{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Introducción a la Programación en MATLAB (C12)\n",
    "\n",
    "Mauricio Tejada\n",
    "\n",
    "ILADES - Universidad Alberto Hurtado\n",
    "\n",
    "Agosto 2017"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Contenidos\n",
    "\n",
    "- [Aplicaciones III](#12.-Aplicaciones-III)\n",
    "    - [Linealización de una Función](#12.1-Linealización-de-una-Función)\n",
    "    - [Esperanza Matemática](#12.2-Esperanza-Matemática)\n",
    "    - [Duopolio de Cournot](#12.3-Modelo-de-Duopolio-de-Cournot)\n",
    "    - [Estimación por Máximo Verosimilitud](#12.4-Estimación-por-Máximo-Verosimilitud)\n",
    "    - [El Problema de Maximización del Consumidor](#12.5-El-Problema-de-Maximización-del-Consumidor)\n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 12. Aplicaciones III"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 12.1 Linealización de una Función\n",
    "\n",
    "Calculemos la aproximación de Taylor de primer orden de la función $$f (x, y) = xe^{-x^2-y^2}$$ alrededor del punto (1,1), esto es: $$f(x,y) ≈ f(1,1)+fx(1,1)(x−1)+fy(1,1)(y−1)$$\n",
    "\n",
    "El ejercicio consisten entonces en evaluar la función en el punto de aproximación f(1,1) y encontrar las derivadas parciales con respecto a x e y, y evaluarlas también en el punto de aproximación: $f_x(1,1)$ y $f_y(1,1)$.\n",
    "\n",
    "El primer paso es definir la función:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "fxy =\n",
      "\n",
      "  function_handle with value:\n",
      "\n",
      "    @(x)x(1)*exp(-x(1)^2-x(2)^2)\n"
     ]
    }
   ],
   "source": [
    "clear all;\n",
    "fxy = @(x) x(1)*exp(-x(1)^2-x(2)^2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Evaluamos la función en el punto $(1,1)$ y calculamos las derivadas parciales evaluada en ese mismo punto:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "fc =\n",
      "\n",
      "    0.1353\n",
      "\n",
      "\n",
      "df =\n",
      "\n",
      "   -0.1353   -0.2707\n",
      "\n",
      "\n",
      "fx =\n",
      "\n",
      "   -0.1353\n",
      "\n",
      "\n",
      "fy =\n",
      "\n",
      "   -0.2707\n",
      "\n",
      "\n",
      "fxyaprox =\n",
      "\n",
      "  function_handle with value:\n",
      "\n",
      "    @(x)fc-fx-fy+fx*x(1)+fy*x(2)\n"
     ]
    }
   ],
   "source": [
    "fc = fxy([1; 1])\n",
    "df = fdjac(fxy,[1; 1])\n",
    "fx = df(1)\n",
    "fy = df(2)\n",
    "\n",
    "fxyaprox = @(x) fc - fx - fy + fx*x(1) + fy*x(2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ans =\n",
      "\n",
      "    0.0067\n",
      "\n",
      "\n",
      "ans =\n",
      "\n",
      "   -0.1353\n"
     ]
    }
   ],
   "source": [
    "x=[1; 2];\n",
    "fxy(x)\n",
    "fxyaprox(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Así luce la aproximación:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
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eAAAwaTj3X8O4hvTfGEjcTF9zZl+lZgQ36ELjPGd+9Y9qiGdaWtOrvt5u2oqH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\nYDAYToAFCYPBYDCc4P8DuE6bFV7oJX0AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = 0.5:0.1:1.5;\n",
    "n = length(x);\n",
    "\n",
    "forig = zeros(n,n);\n",
    "faprox = zeros(n,n);\n",
    "X = zeros(n,n);\n",
    "\n",
    "for i = 1:n;\n",
    "    for j=1:n;\n",
    "        forig(i,j) = fxy([x(i);x(j)]);\n",
    "        faprox(i,j) = fxyaprox([x(i);x(j)]);\n",
    "        X(i,j) = x(j);\n",
    "    end;\n",
    "end;\n",
    "\n",
    "surf(x,x,forig);\n",
