{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Monopolist's Effective Supply Function\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: **demapp10.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": {}, "source": [ "## Initial tasks" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from compecon import BasisChebyshev, NLP" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Residual Function" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "def resid(c):\n", " Q.c = c\n", " q = Q(p)\n", " marginal_income = p + q / (-3.5 * p **(-4.5))\n", " marginal_cost = np.sqrt(q) + q ** 2\n", " return marginal_income - marginal_cost " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Approximation structure" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "n, a, b = 21, 0.5, 2.5\n", "Q = BasisChebyshev(n, a, b)\n", "c0 = np.zeros(n)\n", "c0[0] = 2\n", "p = Q.nodes" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Solve for effective supply function" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "monopoly = NLP(resid)\n", "Q.c = monopoly.broyden(c0)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Plot effective supply" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "nplot = 1000\n", "p = np.linspace(a, b, nplot)\n", "rplot = resid(Q.c)" ] }, { "cell_type": "code", "execution_count": 6, "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=\"Monopolist's Effective Supply Curve\",\n", " xlabel='Quantity', \n", " ylabel='Price')\n", "ax.plot(Q(p), p);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Plot residual" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig2, ax = plt.subplots()\n", "ax.set(title='Functional Equation Residual',\n", " xlabel='Price',\n", " ylabel='Residual')\n", "ax.hlines(0, a, b, 'k', '--')\n", "ax.plot(p, rplot);" ] } ], "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 }