{ "cells": [ { "cell_type": "markdown", "source": [ "# Deterministic Renewable Resource Model\n", "\n", "**Randall Romero Aguilar, PhD**\n", "\n", "This demo is based on the original Matlab demo accompanying the Computational Economics and Finance 2001 textbook by Mario Miranda and Paul Fackler.\n", "\n", "Original (Matlab) CompEcon file: **demdoc04.m**\n", "\n", "Running this file requires the Python version of CompEcon. This can be installed with pip by running\n", "\n", " !pip install compecon --upgrade\n", "\n", "Last updated: 2021-Oct-01\n", "
" ], "metadata": { "collapsed": false } }, { "cell_type": "markdown", "source": [ "## About\n", "\n", "Welfare maximizing social planner must decide the rate at which a renewable resource should be harvested.\n", "\n", "* State\n", " - s resource stock\n", "* Control\n", " - q harvest rate\n", "* Parameters\n", " - 𝛼 biological growth function scale factor\n", " - β biological growth function elasticity\n", " - κ harvest unit cost scale factor\n", " - γ harvest unit cost elasticity\n", " - η inverse elasticity of demand\n", " - 𝜌 continuous discount rate\n", "\n", "## Preliminary tasks\n", "\n", "### Import relevant packages" ], "metadata": { "collapsed": false, "pycharm": { "name": "#%% md\n" } } }, { "cell_type": "code", "execution_count": 1, "outputs": [], "source": [ "import numpy as np\n", "import pandas as pd\n", "import matplotlib.pyplot as plt\n", "from compecon import BasisChebyshev, OCmodel, NLP" ], "metadata": { "collapsed": false, "pycharm": { "name": "#%%\n" } } }, { "cell_type": "markdown", "source": [ "### Model parameters" ], "metadata": { "collapsed": false } }, { "cell_type": "code", "execution_count": 2, "outputs": [], "source": [ "𝛼 = 0.25 # biological growth function scale factor\n", "β = 0.50 # biological growth function elasticity\n", "κ = 5.00 # harvest unit cost scale factor\n", "γ = 1.50 # harvest unit cost elasticity\n", "η = 1.50 # inverse elasticity of demand\n", "𝜌 = 0.05 # continuous discount rate" ], "metadata": { "collapsed": false, "pycharm": { "name": "#%%\n" } } }, { "cell_type": "markdown", "source": [ "### Approximation structure" ], "metadata": { "collapsed": false } }, { "cell_type": "code", "execution_count": 3, "outputs": [], "source": [ "n = 20 # number of basis functions\n", "smin = 0.2 # minimum state\n", "smax = 1.0 # maximum state\n", "basis = BasisChebyshev(n, smin, smax, labels=['q']) # basis functions" ], "metadata": { "collapsed": false, "pycharm": { "name": "#%%\n" } } }, { "cell_type": "markdown", "source": [ "### Steady-state" ], "metadata": { "collapsed": false } }, { "cell_type": "code", "execution_count": 4, "outputs": [ { "data": { "text/plain": "Resource stock 0.366728\nRate of harvest 0.036161\ndtype: float64" }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sstar = 0.6\n", "qstar = 𝛼 * sstar * (1-sstar**β)\n", "xstar = np.array((sstar, qstar))\n", "\n", "def funcss(x):\n", " s, q = x\n", " p = q**(-η) # inverse demand function\n", " pder = -η * q**(-η-1) # inverse demand derivative\n", " g = 𝛼 * s* (1-s**β) # biological growth function\n", " gder = 𝛼 * (1-(1 + β) * s**β) # marginal biological growth function\n", " k = κ * s** (-γ) # harvest unit cost function\n", " kder = -κ * γ * s**(-γ-1) # harvest unit cost derivative\n", " return np.array([g-q, ((𝜌 - gder) * (p-k) + kder * g) / pder])\n", "\n", "sstar, qstar = NLP(funcss).broyden(xstar)\n", "\n", "steadystate = pd.Series([sstar, qstar],\n", " index=['Resource stock', 'Rate of harvest'])\n", "\n", "steadystate" ], "metadata": { "collapsed": false, "pycharm": { "name": "#%%\n" } } }, { "cell_type": "markdown", "source": [ "## Solve HJB equation by collocation\n" ], "metadata": { "collapsed": false } }, { "cell_type": "code", "execution_count": 5, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Solving optimal control model\n", "iter change time \n", "------------------------------\n", " 0 4.7e+02 0.0020\n", " 1 2.5e+02 0.0030\n", " 2 3.9e+00 0.0030\n", " 3 1.4e-02 0.0030\n", " 4 1.1e-06 0.0040\n", " 5 8.5e-14 0.0050\n", "Elapsed Time = 0.00 Seconds\n" ] } ], "source": [ "def control(s, Vs, 𝛼, β, κ, γ, η, 𝜌):\n", " k = κ * s**(-γ)\n", " return (Vs + k)**(-1/η)\n", "\n", "def reward(s, q, 𝛼, β, κ, γ, η, 𝜌):\n", " u = (1/(1-η)) * q **(1-η)\n", " k = κ * s**(-γ)\n", " return u - k*q\n", "\n", "def transition(s, q, 𝛼, β, κ, γ, η, 𝜌):\n", " g = 𝛼 * s * (1-s**β)\n", " return g - q\n", "\n", "model = OCmodel(basis, control, reward, transition, rho=𝜌, params=[𝛼, β, κ, γ, η, 𝜌])\n", "data = model.solve()" ], "metadata": { "collapsed": false, "pycharm": { "name": "#%%\n" } } }, { "cell_type": "markdown", "source": [ "## Plots\n", "\n", "### Optimal policy" ], "metadata": { "collapsed": false } }, { "cell_type": "code", "execution_count": 6, "outputs": [ { "data": { "text/plain": "
