{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Introducción a la Programación en MATLAB (C1)\n",
    "\n",
    "Mauricio Tejada\n",
    "\n",
    "ILADES - Universidad Alberto Hurtado\n",
    "\n",
    "Agosto 2017\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Descripción**\n",
    "\n",
    "Este curso enseña programación en Matlab a aquellos que tienen muy poca o ninguna experiencia previa en el tema. Matlab es usado como programa base porque es fácil de aprender, es versátil, y es muy útil para el análisis numérico. Además es, por ahora, el estándar en la profesión. Cómo complemento, a lo largo del curso se presentarán diversas aplicaciones a problemas económicos. El curso requiere que el alumno acompañe las clases con su computador para replicar los ejercicios y aplicaciones provistas.\n",
    "\n",
    "**Material**\n",
    "\n",
    "[www.mauriciotejada.com](https://mauriciotejada.com) en la sección *Teaching* encontrarán *Introduction to Programming in Matlab*. Ahí estarán disponibles todos los *notebooks* y los archivos complementarios asociados a las clases.\n",
    "\n",
    "**Consultas y horas de oficina**\n",
    "\n",
    "Erasmo Escala 1835 Oficina 211 (Segundo Piso)\n",
    "\n",
    "[matejada@uahurtado.cl](mailto:matejada@uahurtado.cl)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Contenidos\n",
    "\n",
    "- [Motivación](#1.-Motivación:-Soluciones-Numéricas-vs-Soluciones-Algebraicas)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1. Motivación: Soluciones Numéricas vs Soluciones Algebraicas"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Para motivar tomamos el ejemplo presentado en el capítulo introductorio del libro de [Miranda y Fackler](https://mitpress.mit.edu/books/applied-computational-economics-and-finance).\n",
    "\n",
    "Consideremos la siguiente función de demanda: \n",
    "$$q=p^{-0.2}$$\n",
    "\n",
    "Dos preguntas fáciles de responder: \n",
    "\n",
    "1. ¿Cuál es la función inversa de demanda?\n",
    "2. ¿Cuál es el precio que clarea el mercado cuando la cantidad es 2?\n",
    "\n",
    "Respuestas:\n",
    "\n",
    "1. Solución algebraica:\n",
    "$$p=q^{-5}$$\n",
    "\n",
    "2. Usando una calculadora:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "p =\n",
      "\n",
      "    0.0312\n"
     ]
    }
   ],
   "source": [
    "p=2^-5"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ahora intentemos con una función de demanda algo diferente:\n",
    "$$q=0.5p^{-0.2} + 0.5p^{-0.5}$$\n",
    "\n",
    "Esta función contiene dos términos: \n",
    "- Una demanda doméstica.\n",
    "- Una demanda por exportación.\n",
    "\n",
    "Usando argumentos formales basados en los teoremas del Valor Intermedio y de la Función Implícita se puede establecer que la función inversa de demanda está bien definida, es continua y estrictamente decreciente. Por tanto, existe un único precio que clarea el mercado.\n",
