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quantecon-services committed May 3, 2024
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85 changes: 42 additions & 43 deletions BCG_complete_mkts.ipynb
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"cells": [
{
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"metadata": {},
"source": [
"\n",
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},
{
"cell_type": "markdown",
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"metadata": {},
"source": [
"# Irrelevance of Capital Structures with Complete Markets"
]
},
{
"cell_type": "markdown",
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"metadata": {},
"source": [
"## Contents\n",
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},
{
"cell_type": "markdown",
"id": "05120edf",
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"source": [
"In addition to what’s in Anaconda, this lecture will need the following libraries:"
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{
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"source": [
"!pip install --upgrade quantecon\n",
"!pip install interpolation\n",
"!conda install -y -c plotly plotly plotly-orca"
]
},
{
"cell_type": "markdown",
"id": "aec21c4d",
"id": "c2f0a35f",
"metadata": {},
"source": [
"## Introduction\n",
"\n",
"This is a prolegomenon to another lecture [Equilibrium Capital Structures with Incomplete Markets](https://python-advanced.quantecon.org/BCG_incomplete_mkts.html) about a model with\n",
"incomplete markets authored by Bisin, Clementi, and Gottardi [[BCG18](https://python-advanced.quantecon.org/zreferences.html#id29)].\n",
"incomplete markets authored by Bisin, Clementi, and Gottardi [[Bisin *et al.*, 2018](https://python-advanced.quantecon.org/zreferences.html#id29)].\n",
"\n",
"We adopt specifications of preferences and technologies very close to\n",
"Bisin, Clemente, and Gottardi’s but unlike them assume that there are complete\n",
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"- illustrating classic complete markets outcomes that include \n",
" - indeterminacy of consumers’ portfolio choices \n",
" - indeterminacy of firms’ financial structures that underlies a\n",
" Modigliani-Miller theorem [[MM58](https://python-advanced.quantecon.org/zreferences.html#id30)] \n",
" Modigliani-Miller theorem [[Modigliani and Miller, 1958](https://python-advanced.quantecon.org/zreferences.html#id30)] \n",
"- introducing `Big K, little k` issues in a simple context that will\n",
" recur in the BCG incomplete markets environment \n",
"\n",
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},
{
"cell_type": "markdown",
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"id": "0d77e017",
"metadata": {},
"source": [
"### Setup\n",
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},
{
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"metadata": {},
"source": [
"### Endowments\n",
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},
{
"cell_type": "markdown",
"id": "78d8b8fc",
"id": "15ebc952",
"metadata": {},
"source": [
"### Technology:\n",
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},
{
"cell_type": "markdown",
"id": "1bc6cdb3",
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"metadata": {},
"source": [
"### Preferences:\n",
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},
{
"cell_type": "markdown",
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"id": "15288344",
"metadata": {},
"source": [
"### Parameterizations\n",
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},
{
"cell_type": "markdown",
"id": "8279204d",
"id": "597096c0",
"metadata": {},
"source": [
"### Pareto criterion and planning problem\n",
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},
{
"cell_type": "markdown",
"id": "75426d8b",
"id": "bce4acd5",
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"source": [
"### Helpful observations and bookkeeping\n",
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},
{
"cell_type": "markdown",
"id": "b7e6f121",
"id": "99772d3a",
"metadata": {},
"source": [
"#### Remarks\n",
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},
{
"cell_type": "markdown",
"id": "016e5e9d",
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"metadata": {},
"source": [
"## Competitive equilibrium\n",
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},
{
"cell_type": "markdown",
"id": "9537825e",
"id": "43168c40",
"metadata": {},
"source": [
"### Measures of agents and firms\n",
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},
{
"cell_type": "markdown",
"id": "661e2910",
"id": "c177cb0d",
"metadata": {},
"source": [
"#### Ownership\n",
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},
{
"cell_type": "markdown",
"id": "b0499956",
"id": "b625503d",
"metadata": {},
"source": [
"#### Asset markets\n",
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},
{
"cell_type": "markdown",
"id": "ece861b1",
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"metadata": {},
"source": [
"### Objects appearing in a competitive equilibrium\n",
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},
{
"cell_type": "markdown",
"id": "09771b13",
"id": "c84b2c84",
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"source": [
"### A representative firm’s problem\n",
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},
{
"cell_type": "markdown",
"id": "a8dcfea3",
"id": "41108067",
"metadata": {},
"source": [
"### A consumer’s problem\n",
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},
{
"cell_type": "markdown",
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"metadata": {},
"source": [
"### Computing competitive equilibrium prices and quantities\n",
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},
{
"cell_type": "markdown",
"id": "d2096d52",
"id": "0ce4ae56",
"metadata": {},
"source": [
"### Modigliani-Miller theorem\n",
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"which is the same expression that we obtained above when we assumed that\n",
"the firm issued only equity.\n",
"\n",
"We thus obtain a version of the celebrated Modigliani-Miller theorem [[MM58](https://python-advanced.quantecon.org/zreferences.html#id30)]\n",
"We thus obtain a version of the celebrated Modigliani-Miller theorem [[Modigliani and Miller, 1958](https://python-advanced.quantecon.org/zreferences.html#id30)]\n",
"about firms’ finance:\n",
"\n",
"**Modigliani-Miller theorem:**\n",
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},
{
"cell_type": "markdown",
"id": "45f66c33",
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"source": [
"## Code\n",
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{
"cell_type": "code",
"execution_count": null,
"id": "5fe33904",
"id": "01997564",
"metadata": {
"hide-output": false
},
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},
{
"cell_type": "markdown",
"id": "1a1e4fa2",
"id": "8af4a77d",
"metadata": {},
"source": [
"### Examples\n",
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},
{
"cell_type": "markdown",
"id": "ec9fc988",
"id": "0c4f9d1d",
"metadata": {},
"source": [
"#### 1st example\n",
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{
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"execution_count": null,
"id": "9d5f31f1",
"id": "7fd8ca9b",
"metadata": {
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},
{
"cell_type": "markdown",
"id": "7739b0c3",
"id": "cef67a04",
"metadata": {},
"source": [
"Let’s plot the agents’ time-1 endowments with respect to shocks to see\n",
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{
"cell_type": "code",
"execution_count": null,
"id": "b43f1d9d",
"id": "838c1b3c",
"metadata": {
"hide-output": false
},
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},
{
"cell_type": "markdown",
"id": "fdd12701",
"id": "e77dbc46",
"metadata": {},
"source": [
"Let’s also compare the optimal capital stock, $ k $, and optimal\n",
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{
"cell_type": "code",
"execution_count": null,
"id": "db23c700",
"id": "fa49efab",
"metadata": {
"hide-output": false
},
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},
{
"cell_type": "markdown",
"id": "e58214e0",
"id": "f19985ad",
"metadata": {},
"source": [
"#### 2nd example\n",
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{
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"execution_count": null,
"id": "66ba5efa",
"id": "48ee014b",
"metadata": {
"hide-output": false
},
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{
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"id": "0bc3b9ee",
"id": "02cae004",
"metadata": {
"hide-output": false
},
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{
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"id": "94d0939d",
"metadata": {
"hide-output": false
},
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{
"cell_type": "code",
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"metadata": {
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},
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}
],
"metadata": {
"date": 1705369584.2645504,
"date": 1714698769.0995438,
"filename": "BCG_complete_mkts.md",
"kernelspec": {
"display_name": "Python",
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