,7 +503,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "d0e1c668",
+   "id": "5eb17677",
    "metadata": {
     "hide-output": false
    },
@@ -517,7 +517,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "63dbef2b",
+   "id": "da42f413",
    "metadata": {
     "hide-output": false
    },
@@ -530,7 +530,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "d043a643",
+   "id": "3c2c01ef",
    "metadata": {
     "hide-output": false
    },
@@ -544,7 +544,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "142cc9f4",
+   "id": "5dcbf197",
    "metadata": {},
    "source": [
     "Let’s look at the value function matrices and the decision rules for\n",
@@ -554,7 +554,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "c01ccca6",
+   "id": "a378ded5",
    "metadata": {
     "hide-output": false
    },
@@ -567,7 +567,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "eb72c392",
+   "id": "c78794de",
    "metadata": {
     "hide-output": false
    },
@@ -580,7 +580,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "07401214",
+   "id": "75ffeee7",
    "metadata": {
     "hide-output": false
    },
@@ -592,7 +592,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6b19b04f",
+   "id": "d4504d60",
    "metadata": {},
    "source": [
     "Now we’ll plot the decision rules and see if they make sense"
@@ -601,7 +601,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "b35eb1f2",
+   "id": "e4a1fc8b",
    "metadata": {
     "hide-output": false
    },
@@ -633,7 +633,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "fb9aa5bc",
+   "id": "34f93bd4",
    "metadata": {},
    "source": [
     "The above graph plots $ k_{t+1}= k_t + u_t = k_t - F x_t $ as an affine\n",
@@ -659,7 +659,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "3da4dea4",
+   "id": "2adac01c",
    "metadata": {
     "hide-output": false
    },
@@ -680,7 +680,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3d6d03d5",
+   "id": "90f6009f",
    "metadata": {},
    "source": [
     "Now we’ll depart from the preceding transition matrix that made the\n",
@@ -699,7 +699,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "b4c7133b",
+   "id": "01dc6779",
    "metadata": {
     "hide-output": false
    },
@@ -717,7 +717,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "b587e03d",
+   "id": "0e43d745",
    "metadata": {
     "hide-output": false
    },
@@ -734,7 +734,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e2ab6c3f",
+   "id": "b334c646",
    "metadata": {},
    "source": [
     "We can plot optimal decision rules associated with different\n",
@@ -744,7 +744,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "e010e1f6",
+   "id": "6c2306d2",
    "metadata": {
     "hide-output": false
    },
@@ -767,7 +767,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "b7319f63",
+   "id": "833f2685",
    "metadata": {
     "hide-output": false
    },
@@ -787,7 +787,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "fc10690f",
+   "id": "fb6f1485",
    "metadata": {},
    "source": [
     "Notice how the decision rules’ constants and slopes behave as functions\n",
@@ -812,7 +812,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "01fd848b",
+   "id": "d6844e76",
    "metadata": {
     "hide-output": false
    },
@@ -829,7 +829,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "71c6444f",
+   "id": "df5f9422",
    "metadata": {},
    "source": [
     "We can plot optimal decision rules for different $ \\lambda $ and\n",
@@ -839,7 +839,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "49e0cd34",
+   "id": "55177f9f",
    "metadata": {
     "hide-output": false
    },
@@ -869,7 +869,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "5ab51787",
+   "id": "4a7f1dcd",
    "metadata": {
     "hide-output": false
    },
@@ -891,7 +891,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "bda21b71",
+   "id": "ad35e018",
    "metadata": {},
    "source": [
     "The following code defines a wrapper function that computes optimal\n",
@@ -901,7 +901,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "b2623d54",
+   "id": "c1957981",
    "metadata": {
     "hide-output": false
    },
@@ -1002,7 +1002,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "2bf05e98",
+   "id": "6200869d",
    "metadata": {},
    "source": [
     "To illustrate the code with another example, we shall set\n",
@@ -1054,7 +1054,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "bafe7cea",
+   "id": "eec1c63e",
    "metadata": {
     "hide-output": false
    },
@@ -1065,7 +1065,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c7e29b07",
+   "id": "c14a7c89",
    "metadata": {},
    "source": [
     "Set $ f_{1,{s_t}} $ and $ d_{s_t} $ as constant functions and\n",
@@ -1078,7 +1078,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "42ed59db",
+   "id": "b4686d7d",
    "metadata": {
     "hide-output": false
    },
@@ -1089,7 +1089,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b9f6d356",
+   "id": "2160f889",
    "metadata": {},
    "source": [
     "## Example 2\n",
@@ -1159,7 +1159,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "7d93ba76",
+   "id": "1e0d28bd",
    "metadata": {
     "hide-output": false
    },
@@ -1212,7 +1212,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "cffd8802",
+   "id": "8b3ff53f",
    "metadata": {
     "hide-output": false
    },
@@ -1223,7 +1223,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "0fdb06d4",
+   "id": "3524ca2b",
    "metadata": {},
    "source": [
     "Only $ d_{s_t} $ depends on $ s_t $."
@@ -1232,7 +1232,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "d844aa28",
+   "id": "9ebfa635",
    "metadata": {
     "hide-output": false
    },
@@ -1243,7 +1243,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "fc05dfae",
+   "id": "fffba2c2",
    "metadata": {},
    "source": [
     "Only $ f_{1,{s_t}} $ depends on $ s_t $."
@@ -1252,7 +1252,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "b324f250",
+   "id": "3db5e03d",
    "metadata": {
     "hide-output": false
    },
@@ -1263,7 +1263,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9b871b54",
+   "id": "2fa79a41",
    "metadata": {},
    "source": [
     "Only $ f_{2,{s_t}} $ depends on $ s_t $."
@@ -1272,7 +1272,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "fae4aef3",
+   "id": "20083c82",
    "metadata": {
     "hide-output": false
    },
@@ -1283,7 +1283,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5325e3ee",
+   "id": "0f0acf92",
    "metadata": {},
    "source": [
     "Only $ \\alpha_0(s_t) $ depends on $ s_t $."
@@ -1292,7 +1292,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "509e773e",
+   "id": "1645c891",
    "metadata": {
     "hide-output": false
    },
@@ -1303,7 +1303,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "28ee4aaa",
+   "id": "c96813aa",
    "metadata": {},
    "source": [
     "Only $ \\rho_{s_t} $ depends on $ s_t $."
@@ -1312,7 +1312,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "53d29fa7",
+   "id": "dfe5bf16",
    "metadata": {
     "hide-output": false
    },
@@ -1323,7 +1323,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f92bc853",
+   "id": "56803c2f",
    "metadata": {},
    "source": [
     "Only $ \\sigma_{s_t} $ depends on $ s_t $."
@@ -1332,7 +1332,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "353f1475",
+   "id": "b7c9055b",
    "metadata": {
     "hide-output": false
    },
@@ -1343,7 +1343,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a43622f3",
+   "id": "57c86b30",
    "metadata": {},
    "source": [
     "## More examples\n",
@@ -1358,7 +1358,7 @@
   }
  ],
  "metadata": {
-  "date": 1680677526.1009736,
+  "date": 1685490452.990838,
   "filename": "markov_jump_lq.md",
   "kernelspec": {
    "display_name": "Python",
diff --git a/matsuyama.ipynb b/matsuyama.ipynb
index b4faaf5..3d6a06e 100644
--- a/matsuyama.ipynb
+++ b/matsuyama.ipynb
@@ -2,7 +2,7 @@
  "cells": [
   {
    "cell_type": "markdown",
-   "id": "2f3517f8",
+   "id": "1dfcecc9",
    "metadata": {},
    "source": [
     "\n",
@@ -11,7 +11,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "da4184cb",
+   "id": "f8553ab2",
    "metadata": {},
    "source": [
     "# Globalization and Cycles"
@@ -19,7 +19,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d1742543",
+   "id": "e4696560",
    "metadata": {},
    "source": [
     "## Contents\n",
@@ -34,7 +34,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c4fa610e",
+   "id": "ec50776c",
    "metadata": {},
    "source": [
     "## Overview\n",
@@ -59,7 +59,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "6ec38972",
+   "id": "4553990e",
    "metadata": {
     "hide-output": false
    },
@@ -75,7 +75,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "367c24ee",
+   "id": "2b097f9d",
    "metadata": {},
    "source": [
     "### Background\n",
@@ -91,7 +91,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7ec6ecc1",
+   "id": "7a13dd4a",
    "metadata": {},
    "source": [
     "## Key Ideas\n",
@@ -101,7 +101,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "32083ec6",
+   "id": "c2852f83",
    "metadata": {},
    "source": [
     "### Innovation Cycles\n",
@@ -129,7 +129,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4c23d2bd",
+   "id": "a2a360bc",
    "metadata": {},
    "source": [
     "### Synchronization\n",
@@ -145,7 +145,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "8658f828",
+   "id": "c465a2b7",
    "metadata": {},
    "source": [
     "## Model\n",
@@ -193,7 +193,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f616d7a4",
+   "id": "8fdf072a",
    "metadata": {},
    "source": [
     "### Prices\n",
@@ -283,7 +283,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b66a7f82",
+   "id": "e3335bef",
    "metadata": {},
    "source": [
     "### New Varieties\n",
@@ -315,7 +315,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4b020e65",
+   "id": "aff01090",
    "metadata": {},
    "source": [
     "### Law of Motion\n",
@@ -394,7 +394,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "88a31faf",
+   "id": "ccd24b5b",
    "metadata": {},
    "source": [
     "## Simulation\n",
@@ -421,7 +421,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "e8755341",
+   "id": "7157952c",
    "metadata": {
     "hide-output": false
    },
@@ -734,7 +734,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "be245e21",
+   "id": "7a4f8fcf",
    "metadata": {},
    "source": [
     "### Time Series of Firm Measures\n",
@@ -751,7 +751,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "17c2a9b2",
+   "id": "c73ef901",
    "metadata": {
     "hide-output": false
    },
@@ -791,7 +791,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b93a6692",
+   "id": "64ae42fe",
    "metadata": {},
    "source": [
     "In the first case, innovation in the two countries does not synchronize.\n",
@@ -802,7 +802,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "2f61ad3a",
+   "id": "59a4b774",
    "metadata": {},
    "source": [
     "### Basin of Attraction\n",
@@ -837,7 +837,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1d536b9f",
+   "id": "f81bfad4",
    "metadata": {},
    "source": [
     "## Exercises"
@@ -845,7 +845,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "39fe1ebf",
+   "id": "d9cfcd9b",
    "metadata": {},
    "source": [
     "## Exercise 14.1\n",
@@ -855,7 +855,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "193b7017",
+   "id": "d3f4fdf5",
    "metadata": {},
    "source": [
     "## Solution to[ Exercise 14.1](https://python-advanced.quantecon.org/#matsuyama_ex1)"
@@ -864,7 +864,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "ce2ac0e2",
+   "id": "2ae7a5c5",
    "metadata": {
     "hide-output": false
    },
@@ -920,7 +920,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6255e3d5",
+   "id": "9d63bf31",
    "metadata": {},
    "source": [
     "Additionally, instead of just seeing 4 plots at once, we might want to\n",
@@ -933,7 +933,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "98440189",
+   "id": "7d678611",
    "metadata": {
     "hide-output": false
    },
@@ -960,7 +960,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "5b7c7ea0",
+   "id": "034d2f42",
    "metadata": {
     "hide-output": false
    },
@@ -974,7 +974,7 @@
   }
  ],
  "metadata": {
-  "date": 1680677526.1313648,
+  "date": 1685490453.021407,
   "filename": "matsuyama.md",
   "kernelspec": {
    "display_name": "Python",
diff --git a/muth_kalman.ipynb b/muth_kalman.ipynb
index cf4e18b..17b0259 100644
--- a/muth_kalman.ipynb
+++ b/muth_kalman.ipynb
@@ -2,7 +2,7 @@
  "cells": [
   {
    "cell_type": "markdown",
-   "id": "a90a3905",
+   "id": "be07e83d",
    "metadata": {},
    "source": [
     "\n",
@@ -13,7 +13,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "442702a3",
+   "id": "a0933dd7",
    "metadata": {},
    "source": [
     "# Reverse Engineering a la Muth"
@@ -21,7 +21,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "906430bf",
+   "id": "c5ac9f42",
    "metadata": {},
    "source": [
     "## Contents\n",
@@ -37,7 +37,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7d295d86",
+   "id": "a2930c7f",
    "metadata": {},
    "source": [
     "In addition to what’s in Anaconda, this lecture uses the quantecon library."