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\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots()\n", "data['control'].plot(ax=ax)\n", "ax.set(title='Optimal Harvest Policy',\n", " xlabel='Resource Stock',\n", " ylabel='Rate of Harvest',\n", " xlim=[smin, smax])\n", "ax.set_ylim(bottom=0)\n", "ax.hlines(qstar, 0, sstar, colors=['gray'], linestyles=['--'])\n", "ax.vlines(sstar, 0, qstar, colors=['gray'], linestyles=['--'])\n", "ax.annotate('$q^*$', (smin, qstar))\n", "ax.annotate('$k^*$', (sstar, 0))\n", "ax.plot(sstar, qstar, '.', ms=20);" ], "metadata": { "collapsed": false, "pycharm": { "name": "#%%\n" } } }, { "cell_type": "markdown", "source": [ "### Value function" ], "metadata": { "collapsed": false } }, { "cell_type": "code", "execution_count": 7, "outputs": [ { "data": { "text/plain": "
", "image/png": 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\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots()\n", "data['value'].plot(ax=ax)\n", "ax.set(title='Value Function',\n", " xlabel='Resource Stock',\n", " ylabel='Social Welfare',\n", " xlim=[smin, smax])\n", "\n", "lb = ax.get_ylim()[0]\n", "vstar = model.Value(sstar)\n", "ax.vlines(sstar, lb , vstar, colors=['gray'], linestyles=['--'])\n", "ax.annotate('$s^*$', (sstar, lb))\n", "ax.plot(sstar, vstar, '.', ms=20);" ], "metadata": { "collapsed": false, "pycharm": { "name": "#%%\n" } } }, { "cell_type": "markdown", "source": [ "### Shadow price" ], "metadata": { "collapsed": false } }, { "cell_type": "code", "execution_count": 8, "outputs": [ { "data": { "text/plain": "
", "image/png": 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\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "data['shadow'] = model.Value(data.index, 1)\n", "\n", "fig, ax = plt.subplots()\n", "data['shadow'].plot(ax=ax)\n", "ax.set(title='Shadow Price Function',\n", " xlabel='Resource Stock',\n", " ylabel='Shadow Price',\n", " xlim=[smin, smax])\n", "\n", "pstar = model.Value(sstar, 1)\n", "ax.set_ylim(bottom=0)\n", "ax.hlines(pstar, 0, sstar, colors=['gray'], linestyles=['--'])\n", "ax.vlines(sstar, 0 , pstar, colors=['gray'], linestyles=['--'])\n", "ax.annotate('$\\lambda^*$', (smin, pstar))\n", "ax.annotate('$k^*$', (pstar, 0))\n", "ax.plot(sstar, pstar, '.', ms=20);" ], "metadata": { "collapsed": false, "pycharm": { "name": "#%%\n" } } }, { "cell_type": "markdown", "source": [ "### Residual" ], "metadata": { "collapsed": false } }, { "cell_type": "code", "execution_count": 9, "outputs": [ { "data": { "text/plain": "
", "image/png": 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\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots()\n", "ax.axhline(0, c='white')\n", "data['resid'].plot(ax=ax)\n", "ax.set(title='HJB Equation Residual',\n", " xlabel='Resource Stock',\n", " ylabel='Residual',\n", " xlim=[smin, smax]);" ], "metadata": { "collapsed": false, "pycharm": { "name": "#%%\n" } } }, { "cell_type": "markdown", "source": [ "## Simulate the model" ], "metadata": { "collapsed": false } }, { "cell_type": "markdown", "source": [ "### Initial state and time horizon" ], "metadata": { "collapsed": false } }, { "cell_type": "code", "execution_count": 10, "outputs": [], "source": [ "s0 = smax # initial capital stock\n", "T = 20 # time horizon" ], "metadata": { "collapsed": false, "pycharm": { "name": "#%%\n" } } }, { "cell_type": "markdown", "source": [ "### Simulation and plot" ], "metadata": { "collapsed": false } }, { "cell_type": "code", "execution_count": 11, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "PARAMETER xnames NO LONGER VALID. SET labels= AT OBJECT CREATION\n" ] }, { "data": { "text/plain": "
", "image/png": 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\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots()\n", "model.simulate([s0], T).plot(ax=ax)\n", "ax.set(title='Simulated Resource Stock and Rate of Harvest',\n", " xlabel='Time',\n", " ylabel='Quantity',\n", " xlim=[0, T],\n", " xticks=np.arange(0,T+1,5))\n", "\n", "ax.axhline(sstar, ls='--', c='C0')\n", "ax.axhline(qstar, ls='--', c='C1')\n", "\n", "ax.annotate('$s^*$', (0, sstar), color='C0', va='top')\n", "ax.annotate('$q^*$', (0, qstar), color='C1', va='bottom')\n", "\n", "ax.annotate('\\nResource Stock', (T, sstar), color='C0', ha='right', va='top')\n", "ax.annotate('\\nRate of harvest', (T, qstar), color='C1', ha='right', va='top')\n", "\n", "ax.legend([]);" ], "metadata": { "collapsed": false, "pycharm": { "name": "#%%\n" } } }, { "cell_type": "code", "execution_count": 11, "outputs": [], "source": [], "metadata": { "collapsed": false, "pycharm": { "name": "#%%\n" } } } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 2 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython2", "version": "2.7.6" } }, "nbformat": 4, "nbformat_minor": 0 }