{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Cournot Equilibrium 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: **demslv05.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-Sept-04\n", "
\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "- There are two firms producing same good\n", "- Total cost of producing $q_i$ in firm $i$:\n", "\\begin{equation*}\n", "C_i(q_i)=\\frac{\\beta_i}{2} q_i^2\n", "\\end{equation*}\n", "- Inverse demand function:\n", "\\begin{equation*}\n", "P(q_1+q_2)=(q_1+q_2)^{-\\alpha}\n", "\\end{equation*}\n", "- Firm $i$'s profits:\n", "\\begin{equation*}\n", "\\pi_i(q_1,q_2)=P(q_1+q_2)q_i-C_i(q_i),\n", "\\end{equation*}\n", "- Marginal profit for firm $i$:\n", "\\begin{equation*}\n", "\\frac{\\partial \\pi_i}{\\partial q_i} = P+P'q_i-C_i'=0\n", "\\end{equation*}\n", "- Therefore, equilibrium is characterized by solution to \n", "\\begin{equation*}\n", "f(q)=\\begin{bmatrix}P+P'q_1-C_1'\\\\ P+P'q_2-C_2' \\end{bmatrix} = \\begin{bmatrix}0\\\\ 0 \\end{bmatrix}\n", "\\end{equation*}\n", "- The Jacobian matrix for this function is\n", "\\begin{equation*}\n", "f'(q)= \\begin{bmatrix}2P'+P''q_1-C_1'' & P'+P''q_1\\\\ P'+P''q_2 & 2P'+P''q_2-C_2''\\end{bmatrix}\n", "\\end{equation*}\n", "- Define \n", "\\begin{align*}\n", "q &= \\begin{bmatrix}q_1\\\\ q_2\\end{bmatrix}; & \\beta &= \\begin{bmatrix}\\beta_1\\\\ \\beta_2\\end{bmatrix}; & C' &= \\begin{bmatrix}C'_1\\\\ C'_2\\end{bmatrix}= \\begin{bmatrix}\\beta_1q_1\\\\ \\beta_2q_2\\end{bmatrix} = \\beta \\odot q\n", "\\end{align*}\n", "where $\\odot$ denotes the Hadamard (element-by-element) product of two matrices.\n", "- Then we can rewrite the $f$ function and its Jacobian matrix as:\n", "\\begin{align*}\n", "f(q) &= P + (P' - \\beta) \\odot q \\\\\n", "f'(q) &= \\text{diag}(2P'+P''q - \\beta) + \\text{diag}(P'+P''q) \\begin{bmatrix}0 & 1\\\\ 1 & 0\\end{bmatrix}\n", "\\end{align*}\n" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from compecon import NLP, gridmake" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Parameters and initial value" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": true }, "outputs": [], "source": [ "alpha = 0.625\n", "beta = np.array([0.6, 0.8])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Set up the Cournot function" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def market(q):\n", " quantity = q.sum()\n", " price = quantity ** (-alpha)\n", " return price, quantity" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def cournot(q):\n", " P, Q = market(q)\n", " P1 = -alpha * P/Q\n", " P2 = (-alpha - 1) * P1 / Q\n", " fval = P + (P1 - beta) * q\n", " fjac = np.diag(2 * P1 + P2 * q - beta) + np.fliplr(np.diag(P1 + P2 * q))\n", " return fval, fjac" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We could also write the function and its Jacobian matrix more explicitly:\n", "\n", " def cournot(q):\n", " P, Q = market(q)\n", " P1 = -alpha * P/Q\n", " P2 = (-alpha - 1) * P1 / Q\n", " fval = [P + (P1 - beta[0]) * q[0], P + (P1 - beta[0]) * q[0]]\n", " fjac = [[2 * P1 + P2 * q[0] - beta[0], P1 + P2 * q[0]],\n", " [P1 + P2 * q[1], 2 * P1 + P2 * q[1] - beta[1]]]\n", " return fval, fjac\n", "\n", "However, the way it was defined earlier, in terms of matrix operations, is more convenient if we were to change the number of firms. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Compute equilibrium using Newton method (explicitly)" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Company 1 produces 0.8396 units, while company 2 produces 0.6888 units.