@@ -46,7 +46,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "f54d7d28",
+   "id": "64e4bcd3",
    "metadata": {
     "hide-output": false
    },
@@ -57,7 +57,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "af7d2e1e",
+   "id": "2a1301bb",
    "metadata": {},
    "source": [
     "We’ll also need the following imports:"
@@ -66,7 +66,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "6d8b9358",
+   "id": "f72d72a9",
    "metadata": {
     "hide-output": false
    },
@@ -85,7 +85,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "0721e6e4",
+   "id": "443d5257",
    "metadata": {},
    "source": [
     "This lecture uses the Kalman filter to reformulate John F. Muth’s first\n",
@@ -98,7 +98,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "2fe9f3fb",
+   "id": "f7f3a172",
    "metadata": {},
    "source": [
     "## Friedman (1956) and Muth (1960)\n",
@@ -149,7 +149,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "73e6dfb6",
+   "id": "c679aa68",
    "metadata": {},
    "source": [
     "## A Process for Which Adaptive Expectations are Optimal\n",
@@ -217,7 +217,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "4a2431e0",
+   "id": "663d2028",
    "metadata": {
     "hide-output": false
    },
@@ -250,7 +250,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1f46d193",
+   "id": "c93fe4b3",
    "metadata": {},
    "source": [
     "## Some Useful State-Space Math\n",
@@ -307,7 +307,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "fae99dfc",
+   "id": "70b2cbc1",
    "metadata": {
     "hide-output": false
    },
@@ -340,7 +340,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a48cb648",
+   "id": "fb3e6b6b",
    "metadata": {},
    "source": [
     "Now that we have simulated our joint system, we have $ x_t $,\n",
@@ -352,7 +352,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9c266ba0",
+   "id": "b36b1c60",
    "metadata": {},
    "source": [
     "## Estimates of Unobservables\n",
@@ -365,7 +365,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "933fe234",
+   "id": "883952b0",
    "metadata": {
     "hide-output": false
    },
@@ -382,7 +382,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "436a7145",
+   "id": "9e3a752b",
    "metadata": {},
    "source": [
     "Note how $ x_t $ and $ \\hat{x_t} $ differ.\n",
@@ -393,7 +393,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ff5e3269",
+   "id": "b6db578c",
    "metadata": {},
    "source": [
     "## Relationship of Unobservables to Observables\n",
@@ -406,7 +406,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "e2a82432",
+   "id": "70f7c1b9",
    "metadata": {
     "hide-output": false
    },
@@ -423,7 +423,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b44bada2",
+   "id": "df3d8916",
    "metadata": {},
    "source": [
     "We see above that $ y $ seems to look like white noise around the\n",
@@ -432,7 +432,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "0df3035e",
+   "id": "e63a50bf",
    "metadata": {},
    "source": [
     "### Innovations\n",
@@ -444,7 +444,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "62949de4",
+   "id": "e3201a09",
    "metadata": {
     "hide-output": false
    },
@@ -460,7 +460,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6b15a94f",
+   "id": "30ee2cb6",
    "metadata": {},
    "source": [
     "## MA and AR Representations\n",
@@ -481,7 +481,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "2b4d6356",
+   "id": "0e342fc4",
    "metadata": {
     "hide-output": false
    },
@@ -507,7 +507,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a8c1111c",
+   "id": "c7fa40b5",
    "metadata": {},
    "source": [
     "The **moving average** coefficients in the top panel show tell-tale\n",
@@ -524,7 +524,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "654c4886",
+   "id": "4c36e61f",
    "metadata": {
     "hide-output": false
    },
@@ -535,7 +535,7 @@
   }
  ],
  "metadata": {
-  "date": 1680677526.3896594,
+  "date": 1685490453.0489576,
   "filename": "muth_kalman.md",
   "kernelspec": {
    "display_name": "Python",
diff --git a/opt_tax_recur.ipynb b/opt_tax_recur.ipynb
index fad17e5..32607c7 100644
--- a/opt_tax_recur.ipynb
+++ b/opt_tax_recur.ipynb
@@ -2,7 +2,7 @@
  "cells": [
   {
    "cell_type": "markdown",
-   "id": "83848ae9",
+   "id": "0d276c32",
    "metadata": {},
    "source": [
     "\n",
@@ -11,7 +11,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "04fe5f56",
+   "id": "a385390d",
    "metadata": {},
    "source": [
     "# Optimal Taxation with State-Contingent Debt"
@@ -19,7 +19,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "93c4fc38",
+   "id": "4c7737be",
    "metadata": {},
    "source": [
     "## Contents\n",
@@ -33,7 +33,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4f49b77e",
+   "id": "d41aa74b",
    "metadata": {},
    "source": [
     "In addition to what’s in Anaconda, this lecture will need the following libraries:"
@@ -42,7 +42,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "91c7de3c",
+   "id": "ca700046",
    "metadata": {
     "hide-output": false
    },
@@ -54,7 +54,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "964f187a",
+   "id": "c2be612d",
    "metadata": {},
    "source": [
     "## Overview\n",
@@ -95,7 +95,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "70314beb",
+   "id": "86c93164",
    "metadata": {
     "hide-output": false
    },
@@ -114,7 +114,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b98ca35b",
+   "id": "22b67d24",
    "metadata": {},
    "source": [
     "## A Competitive Equilibrium with Distorting Taxes\n",
@@ -231,7 +231,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3fdc76de",
+   "id": "49b283d3",
    "metadata": {},
    "source": [
     "### Arrow-Debreu Version of Price System\n",
@@ -259,7 +259,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a7c42e31",
+   "id": "aabd81c0",
    "metadata": {},
    "source": [
     "### Primal Approach\n",
@@ -291,7 +291,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "828c14cb",
+   "id": "a2b7f6e3",
    "metadata": {},
    "source": [
     "### The Implementability Constraint\n",
@@ -367,7 +367,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "79ecb9d1",
+   "id": "2e78c718",
    "metadata": {},
    "source": [
     "### Solution Details\n",
@@ -509,7 +509,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "0da9849d",
+   "id": "7771be3c",
    "metadata": {},
    "source": [
     "### The Ramsey Allocation for a Given Multiplier\n",
@@ -545,7 +545,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "295c1f8e",
+   "id": "223645a4",
    "metadata": {},
    "source": [
     "### Further Specialization\n",
@@ -567,7 +567,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "68dd4c85",
+   "id": "5379b7c2",
    "metadata": {},
    "source": [
     "### Determining the Lagrange Multiplier\n",
@@ -703,7 +703,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "da64da3c",
+   "id": "7ed6b0cb",
    "metadata": {},
    "source": [
     "### Time Inconsistency\n",
@@ -734,7 +734,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7aca615f",
+   "id": "ef050872",
    "metadata": {},
    "source": [
     "### Specification with CRRA Utility\n",
@@ -819,7 +819,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "30487e80",
+   "id": "e0422e0f",
    "metadata": {},
    "source": [
     "### Sequence Implementation\n",
@@ -830,7 +830,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "2af41119",
+   "id": "0fe9b7fd",
    "metadata": {
     "hide-output": false
    },
@@ -1038,7 +1038,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e49e23b5",
+   "id": "dd847405",
    "metadata": {},
    "source": [
     "## Recursive Formulation of the Ramsey Problem\n",
@@ -1055,7 +1055,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "efb270f2",
+   "id": "b8cba3d2",
    "metadata": {},
    "source": [
     "### Intertemporal Delegation\n",
@@ -1104,7 +1104,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3f81bc00",
+   "id": "dc043a4d",
    "metadata": {},
    "source": [
     "### Two Bellman Equations\n",
@@ -1123,7 +1123,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "07743edc",
+   "id": "ecf71eae",
    "metadata": {},
    "source": [
     "### The Continuation Ramsey Problem\n",
@@ -1168,7 +1168,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f0d5ee87",
+   "id": "907f7db3",
    "metadata": {},
    "source": [
     "### The Ramsey Problem\n",
@@ -1221,7 +1221,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c7b95e31",
+   "id": "7e37aaaf",
    "metadata": {},
    "source": [
     "### First-Order Conditions\n",
@@ -1305,7 +1305,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5ecf1585",
+   "id": "01249658",
    "metadata": {},
    "source": [
     "### State Variable Degeneracy\n",
@@ -1333,7 +1333,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3ae9845a",
+   "id": "452a1b4f",
    "metadata": {},
    "source": [
     "### Manifestations of Time Inconsistency\n",
@@ -1383,7 +1383,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "61151097",
+   "id": "c8a3684f",
    "metadata": {},
    "source": [
     "### Recursive Implementation\n",
@@ -1394,7 +1394,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "31c8392e",
+   "id": "ff4d714b",
    "metadata": {
     "hide-output": false
    },
@@ -1648,7 +1648,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ece7fb3e",
+   "id": "afb92a84",
    "metadata": {},
    "source": [
     "## Examples\n",
@@ -1658,7 +1658,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "05be1d69",
+   "id": "9fbbd35f",
    "metadata": {},
    "source": [
     "### Anticipated One-Period War\n",
@@ -1714,7 +1714,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "d3e4f159",
+   "id": "052ae6d6",
    "metadata": {
     "hide-output": false
    },
@@ -1770,7 +1770,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ea372b22",
+   "id": "77b784c6",
    "metadata": {},
    "source": [
     "We set initial government debt $ b_0 = 1 $.\n",
@@ -1784,7 +1784,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "cff96ebe",
+   "id": "707e66c5",
    "metadata": {
     "hide-output": false
    },
@@ -1825,7 +1825,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a4657348",
+   "id": "a0100aeb",
    "metadata": {},
    "source": [
     "**Tax smoothing**\n",
@@ -1871,7 +1871,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "508dea50",
+   "id": "2ab5fc53",
    "metadata": {
     "hide-output": false
    },
@@ -1886,7 +1886,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e61bbe7b",
+   "id": "236c6176",
    "metadata": {},
    "source": [
     "### Government Saving\n",
@@ -1922,7 +1922,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b30073cc",
+   "id": "846c6ca9",
    "metadata": {},
    "source": [
     "### Time 0 Manipulation of Interest Rate\n",
@@ -1940,7 +1940,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "bb0d9121",
+   "id": "d661b9bc",
    "metadata": {},
    "source": [
     "### Time 0 and Time-Inconsistency\n",
@@ -1960,7 +1960,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "a8ea1146",
+   "id": "2f152d92",
    "metadata": {
     "hide-output": false
    },
@@ -1994,7 +1994,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "fb51af00",
+   "id": "8128c02e",
    "metadata": {},
    "source": [
     "The figure indicates  that if the government enters with  positive debt, it sets\n",
@@ -2044,7 +2044,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "4fabfdd2",
+   "id": "991b1abd",
    "metadata": {
     "hide-output": false
    },
@@ -2074,7 +2074,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "2b7cf2e4",
+   "id": "5edaf095",
    "metadata": {},
    "source": [
     "The tax rates in the figure are equal  for only two values of initial government debt."
