{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Private Non-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: **demdp09.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-23\n", "
" ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "## About\n", "\n", "Profit maximizing mine owner must decide how much ore to extract\n", "\n", "- States\n", " - s: ore stock\n", "- Actions\n", " - q: ore extracted and sold\n", "- Parameters\n", " - a0,a1: demand function parameters\n", " - b0,b1: supply function parameters\n", " - $\\delta$: discount factor" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from compecon import BasisSpline, DPmodel, DPoptions, qnwnorm" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Model parameters" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "a0, a1, b0, b1, δ = 5, 0.8, 7, 1.0, 0.9" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### State space\n", "The state variable is s=\"Stock\", which is restricted to $s\\in[0, 10]$. \n", "\n", "Here, we represent it with a cubic spline basis, with $n=101$ nodes." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "n, smin, smax = 101, 0, 10\n", "basis = BasisSpline(n, smin, smax, labels=['Ore Stock'])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Action space\n", "The choice variable q=\"Ore extracted\" must be nonnegative." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "def bounds(s, i=None, j=None):\n", " return np.zeros_like(s), s[:]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Reward function\n", "The reward function is the utility of harvesting $q$ units." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "def reward(s, q, i=None, j=None):\n", " u = (a0-b0+b1*s)*q - (a1+b1/2)*q**2\n", " ux = (a0-b0+b1*s) - (2*a1+b1)*q\n", " uxx = -2*(a1+b1/2)*np.ones_like(s) \n", " return u, ux, uxx" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### State transition function\n", "Next period, the stock will be equal that is $s' = \\alpha (s-q) - 0.5\\beta(s-q)^2$" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "def transition(s, q, i=None, j=None, in_=None, e=None):\n", " g = s-q\n", " gx = -np.ones_like(s)\n", " gxx = np.zeros_like(s)\n", " return g, gx, gxx" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Model structure\n", "The value of wealth $s$ satisfies the Bellman equation\n", "\\begin{equation*}\n", "V(s) = \\max_q\\left\\{(a_0-b_0+b_1 s)q - (a_1+b_1/2)q^2 + \\delta V(s') \\right\\}\n", "\\end{equation*}\n", "\n", "To solve and simulate this model,use the CompEcon class `DPmodel`" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "model = DPmodel(basis, reward, transition, bounds,\n", " x=['Ore Extracted'],\n", " discount=δ)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Solving the model\n", "\n", "Solving the growth model by collocation" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Solving infinite-horizon model collocation equation by Newton's method\n", "iter change time \n", "------------------------------\n", " 0 1.9e+01 0.0219\n", " 1 3.5e+00 0.0369\n", " 2 2.2e-01 0.0489\n", " 3 1.0e-03 0.0659\n", " 4 2.2e-08 0.0778\n", " 5 1.9e-14 0.0878\n", "Elapsed Time = 0.09 Seconds\n" ] }, { "data": { "text/html": [ "
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Ore StockvalueresidOre Extracted
Ore Stock
0.0000000.0000000.000000e+000.000000e+000.000000e+00
0.0099110.009911-3.725252e-16-3.725252e-173.016346e-15
0.0198220.019822-3.915019e-16-3.915019e-173.170001e-15
0.0297320.029732-1.557981e-16-1.557981e-171.261501e-15
0.0396430.0396432.357181e-162.357181e-17-1.908615e-15
\n", "
" ], "text/plain": [ " Ore Stock value resid Ore Extracted\n", "Ore Stock \n", "0.000000 0.000000 0.000000e+00 0.000000e+00 0.000000e+00\n", "0.009911 0.009911 -3.725252e-16 -3.725252e-17 3.016346e-15\n", "0.019822 0.019822 -3.915019e-16 -3.915019e-17 3.170001e-15\n", "0.029732 0.029732 -1.557981e-16 -1.557981e-17 1.261501e-15\n", "0.039643 0.039643 2.357181e-16 2.357181e-17 -1.908615e-15" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "S = model.solve()\n", "S.head()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "`DPmodel.solve` returns a pandas `DataFrame` with the following data:" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Compute and print abandonment point" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Abandonment Point = 2.00\n" ] } ], "source": [ "sstar = (b0-a0)/b1\n", "print(f'Abandonment Point = {sstar:5.2f}')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We are also interested in the shadow price of ore (the first derivative of the value function)." ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [], "source": [ "S['shadow price'] = model.Value(S['Ore Stock'],1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Plotting the results" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Optimal Policy" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig1, ax = plt.subplots()\n", "ax.set(title='Optimal Extraction', xlabel='Ore Stock', ylabel='Ore Extracted')\n", "ax.plot(S['Ore Extracted'])\n", "\n", "ax.plot(sstar, 0, 'wo')\n", "ax.annotate(f\"$s^*$ = {sstar:.2f}\",[sstar, 0], va='top');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Value Function" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig2, ax = plt.subplots()\n", "\n", "ax.set(title='Value Function', xlabel='Ore Stock', ylabel='Value')\n", "ax.plot(S.value);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Shadow Price Function" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig3,ax = plt.subplots()\n", "ax.set(title='Shadow Price Function', xlabel='Ore Stock', ylabel='Shadow Price')\n", "ax.plot(S['shadow price']);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Residual" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "scrolled": false }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig4, ax = plt.subplots()\n", "ax.set(title='Bellman Equation Residual', xlabel='Ore Stock', ylabel='Residual')\n", "ax.axhline(0, color='white')\n", "ax.plot(S['resid'])\n", "ax.ticklabel_format(style='sci', axis='y', scilimits=(-1,1))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Simulating the model\n", "\n", "We simulate 21 periods of the model starting from $s=s_{\\max}$" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [], "source": [ "T = 21\n", "data = model.simulate(T, smax)" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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timeOre StockOre Extracted
0010.0000001.506241
118.4937591.222646
227.2711130.992446
336.2786670.805588
445.4730790.653912
\n", "
" ], "text/plain": [ " time Ore Stock Ore Extracted\n", "0 0 10.000000 1.506241\n", "1 1 8.493759 1.222646\n", "2 2 7.271113 0.992446\n", "3 3 6.278667 0.805588\n", "4 4 5.473079 0.653912" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "data.head()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Simulated State and Policy Paths" ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "scrolled": false }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig5, ax = plt.subplots()\n", "ax.set(title='State and Policy Paths',\n", " xlabel='Period', \n", " ylabel='Stock/Extraction',\n", " xlim=[0, T + 0.5])\n", "\n", "ax.plot(data[['Ore Stock', 'Ore Extracted']])\n", "ax.axhline(sstar, linestyle='--')\n", "\n", "\n", "ax.annotate(f'$s^* = {sstar:.2f}$', [T, sstar], ha='right', va='top', color='C0');" ] } ], "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": 1 }