{ "cells": [ { "cell_type": "markdown", "metadata": { "Collapsed": "false" }, "source": [ "# Timber Harvesting -- using cubic splines\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: **demdp01b.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: 2022-Oct-22\n", "
" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "## About\n", "\n", "Profit maximizing owner of a commercial tree stand must decide when to clearcut the stand.\n" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "Collapsed": "false" }, "outputs": [], "source": [ "import numpy as np\n", "from compecon import NLP, BasisSpline\n", "import matplotlib.pyplot as plt" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "Collapsed": "false" }, "outputs": [], "source": [ "price = 1.0 # price of biomass\n", "κ = 0.2 # clearcut-replant cost\n", "smax = 0.5 # stand carrying capacity\n", "ɣ = 0.1 # biomass growth parameter\n", "δ = 0.9 # discount factor" ] }, { "cell_type": "markdown", "metadata": { "Collapsed": "false" }, "source": [ "### Code the growth function" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "Collapsed": "false" }, "outputs": [], "source": [ "def h(s): return np.array(s + ɣ*(smax - s))" ] }, { "cell_type": "markdown", "metadata": { "Collapsed": "false" }, "source": [ "## SOLUTION\n", "\n", "### Code the approximant and the residual" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "Collapsed": "false" }, "outputs": [], "source": [ "ns = 200\n", "vhat = BasisSpline(ns,0,smax,k=3)" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "Collapsed": "false" }, "outputs": [], "source": [ "def vhat1(s): return price*s - κ + δ * vhat(h(0))\n", "def vhat0(s): return δ * vhat(h(s))" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "Collapsed": "false" }, "outputs": [], "source": [ "def resid(c,s=vhat.nodes):\n", " vhat.c = c\n", " return vhat(s) - np.maximum(vhat0(s), vhat1(s))" ] }, { "cell_type": "markdown", "metadata": { "Collapsed": "false" }, "source": [ "### Solve collocation equation" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "Collapsed": "false" }, "outputs": [], "source": [ "cc = NLP(resid).broyden(vhat.c)" ] }, { "cell_type": "markdown", "metadata": { "Collapsed": "false" }, "source": [ "### Compute critical biomass" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "Collapsed": "false" }, "outputs": [], "source": [ "scrit = NLP(lambda s: vhat0(s)-vhat1(s)).broyden(0.0)" ] }, { "cell_type": "markdown", "metadata": { "Collapsed": "false" }, "source": [ "## ANALYSIS" ] }, { "cell_type": "markdown", "metadata": { "Collapsed": "false" }, "source": [ "### Compute refined state grid" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "Collapsed": "false" }, "outputs": [], "source": [ "ss = np.linspace(0,smax,1000)" ] }, { "cell_type": "markdown", "metadata": { "Collapsed": "false" }, "source": [ "### Plot Conditional Value Functions" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "Collapsed": "false" }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Optimal Biomass Harvest Level = 0.3067\n" ] }, { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig1, ax = plt.subplots()\n", "\n", "ax.plot(ss, vhat0(ss), label='Grow')\n", "ax.plot(ss, vhat1(ss), label='Clear-Cut')\n", "\n", "\n", "ax.set(title='Conditional Value Functions',\n", " xlabel='Biomass',\n", " ylabel='Value of Stand')\n", "ax.legend()\n", "\n", "vcrit = vhat(scrit)\n", "ymin = ax.get_ylim()[0]\n", "ax.vlines(scrit, ymin,vcrit,'grey',linestyles='--')\n", "\n", "ax.annotate('$s^*$', [scrit,ymin])\n", "ax.plot(scrit,vcrit,'wo')\n", "print(f'Optimal Biomass Harvest Level = {scrit:.4f}') " ] }, { "cell_type": "markdown", "metadata": { "Collapsed": "false" }, "source": [ "### Plot Value Function Residual" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "Collapsed": "false" }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig2, ax = plt.subplots()\n", "\n", "ax.set(title='Bellman Equation Residual', xlabel='Biomass', ylabel='Percent Residual')\n", "ax.plot(ss, 100*resid(cc,ss) / vhat(ss))\n", "ax.hlines(0,0,smax,linestyles='--')" ] }, { "cell_type": "markdown", "metadata": { "Collapsed": "false" }, "source": [ "### Compute ergodic mean annual harvest " ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "Collapsed": "false" }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Ergodic Mean Annual Harvest = 0.0362 after 10 iterations\n" ] } ], "source": [ "s = h(0)\n", "for n in range(100):\n", " if s > scrit: break\n", " s = h(s)\n", " \n", "print(f'Ergodic Mean Annual Harvest = {s/n:.4f} after {n+1} iterations') " ] } ], "metadata": { "kernelspec": { "display_name": "Python 3.9.7 ('base')", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.9.7" }, "vscode": { "interpreter": { "hash": "ad2bdc8ecc057115af97d19610ffacc2b4e99fae6737bb82f5d7fb13d2f2c186" } } }, "nbformat": 4, "nbformat_minor": 4 }