@@ -2082,7 +2082,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "423c8abb",
+   "id": "a465e780",
    "metadata": {},
    "source": [
     "### Tax Smoothing and non-CRRA Preferences\n",
@@ -2119,7 +2119,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "df5bf32b",
+   "id": "735c9d72",
    "metadata": {
     "hide-output": false
    },
@@ -2165,7 +2165,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "94857735",
+   "id": "e8c2dab4",
    "metadata": {},
    "source": [
     "Also, suppose that $ g_t $ follows a two-state IID process with equal\n",
@@ -2179,7 +2179,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "7943da8a",
+   "id": "79053e59",
    "metadata": {
     "hide-output": false
    },
@@ -2221,7 +2221,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "bc55f0a0",
+   "id": "d5e24b7f",
    "metadata": {},
    "source": [
     "As should be expected, the recursive and sequential solutions produce almost\n",
@@ -2234,7 +2234,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1d0fecc0",
+   "id": "4c27e111",
    "metadata": {},
    "source": [
     "### Further Comments\n",
@@ -2255,7 +2255,7 @@
   }
  ],
  "metadata": {
-  "date": 1680677526.4970841,
+  "date": 1685490453.3169343,
   "filename": "opt_tax_recur.md",
   "kernelspec": {
    "display_name": "Python",
diff --git a/orth_proj.ipynb b/orth_proj.ipynb
index 9fe69fe..ca3b213 100644
--- a/orth_proj.ipynb
+++ b/orth_proj.ipynb
@@ -2,7 +2,7 @@
  "cells": [
   {
    "cell_type": "markdown",
-   "id": "f88fdbed",
+   "id": "f7434317",
    "metadata": {},
    "source": [
     "\n",
@@ -11,7 +11,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "378aee7f",
+   "id": "f5fa7483",
    "metadata": {},
    "source": [
     "# Orthogonal Projections and Their Applications\n",
@@ -22,7 +22,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5b07c0d5",
+   "id": "cffafe6e",
    "metadata": {},
    "source": [
     "## Contents\n",
@@ -40,7 +40,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "59e93231",
+   "id": "ab71009d",
    "metadata": {},
    "source": [
     "## Overview\n",
@@ -69,7 +69,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "57363018",
+   "id": "614c26da",
    "metadata": {
     "hide-output": false
    },
@@ -81,7 +81,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "09229a55",
+   "id": "a808c60a",
    "metadata": {},
    "source": [
     "### Further Reading\n",
@@ -97,7 +97,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "50b39f87",
+   "id": "af24e290",
    "metadata": {},
    "source": [
     "## Key Definitions\n",
@@ -161,7 +161,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4f5f93e1",
+   "id": "57f08b18",
    "metadata": {},
    "source": [
     "### Linear Independence vs Orthogonality\n",
@@ -175,7 +175,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "8114b3d6",
+   "id": "ce84ec22",
    "metadata": {},
    "source": [
     "## The Orthogonal Projection Theorem\n",
@@ -206,7 +206,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "143ffbaa",
+   "id": "3e42dc18",
    "metadata": {},
    "source": [
     "### Proof of Sufficiency\n",
@@ -232,7 +232,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4874f726",
+   "id": "4cedd791",
    "metadata": {},
    "source": [
     "### Orthogonal Projection as a Mapping\n",
@@ -273,7 +273,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e795935c",
+   "id": "8ba93e31",
    "metadata": {},
    "source": [
     "#### Orthogonal Complement\n",
@@ -314,7 +314,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "77f3de8b",
+   "id": "ea6d3f94",
    "metadata": {},
    "source": [
     "## Orthonormal Basis\n",
@@ -360,7 +360,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6f127b31",
+   "id": "c44065b5",
    "metadata": {},
    "source": [
     "### Projection onto an Orthonormal Basis\n",
@@ -398,7 +398,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "68ee810a",
+   "id": "03fe950c",
    "metadata": {},
    "source": [
     "## Projection Via Matrix Algebra\n",
@@ -460,7 +460,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c6df1635",
+   "id": "61871089",
    "metadata": {},
    "source": [
     "### Starting with the Basis\n",
@@ -482,7 +482,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "71405585",
+   "id": "4295327e",
    "metadata": {},
    "source": [
     "### The Orthonormal Case\n",
@@ -513,7 +513,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "af758339",
+   "id": "49494b5d",
    "metadata": {},
    "source": [
     "### Application: Overdetermined Systems of Equations\n",
@@ -570,7 +570,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "59e4d89c",
+   "id": "36e2e7fb",
    "metadata": {},
    "source": [
     "## Least Squares Regression\n",
@@ -584,7 +584,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "554b8e39",
+   "id": "fde7896b",
    "metadata": {},
    "source": [
     "### Squared Risk Measures\n",
@@ -622,7 +622,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "81715a3f",
+   "id": "b4a69b6f",
    "metadata": {},
    "source": [
     "### Solution\n",
@@ -731,7 +731,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "28450dca",
+   "id": "e4617edc",
    "metadata": {},
    "source": [
     "## Orthogonalization and Decomposition\n",
@@ -748,7 +748,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e2c2b152",
+   "id": "fb5dd89d",
    "metadata": {},
    "source": [
     "### Gram-Schmidt Orthogonalization\n",
@@ -781,7 +781,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4b5e0570",
+   "id": "c42f6566",
    "metadata": {},
    "source": [
     "### QR Decomposition\n",
@@ -813,7 +813,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1ca97ba9",
+   "id": "98e2f4e9",
    "metadata": {},
    "source": [
     "### Linear Regression via QR Decomposition\n",
@@ -838,7 +838,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4f5b7bbc",
+   "id": "68fa3dd3",
    "metadata": {},
    "source": [
     "## Exercises"
@@ -846,7 +846,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "bfa02164",
+   "id": "9b88cf64",
    "metadata": {},
    "source": [
     "## Exercise 1.1\n",
@@ -856,7 +856,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "37699254",
+   "id": "7a161566",
    "metadata": {},
    "source": [
     "## Solution to[ Exercise 1.1](https://python-advanced.quantecon.org/#op_ex1)\n",
@@ -867,7 +867,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c4ebc38b",
+   "id": "693de976",
    "metadata": {},
    "source": [
     "## Exercise 1.2\n",
@@ -879,7 +879,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d0e680fb",
+   "id": "742ebdb0",
    "metadata": {},
    "source": [
     "## Solution to[ Exercise 1.2](https://python-advanced.quantecon.org/#op_ex2)\n",
@@ -895,7 +895,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b864be06",
+   "id": "684e10b4",
    "metadata": {},
    "source": [
     "## Exercise 1.3\n",
@@ -930,7 +930,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b26c3a73",
+   "id": "d7a31554",
    "metadata": {},
    "source": [
     "## Solution to[ Exercise 1.3](https://python-advanced.quantecon.org/#op_ex3)\n",
@@ -942,7 +942,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "64735679",
+   "id": "47f6f45f",
    "metadata": {
     "hide-output": false
    },
@@ -988,7 +988,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "fde39a19",
+   "id": "2937b44e",
    "metadata": {},
    "source": [
     "Here are the arrays we’ll work with"
@@ -997,7 +997,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "381fef46",
+   "id": "cec6eab2",
    "metadata": {
     "hide-output": false
    },
@@ -1014,7 +1014,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "8e5ee1d6",
+   "id": "94f9d47b",
    "metadata": {},
    "source": [
     "First, let’s try projection of $ y $ onto the column space of\n",
@@ -1024,7 +1024,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "6aa440c5",
+   "id": "0bae447e",
    "metadata": {
     "hide-output": false
    },
@@ -1036,7 +1036,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1b05aa88",
+   "id": "b15328c4",
    "metadata": {},
    "source": [
     "Now let’s do the same using an orthonormal basis created from our\n",
@@ -1046,7 +1046,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "08453861",
+   "id": "0e0e0a53",
    "metadata": {
     "hide-output": false
    },
@@ -1059,7 +1059,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "4cd9cc2c",
+   "id": "1a090da4",
    "metadata": {
     "hide-output": false
    },
@@ -1071,7 +1071,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "185e330f",
+   "id": "8e542d29",
    "metadata": {},
    "source": [
     "This is the same answer. So far so good. Finally, let’s try the same\n",
@@ -1081,7 +1081,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "14f5f159",
+   "id": "f82aa064",
    "metadata": {
     "hide-output": false
    },
@@ -1094,7 +1094,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "cb0e337c",
+   "id": "49993acc",
    "metadata": {
     "hide-output": false
    },
@@ -1106,7 +1106,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ead6e643",
+   "id": "ce14c47b",
    "metadata": {},
    "source": [
     "Again, we obtain the same answer."
@@ -1114,7 +1114,7 @@
   }
  ],
  "metadata": {
-  "date": 1680677526.5567663,
+  "date": 1685490453.3759506,
   "filename": "orth_proj.md",
   "kernelspec": {
    "display_name": "Python",
diff --git a/permanent_income_dles.ipynb b/permanent_income_dles.ipynb
index 5b16f72..3febf66 100644
--- a/permanent_income_dles.ipynb
+++ b/permanent_income_dles.ipynb
@@ -2,7 +2,7 @@
  "cells": [
   {
    "cell_type": "markdown",
-   "id": "744882b6",
+   "id": "84c0a45b",
    "metadata": {},
    "source": [
     "\n",
@@ -13,7 +13,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "811b2a39",
+   "id": "2d66e458",
    "metadata": {},
    "source": [
     "# Permanent Income Model using the DLE Class"
@@ -21,7 +21,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "fe8c0c19",
+   "id": "27f4efda",
    "metadata": {},
    "source": [
     "## Contents\n",
@@ -32,7 +32,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c1d5c353",
+   "id": "5e5ecc6f",
    "metadata": {},
    "source": [
     "This lecture is part of a suite of lectures that use the quantecon DLE class to instantiate models within the\n",
@@ -44,7 +44,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "2be2ae53",
+   "id": "cb2d9a65",
    "metadata": {
     "hide-output": false
    },
@@ -55,7 +55,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7372711f",
+   "id": "6e2bdb3b",
    "metadata": {},
    "source": [
     "This lecture adds a third solution method for the\n",
@@ -76,7 +76,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "83d8246a",
+   "id": "22c80fe2",
    "metadata": {
     "hide-output": false
    },
@@ -94,7 +94,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "73f686dc",
+   "id": "cb596946",
    "metadata": {},
    "source": [
     "## The Permanent Income Model\n",
@@ -194,7 +194,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e700fd08",
+   "id": "8b341913",
    "metadata": {},
    "source": [
     "### Solution with the DLE Class\n",
@@ -253,7 +253,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "dca05154",
+   "id": "7831daea",
    "metadata": {
     "hide-output": false
    },
@@ -293,7 +293,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "33d879b5",
+   "id": "4f7972df",
    "metadata": {},
    "source": [
     "To check the solution of this model with that from the **LQ** problem,\n",
@@ -310,7 +310,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "f01ccebe",
+   "id": "fee648a2",
    "metadata": {
     "hide-output": false
    },
@@ -321,7 +321,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b8b6973e",
+   "id": "fbe625ef",
    "metadata": {},
    "source": [
     "The state vector in the DLE class is:\n",
@@ -351,7 +351,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "3efd36ce",
+   "id": "90bfad01",
    "metadata": {
     "hide-output": false
    },
@@ -377,7 +377,7 @@
   }
  ],
  "metadata": {
-  "date": 1680677526.5780478,
+  "date": 1685490453.3982115,
   "filename": "permanent_income_dles.md",
   "kernelspec": {
    "display_name": "Python",
diff --git a/rob_markov_perf.ipynb b/rob_markov_perf.ipynb
index fc06bbe..8a54297 100644
--- a/rob_markov_perf.ipynb
+++ b/rob_markov_perf.ipynb
@@ -2,7 +2,7 @@
  "cells": [
   {
    "cell_type": "markdown",
-   "id": "a0e4bbe8",
+   "id": "7e570c1b",
    "metadata": {},
    "source": [
     "\n",
@@ -11,7 +11,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "915e79cb",
+   "id": "d28f263d",
    "metadata": {},
    "source": [
     "# Robust Markov Perfect Equilibrium"
@@ -19,7 +19,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1de29429",
+   "id": "94a7b45f",
    "metadata": {},
    "source": [
     "## Contents\n",
@@ -32,7 +32,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c6d40341",
+   "id": "b35aad5a",
    "metadata": {},
    "source": [
     "In addition to what’s in Anaconda, this lecture will need the following libraries:"
@@ -41,7 +41,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "52472702",
+   "id": "8ac438cc",
    "metadata": {
     "hide-output": false
    },
@@ -52,7 +52,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4bac418f",
+   "id": "71f5e103",
    "metadata": {},
    "source": [
     "## Overview\n",
@@ -79,7 +79,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "069f1d10",
+   "id": "d44c62d0",
    "metadata": {
     "hide-output": false
    },
@@ -94,7 +94,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "37f0e32f",
+   "id": "1ff44f7d",
    "metadata": {},
    "source": [
     "### Basic Setup\n",
@@ -128,7 +128,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4a096ec7",
+   "id": "141f661a",
    "metadata": {},
    "source": [
     "## Linear Markov Perfect Equilibria with Robust Agents\n",
@@ -143,7 +143,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9f1dff46",
+   "id": "70f2b690",
    "metadata": {},
    "source": [
     "### Modified Coupled Linear Regulator Problems\n",
@@ -220,7 +220,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "506c1cda",
+   "id": "23b677b2",
    "metadata": {},
    "source": [
     "### Computing Equilibrium\n",
@@ -337,7 +337,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "48ba56f8",
+   "id": "13656cdc",
    "metadata": {},
    "source": [
     "### Key Insight\n",
@@ -357,7 +357,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e74501fb",
+   "id": "440aa13d",
    "metadata": {},
    "source": [
     "### Worst-case Shocks\n",
@@ -377,7 +377,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "bb9b0864",
+   "id": "fb3fe1a0",
    "metadata": {},
    "source": [
     "### Infinite Horizon\n",
@@ -391,7 +391,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "14718a18",
+   "id": "cedc439b",
    "metadata": {},
    "source": [
     "### Implementation\n",
@@ -403,7 +403,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "2517bd64",
+   "id": "fdf8b917",
    "metadata": {},
    "source": [
     "## Application\n",
@@ -414,7 +414,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b6fce28e",
+   "id": "a619e8d4",
    "metadata": {},
    "source": [
     "### A Duopoly Model\n",
@@ -544,7 +544,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a1585488",
+   "id": "b7706b6e",
    "metadata": {},
    "source": [
     "### Parameters and Solution\n",
@@ -563,7 +563,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "162981d1",
+   "id": "05af8d5a",
    "metadata": {
     "hide-output": false
    },
@@ -609,7 +609,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d798e11c",
+   "id": "1d4bdc81",
    "metadata": {},
    "source": [
     "#### Markov Perfect Equilibrium with Robustness\n",
@@ -628,7 +628,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "3d96383a",
+   "id": "2b7e990f",
    "metadata": {
     "hide-output": false
    },
@@ -800,7 +800,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3626a664",
+   "id": "724d40cd",
    "metadata": {},
    "source": [
     "### Some Details\n",
@@ -874,7 +874,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "0a1395c3",
+   "id": "405ea9b4",
    "metadata": {
     "hide-output": false
    },
@@ -907,7 +907,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "069df073",
+   "id": "6c398d31",
    "metadata": {},
    "source": [
     "#### Consistency Check\n",
@@ -919,7 +919,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "d4e0be4b",
+   "id": "f9237480",
    "metadata": {
     "hide-output": false
    },
@@ -943,7 +943,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "8d7ac961",
+   "id": "9097d8da",
    "metadata": {},
    "source": [
     "We can see that the results are consistent across the two functions."