\n", "Total production is 1.5284 and price is 0.7671\n" ] } ], "source": [ "q = np.array([0.2, 0.2])\n", "\n", "for it in range(40):\n", " f, J = cournot(q)\n", " step = -np.linalg.solve(J, f)\n", " q += step\n", " if np.linalg.norm(step) < 1.e-10: break\n", "\n", "price, quantity = market(q)\n", "print(f'Company 1 produces {q[0]:.4f} units, while company 2 produces {q[1]:.4f} units.')\n", "print(f'Total production is {quantity:.4f} and price is {price:.4f}')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Using a NLP object" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Solving nonlinear equations by Newton's method\n", "it bstep change\n", "--------------------\n", " 0 0 4.64e-01\n", " 1 0 9.53e-02\n", " 2 0 3.47e-03\n", " 3 0 4.20e-06\n", " 4 0 5.77e-12\n", "\n", "Company 1 produces 0.8396 units, while company 2 produces 0.6888 units.\n", "Total production is 1.5284 and price is 0.7671\n" ] } ], "source": [ "q0 = [0.2, 0.2]\n", "cournot_problem = NLP(cournot)\n", "q = cournot_problem.newton(q0, show=True)\n", "\n", "price, quantity = market(q)\n", "print(f'\\nCompany 1 produces {q[0]:.4f} units, while company 2 produces {q[1]:.4f} units.')\n", "print(f'Total production is {quantity:.4f} and price is {price:.4f}')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Generate data for contour plot" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": true }, "outputs": [], "source": [ "n = 100\n", "q1 = np.linspace(0.1, 1.5, n)\n", "q2 = np.linspace(0.1, 1.5, n)\n", "z = np.array([cournot(q)[0] for q in gridmake(q1, q2).T]).T" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Plot figures" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "pycharm": { "name": "#%%\n" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Solving nonlinear equations by Newton's method\n", "it bstep change\n", "--------------------\n", " 0 0 1.10e+00\n", " 1 0 4.64e-01\n", " 2 0 9.53e-02\n", " 3 0 3.47e-03\n", " 4 0 4.20e-06\n", "Solving nonlinear equations by Broyden's method\n", "it bstep change\n", "--------------------\n", " 0 0 4.64e-01\n", " 1 0 2.17e-01\n", " 2 0 5.45e-02\n", " 3 0 1.53e-02\n", " 4 0 1.04e-02\n", " 5 0 4.55e-03\n", " 6 0 1.33e-04\n", " 7 0 2.94e-07\n", " 8 0 1.34e-09\n" ] }, { "data": { "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "steps_options = {'marker': 'o',\n", " 'color': (0.2, 0.2, .81),\n", " 'linewidth': 1.0,\n", " 'markersize': 9,\n", " 'markerfacecolor': 'white',\n", " 'markeredgecolor': 'red'}\n", "\n", "contour_options = {'levels': [0.0],\n", " 'colors': '0.25',\n", " 'linewidths': 0.5}\n", "\n", "\n", "Q1, Q2 = np.meshgrid(q1, q2)\n", "Z0 = np.reshape(z[0], (n,n), order='F')\n", "Z1 = np.reshape(z[1], (n,n), order='F')\n", "\n", "methods = ['newton', 'broyden']\n", "cournot_problem.opts['maxit', 'maxsteps', 'all_x'] = 10, 0, True\n", "\n", "qmin, qmax = 0.1, 1.3\n", "\n", "fig, axs = plt.subplots(1,2,figsize=[12,6], sharey=True)\n", "for ax, method in zip(axs, methods):\n", " x = cournot_problem.zero(method=method)\n", " ax.set(title=method.capitalize() + \"'s method\",\n", " xlabel='$q_1$',\n", " ylabel='$q_2$',\n", " xlim=[qmin, qmax],\n", " ylim=[qmin, qmax])\n", " ax.contour(Q1, Q2, Z0, **contour_options)\n", " ax.contour(Q1, Q2, Z1, **contour_options)\n", " ax.plot(cournot_problem.x_sequence['x_0'], cournot_problem.x_sequence['x_1'], **steps_options)\n", "\n", " ax.annotate('$\\pi_1 = 0$', (0.85, qmax), ha='left', va='top')\n", " ax.annotate('$\\pi_2 = 0$', (qmax, 0.55), ha='right', va='center')" ] } ], "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 }