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‎lectures/_static/lecture_specific/finite_markov/figures.ipynb

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{
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"cells": [
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{
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"cell_type": "markdown",
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"id": "b5a640be-e2e4-4841-bcda-95f6660fd9fe",
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"metadata": {},
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"source": [
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"# Figures for Markov Chain II"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 1,
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"id": "f8a64d7b-2ffd-4974-a1dd-ec14d8e44102",
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"Collecting graphviz\n",
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" Obtaining dependency information for graphviz from https://files.pythonhosted.org/packages/00/be/d59db2d1d52697c6adc9eacaf50e8965b6345cc143f671e1ed068818d5cf/graphviz-0.20.3-py3-none-any.whl.metadata\n",
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" Downloading graphviz-0.20.3-py3-none-any.whl.metadata (12 kB)\n",
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"Downloading graphviz-0.20.3-py3-none-any.whl (47 kB)\n",
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"\u001b[2K \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m47.1/47.1 kB\u001b[0m \u001b[31m1.4 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n",
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"\u001b[?25hInstalling collected packages: graphviz\n",
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"Successfully installed graphviz-0.20.3\n"
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]
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}
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],
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"source": [
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"!pip install graphviz"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 2,
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"id": "43d55bea-fd00-4583-8d89-830151b6c36c",
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"metadata": {},
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"outputs": [],
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"source": [
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"from graphviz import Digraph"
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]
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},
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{
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"cell_type": "markdown",
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"id": "4185ae75-3a1c-4f89-ad74-1950d344ba56",
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"metadata": {},
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"source": [
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"## Irreducibility"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 3,
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"id": "53a8bb26-a6e8-421c-abcc-535031d5a69b",
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"'mc_irreducibility1.png'"
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]
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},
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"execution_count": 3,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"dot = Digraph(format='png')\n",
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"dot.attr(rankdir='LR')\n",
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"dot.node(\"贫穷\")\n",
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"dot.node(\"中产\")\n",
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"dot.node(\"富裕\")\n",
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"\n",
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"dot.edge(\"贫穷\", \"贫穷\", label=\"0.9\")\n",
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"dot.edge(\"贫穷\", \"中产\", label=\"0.1\")\n",
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"dot.edge(\"中产\", \"贫穷\", label=\"0.4\")\n",
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"dot.edge(\"中产\", \"中产\", label=\"0.4\")\n",
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"dot.edge(\"中产\", \"富裕\", label=\"0.2\")\n",
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"dot.edge(\"富裕\", \"贫穷\", label=\"0.1\")\n",
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"dot.edge(\"富裕\", \"中产\", label=\"0.1\")\n",
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"dot.edge(\"富裕\", \"富裕\", label=\"0.8\")\n",
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"\n",
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"dot\n",
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"dot.render(filename='mc_irreducibility1')"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 4,
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"id": "4e96fd64-a1ab-4a6e-a5d6-a64767f6181e",
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"'mc_irreducibility2.png'"
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]
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},
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"execution_count": 4,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"dot = Digraph(format='png')\n",
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"dot.attr(rankdir='LR')\n",
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"dot.node(\"贫穷\")\n",
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"dot.node(\"中产\")\n",
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"dot.node(\"富裕\")\n",
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"\n",
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"dot.edge(\"贫穷\", \"贫穷\", label=\"1.0\")\n",
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"dot.edge(\"中产\", \"贫穷\", label=\"0.1\")\n",
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"dot.edge(\"中产\", \"中产\", label=\"0.8\")\n",
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"dot.edge(\"中产\", \"富裕\", label=\"0.1\")\n",
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"dot.edge(\"富裕\", \"中产\", label=\"0.2\")\n",
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"dot.edge(\"富裕\", \"富裕\", label=\"0.8\")\n",
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"\n",
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"dot\n",
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"dot.render(filename='mc_irreducibility2')"
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]
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},
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{
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"cell_type": "markdown",
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"id": "1d7441a9-7753-4922-8276-3d26a26798cf",
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"metadata": {},
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"source": [
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"## Example 4"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 6,
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"id": "5f9c4db0-812a-4131-803f-024ae5b61772",
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"'hamilton_graph.png'"
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]
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},
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"execution_count": 6,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"dot = Digraph(format='png')\n",
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"dot.attr(rankdir='LR')\n",
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"dot.node(\"ng\")\n",
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"dot.node(\"mr\")\n",
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"dot.node(\"sr\")\n",
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"\n",
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"dot.edge(\"ng\", \"ng\", label=\"0.971\")\n",
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"dot.edge(\"ng\", \"mr\", label=\"0.029\")\n",
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"dot.edge(\"mr\", \"ng\", label=\"0.145\")\n",
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"\n",
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"dot.edge(\"mr\", \"mr\", label=\"0.778\")\n",
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"dot.edge(\"mr\", \"sr\", label=\"0.077\")\n",
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"dot.edge(\"sr\", \"mr\", label=\"0.508\")\n",
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"\n",
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"dot.edge(\"sr\", \"sr\", label=\"0.492\")\n",
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"dot\n",
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"\n",
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"dot.render(filename='hamilton_graph')"
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]
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}
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],
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"metadata": {
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"kernelspec": {
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"display_name": "quantecon",
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"language": "python",
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"name": "python3"
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},
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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"version": 3
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.11.5"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 5
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}