@@ -951,7 +951,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5db9883e",
+   "id": "45ec5b59",
    "metadata": {},
    "source": [
     "#### Comparative Dynamics under Baseline Transition Dynamics\n",
@@ -995,7 +995,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "65e8382a",
+   "id": "74f5676d",
    "metadata": {
     "hide-output": false
    },
@@ -1066,7 +1066,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3ad6e5d6",
+   "id": "10372e8c",
    "metadata": {},
    "source": [
     "The following code prepares graphs that compare market-wide output $ q_{1t} + q_{2t} $ and  the price of the good\n",
@@ -1080,7 +1080,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "c54816ae",
+   "id": "d08131d3",
    "metadata": {
     "hide-output": false
    },
@@ -1104,7 +1104,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4c47b85e",
+   "id": "843a6432",
    "metadata": {},
    "source": [
     "Under the dynamics associated with the baseline model, the price path is higher with the Markov perfect equilibrium robust decision rules\n",
@@ -1120,7 +1120,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "3df0cd54",
+   "id": "3fb1af2f",
    "metadata": {
     "hide-output": false
    },
@@ -1144,7 +1144,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9212532f",
+   "id": "0d05cc82",
    "metadata": {},
    "source": [
     "Evidently, firm 1’s output path is substantially lower when firms are  robust firms while\n",
@@ -1167,7 +1167,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6ef5c010",
+   "id": "e8b02a6e",
    "metadata": {},
    "source": [
     "#### Heterogeneous Beliefs\n",
@@ -1198,7 +1198,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "7e6b6455",
+   "id": "47e57587",
    "metadata": {
     "hide-output": false
    },
@@ -1214,7 +1214,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "1d250e33",
+   "id": "cdf685b2",
    "metadata": {
     "hide-output": false
    },
@@ -1245,7 +1245,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "2fb3fb18",
+   "id": "f48a6f46",
    "metadata": {},
    "source": [
     "We see from the above graph that under robustness concerns, player 1 and\n",
@@ -1265,7 +1265,7 @@
   }
  ],
  "metadata": {
-  "date": 1680677526.624691,
+  "date": 1685490453.4445932,
   "filename": "rob_markov_perf.md",
   "kernelspec": {
    "display_name": "Python",
diff --git a/robustness.ipynb b/robustness.ipynb
index f5b8b9a..911df21 100644
--- a/robustness.ipynb
+++ b/robustness.ipynb
@@ -2,7 +2,7 @@
  "cells": [
   {
    "cell_type": "markdown",
-   "id": "dfe96ea3",
+   "id": "c6b40439",
    "metadata": {},
    "source": [
     "\n",
@@ -11,7 +11,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1a280dba",
+   "id": "6efb370f",
    "metadata": {},
    "source": [
     "# Robustness\n",
@@ -22,7 +22,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "12c795c6",
+   "id": "65701d85",
    "metadata": {},
    "source": [
     "## Contents\n",
@@ -40,7 +40,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "eece39bb",
+   "id": "e23542d0",
    "metadata": {},
    "source": [
     "In addition to what’s in Anaconda, this lecture will need the following libraries:"
@@ -49,7 +49,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "c1aff0f5",
+   "id": "7b06dd2f",
    "metadata": {
     "hide-output": false
    },
@@ -60,7 +60,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a3535b1f",
+   "id": "7457b8d1",
    "metadata": {},
    "source": [
     "## Overview\n",
@@ -109,7 +109,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "3f70703c",
+   "id": "3c55f723",
    "metadata": {
     "hide-output": false
    },
@@ -125,7 +125,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "36ba758b",
+   "id": "6e4fe55a",
    "metadata": {},
    "source": [
     "\n",
@@ -134,7 +134,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7e947caf",
+   "id": "7af8ed2b",
    "metadata": {},
    "source": [
     "### Sets of Models Imply Sets Of Values\n",
@@ -201,7 +201,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5d83d732",
+   "id": "0b7ffb1c",
    "metadata": {},
    "source": [
     "### Inspiring Video\n",
@@ -211,7 +211,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9bcd2a3d",
+   "id": "186ea999",
    "metadata": {},
    "source": [
     "### Other References\n",
@@ -224,7 +224,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "144dfe34",
+   "id": "ce253937",
    "metadata": {},
    "source": [
     "## The Model\n",
@@ -278,7 +278,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7c85630a",
+   "id": "c47c7afa",
    "metadata": {},
    "source": [
     "## Constructing More Robust Policies\n",
@@ -327,7 +327,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d8dd2bac",
+   "id": "abb5ee43",
    "metadata": {},
    "source": [
     "### Analyzing the Bellman Equation\n",
@@ -433,7 +433,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "19458546",
+   "id": "c1f6fba5",
    "metadata": {},
    "source": [
     "## Robustness as Outcome of a Two-Person Zero-Sum Game\n",
@@ -454,7 +454,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "46a83530",
+   "id": "74e51dac",
    "metadata": {},
    "source": [
     "### Agent 2’s Problem\n",
@@ -561,7 +561,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "37a1517a",
+   "id": "8572b5ca",
    "metadata": {},
    "source": [
     "### Using Agent 2’s Problem to Construct Bounds on the Value Sets"
@@ -569,7 +569,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f20003ff",
+   "id": "fbbe42ad",
    "metadata": {},
    "source": [
     "#### The Lower Bound\n",
@@ -628,7 +628,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d8d992e4",
+   "id": "bfdd7d66",
    "metadata": {},
    "source": [
     "#### The Upper Bound\n",
@@ -691,7 +691,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "63967aa7",
+   "id": "3cfb18a8",
    "metadata": {},
    "source": [
     "#### Reshaping the Set of Values\n",
@@ -701,7 +701,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "0a87b1b7",
+   "id": "cdfd546a",
    "metadata": {},
    "source": [
     "### Agent 1’s Problem\n",
@@ -748,7 +748,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ac7c86b0",
+   "id": "10b9504f",
    "metadata": {},
    "source": [
     "### Nash Equilibrium\n",
@@ -782,7 +782,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c02d1c43",
+   "id": "643ed46c",
    "metadata": {},
    "source": [
     "## The Stochastic Case\n",
@@ -831,7 +831,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "eee5f930",
+   "id": "b655f4f1",
    "metadata": {},
    "source": [
     "### Solving the Model\n",
@@ -929,7 +929,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "0c5abb50",
+   "id": "0945cffa",
    "metadata": {},
    "source": [
     "### Computing Other Quantities\n",
@@ -939,7 +939,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "0715ec91",
+   "id": "f46aed07",
    "metadata": {},
    "source": [
     "#### Worst-Case Value of a Policy\n",
@@ -997,7 +997,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "21f2ab87",
+   "id": "25736fe6",
    "metadata": {},
    "source": [
     "## Implementation\n",
@@ -1023,7 +1023,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "fb0cd8bf",
+   "id": "49c4af08",
    "metadata": {},
    "source": [
     "## Application\n",
@@ -1123,7 +1123,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "40729e65",
+   "id": "886a83f9",
    "metadata": {
     "hide-output": false
    },
@@ -1300,7 +1300,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f9241593",
+   "id": "50faafb4",
    "metadata": {},
    "source": [
     "Here’s another such figure, with $ \\theta = 0.002 $ instead of $ 0.02 $\n",
@@ -1316,7 +1316,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9a4d3b65",
+   "id": "8419bb2e",
    "metadata": {},
    "source": [
     "## Appendix\n",
@@ -1390,7 +1390,7 @@
   }
  ],
  "metadata": {
-  "date": 1680677526.6891966,
+  "date": 1685490453.5090854,
   "filename": "robustness.md",
   "kernelspec": {
    "display_name": "Python",
diff --git a/rosen_schooling_model.ipynb b/rosen_schooling_model.ipynb
index 6873675..cf626eb 100644
--- a/rosen_schooling_model.ipynb
+++ b/rosen_schooling_model.ipynb
@@ -2,7 +2,7 @@
  "cells": [
   {
    "cell_type": "markdown",
-   "id": "0c27d932",
+   "id": "d1b3ee98",
    "metadata": {},
    "source": [
     "\n",
@@ -13,7 +13,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ba5910f0",
+   "id": "cac48258",
    "metadata": {},
    "source": [
     "# Rosen Schooling Model"
@@ -21,7 +21,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "93f3ea33",
+   "id": "28f49292",
    "metadata": {},
    "source": [
     "## Contents\n",
@@ -33,7 +33,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "2c9d6906",
+   "id": "2ba49a4f",
    "metadata": {},
    "source": [
     "This lecture is yet another part of a suite of lectures that use the quantecon DLE class to instantiate models within the\n",
@@ -45,7 +45,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "798db44a",
+   "id": "34799b44",
    "metadata": {
     "hide-output": false
    },
@@ -56,7 +56,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "22896251",
+   "id": "c6b90259",
    "metadata": {},
    "source": [
     "We’ll also need the following imports:"
@@ -65,7 +65,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "1d89d4cb",
+   "id": "d48130d7",
    "metadata": {
     "hide-output": false
    },
@@ -82,7 +82,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5b28801e",
+   "id": "f1291d21",
    "metadata": {},
    "source": [
     "## A One-Occupation Model\n",
@@ -130,7 +130,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1bfcbec1",
+   "id": "6c84728e",
    "metadata": {},
    "source": [
     "## Mapping into HS2013 Framework\n",
@@ -145,7 +145,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c4b5f7bb",
+   "id": "feddb0cd",
    "metadata": {},
    "source": [
     "### Preferences\n",
@@ -177,7 +177,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "0504a88f",
+   "id": "5c4a4be3",
    "metadata": {},
    "source": [
     "### Technology\n",
@@ -198,7 +198,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ad2e55e6",
+   "id": "376f6774",
    "metadata": {},
    "source": [
     "### Information\n",
@@ -231,7 +231,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "9e73a25b",
+   "id": "0f75bc8c",
    "metadata": {
     "hide-output": false
    },
@@ -244,7 +244,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c35994ba",
+   "id": "fcf86963",
    "metadata": {},
    "source": [
     "### Effects of Changes in Education Technology and Demand\n",
@@ -263,7 +263,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "f7b9bc53",
+   "id": "e05785de",
    "metadata": {
     "hide-output": false
    },
@@ -318,7 +318,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b249ea16",
+   "id": "e4d9c5a2",
    "metadata": {},
    "source": [
     "We create three other instances by:\n",
@@ -331,7 +331,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "9128efb3",
+   "id": "029bdc6b",
    "metadata": {
     "hide-output": false
    },
@@ -378,7 +378,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1a2b64f6",
+   "id": "cba4dd3f",
    "metadata": {},
    "source": [
     "The first figure plots the impulse response of $ n_t $ (on the left)\n",
@@ -406,7 +406,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "e5a932a4",
+   "id": "abee6fa9",
    "metadata": {
     "hide-output": false
    },
@@ -427,7 +427,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ec546ed7",
+   "id": "1d949958",
    "metadata": {},
    "source": [
     "The next figure plots the impulse response of $ n_t $ (on the left)\n",
@@ -438,7 +438,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "6d877d5e",
+   "id": "0da95ab2",
    "metadata": {
     "hide-output": false
    },
@@ -461,7 +461,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "25cd428e",
+   "id": "84777b4e",
    "metadata": {},
    "source": [
     "Both panels in the above figure show that raising $ k $ lowers the effect of\n",
@@ -475,7 +475,7 @@
   }
  ],
  "metadata": {
-  "date": 1680677526.7109072,
+  "date": 1685490453.5316172,
   "filename": "rosen_schooling_model.md",
   "kernelspec": {
    "display_name": "Python",
diff --git a/smoothing.ipynb b/smoothing.ipynb
index 332d14a..da43260 100644
--- a/smoothing.ipynb
+++ b/smoothing.ipynb
@@ -2,7 +2,7 @@
  "cells": [
   {
    "cell_type": "markdown",
-   "id": "7e35f20b",
+   "id": "6d15abd1",
    "metadata": {},
    "source": [
     "\n",
@@ -11,7 +11,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4bcb20e1",
+   "id": "a886c291",
    "metadata": {},
    "source": [
     "# Consumption Smoothing with Complete and Incomplete Markets\n",
@@ -22,7 +22,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "65ef00d1",
+   "id": "96dd1081",
    "metadata": {},
    "source": [
     "## Contents\n",
@@ -37,7 +37,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f190f18a",
+   "id": "d4edaee8",
    "metadata": {},
    "source": [
