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auto publishing updates to notebooks
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quantecon-services committed Oct 8, 2024
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80 changes: 40 additions & 40 deletions BCG_complete_mkts.ipynb
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"cells": [
{
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"metadata": {},
"source": [
"\n",
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},
{
"cell_type": "markdown",
"id": "f187a184",
"id": "7a190309",
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"source": [
"# Irrelevance of Capital Structures with Complete Markets\n",
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{
"cell_type": "code",
"execution_count": null,
"id": "04a85532",
"id": "5cebe13a",
"metadata": {
"hide-output": false
},
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},
{
"cell_type": "markdown",
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"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 [[Bisin *et al.*, 2018](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#id30)].\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 [[Modigliani and Miller, 1958](https://python-advanced.quantecon.org/zreferences.html#id30)] \n",
" Modigliani-Miller theorem [[Modigliani and Miller, 1958](https://python-advanced.quantecon.org/zreferences.html#id31)] \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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"source": [
"### Setup\n",
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},
{
"cell_type": "markdown",
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"metadata": {},
"source": [
"### Endowments\n",
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},
{
"cell_type": "markdown",
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"metadata": {},
"source": [
"### Technology:\n",
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},
{
"cell_type": "markdown",
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"metadata": {},
"source": [
"### Preferences:\n",
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},
{
"cell_type": "markdown",
"id": "d3c99898",
"id": "97c078cc",
"metadata": {},
"source": [
"### Parameterizations\n",
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},
{
"cell_type": "markdown",
"id": "0b911518",
"id": "13b637a3",
"metadata": {},
"source": [
"### Pareto criterion and planning problem\n",
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},
{
"cell_type": "markdown",
"id": "947213a7",
"id": "1ee74d5a",
"metadata": {},
"source": [
"### Helpful observations and bookkeeping\n",
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},
{
"cell_type": "markdown",
"id": "6306f398",
"id": "6caa3524",
"metadata": {},
"source": [
"#### Remarks\n",
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},
{
"cell_type": "markdown",
"id": "c1f60461",
"id": "6c09cb5b",
"metadata": {},
"source": [
"## Competitive equilibrium\n",
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},
{
"cell_type": "markdown",
"id": "612b14a8",
"id": "6799104a",
"metadata": {},
"source": [
"### Measures of agents and firms\n",
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},
{
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"id": "2b71afd5",
"id": "4ba71217",
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"source": [
"#### Ownership\n",
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},
{
"cell_type": "markdown",
"id": "586e1ae6",
"id": "c578d4c0",
"metadata": {},
"source": [
"#### Asset markets\n",
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},
{
"cell_type": "markdown",
"id": "ef40b69a",
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"metadata": {},
"source": [
"### Objects appearing in a competitive equilibrium\n",
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},
{
"cell_type": "markdown",
"id": "472550a2",
"id": "be0b84b6",
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"source": [
"### A representative firm’s problem\n",
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},
{
"cell_type": "markdown",
"id": "59b4fc2b",
"id": "8dfe0b80",
"metadata": {},
"source": [
"### A consumer’s problem\n",
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},
{
"cell_type": "markdown",
"id": "58c5c404",
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"source": [
"### Computing competitive equilibrium prices and quantities\n",
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},
{
"cell_type": "markdown",
"id": "d888ed5d",
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"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 [[Modigliani and Miller, 1958](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#id31)]\n",
"about firms’ finance:\n",
"\n",
"**Modigliani-Miller theorem:**\n",
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},
{
"cell_type": "markdown",
"id": "c0fa5ef0",
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"metadata": {},
"source": [
"## Code\n",
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{
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"id": "024ebc28",
"id": "1ae11a90",
"metadata": {
"hide-output": false
},
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{
"cell_type": "code",
"execution_count": null,
"id": "5ebeaf90",
"id": "27489317",
"metadata": {
"hide-output": false
},
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},
{
"cell_type": "markdown",
"id": "2bbd853a",
"id": "2012e598",
"metadata": {},
"source": [
"### Examples\n",
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},
{
"cell_type": "markdown",
"id": "de2a9267",
"id": "d097b234",
"metadata": {},
"source": [
"#### 1st example\n",
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{
"cell_type": "code",
"execution_count": null,
"id": "0d19519c",
"id": "39911897",
"metadata": {
"hide-output": false
},
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},
{
"cell_type": "markdown",
"id": "a5f707e1",
"id": "c9bda2c7",
"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": "6c7f7f19",
"id": "6198bcf2",
"metadata": {
"hide-output": false
},
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},
{
"cell_type": "markdown",
"id": "6134bcc5",
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"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": "74abae50",
"id": "9a303e5f",
"metadata": {
"hide-output": false
},
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},
{
"cell_type": "markdown",
"id": "b4773f6b",
"id": "44bf72a2",
"metadata": {},
"source": [
"#### 2nd example\n",
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{
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"id": "afcbb87d",
"id": "39820c9a",
"metadata": {
"hide-output": false
},
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{
"cell_type": "code",
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"id": "84f802a8",
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"metadata": {
"hide-output": false
},
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{
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"metadata": {
"hide-output": false
},
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{
"cell_type": "code",
"execution_count": null,
"id": "f137ef5b",
"id": "06d570ed",
"metadata": {
"hide-output": false
},
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}
],
"metadata": {
"date": 1724218392.944995,
"date": 1728369867.2445648,
"filename": "BCG_complete_mkts.md",
"kernelspec": {
"display_name": "Python",
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