‎lectures/_static/lecture_specific/finite_markov/hamilton_grah

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digraph {
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rankdir=LR
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ng
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mr
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sr
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ng -> ng [label=0.971]
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ng -> mr [label=0.029]
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mr -> ng [label=0.145]
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mr -> mr [label=0.778]
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mr -> sr [label=0.077]
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sr -> mr [label=0.508]
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sr -> sr [label=0.492]
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}

‎lectures/_static/lecture_specific/finite_markov/hamilton_graph

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digraph {
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rankdir=LR
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ng
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mr
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sr
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ng -> ng [label=0.971]
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ng -> mr [label=0.029]
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mr -> ng [label=0.145]
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mr -> mr [label=0.778]
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mr -> sr [label=0.077]
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sr -> mr [label=0.508]
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sr -> sr [label=0.492]
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}

‎lectures/_static/lecture_specific/finite_markov/hamilton_graph.png

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‎lectures/_static/lecture_specific/finite_markov/mc_irreducibility1

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digraph {
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rankdir=LR
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"贫穷"
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"中产"
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"富裕"
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"贫穷" -> "贫穷" [label=0.9]
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"贫穷" -> "中产" [label=0.1]
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"中产" -> "贫穷" [label=0.4]
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"中产" -> "中产" [label=0.4]
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"中产" -> "富裕" [label=0.2]
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"富裕" -> "贫穷" [label=0.1]
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"富裕" -> "中产" [label=0.1]
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"富裕" -> "富裕" [label=0.8]
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}

‎lectures/_static/lecture_specific/finite_markov/mc_irreducibility1.png

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‎lectures/_static/lecture_specific/finite_markov/mc_irreducibility2

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digraph {
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rankdir=LR
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"贫穷"
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"中产"
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"富裕"
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"贫穷" -> "贫穷" [label=1.0]
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"中产" -> "贫穷" [label=0.1]
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"中产" -> "中产" [label=0.8]
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"中产" -> "富裕" [label=0.1]
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"富裕" -> "中产" [label=0.2]
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"富裕" -> "富裕" [label=0.8]
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}

‎lectures/_static/lecture_specific/finite_markov/mc_irreducibility2.png

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‎lectures/aiyagari.md

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@@ -169,9 +169,9 @@ w(r) = A (1 - \alpha) (A \alpha / (r + \delta))^{\alpha / (1 - \alpha)}
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* 价格诱导的行为产生的总量与价格一致
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* 总量和价格随时间保持不变
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更详细地说，SREE列出了价格、储蓄和生产政策的集合，使得：
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更详细地说，SREE列出了价格、储蓄和生产策略的集合，使得：
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* 家庭在给定价格下选择指定的储蓄政策
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* 家庭在给定价格下选择指定的储蓄策略
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* 企业在相同价格下最大化利润
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* 产生的总量与价格一致；特别是，资本需求等于供给
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* 总量（定义为横截面平均值）保持不变
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1. 选择一个提议的总资本量 $K$
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2. 确定相应的价格，其中利率 $r$ 由 {eq}`aiy_rgk` 决定，工资率 $w(r)$ 由 {eq}`aiy_wgr` 给出
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3. 确定给定这些价格下家庭的共同最优储蓄政策
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4. 计算给定这个储蓄政策下的稳态资本平均值
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3. 确定给定这些价格下家庭的共同最优储蓄策略
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4. 计算给定这个储蓄策略下的稳态资本平均值
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如果最终数量与 $K$ 一致，那么我们就得到了一个SREE。
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class Household:
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"""
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这个类接收定义家庭资产积累问题的参数，并计算相应的回报和转移矩阵R
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和Q，这些矩阵是生成DiscreteDP实例所必需的，从而求解最优政策。
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和Q，这些矩阵是生成DiscreteDP实例所必需的，从而求解最优策略。
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关于索引的说明：我们需要将状态空间S枚举为序列S = {0, ..., n}。
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为此，(a_i, z_i)索引对根据以下规则映射到s_i索引：
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return a_probs
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```
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作为第一个例子，让我们计算并绘制在固定价格下的最优积累政策。
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作为第一个例子，让我们计算并绘制在固定价格下的最优积累策略。
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```{code-cell} python3
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# 示例价格
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plt.show()
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```
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该图显示了在不同外生状态值下的资产积累政策。
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该图显示了在不同外生状态值下的资产积累策略。
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现在我们要计算均衡。
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w = r_to_w(r)
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am.set_prices(r, w)
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aiyagari_ddp = DiscreteDP(am.R, am.Q, β)
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# 计算最优政策
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# 计算最优策略
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results = aiyagari_ddp.solve(method='policy_iteration')
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# 计算稳态分布
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stationary_probs = results.mc.stationary_distributions[0]

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