     "In addition to what’s in Anaconda, this lecture uses the  library:"
@@ -46,7 +46,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "c4d72523",
+   "id": "4247e5ae",
    "metadata": {
     "hide-output": false
    },
@@ -57,7 +57,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5ec5a68c",
+   "id": "a0db313d",
    "metadata": {},
    "source": [
     "## Overview\n",
@@ -109,7 +109,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "83291e59",
+   "id": "5d53c0b4",
    "metadata": {
     "hide-output": false
    },
@@ -124,7 +124,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "99c6b260",
+   "id": "4040b103",
    "metadata": {},
    "source": [
     "### Relationship to Other Lectures\n",
@@ -136,7 +136,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "fc405e0d",
+   "id": "ea14df1e",
    "metadata": {},
    "source": [
     "## Background\n",
@@ -171,7 +171,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "0541ef5f",
+   "id": "5065b250",
    "metadata": {},
    "source": [
     "## Linear State Space Version of Complete Markets Model\n",
@@ -332,7 +332,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "987878eb",
+   "id": "e1aba217",
    "metadata": {
     "hide-output": false
    },
@@ -415,7 +415,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d5bac5b2",
+   "id": "0d0bf45f",
    "metadata": {},
    "source": [
     "### Interpretation of Graph\n",
@@ -433,7 +433,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b1295b06",
+   "id": "178b89fc",
    "metadata": {},
    "source": [
     "### Incomplete Markets Version\n",
@@ -446,7 +446,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "48bf78ba",
+   "id": "cdc7f1d2",
    "metadata": {},
    "source": [
     "### Finite State Markov Income Process\n",
@@ -497,7 +497,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "166297b0",
+   "id": "7137e06b",
    "metadata": {},
    "source": [
     "### Market Structure\n",
@@ -516,7 +516,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "185fa335",
+   "id": "170e67b3",
    "metadata": {},
    "source": [
     "## Model 1 (Complete Markets)\n",
@@ -695,7 +695,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b50a9efe",
+   "id": "7d37c1da",
    "metadata": {},
    "source": [
     "### Key Outcomes\n",
@@ -723,7 +723,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "86aafb5d",
+   "id": "be3b22f3",
    "metadata": {},
    "source": [
     "### Code\n",
@@ -737,7 +737,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "6bc0b6b3",
+   "id": "d2b32aa1",
    "metadata": {
     "hide-output": false
    },
@@ -867,7 +867,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f0d8da7e",
+   "id": "332666a3",
    "metadata": {},
    "source": [
     "Let’s test by checking that $ \\bar c $ and $ b_2 $ satisfy the budget constraint"
@@ -876,7 +876,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "c9f5174a",
+   "id": "c742a61b",
    "metadata": {
     "hide-output": false
    },
@@ -889,7 +889,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "0528d2eb",
+   "id": "ec4a068d",
    "metadata": {},
    "source": [
     "Below, we’ll take the outcomes produced by this code – in particular the implied\n",
@@ -899,7 +899,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6d4f3854",
+   "id": "36926c68",
    "metadata": {},
    "source": [
     "## Model 2 (One-Period Risk-Free Debt Only)\n",
@@ -1028,7 +1028,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7ad3fbde",
+   "id": "8706e8eb",
    "metadata": {},
    "source": [
     "### Summary of Outcomes\n",
@@ -1050,7 +1050,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f3108440",
+   "id": "35093443",
    "metadata": {},
    "source": [
     "### The Incomplete Markets Model\n",
@@ -1067,7 +1067,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "b1b86c65",
+   "id": "3a8a0e7b",
    "metadata": {
     "hide-output": false
    },
@@ -1105,7 +1105,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f3d8da4d",
+   "id": "5268614a",
    "metadata": {},
    "source": [
     "In the graph on the left, for the same sample path of nonfinancial\n",
@@ -1120,7 +1120,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "08ce95b2",
+   "id": "f459a7c0",
    "metadata": {},
    "source": [
     "### A sequel\n",
@@ -1131,7 +1131,7 @@
   }
  ],
  "metadata": {
-  "date": 1680677526.9914355,
+  "date": 1685490453.7613523,
   "filename": "smoothing.md",
   "kernelspec": {
    "display_name": "Python",
diff --git a/smoothing_tax.ipynb b/smoothing_tax.ipynb
index 1084a6f..9c8a2ea 100644
--- a/smoothing_tax.ipynb
+++ b/smoothing_tax.ipynb
@@ -2,7 +2,7 @@
  "cells": [
   {
    "cell_type": "markdown",
-   "id": "1a379fb0",
+   "id": "1e030e93",
    "metadata": {},
    "source": [
     "\n",
@@ -11,7 +11,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "08886169",
+   "id": "a79076d3",
    "metadata": {},
    "source": [
     "# Tax Smoothing with Complete and Incomplete Markets\n",
@@ -22,7 +22,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "de5e757d",
+   "id": "17d5d377",
    "metadata": {},
    "source": [
     "## Contents\n",
@@ -36,7 +36,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5a1ba522",
+   "id": "b3e45ff9",
    "metadata": {},
    "source": [
     "In addition to what’s in Anaconda, this lecture uses the  library:"
@@ -45,7 +45,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "adecc6a9",
+   "id": "070ee188",
    "metadata": {
     "hide-output": false
    },
@@ -56,7 +56,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "673805de",
+   "id": "eb0f11b6",
    "metadata": {},
    "source": [
     "## Overview\n",
@@ -94,7 +94,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "08855cf3",
+   "id": "b716fce5",
    "metadata": {},
    "source": [
     "### Isomorphism between Consumption and Tax Smoothing\n",
@@ -120,7 +120,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "151cb7cb",
+   "id": "658882d2",
    "metadata": {},
    "source": [
     "#### Link to History\n",
@@ -134,7 +134,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "fd415cc7",
+   "id": "d6a2386a",
    "metadata": {
     "hide-output": false
    },
@@ -149,7 +149,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1d36a985",
+   "id": "db6c105f",
    "metadata": {},
    "source": [
     "To exploit the isomorphism between consumption-smoothing and tax-smoothing models, we  simply use code from [Consumption Smoothing with Complete and Incomplete Markets](https://python-advanced.quantecon.org/smoothing.html)"
@@ -157,7 +157,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f134b54e",
+   "id": "96eddc84",
    "metadata": {},
    "source": [
     "### Code\n",
@@ -171,7 +171,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "a7964ff5",
+   "id": "10d2a964",
    "metadata": {
     "hide-output": false
    },
@@ -301,7 +301,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "11593f73",
+   "id": "ef038db1",
    "metadata": {},
    "source": [
     "### Revisiting the consumption-smoothing model\n",
@@ -318,7 +318,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "41bd1858",
+   "id": "606009e9",
    "metadata": {
     "hide-output": false
    },
@@ -354,7 +354,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "975f6a0d",
+   "id": "50aef490",
    "metadata": {},
    "source": [
     "In the graph on the left, for the same sample path of nonfinancial\n",
@@ -369,7 +369,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "0e727fbc",
+   "id": "e660dafe",
    "metadata": {},
    "source": [
     "#### Relabeling variables to create tax-smoothing models\n",
@@ -380,7 +380,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "7e7b7d92",
+   "id": "6cd4ed41",
    "metadata": {
     "hide-output": false
    },
@@ -409,7 +409,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5f5b1df0",
+   "id": "e22045bc",
    "metadata": {},
    "source": [
     "## Tax Smoothing with Complete Markets\n",
@@ -460,7 +460,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "94f4a67e",
+   "id": "02653da3",
    "metadata": {},
    "source": [
     "## Returns on State-Contingent Debt\n",
@@ -492,7 +492,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "a1a9fb0e",
+   "id": "2cbd9af4",
    "metadata": {
     "hide-output": false
    },
@@ -532,7 +532,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9b08b300",
+   "id": "a42d8cb5",
    "metadata": {},
    "source": [
     "### An Example of Tax Smoothing\n",
@@ -561,7 +561,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "724b5636",
+   "id": "21d707f6",
    "metadata": {
     "hide-output": false
    },
@@ -640,7 +640,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b24a3814",
+   "id": "70dfce65",
    "metadata": {},
    "source": [
     "### Explanation\n",
@@ -666,7 +666,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "df74483a",
+   "id": "ef6c0a30",
    "metadata": {},
    "source": [
     "### Exercise 7.1\n",
@@ -687,7 +687,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "74ac736c",
+   "id": "3190d4e1",
    "metadata": {},
    "source": [
     "## More Finite Markov Chain Tax-Smoothing Examples\n",
@@ -705,7 +705,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "80230211",
+   "id": "37d6cbb5",
    "metadata": {
     "hide-output": false
    },
@@ -825,7 +825,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "38f9f5ed",
+   "id": "e58f6454",
    "metadata": {},
    "source": [
     "### Parameters"
@@ -834,7 +834,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "ad0af56c",
+   "id": "65329cfa",
    "metadata": {
     "hide-output": false
    },
@@ -853,7 +853,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c0ef471a",
+   "id": "04d8cd0d",
    "metadata": {},
    "source": [
     "### Example 1\n",
@@ -885,7 +885,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "07419783",
+   "id": "6d74568e",
    "metadata": {
     "hide-output": false
    },
@@ -902,7 +902,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "26ace3f1",
+   "id": "10cca6f3",
    "metadata": {
     "hide-output": false
    },
@@ -915,7 +915,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "ac1dcf2e",
+   "id": "c31829f7",
    "metadata": {
     "hide-output": false
    },
@@ -929,7 +929,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "8d3957f9",
+   "id": "c0977e1c",
    "metadata": {},
    "source": [
     "### Example 2\n",
@@ -955,7 +955,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "f90a5da1",
+   "id": "af83879d",
    "metadata": {
     "hide-output": false
    },
@@ -972,7 +972,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "f6ef36d6",
+   "id": "25952b4f",
    "metadata": {
     "hide-output": false
    },
@@ -984,7 +984,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f4c16df4",
+   "id": "5ad50753",
    "metadata": {},
    "source": [
     "### Example 3\n",
@@ -1013,7 +1013,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "c26eaee4",
+   "id": "9d1ac176",
    "metadata": {
     "hide-output": false
    },
@@ -1031,7 +1031,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "34d5e9d6",
+   "id": "57958de2",
    "metadata": {
     "hide-output": false
    },
@@ -1043,7 +1043,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "520bd58c",
+   "id": "6e3632fd",
    "metadata": {},
    "source": [
     "### Example 4\n",
@@ -1070,7 +1070,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "d57703e1",
+   "id": "7d586c48",
    "metadata": {
     "hide-output": false
    },
@@ -1089,7 +1089,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "358f0e22",
+   "id": "c4d415fe",
    "metadata": {
     "hide-output": false
    },
@@ -1101,7 +1101,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "781bc96e",
+   "id": "1094a4f2",
    "metadata": {},
    "source": [
     "### Example 5\n",
@@ -1133,7 +1133,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "ff6570d0",
+   "id": "92c6e8be",
    "metadata": {
     "hide-output": false
    },
@@ -1154,7 +1154,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "14cc665d",
+   "id": "b1833f20",
    "metadata": {
     "hide-output": false
    },
@@ -1166,7 +1166,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5be41310",
+   "id": "5c6227dd",
    "metadata": {},
    "source": [
     "### Continuous-State Gaussian Model\n",
@@ -1216,7 +1216,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "cf02d670",
+   "id": "42bda0bf",
    "metadata": {},
    "source": [
     "#### Related Lectures\n",
@@ -1242,7 +1242,7 @@
   }
  ],
  "metadata": {
-  "date": 1680677527.0435083,
+  "date": 1685490453.8118196,
   "filename": "smoothing_tax.md",
   "kernelspec": {
    "display_name": "Python",
diff --git a/stationary_densities.ipynb b/stationary_densities.ipynb
index 74c531a..f843c72 100644
--- a/stationary_densities.ipynb
+++ b/stationary_densities.ipynb
@@ -2,7 +2,7 @@
  "cells": [
   {
    "cell_type": "markdown",
-   "id": "01fdcb8f",
+   "id": "ad48e6e6",
    "metadata": {},
    "source": [
     "\n",
@@ -11,7 +11,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c812b518",