    "view(40, 10); "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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65O622OgKXmys29KlPvsP+B093hg/RHnkqJa/w50VvE3b6559RVWi1PF3kEt++q7XP14O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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "surf(x,x,faprox);\n",
    "view(30, 10);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 12.2 Esperanza Matemática\n",
    "\n",
    "Calculemos la esperanza matemática de una variable aleatoria normal $x$: $$E(x) = \\int^{\\infty}_{-\\infty} x f(x)dx$$ donde $f(x)$ es la función de densidad normal. Para esto escribimos la función en un m-file recordando que:\n",
    "\n",
    "$$f(x) = \\frac{1}{\\sigma \\sqrt {2\\pi}}e^{- \\frac{\\left( x - \\mu  \\right)^2}{2 \\sigma^2} }$$\n",
    "\n",
    "Note: Matlab tiene la densidad normal incorporada en el toolbox de estadísticas pero dejaremos esto para más adelante.\n",
    "\n",
    "```\n",
    "funtion int = integrando(x,mu,sigma)\n",
    "\n",
    "fx = (1./(sigma*sqrt(2*pi))).*exp(-(x-mu).^2./(2*sigma^2));\n",
    "\n",
    "int = x.*fx;\n",
    "\n",
    "end\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Ex =\n",
      "\n",
      "    3.0000\n"
     ]
    }
   ],
   "source": [
    "Ex = integral(@(x) integrando(x,3,2),-Inf,Inf)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "intf =\n",
      "\n",
      "  function_handle with value:\n",
      "\n",
      "    @(x,mu,sigma)x.*normpdf(x,mu,sigma)\n",
      "\n",
      "\n",
      "ans =\n",
      "\n",
      "    3.0000\n"
     ]
    }
   ],
   "source": [
    "intf = @(x,mu,sigma) x.*normpdf(x,mu,sigma)\n",
    "integral(@(x) intf(x,3,2),-Inf,Inf)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Usando la misma lógica calculemos $E(x^2)$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Ex2 =\n",
      "\n",
      "   13.0000\n"
     ]
    }
   ],
   "source": [
    "Ex2 = integral(@(x) integrando2(x,3,2),-Inf,Inf)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finalmente, usemos los dos resultados anteriores para calcular la varianza. Para ello recordemos que $$V(x) = E(x^2) - (E(x))^2$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Vx =\n",
      "\n",
      "    4.0000\n"
     ]
    }
   ],
   "source": [
    "Vx = Ex2 - Ex^2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 12.3 Modelo de Duopolio de Cournot\n",
    "\n",
    "*Aplicación tomada de Miranda y Fackler (2002), Capítulo 3.*\n",
    "\n",
    "Suponga que la demanda de mercado es provista por dos empresas 1 y 2. La función de demanda es:\n",
    "\n",
    "$$P(q) = q^{1/\\eta}$$\n",
    "\n",
    "con $q=q_1+q_2$. Laq función de costos de la empresa $i=1,2$ es:\n",
    "\n",
    "$$C_i(q_i) = 0.5c_iq^2_i$$\n",
    "\n",
    "Con esto es posible escribir la función de beneficios de la empresa $i$ como:\n",
    "\n",
    "$$\\pi(q_1,q_2) = P(q_1+q_2)q_i - C_i(q_i)$$\n",
    "\n",
    "Reemplazando tenemos:\n",
    "\n",
    "$$\\pi(q_1,q_2) = (q_1+q_2)^{1/\\eta}q_i - 0.5c_iq^2_i$$\n",
    "\n",
    "Cada firma busca maximizar su beneficio eligiendo la cantidad que produce y tomando como dada la decisión de la otra empresa.\n",
    "\n",
    "Las condiciones de primer orden son:\n",
    "\n",
    "$$(q_1+q_2)^{-1/\\eta} - (1/\\eta)(q_1+q_2)^{-1/\\eta-1} - c_iq_i = 0, \\ \\ \\ i=1,2$$\n",
    "\n",
    "Note que el equilibrio está caracterizado por la solución del sistema de dos ecuaciones no lineales anterior.\n",
    "\n",
    "Para resolver el modelo escribimos la siguiente función en un m-file:\n",
    "\n",
    "```\n",
    "function fval = cournot(q,c,eta)\n",
    "\n",
    "neq = length(q);\n",
    "fval = zeros(neq,1);\n",
    "\n",
    "q1 = q(1);\n",
