{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Equilibrium"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Prepared for the [QuantEcon](http://quantecon.org/) Workshop on Computational Methods in HCMC\n",
    "\n",
    "#### John Stachurski, Nov 2016"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First we import some functionality from the scientific libraries"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "from scipy.optimize import bisect"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's write routines to compute supply and demand as functions of price and parameters:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "\n",
    "def supply(p, b):\n",
    "    return np.exp(b * p) - 1\n",
    "\n",
    "def demand(p, a, epsilon):\n",
    "    return a * p**(-epsilon)\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next we'll write a function that takes a parameter set and returns a market clearing price via bisection:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from scipy.optimize import bisect\n",
    "\n",
    "def compute_equilibrium(a, b, epsilon):\n",
    "    plow = 0.1\n",
    "    phigh = 10.0\n",
    "    def excess_supply(p):\n",
    "        return supply(p, b) - demand(p, a, epsilon)\n",
    "    pclear = bisect(excess_supply, plow, phigh)\n",
    "    return pclear"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's test it with the original parameter set, the market clearing price for which was 2.9334.  The parameters are\n",
    "\n",
    "$$ a = 1, \\quad b = 0.1, \\quad \\epsilon = 1 $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.9334108855344145"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "compute_equilibrium(1, 0.1, 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.433107128867579"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "compute_equilibrium(1, 0.1, 1.45)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercise\n",
    "\n",
    "For $\\epsilon$ in a grid of values between 1.0 and 1.5, plot the equilibrium price for each $\\epsilon$.\n",
    "\n",
    "One problem is that you need to **loop**.  That is, you need to evaluate \"compute_equilibrium\" for lots of different $\\epsilon$.  Here's a hint on how you might try that."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def f(x):\n",
    "    out = \"negative\" if x < 0 else \"nonnegative\"\n",
    "    return out\n",
    "\n",
    "vals = np.linspace(-1, 1, 5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-1. , -0.5,  0. ,  0.5,  1. ])"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vals"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['negative', 'negative', 'nonnegative', 'nonnegative', 'nonnegative']"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "[f(v) for v in vals]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Solution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The solution is below\n",
      "The solution is below\n",
      "The solution is below\n",
      "The solution is below\n",
      "The solution is below\n",
      "The solution is below\n",
      "The solution is below\n",
      "The solution is below\n",
      "The solution is below\n",
      "The solution is below\n",
      "The solution is below\n",
      "The solution is below\n",
      "The solution is below\n",
      "The solution is below\n",
      "The solution is below\n",
      "The solution is below\n",
      "The solution is below\n",
      "The solution is below\n",
      "The solution is below\n",
      "The solution is below\n",
      "The solution is below\n",
      "The solution is below\n",
      "The solution is below\n",
      "The solution is below\n",
      "The solution is below\n",
      "The solution is below\n",
      "The solution is below\n",
      "The solution is below\n",
      "The solution is below\n",
      "The solution is below\n",
      "The solution is below\n",
      "The solution is below\n",
      "The solution is below\n",
      "The solution is below\n",
      "The solution is below\n",
      "The solution is below\n",
      "The solution is below\n",
      "The solution is below\n",
      "The solution is below\n",
      "The solution is below\n"
     ]
    }
   ],
   "source": [
    "for i in range(40):\n",
    "    print(\"The solution is below\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1.0, 1.5)"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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9jfgX9cO/eO1so9WrV2N8zL4Qr7322hW9oIj4J2tkKDcvSGZuloNDZe3Ut7k5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\nAUcKOf3ullsbAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7facb3a160b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import seaborn as sb  # just to make it look pretty\n",
    "\n",
    "a, b = 1, 0.1\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(9, 6))\n",
    "epsilon_grid = np.linspace(1, 1.5, 100)\n",
    "\n",
    "prices = [compute_equilibrium(a, b, epsilon) for epsilon in epsilon_grid]\n",
    "\n",
    "ax.plot(epsilon_grid, prices, lw=2, alpha=0.6)\n",
    "ax.set_xlabel(\"epsilon\")\n",
    "ax.set_ylabel(\"equilibrium price\")\n",
    "ax.set_xlim(1.0, 1.5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python [default]",
   "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": "3.5.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}