+   "id": "0425ca9d",
    "metadata": {},
    "source": [
     "# Continuous State Markov Chains\n",
@@ -22,7 +22,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "fdf72bd5",
+   "id": "d5e22deb",
    "metadata": {},
    "source": [
     "## Contents\n",
@@ -38,7 +38,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "56208c3a",
+   "id": "59e0096f",
    "metadata": {},
    "source": [
     "In addition to what’s in Anaconda, this lecture will need the following libraries:"
@@ -47,7 +47,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "93619cea",
+   "id": "27dd0f99",
    "metadata": {
     "hide-output": false
    },
@@ -58,7 +58,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "abbb59d3",
+   "id": "928f1fcd",
    "metadata": {},
    "source": [
     "## Overview\n",
@@ -106,7 +106,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "0cc4668b",
+   "id": "4528a54c",
    "metadata": {
     "hide-output": false
    },
@@ -122,7 +122,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a0a0d05d",
+   "id": "1c85a8e6",
    "metadata": {},
    "source": [
     "\n",
@@ -131,7 +131,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ee387d0e",
+   "id": "104ab764",
    "metadata": {},
    "source": [
     "## The Density Case\n",
@@ -151,7 +151,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a8a0ae44",
+   "id": "c2104a6e",
    "metadata": {},
    "source": [
     "### Definitions and Basic Properties\n",
@@ -229,7 +229,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b3220599",
+   "id": "e28466d0",
    "metadata": {},
    "source": [
     "### Connection to Stochastic Difference Equations\n",
@@ -351,7 +351,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "33f84b5c",
+   "id": "bb4076f0",
    "metadata": {},
    "source": [
     "### Distribution Dynamics\n",
@@ -438,7 +438,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d4306f52",
+   "id": "92166bd2",
    "metadata": {},
    "source": [
     "### Computation\n",
@@ -519,7 +519,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "45f9ac19",
+   "id": "c78e4e7d",
    "metadata": {},
    "source": [
     "### Implementation\n",
@@ -544,7 +544,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c88e6d8a",
+   "id": "5d3d154a",
    "metadata": {},
    "source": [
     "### Example\n",
@@ -558,7 +558,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "8d6cf0c3",
+   "id": "4211272f",
    "metadata": {
     "hide-output": false
    },
@@ -608,7 +608,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "8a594fa7",
+   "id": "96357c94",
    "metadata": {},
    "source": [
     "The figure shows part of the density sequence $ \\{\\psi_t\\} $, with each\n",
@@ -623,7 +623,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "66365f6b",
+   "id": "4736a546",
    "metadata": {},
    "source": [
     "## Beyond Densities\n",
@@ -645,7 +645,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e5e1a3ba",
+   "id": "9a99cb21",
    "metadata": {},
    "source": [
     "### Example and Definitions\n",
@@ -702,7 +702,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d22c14b8",
+   "id": "739ae5aa",
    "metadata": {},
    "source": [
     "### Computation\n",
@@ -717,7 +717,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "61c01d7c",
+   "id": "92ac9d0d",
    "metadata": {},
    "source": [
     "## Stability\n",
@@ -733,7 +733,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "73a18487",
+   "id": "3f1631d3",
    "metadata": {},
    "source": [
     "### Theoretical Results\n",
@@ -816,7 +816,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "47f72059",
+   "id": "3b0f598e",
    "metadata": {},
    "source": [
     "### An Example of Stability\n",
@@ -843,7 +843,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "885c556d",
+   "id": "a0cd3356",
    "metadata": {},
    "source": [
     "### Computing Stationary Densities\n",
@@ -895,7 +895,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5c3e8bca",
+   "id": "1b81e19c",
    "metadata": {},
    "source": [
     "## Exercises\n",
@@ -906,7 +906,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c33c9f76",
+   "id": "d5db18b1",
    "metadata": {},
    "source": [
     "## Exercise 2.1\n",
@@ -961,7 +961,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b2762eb7",
+   "id": "5ef27020",
    "metadata": {},
    "source": [
     "## Solution to[ Exercise 2.1](https://python-advanced.quantecon.org/#sd_ex1)\n",
@@ -981,7 +981,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "51a6ad60",
+   "id": "017879e2",
    "metadata": {
     "hide-output": false
    },
@@ -1020,7 +1020,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "0fd25c7d",
+   "id": "5cfec88f",
    "metadata": {},
    "source": [
     "\n",
@@ -1029,7 +1029,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1b7dc89b",
+   "id": "8e5e8b7a",
    "metadata": {},
    "source": [
     "## Exercise 2.2\n",
@@ -1048,7 +1048,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "ff225664",
+   "id": "f3111af5",
    "metadata": {
     "hide-output": false
    },
@@ -1059,7 +1059,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "24769230",
+   "id": "605f3f8e",
    "metadata": {},
    "source": [
     "## Solution to[ Exercise 2.2](https://python-advanced.quantecon.org/#sd_ex2)\n",
@@ -1070,7 +1070,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "fe86c2be",
+   "id": "2a40cc68",
    "metadata": {
     "hide-output": false
    },
@@ -1122,7 +1122,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d120af33",
+   "id": "83dc49fe",
    "metadata": {},
    "source": [
     "\n",
@@ -1131,7 +1131,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5c822bd4",
+   "id": "253eef93",
    "metadata": {},
    "source": [
     "## Exercise 2.3\n",
@@ -1155,7 +1155,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "1956b4d8",
+   "id": "76b00f11",
    "metadata": {
     "hide-output": false
    },
@@ -1177,7 +1177,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a1668171",
+   "id": "dd090cb7",
    "metadata": {},
    "source": [
     "Each data set is represented by a box, where the top and bottom of the box are the third and first quartiles of the data, and the red line in the center is the median.\n",
@@ -1203,7 +1203,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "7eaff244",
+   "id": "9c059040",
    "metadata": {
     "hide-output": false
    },
@@ -1214,7 +1214,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "cd4dcd8d",
+   "id": "343504e8",
    "metadata": {},
    "source": [
     "For each $ X_0 $ in this set,\n",
@@ -1228,7 +1228,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9919fafc",
+   "id": "a7dcb2cd",
    "metadata": {},
    "source": [
     "## Solution to[ Exercise 2.3](https://python-advanced.quantecon.org/#sd_ex3)\n",
@@ -1242,7 +1242,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "133a99a6",
+   "id": "41ffbc50",
    "metadata": {
     "hide-output": false
    },
@@ -1276,7 +1276,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "0b25f5f3",
+   "id": "6f9e238f",
    "metadata": {},
    "source": [
     "## Appendix\n",
@@ -1296,7 +1296,7 @@
   }
  ],
  "metadata": {
-  "date": 1680677527.1191304,
+  "date": 1685490453.8861685,
   "filename": "stationary_densities.md",
   "kernelspec": {
    "display_name": "Python",
diff --git a/status.ipynb b/status.ipynb
index adf703f..2efa44e 100644
--- a/status.ipynb
+++ b/status.ipynb
@@ -2,7 +2,7 @@
  "cells": [
   {
    "cell_type": "markdown",
-   "id": "94297ca2",
+   "id": "84469410",
    "metadata": {},
    "source": [
     "# Execution Statistics\n",
@@ -11,64 +11,64 @@
     "\n",
     "[](https://python-advanced.quantecon.org/BCG_complete_mkts.html)[](https://python-advanced.quantecon.org/BCG_incomplete_mkts.html)[](https://python-advanced.quantecon.org/additive_functionals.html)[](https://python-advanced.quantecon.org/amss.html)[](https://python-advanced.quantecon.org/amss2.html)[](https://python-advanced.quantecon.org/amss3.html)[](https://python-advanced.quantecon.org/arellano.html)[](https://python-advanced.quantecon.org/arma.html)[](https://python-advanced.quantecon.org/asset_pricing_lph.html)[](https://python-advanced.quantecon.org/black_litterman.html)[](https://python-advanced.quantecon.org/calvo.html)[](https://python-advanced.quantecon.org/cattle_cycles.html)[](https://python-advanced.quantecon.org/chang_credible.html)[](https://python-advanced.quantecon.org/chang_ramsey.html)[](https://python-advanced.quantecon.org/classical_filtering.html)[](https://python-advanced.quantecon.org/coase.html)[](https://python-advanced.quantecon.org/cons_news.html)[](https://python-advanced.quantecon.org/discrete_dp.html)[](https://python-advanced.quantecon.org/dyn_stack.html)[](https://python-advanced.quantecon.org/entropy.html)[](https://python-advanced.quantecon.org/estspec.html)[](https://python-advanced.quantecon.org/five_preferences.html)[](https://python-advanced.quantecon.org/growth_in_dles.html)[](https://python-advanced.quantecon.org/hs_invertibility_example.html)[](https://python-advanced.quantecon.org/hs_recursive_models.html)[](https://python-advanced.quantecon.org/intro.html)[](https://python-advanced.quantecon.org/irfs_in_hall_model.html)[](https://python-advanced.quantecon.org/knowing_forecasts_of_others.html)[](https://python-advanced.quantecon.org/lqramsey.html)[](https://python-advanced.quantecon.org/lu_tricks.html)[](https://python-advanced.quantecon.org/lucas_asset_pricing_dles.html)[](https://python-advanced.quantecon.org/lucas_model.html)[](https://python-advanced.quantecon.org/markov_jump_lq.html)[](https://python-advanced.quantecon.org/matsuyama.html)[](https://python-advanced.quantecon.org/muth_kalman.html)[](https://python-advanced.quantecon.org/opt_tax_recur.html)[](https://python-advanced.quantecon.org/orth_proj.html)[](https://python-advanced.quantecon.org/permanent_income_dles.html)[](https://python-advanced.quantecon.org/rob_markov_perf.html)[](https://python-advanced.quantecon.org/robustness.html)[](https://python-advanced.quantecon.org/rosen_schooling_model.html)[](https://python-advanced.quantecon.org/smoothing.html)[](https://python-advanced.quantecon.org/smoothing_tax.html)[](https://python-advanced.quantecon.org/stationary_densities.html)[](https://python-advanced.quantecon.org/.html)[](https://python-advanced.quantecon.org/tax_smoothing_1.html)[](https://python-advanced.quantecon.org/tax_smoothing_2.html)[](https://python-advanced.quantecon.org/tax_smoothing_3.html)[](https://python-advanced.quantecon.org/troubleshooting.html)[](https://python-advanced.quantecon.org/un_insure.html)[](https://python-advanced.quantecon.org/zreferences.html)|Document|Modified|Method|Run Time (s)|Status|\n",
     "|:------------------:|:------------------:|:------------------:|:------------------:|:------------------:|\n",
-    "|BCG_complete_mkts|2023-04-05 03:30|cache|64.4|✅|\n",
-    "|BCG_incomplete_mkts|2023-04-05 03:32|cache|104.34|✅|\n",
-    "|additive_functionals|2023-04-05 03:32|cache|21.22|✅|\n",
-    "|amss|2023-04-05 03:41|cache|507.39|✅|\n",
-    "|amss2|2023-04-05 03:42|cache|75.15|✅|\n",
-    "|amss3|2023-04-05 03:47|cache|331.37|✅|\n",
-    "|arellano|2023-04-05 03:57|cache|561.9|✅|\n",
-    "|arma|2023-04-05 03:57|cache|12.05|✅|\n",
-    "|asset_pricing_lph|2023-04-05 03:57|cache|3.39|✅|\n",
-    "|black_litterman|2023-04-05 03:58|cache|74.42|✅|\n",
-    "|calvo|2023-04-05 03:58|cache|7.93|✅|\n",
-    "|cattle_cycles|2023-04-05 03:58|cache|7.1|✅|\n",
-    "|chang_credible|2023-04-05 04:02|cache|217.95|✅|\n",
-    "|chang_ramsey|2023-04-05 04:09|cache|429.46|✅|\n",
-    "|classical_filtering|2023-04-05 04:09|cache|1.65|✅|\n",
-    "|coase|2023-04-05 04:09|cache|9.68|✅|\n",
-    "|cons_news|2023-04-05 04:10|cache|7.58|✅|\n",
-    "|discrete_dp|2023-04-05 04:10|cache|52.02|✅|\n",
-    "|dyn_stack|2023-04-05 04:11|cache|9.49|✅|\n",
-    "|entropy|2023-04-05 04:11|cache|1.05|✅|\n",
-    "|estspec|2023-04-05 04:11|cache|8.47|✅|\n",
-    "|five_preferences|2023-04-05 04:12|cache|54.13|✅|\n",
-    "|growth_in_dles|2023-04-05 04:12|cache|7.15|✅|\n",
-    "|hs_invertibility_example|2023-04-05 04:12|cache|7.35|✅|\n",
-    "|hs_recursive_models|2023-04-05 04:12|cache|4.02|✅|\n",
-    "|intro|2023-04-05 04:12|cache|4.02|✅|\n",
-    "|irfs_in_hall_model|2023-04-05 04:12|cache|7.23|✅|\n",
-    "|knowing_forecasts_of_others|2023-04-05 04:13|cache|29.35|✅|\n",
-    "|lqramsey|2023-04-05 04:13|cache|9.73|✅|\n",
-    "|lu_tricks|2023-04-05 04:13|cache|2.96|✅|\n",
-    "|lucas_asset_pricing_dles|2023-04-05 04:13|cache|7.25|✅|\n",
-    "|lucas_model|2023-04-05 04:13|cache|10.78|✅|\n",
-    "|markov_jump_lq|2023-04-05 04:15|cache|93.59|✅|\n",
-    "|matsuyama|2023-04-05 04:15|cache|8.85|✅|\n",
-    "|muth_kalman|2023-04-05 04:15|cache|7.76|✅|\n",
-    "|opt_tax_recur|2023-04-05 04:16|cache|60.02|✅|\n",
-    "|orth_proj|2023-04-05 04:16|cache|1.48|✅|\n",
-    "|permanent_income_dles|2023-04-05 04:16|cache|7.21|✅|\n",
-    "|rob_markov_perf|2023-04-05 04:16|cache|7.31|✅|\n",
-    "|robustness|2023-04-05 04:16|cache|9.2|✅|\n",