    "q2 = q(2);\n",
    "\n",
    "c1 = c(1);\n",
    "c2 = c(2);\n",
    "\n",
    "fval(1) = (q1+q2)^(-1/eta) - (1/eta)*((q1+q2)^(-(1/eta)-1))*q1 - c1*q1;\n",
    "fval(2) = (q1+q2)^(-1/eta) - (1/eta)*((q1+q2)^(-(1/eta)-1))*q2 - c2*q2;\n",
    "\n",
    "end\n",
    "```\n",
    "\n",
    "Definimos los parámetros:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "clear all;\n",
    "c = [0.6; 0.6];\n",
    "eta = 1.2;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Usamos `fsolve` para encontrar la solución:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Equation solved.\n",
      "\n",
      "fsolve completed because the vector of function values is near zero\n",
      "as measured by the default value of the function tolerance, and\n",
      "the problem appears regular as measured by the gradient.\n",
      "\n",
      "\n",
      "\n",
      "\n",
      "qstar =\n",
      "\n",
      "    0.7186\n",
      "    0.7186\n"
     ]
    }
   ],
   "source": [
    "q0 = [0.2; 0.2];\n",
    "qstar = fsolve(@(x) cournot(x,c,eta),q0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "La idea de escribir la función dejando `c` y `eta` como inputs permite simular la solución bajo distintos niveles de costos y de la elasticidad de la demanda."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 12.4 Estimación por Máximo Verosimilitud \n",
    "\n",
    "Suponga que buscamos estimar el siguiente modelo de regresión lineal:\n",
    "\n",
    "$$y_i = \\beta_0 + \\beta_1 x_{1i}+ \\beta_2 x_{2i} + u_i$$\n",
    "\n",
    "por el método de máximo verosimilitud. Para ello suponemos que:\n",
    "\n",
    "$$u_i \\sim N(0,\\sigma^2)$$ \n",
    "\n",
    "Usaremos los datos que generamos para la aplicación sobre MCO."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "clear all;\n",
    "warning('off');\n",
    "impdata = importdata('DatosMCO.txt');\n",
    "[N, K]= size(impdata);\n",
    "y = impdata(:,1);\n",
    "X1 = impdata(:,2);\n",
    "X2 = impdata(:,3);\n",
    "\n",
    "X = [X1 X2];"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "La función de verosimilitud se define como:\n",
    "\n",
    "$$L(y,x1,x2|\\beta_0,\\beta_1,\\beta_2,\\sigma) = \\prod^n_{i=1} f(u_i)$$\n",
    "\n",
    "donde $f(u_i)$ es la función de densidad normal. Tomando logaritmos:\n",
    "\n",
    "$$\\ln L(y,x1,x2|\\beta_0,\\beta_1,\\beta_2,\\sigma) = \\sum^n_{i=1} \\ln f(u_i)$$\n",
    "\n",
    "El objetivo es maximizar $$\\ln L(y,x1,x2|\\beta_0,\\beta_1,\\beta_2,\\sigma)$$ eligiendo los parámetros $(\\beta_0,\\beta_1,\\beta_2,\\sigma)$.\n",
    "\n",
    "El primer paso es escribir la función de verosimilitud.\n",
    "\n",
    "Para ellos haremos uso del toolbox de estadísticas de Matlab. Dicho toolbox implementa muchas distribuciones, tanto discretas como continuas. Ahora usaremos la distribución normal.\n",
    "\n",
    "Las opciones para usar la distribución normal son:\n",
    "\n",
    "- `normpdf(x,mu,sigma)`: Función de densidad.\n",
    "- `normcdf(x,mu,sigma)`: Función de Distribución Acumulada\n",
    "- `norminv(Prob,mu,sigma)`: Inversa de la Función de Distribución Acumulada.\n",
    "- `normrnd(mu,sigma)`: Generados de números aleatorios.\n",
    "\n",
    "La lista de distribuciones que Matlab tiene implementadas puede verse [aquí](http://www.mathworks.com/help/stats/supported-distributions.html). En general la sintaxis es `distpdf`, `distcdf`, `distinv`, `distrnd` con `dist` el identificador de la distribución.\n",
    "\n",
    "```\n",
    "function lnL = loglike(par,y,X)\n",
    "\n",
    "beta0 = par(1);\n",
    "beta1 = par(2);\n",
    "beta2 = par(3);\n",