-    "|rosen_schooling_model|2023-04-05 04:17|cache|7.19|✅|\n",
-    "|smoothing|2023-04-05 04:17|cache|7.65|✅|\n",
-    "|smoothing_tax|2023-04-05 04:17|cache|11.67|✅|\n",
-    "|stationary_densities|2023-04-05 04:17|cache|13.96|✅|\n",
-    "|status|2023-04-05 04:12|cache|4.02|✅|\n",
-    "|tax_smoothing_1|2023-04-05 04:17|cache|15.07|✅|\n",
-    "|tax_smoothing_2|2023-04-05 04:18|cache|8.26|✅|\n",
-    "|tax_smoothing_3|2023-04-05 04:18|cache|7.8|✅|\n",
-    "|troubleshooting|2023-04-05 04:12|cache|4.02|✅|\n",
-    "|un_insure|2023-04-05 04:18|cache|15.79|✅|\n",
-    "|zreferences|2023-04-05 04:12|cache|4.02|✅|\n",
+    "|BCG_complete_mkts|2023-05-28 04:24|cache|68.48|✅|\n",
+    "|BCG_incomplete_mkts|2023-05-28 04:26|cache|102.58|✅|\n",
+    "|additive_functionals|2023-05-30 23:47|cache|6.83|❌|\n",
+    "|amss|2023-05-28 04:35|cache|514.04|✅|\n",
+    "|amss2|2023-05-28 04:36|cache|74.81|✅|\n",
+    "|amss3|2023-05-28 04:41|cache|334.9|✅|\n",
+    "|arellano|2023-05-28 04:52|cache|614.06|✅|\n",
+    "|arma|2023-05-28 04:52|cache|11.76|✅|\n",
+    "|asset_pricing_lph|2023-05-28 04:52|cache|3.07|✅|\n",
+    "|black_litterman|2023-05-28 04:53|cache|73.48|✅|\n",
+    "|calvo|2023-05-28 04:53|cache|7.91|✅|\n",
+    "|cattle_cycles|2023-05-28 04:53|cache|7.1|✅|\n",
+    "|chang_credible|2023-05-28 04:57|cache|213.91|✅|\n",
+    "|chang_ramsey|2023-05-28 05:04|cache|424.31|✅|\n",
+    "|classical_filtering|2023-05-28 05:04|cache|1.64|✅|\n",
+    "|coase|2023-05-28 05:04|cache|8.97|✅|\n",
+    "|cons_news|2023-05-28 05:04|cache|7.32|✅|\n",
+    "|discrete_dp|2023-05-28 05:05|cache|39.35|✅|\n",
+    "|dyn_stack|2023-05-28 05:05|cache|9.34|✅|\n",
+    "|entropy|2023-05-28 05:05|cache|1.21|✅|\n",
+    "|estspec|2023-05-28 05:05|cache|8.02|✅|\n",
+    "|five_preferences|2023-05-28 05:06|cache|52.45|✅|\n",
+    "|growth_in_dles|2023-05-28 05:06|cache|6.89|✅|\n",
+    "|hs_invertibility_example|2023-05-28 05:06|cache|10.02|✅|\n",
+    "|hs_recursive_models|2023-05-28 05:06|cache|1.2|✅|\n",
+    "|intro|2023-05-28 05:06|cache|1.2|✅|\n",
+    "|irfs_in_hall_model|2023-05-28 05:07|cache|6.92|✅|\n",
+    "|knowing_forecasts_of_others|2023-05-28 05:07|cache|32.24|✅|\n",
+    "|lqramsey|2023-05-28 05:07|cache|9.29|✅|\n",
+    "|lu_tricks|2023-05-28 05:07|cache|2.6|✅|\n",
+    "|lucas_asset_pricing_dles|2023-05-28 05:07|cache|6.97|✅|\n",
+    "|lucas_model|2023-05-28 05:08|cache|10.35|✅|\n",
+    "|markov_jump_lq|2023-05-28 05:09|cache|93.64|✅|\n",
+    "|matsuyama|2023-05-28 05:09|cache|8.78|✅|\n",
+    "|muth_kalman|2023-05-28 05:09|cache|7.69|✅|\n",
+    "|opt_tax_recur|2023-05-28 05:10|cache|59.8|✅|\n",
+    "|orth_proj|2023-05-28 05:11|cache|1.39|✅|\n",
+    "|permanent_income_dles|2023-05-28 05:11|cache|7.01|✅|\n",
+    "|rob_markov_perf|2023-05-28 05:11|cache|7.14|✅|\n",
+    "|robustness|2023-05-30 23:47|cache|6.58|❌|\n",
+    "|rosen_schooling_model|2023-05-28 05:11|cache|6.92|✅|\n",
+    "|smoothing|2023-05-28 05:11|cache|7.38|✅|\n",
+    "|smoothing_tax|2023-05-28 05:11|cache|11.1|✅|\n",
+    "|stationary_densities|2023-05-28 05:12|cache|13.43|✅|\n",
+    "|status|2023-05-28 05:06|cache|1.2|✅|\n",
+    "|tax_smoothing_1|2023-05-28 05:12|cache|14.61|✅|\n",
+    "|tax_smoothing_2|2023-05-28 05:12|cache|7.93|✅|\n",
+    "|tax_smoothing_3|2023-05-28 05:12|cache|7.75|✅|\n",
+    "|troubleshooting|2023-05-28 05:06|cache|1.2|✅|\n",
+    "|un_insure|2023-05-28 05:12|cache|15.51|✅|\n",
+    "|zreferences|2023-05-28 05:06|cache|1.2|✅|\n",
     "These lectures are built on `linux` instances through `github actions` so are\n",
     "executed using the following [hardware specifications](https://docs.github.com/en/actions/reference/specifications-for-github-hosted-runners#supported-runners-and-hardware-resources)"
    ]
   }
  ],
  "metadata": {
-  "date": 1680677527.1518707,
+  "date": 1685490453.920168,
   "filename": "status.md",
   "kernelspec": {
    "display_name": "Python",
diff --git a/tax_smoothing_1.ipynb b/tax_smoothing_1.ipynb
index f19bd8b..3d67d87 100644
--- a/tax_smoothing_1.ipynb
+++ b/tax_smoothing_1.ipynb
@@ -2,7 +2,7 @@
  "cells": [
   {
    "cell_type": "markdown",
-   "id": "7dca66c0",
+   "id": "78145c27",
    "metadata": {},
    "source": [
     "\n",
@@ -13,7 +13,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3bc6f6ef",
+   "id": "321269b9",
    "metadata": {},
    "source": [
     "# How to Pay for a War: Part 1"
@@ -21,7 +21,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a789ede4",
+   "id": "3e342773",
    "metadata": {},
    "source": [
     "## Contents\n",
@@ -36,7 +36,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "094dff69",
+   "id": "1b38c744",
    "metadata": {},
    "source": [
     "In addition to what’s in Anaconda, this lecture will deploy quantecon:"
@@ -45,7 +45,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "b264f59d",
+   "id": "29bccbd1",
    "metadata": {
     "hide-output": false
    },
@@ -56,7 +56,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "56248531",
+   "id": "d8e2189e",
    "metadata": {},
    "source": [
     "## Reader’s Guide\n",
@@ -67,7 +67,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "b7a3f366",
+   "id": "fc4349cf",
    "metadata": {
     "hide-output": false
    },
@@ -81,7 +81,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "0cd16869",
+   "id": "b65b200c",
    "metadata": {},
    "source": [
     "This lecture uses the method of   **Markov jump linear quadratic dynamic programming** that is described in lecture\n",
@@ -185,7 +185,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6e9cc371",
+   "id": "9a44c8ea",
    "metadata": {},
    "source": [
     "## Public Finance Questions\n",
@@ -230,7 +230,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b3759187",
+   "id": "d626f6aa",
    "metadata": {},
    "source": [
     "## Barro (1979) Model\n",
@@ -347,7 +347,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "922495d9",
+   "id": "5856b8f4",
    "metadata": {
     "hide-output": false
    },
@@ -392,7 +392,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "20ab29a9",
+   "id": "3776efa0",
    "metadata": {},
    "source": [
     "We can now create an instance of `LQ`:"
@@ -401,7 +401,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "dbec9ed3",
+   "id": "a35aa24a",
    "metadata": {
     "hide-output": false
    },
@@ -414,7 +414,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "fa905352",
+   "id": "a259e0d0",
    "metadata": {},
    "source": [
     "We can see the isomorphism by noting that consumption is a martingale in\n",
@@ -454,7 +454,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "2b428e1b",
+   "id": "7998fa5c",
    "metadata": {
     "hide-output": false
    },
@@ -465,7 +465,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "92ff6d18",
+   "id": "20b25381",
    "metadata": {},
    "source": [
     "This explains the  fanning out of the conditional empirical  distribution of  taxation across time, computing\n",
@@ -476,7 +476,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "cde383a1",
+   "id": "59fda209",
    "metadata": {
     "hide-output": false
    },
@@ -493,7 +493,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e8b4c812",
+   "id": "afe1d4d5",
    "metadata": {},
    "source": [
     "We can see a similar, but a smoother pattern, if we plot government debt\n",
@@ -503,7 +503,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "1871cb4b",
+   "id": "93513804",
    "metadata": {
     "hide-output": false
    },
@@ -520,7 +520,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d7963705",
+   "id": "29fccc13",
    "metadata": {},
    "source": [
     "## Python Class to Solve Markov Jump Linear Quadratic Control Problems\n",
@@ -549,7 +549,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6fecad85",
+   "id": "4ee65b11",
    "metadata": {},
    "source": [
     "## Barro Model with a Time-varying Interest Rate\n",
@@ -591,7 +591,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "e16ec53f",
+   "id": "3f0f3ed7",
    "metadata": {
     "hide-output": false
    },
@@ -623,7 +623,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6511d6bb",
+   "id": "ae6a164f",
    "metadata": {},
    "source": [
     "The decision rules are now dependent on the Markov state:"
@@ -632,7 +632,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "a5294130",
+   "id": "b864003e",
    "metadata": {
     "hide-output": false
    },
@@ -644,7 +644,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "49e2c7ad",
+   "id": "434e4d43",
    "metadata": {
     "hide-output": false
    },
@@ -655,7 +655,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "57c26da1",
+   "id": "96540c74",
    "metadata": {},
    "source": [
     "Simulating a large number of such economies over time reveals\n",
@@ -668,7 +668,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "c91faf76",
+   "id": "61ecc94d",
    "metadata": {
     "hide-output": false
    },
@@ -686,7 +686,7 @@
   }
  ],
  "metadata": {
-  "date": 1680677527.1923513,
+  "date": 1685490453.9609783,
   "filename": "tax_smoothing_1.md",
   "kernelspec": {
    "display_name": "Python",
diff --git a/tax_smoothing_2.ipynb b/tax_smoothing_2.ipynb
index 455e2f2..5cfeb68 100644
--- a/tax_smoothing_2.ipynb
+++ b/tax_smoothing_2.ipynb
@@ -2,7 +2,7 @@
  "cells": [
   {
    "cell_type": "markdown",
-   "id": "bcbdff97",
+   "id": "e7655da7",
    "metadata": {},
    "source": [
     "\n",
@@ -13,7 +13,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b2e613b6",
+   "id": "fede8d83",
    "metadata": {},
    "source": [
     "# How to Pay for a War: Part 2"
@@ -21,7 +21,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "75f45c1d",
+   "id": "3e3605fa",
    "metadata": {},
    "source": [
     "## Contents\n",
@@ -38,7 +38,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9ebe8562",
+   "id": "688d83fb",
    "metadata": {},
    "source": [
     "In addition to what’s in Anaconda, this lecture  deploys the quantecon library:"
@@ -47,7 +47,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "04f12a4f",
+   "id": "9681fe21",
    "metadata": {
     "hide-output": false
    },
@@ -58,7 +58,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "147d7fbc",
+   "id": "9b9f2a2f",
    "metadata": {},
    "source": [
     "## An Application of Markov Jump Linear Quadratic Dynamic Programming\n",
@@ -106,7 +106,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "d46c0d90",
+   "id": "d1687595",
    "metadata": {
     "hide-output": false
    },
@@ -120,7 +120,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4997f49c",
+   "id": "7cab3358",
    "metadata": {},
    "source": [
     "## Two example specifications\n",
@@ -137,7 +137,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "2770a0d8",
+   "id": "4ea60a54",
    "metadata": {},
    "source": [
     "## One- and Two-period Bonds but No Restructuring\n",
@@ -210,7 +210,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4166f940",
+   "id": "6805fa68",
    "metadata": {},
    "source": [
     "## Mapping into an LQ Markov Jump Problem\n",
@@ -375,7 +375,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "9e9633c2",
+   "id": "41c3bb06",
    "metadata": {
     "hide-output": false
    },
@@ -436,7 +436,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "26b3d26f",
+   "id": "3328ed35",
    "metadata": {},
    "source": [
     "With the above function, we can proceed to solve the model in two steps:\n",
@@ -450,7 +450,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4373ff7b",
+   "id": "256a64a6",
    "metadata": {},
    "source": [
     "## Penalty on Different Issuance Across Maturities\n",
@@ -503,7 +503,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "8293f992",
+   "id": "da1ea74f",
    "metadata": {
     "hide-output": false
    },
@@ -557,7 +557,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5405975b",
+   "id": "6ced945b",
    "metadata": {},
    "source": [
     "The above simulations show that when no penalty is imposed on different\n",
@@ -574,7 +574,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "d2474627",
+   "id": "9eef7c33",
    "metadata": {
     "hide-output": false
    },
@@ -618,7 +618,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "44855f31",
+   "id": "e462d249",
    "metadata": {},
    "source": [
     "## A Model with Restructuring\n",
@@ -795,7 +795,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ac401efe",
+   "id": "30da82c0",
    "metadata": {},
    "source": [
     "## Restructuring as a Markov Jump Linear Quadratic Control Problem\n",
@@ -808,7 +808,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "6c315c2e",
+   "id": "47dd11d3",
    "metadata": {
     "hide-output": false
    },
@@ -863,7 +863,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5b398fd1",
+   "id": "280a79fe",
    "metadata": {},
    "source": [
     "### Example with Restructuring\n",
@@ -894,7 +894,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "aaed30e8",
+   "id": "11678cca",
    "metadata": {
     "hide-output": false
    },
@@ -939,7 +939,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "04d93c3b",
+   "id": "951606df",
    "metadata": {
     "hide-output": false
    },
@@ -967,7 +967,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "6c41dd8d",
+   "id": "4bc1460a",
    "metadata": {
     "hide-output": false
    },
@@ -984,7 +984,7 @@
   }
  ],
  "metadata": {
-  "date": 1680677527.2279928,
+  "date": 1685490453.9983878,
   "filename": "tax_smoothing_2.md",
   "kernelspec": {
    "display_name": "Python",
diff --git a/tax_smoothing_3.ipynb b/tax_smoothing_3.ipynb
index 6c76c17..26de76f 100644
--- a/tax_smoothing_3.ipynb
+++ b/tax_smoothing_3.ipynb
@@ -2,7 +2,7 @@
  "cells": [
   {
    "cell_type": "markdown",
-   "id": "b21a1a72",
+   "id": "e26be8e2",
    "metadata": {},
    "source": [
     "\n",
@@ -13,7 +13,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "0e93319c",
+   "id": "ec6ac92c",
    "metadata": {},
    "source": [
     "# How to Pay for a War: Part 3"
@@ -21,7 +21,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "dc045458",
+   "id": "431dbc38",
    "metadata": {},
    "source": [
     "## Contents\n",
@@ -35,7 +35,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7f380f4b",
+   "id": "68cec30f",
    "metadata": {},
    "source": [
     "In addition to what’s in Anaconda, this lecture deploys the quantecon library:"
@@ -44,7 +44,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "ef6a0e80",
+   "id": "4a1ce279",
    "metadata": {
     "hide-output": false
    },
@@ -55,7 +55,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d5d583f4",
+   "id": "c9f81bc9",
    "metadata": {},
    "source": [
     "## Another Application of Markov Jump Linear Quadratic Dynamic Programming\n",
@@ -84,7 +84,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "ce1a10bd",
+   "id": "cbe27afc",
    "metadata": {
     "hide-output": false
    },
@@ -98,7 +98,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e3074e28",
+   "id": "12533c4f",
    "metadata": {},
    "source": [
     "## Roll-Over Risk\n",
@@ -150,7 +150,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "8c8c7be7",
+   "id": "6a5d5e1b",
    "metadata": {},
    "source": [
     "## A Dead End\n",
@@ -188,7 +188,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "465322eb",
+   "id": "4466bc1b",
    "metadata": {},
    "source": [
     "## Better Representation of Roll-Over Risk\n",
@@ -242,7 +242,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "c0dfccb2",
+   "id": "2c133b15",
    "metadata": {
     "hide-output": false
    },
@@ -302,7 +302,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "80aefc0b",
+   "id": "e78d4f2c",
    "metadata": {},
    "source": [
     "This model is simulated below, using the same process for $ G_t $ as\n",
@@ -325,7 +325,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "524dfb94",
+   "id": "5640b9dc",
    "metadata": {
     "hide-output": false
    },
@@ -353,7 +353,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7bae94c8",
+   "id": "f8c60120",
    "metadata": {},
    "source": [
     "We can adjust the model so that, rather than having debt fluctuate\n",
@@ -367,7 +367,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "cab38e51",
+   "id": "35e36df9",
    "metadata": {
     "hide-output": false
    },
@@ -408,7 +408,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b8ce71c0",
+   "id": "4557ca94",
    "metadata": {},
    "source": [
     "With a lower interest rate, the government has an incentive to\n",
@@ -424,7 +424,7 @@
   }
  ],
  "metadata": {
-  "date": 1680677527.2495377,
+  "date": 1685490454.0195963,
   "filename": "tax_smoothing_3.md",
   "kernelspec": {
    "display_name": "Python",
diff --git a/troubleshooting.ipynb b/troubleshooting.ipynb
index df929ff..1c32f62 100644
--- a/troubleshooting.ipynb
+++ b/troubleshooting.ipynb
@@ -2,7 +2,7 @@
  "cells": [
   {
    "cell_type": "markdown",
-   "id": "10272db4",
+   "id": "5f81e47b",
    "metadata": {},
    "source": [
     "\n",
@@ -11,7 +11,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "74e79bb7",
+   "id": "96e6630d",
    "metadata": {},
    "source": [
     "# Troubleshooting"
@@ -19,7 +19,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "783634d9",
+   "id": "427be46e",
    "metadata": {},
    "source": [
     "## Contents\n",
@@ -31,7 +31,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6a62e385",
+   "id": "55e6ef37",
    "metadata": {},
    "source": [
     "This page is for readers experiencing errors when running the code from the lectures."
@@ -39,7 +39,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f9a95076",
+   "id": "7005087c",
    "metadata": {},
    "source": [
     "## Fixing Your Local Environment\n",
@@ -81,7 +81,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "dd2ad606",
+   "id": "01180b3a",
    "metadata": {},
    "source": [
     "## Reporting an Issue\n",
@@ -98,7 +98,7 @@
   }
  ],
  "metadata": {
-  "date": 1680677527.2562194,
+  "date": 1685490454.0263243,
   "filename": "troubleshooting.md",
   "kernelspec": {
    "display_name": "Python",
diff --git a/un_insure.ipynb b/un_insure.ipynb
index 8c2cf80..c4ac326 100644
--- a/un_insure.ipynb
+++ b/un_insure.ipynb
@@ -2,7 +2,7 @@
  "cells": [
   {
    "cell_type": "markdown",
-   "id": "26344b53",
+   "id": "2d3c427b",
    "metadata": {},
    "source": [
     "# Optimal Unemployment Insurance"
@@ -10,7 +10,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "770b8665",
+   "id": "e0f405b3",
    "metadata": {},
    "source": [
     "## Overview\n",
@@ -28,7 +28,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9a7af76f",
+   "id": "63ad2dbb",
    "metadata": {},
    "source": [
     "## Shavell and Weiss’s Model\n",
@@ -88,7 +88,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7e594661",
+   "id": "59969ec4",
    "metadata": {},
    "source": [
     "### Autarky\n",
@@ -160,7 +160,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "2e3a0bfa",
+   "id": "a069219a",
    "metadata": {},
    "source": [
     "### Full Information\n",
@@ -274,7 +274,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ee760c94",
+   "id": "f68ed0c1",
    "metadata": {},
    "source": [
     "### Incentive Problem\n",
@@ -340,7 +340,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "fefff189",
+   "id": "4081f5b3",
    "metadata": {},
    "source": [
     "## Private Information\n",
@@ -445,7 +445,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6c94cdc0",
+   "id": "269b7ef7",
    "metadata": {},
    "source": [
     "### Computational Details\n",
@@ -534,7 +534,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a13302ea",
+   "id": "0ecca755",
    "metadata": {},
    "source": [
     "### Python Computations\n",
@@ -547,7 +547,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "dcceb453",
+   "id": "33b2fa56",
    "metadata": {
     "hide-output": false
    },
@@ -562,7 +562,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "0d0d324f",
+   "id": "fa55eef6",
    "metadata": {},
    "source": [
     "We first create a class to set up a particular parametrization."
@@ -571,7 +571,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "935cfd96",
+   "id": "52cd71ba",
    "metadata": {
     "hide-output": false
    },
@@ -594,7 +594,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ff6f62c4",
+   "id": "14576702",
    "metadata": {},
    "source": [
     "### Parameter Values\n",
@@ -609,7 +609,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "ad663dad",
+   "id": "6335d604",
    "metadata": {
     "hide-output": false
    },
@@ -635,7 +635,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3e49b6ce",
+   "id": "5c370224",
    "metadata": {},
    "source": [
     "Recall that under  autarky the value for an unemployed worker\n",
@@ -674,7 +674,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "2110e37d",
+   "id": "971a4ec7",
    "metadata": {
     "hide-output": false
    },
@@ -693,7 +693,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "25ad67a5",
+   "id": "786a6c01",
    "metadata": {},
    "source": [
     "Since the calibration exercise is to match the hazard rate under autarky to the data, we must find an interest rate $ r $ to match `p(a,r) = 0.1`.\n",
@@ -706,7 +706,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "2b95c5d0",
+   "id": "f0bf169c",
    "metadata": {
     "hide-output": false
    },
@@ -724,7 +724,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7c926a84",
+   "id": "ab1c512e",
    "metadata": {},
    "source": [
     "Now, let us create an instance of the model with our parametrization"
@@ -733,7 +733,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "1abf470a",
+   "id": "88855eba",
    "metadata": {
     "hide-output": false
    },
@@ -747,7 +747,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f131c64f",
+   "id": "3f2e1d60",
    "metadata": {},
    "source": [
     "We want to compute an  $ r $ that is consistent with the hazard rate 0.1 in autarky.\n",
@@ -758,7 +758,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "25f6a932",
+   "id": "ea8ec262",
    "metadata": {
     "hide-output": false
    },
@@ -775,7 +775,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e3c4ef2c",
+   "id": "4d2769c3",
    "metadata": {},
    "source": [
     "Now that we have calibrated our interest rate $ r $, we can continue with solving the  model with private information."
@@ -783,7 +783,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c1b38526",
+   "id": "1db4efc1",
    "metadata": {},
    "source": [
     "### Computation under Private Information\n",
@@ -808,7 +808,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "b2b3f2a7",
+   "id": "477be95f",
    "metadata": {
     "hide-output": false
    },
@@ -838,7 +838,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "660f3d6f",
+   "id": "741589f9",
    "metadata": {},
    "source": [
     "With these analytical solutions for optimal $ c $ and $ a $ in hand, we can reduce the minimization to  [(39.12)](#equation-eq-hugo23)  in the single variable\n",
@@ -849,7 +849,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1a3d6f09",
+   "id": "26be8106",
    "metadata": {},
    "source": [
     "### Algorithm\n",
@@ -868,7 +868,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "4c7ecd83",
+   "id": "52fab446",
    "metadata": {
     "hide-output": false
    },
@@ -921,7 +921,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5c4a7408",
+   "id": "a3e69f54",
    "metadata": {},
    "source": [
     "The below code executes steps 4 and 5 in the Algorithm  until convergence to a function $ C^*(V) $."
@@ -930,7 +930,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "524f1ba6",
+   "id": "c2f96b53",
    "metadata": {
     "hide-output": false
    },
@@ -958,7 +958,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "8b837096",
+   "id": "a7b529fe",
    "metadata": {},
    "source": [
     "## Outcomes\n",
@@ -969,7 +969,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "072e90d2",
+   "id": "8cb90db3",
    "metadata": {
     "hide-output": false
    },
@@ -995,7 +995,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "20377cbe",
+   "id": "beadf9b2",
    "metadata": {},
    "source": [
     "### Replacement Ratios and Continuation Values\n",
@@ -1010,7 +1010,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "8ff02035",
+   "id": "c22e2b45",
    "metadata": {
     "hide-output": false
    },
@@ -1030,7 +1030,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "d31730d1",
+   "id": "ee604be8",
    "metadata": {
     "hide-output": false
    },
@@ -1047,7 +1047,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "6f3341ac",
+   "id": "cca2e11f",
    "metadata": {
     "hide-output": false
    },
@@ -1083,7 +1083,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "52d1c2b7",
+   "id": "34e7c019",
    "metadata": {},
    "source": [
     "For an initial promised value $ V^u = V_{\\rm aut} $, the planner chooses the autarky level of $ 0 $ for the replacement ratio and instructs the worker to search at the autarky search intensity, regardless of the duration of unemployment\n",
@@ -1093,7 +1093,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6e39d545",
+   "id": "6f95f10d",
    "metadata": {},
    "source": [
     "### Interpretations\n",
@@ -1147,7 +1147,7 @@
   }
  ],
  "metadata": {
-  "date": 1680677527.3145578,
+  "date": 1685490454.0849657,
   "filename": "un_insure.md",
   "kernelspec": {
    "display_name": "Python",
diff --git a/zreferences.ipynb b/zreferences.ipynb
index 25663cc..1c71319 100644
--- a/zreferences.ipynb
+++ b/zreferences.ipynb
@@ -2,7 +2,7 @@
  "cells": [
   {
    "cell_type": "markdown",
-   "id": "bfd24c46",
+   "id": "2d2542c2",
    "metadata": {},
    "source": [
     "\n",
@@ -11,7 +11,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "367fa281",
+   "id": "1871e063",
    "metadata": {},
    "source": [
     "# References\n",
@@ -322,7 +322,7 @@
   }
  ],
  "metadata": {
-  "date": 1680677527.3586204,
+  "date": 1685490454.1281092,
   "filename": "zreferences.md",
   "kernelspec": {
    "display_name": "Python",