    "sig   = exp(par(4));\n",
    "\n",
    "N = length(y);\n",
    "\n",
    "L = zeros(N,1);\n",
    "\n",
    "for i=1:N\n",
    "    ui = y(i) - beta0 - beta1*X(i,1) - beta2*X(i,2);\n",
    "    L(i) = normpdf(ui,0,sig);\n",
    "end\n",
    "\n",
    "lnL = -sum(log(L));\n",
    "\n",
    "end\n",
    "```\n",
    "\n",
    "Maximizamos la función de verosimilitud:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Local minimum found.\n",
      "\n",
      "Optimization completed because the size of the gradient is less than\n",
      "the default value of the optimality tolerance.\n",
      "\n",
      "\n",
      "\n",
      "    2.9913    0.5640    0.8020   -0.0170\n"
     ]
    }
   ],
   "source": [
    "par0 = [2 0.1 0.1 log(2)];\n",
    "par = fminunc(@(x) loglike(x,y,X),par0);\n",
    "disp(par)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Recordemos que los datos fueron generados bajo el siguiente modelo:\n",
    "\n",
    "$$y_i = 3 + 0.5X_{1i} + 0.9X_{2i} + u_i$$\n",
    "\n",
    "donde $u_i \\sim N(0,1)$.\n",
    "\n",
    "Finalmente, la desviación estándar será: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "sig =\n",
      "\n",
      "    0.9832\n"
     ]
    }
   ],
   "source": [
    "sig = exp(par(4))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 12.5 El Problema de Maximización del Consumidor\n",
    "\n",
    "Suponga que un consumidor busca maximizar la siguiente función de utilidad:\n",
    "\n",
    "$$U(x_1,x_2,...,x_n) = \\sum^{n}_{i=1}x^{\\alpha_i}_i$$\n",
    "\n",
    "con $\\sum^{n}_{i=1}\\alpha_i = 1$. Sujeto a la restricción presupuestaria:\n",
    "\n",
    "$$p_1x_1 + p_2x_2 + ... + p_nx_n \\leq m$$ \n",
    "\n",
    "y las restricciones de no negatividad:\n",
    "\n",
    "$$x_i \\geq 0 $$\n",
    "\n",
    "con $m$ es ingreso y $p_i$ el precio del bien $i$.\n",
    "\n",
    "Escribimos una función en un m-file que tome un número arbitrario de bienes.\n",
    "\n",
    "```\n",
    "function u = utility(x,alpha)\n",
    "\n",
    "u = - sum(x.^alpha)\n",
    "\n",
    "end\n",
    "```\n",
    "\n",
    "Note que definimos la función de utilidad como negativa para maximizar (recuerde que `fmincon` minimiza).\n",
    "\n",
    "Maximicemos la utilidad bajo el supuesto que existen 4 bienes. \n",
    "\n",
    "Definimos los parámetros del modelo:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "clear all;\n",
    "alpha = [0.2 0.4 0.1 0.3]';\n",
    "p = [2 3 4 5];\n",
    "m = 100;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ahora definimos los parámetros de optimización:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "AI = p;\n",
    "bI = m;\n",
    "lb = [0 0 0 0]';\n",
    "ub = [Inf Inf Inf Inf]';"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Optimizamos:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Local minimum found that satisfies the constraints.\n",
      "\n",
      "Optimization completed because the objective function is non-decreasing in \n",
      "feasible directions, to within the default value of the optimality tolerance,\n",
      "and constraints are satisfied to within the default value of the constraint tolerance.\n",
      "\n",
      "\n",
      "\n",
      "    6.6759\n",
      "   20.3037\n",
      "    1.1586\n",
      "    4.2205\n"
     ]
    }
   ],
   "source": [
    "x0 = [1 1 1 1]';\n",
    "x = fmincon(@(x) utility(x,alpha),x0,AI,bI,[],[],lb,ub);\n",
    "disp(x);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ans =\n",
      "\n",
      "  100.0000\n"
     ]
    }
   ],
   "source": [
    "p*x"
   ]
  }
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