    "\n",
    "Solución a las preguntas (1) y (2): No existe un solución cerrada para la función inversa de demanda. ¿Cómo calculamos el precio que clarea el mercado?\n",
    "\n",
    "**Alternativa:** Solución numérica."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.1542\n"
     ]
    }
   ],
   "source": [
    "p = 0.25;\n",
    "for i=1:100\n",
    "  deltap = (.5*p^-.2+.5*p^-.5-2)/(.1*p^-1.2 + .25*p^-1.5);\n",
    "  p = p + deltap;\n",
    "  if abs(deltap) < 1.e-8, break, end\n",
    "end \n",
    "disp(p);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Incluso podemos ver como luce la función de demanda inversa usando la misma idea:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.5000    8.3553\n",
      "    0.6000    4.6392\n",
      "    0.7000    2.8710\n",
      "    0.8000    1.9178\n",
      "    0.9000    1.3553\n",
      "    1.0000    1.0000\n",
      "    1.1000    0.7634\n",
      "    1.2000    0.5990\n",
      "    1.3000    0.4808\n",
      "    1.4000    0.3932\n",
      "    1.5000    0.3268\n",
      "    1.6000    0.2753\n",
      "    1.7000    0.2348\n",
      "    1.8000    0.2023\n",
      "    1.9000    0.1759\n",
      "    2.0000    0.1542\n",
      "    2.1000    0.1362\n",
      "    2.2000    0.1210\n"
     ]
    }
   ],
   "source": [
    "q = (0.5:0.1:2.2)';\n",
    "P = zeros(length(q),1);\n",
    "for j=1:length(q)\n",
    "    p = 0.25;\n",
    "    for i=1:100\n",
    "        deltap = (.5*p^-.2+.5*p^-.5-q(j))/(.1*p^-1.2 + .25*p^-1.5);\n",
    "        p = p + deltap;\n",
    "        if abs(deltap) < 1.e-8, break, end\n",
    "    end \n",
    "    P(j) = p;\n",
    "end;\n",
    "\n",
    "disp([q P]);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
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9Z84c65ZoH1HBOt7UBwAqsnzqufDw8M8++0wIcfHixbq6uu7du1uvKhUE6rXJB4oY1wAA\narHCXKhdu3Zt/0ZUZ9BrGdcAACoyK5AOHjy4bds2jUYzc+ZMIcSyZcsuX77c+iqzZ8+2QnV2ZNB5\nM6gBAFRkViAdOXIkKSnJ09NTCaQ1a9YUFxe3vorjBdL1CYR4SBYAVGFWIA0ZMmTu3LmmaRFmzpxp\nGlPnZPJLq0Ww2kUAgEsyK5D69u3bt29f06+PPfaYzepRU1SwroCrdgCgEsvngjt16tS6detMvx4+\nfPif//xnSUmJNapSx/AQ5vwGANVYGEiJiYl//OMf33vvPVNLQUHBnDlzRowYYd13T9gTEwgBgIos\nCaRNmzZ9/PHHQoj77rvP1BgRETF48OBr167Fx8dv2bLFagXaERMIAYCKLAmkzz//XPnv0qVLTY1B\nQUGrV69OSkoSQjTuOTkWZQIhtasAAFfU5kCqrq7Oycn53e9+98ADDzT/9P777+/bt+/Zs2cd9GYS\nEwgBgFraHEgXL15saGi48847b7ZAVFSUEKKwsLA9ZamIcQ0AoIo2B9Ltt9+u1WqPHz9+swWKioqE\nED169GhXXSoZHtKFcQ0AoIo2B5JGo+nXr9+xY8d2797d/NO8vLwffvjB39/f39/fGuXZm0HnrXYJ\nAOCiLBnU8OKLL9bX17/yyivLly8/d+6c0lhZWfmPf/xj4sSJFRUVEydOtGaNdqS8D4mrdgBgf5bM\n9j1ixIi4uLjExMSlS5cuXbrU09PTy8ursrJS+fT++++PjY21apF2ZdDxjj4AUIGFD8ZOmzZt/fr1\nUVFRygv6KisrPTw8+vXr9/7773/++eemWe8cEQPtAEAVlr8PacCAAStWrBBClJeXX7169fbbb3fo\nHDIZHtJlXkYeb+oDADuzPJAaGhr27t377bffFhcXDxw48OWXX05NTR04cGBwsGNPl80EQgCgCgsD\n6eTJk1OmTCkoKFB+9fX1FUKsXbv2jTfeeOGFF2bNmuXm5ma1Gu3LNIGQMsABAGAfllxky83NHT9+\nfEFBwahRo+bMmWNqHzt2rLe3d1JS0tdff229ClXABEIAYH+WBFJiYmJJScmcOXMSExPHjh1ran/u\nuee2bNni7e29YsWK+vp66xVpbwa9N+MaAMDOLAmk/fv3h4aGjh8/vvlHPXr0uPfee0tKSkzPJzki\ng07Lo0gAYGdtDqTi4uLz588PHDjwZgtEREQIIRx0clXF8JAuapcAAC6nzYHk7++v1WovXLhwswXy\n8vKEEAaDoT1lqYuBdgBgf5bMZRcREbFv377c3Nzmn546dWrnzp09e/b08/OzRnnqYAIhALA/S+4h\nzZ49u66uLjY2NjMzs6amRmk0Go0//PDD5MmTr1y58vLLL1u1SBUwgRAA2JlbQ0ODBaulpKQsXry4\nrq7O3d29rq7O09PTaDQajUYhxJ///Of58+dbu05LhIWFtfKajNbNy8gTQsTHMF8DAKfSnhOjrVk4\n2c/48eM3b948cuTITp06CSFqamp8fHyGDh26atUqSdKonYaHdOGSHQDYk+VTBwUHB3/66adCiNLS\n0vr6egd9AdLNMK4BAOyszYF0+fLlt956y9PTc/HixUqLXq+3dlVSyC8lkADAftp8yc7X1/eXX35J\nTU116CeNbsmg10YFc9UOAOzHkntIkZGRQohdu3ZZuxi5RAXrkg848HwTAOBYLAmk119//a677lqw\nYIG0QzWsYkJkAD0kALAbSwY1nD17durUqYsXL/7Tn/704IMPDhgwoHv37l5eXo2XeeSRR6xUoWoM\neq0yqV1UsE7tWgDA+VnyHNIDDzxQXFzc+jIydJ7aP9x+5YGi5ANF2+PutlZJAKAumZ9DsqSH9Oij\nj1ZWVlq9FAlFBevmbc2jkwQAdmBJIM2aNcvqdchJuWq3M6ecQAIAW7NkUINlsw05qPiYoJU/Fald\nBQA4vzYE0okTJ6ZMmRIVFdW/f/9Ro0bNmjWrsLDQdpVJIipYx/v6AMAOzA2kH3744bHHHsvMzCwq\nKjIajadPn/7Xv/718MMPHzt2zKb1yYAHkgDADswKpJqamnnz5hmNxoEDByYmJm7YsOH9998PDAys\nqqqaO3eujStUHw8kAYAdmDWoITs7+8yZM926dVu1apVWqxVC9O/ff8iQIaNGjTp48OClS5c6d+5s\n4zrVxANJAGAHZvWQlLeSjx49WkkjRbdu3YYOHSqEKCgosFFx8pgQGaC8IQkAYCNmBVJ5ebkQokeP\nHk3au3fvLoS4dOmS1cuSTVSwbsfJci7cAYDttGGUXZPJgVpscVYGvXZiZMDOnHK1CwEAp2XhG2NV\nVFVV9dRTT/33f/+3nb93QuTtPJAEALbjeIG0cOHCQ4cO2f9tTDyQBAA25WCBlJmZuWHDhsZjK+yJ\nB5IAwHbaMJfdggULFi5c2Lilvr5eCPHiiy+6ubk1WfjIkSPtL66JkpKSOXPmTJkyZf369VbfuDkm\nRAY8uCxLla8GAKfXhh6S0Wisu5ESSM3b6+rqbFHrX//614CAgClTpthi4+ZQHkhaeYA7SQBgfWb1\nkB566KE777zT1qW0bu3atbt3796wYYNGo1GxjPiYoHkZeRMjA1SsAQCcklmB1LVr165du9q6lFbk\n5+cvWrRo+vTpffv2VbEMIYRB5608kMSsDQBgXQ4wqMFoNM6ePTs8PPz5559v67ph1yUkJFilGB5I\nAuBwEhISTCdDtWtpjSUv6LOzxMTE7OzsTZs2dejQ5vi0xZt6J0TePmnt0fiYIKtvGQBsYerUqVOn\nTlV+ljmTZO8hHTp0aPny5VOmTNHr9ZXX1dfX19fXV1ZWXr161f4l8UASANiC7D2kw4cPG43GDz74\n4IMPPmjcfu7cucGDB/fr12/Tpk32r0qZazUqjttIAGA1sgdS//794+LimjSmpKR4e3s//fTT/v7+\nqlQVFaybt5XJvwHAmmQPpDvuuOOOO+5o0piamqrT6aZPn65KSaLRA0mM/wYAa5H9HpK04mOCknlC\nFgCsh0CykOmBJLULAQAnIfsluxZt375d7RL+80BS8oFzPCELAFZBD8ly8dFB9JAAwFoIJMspQxvI\nJACwCgKpXZQHktSuAgCcAYHULlHBuvyyarWrAABnQCC1C29IAgBrIZDaKz4miFkbAKD9CKT2Mui8\n80urGdoAAO1EILWXQa+dGx2UfOCc2oUAgGMjkKxgQmQAPSQAaCcCyQp4IAkA2o9Asg4eSAKAdiKQ\nrIMHkgCgnQgk61Cu2tFJAgCLEUhWEx8TtPInnpAFAAsRSFZj0HkLIRjaAACWIZCsxqDXbp9y96S1\nR9UuBAAcEoFkTYz/BgCLEUhWxvhvALAMgWRlyvjv/FKGgANA2xBIVqZctUvmhRQA0EYEkvUx/hsA\nLEAgWZ9B583QBgBoKwLJ+gx6bVSwjhdSAECbEEg2wQspAKCtCCSb4IEkAGgrAslWeCAJANqEQLIV\n5YEkOkkAYCYCyVYMem18dBBT2wGAmQgkG5oYGRAVrCOTAMAcBJJtxUcH7ThZxoU7ALglAsm2DHrt\nV+PCJ609yux2ANA6AsnmooJ1EwcHTFr7m9qFAIDUCCR7mBAZIIRgFDgAtIJAsgeDXvvVuIiVPxVx\n4Q4AboZAshODXjtxcMCDy7LULgQAJEUg2c+EyACDTsuFOwBoEYFkP6YLd4wCB4DmCCS7YvoGALgZ\nAsnemL4BAFpEIKmA6RsAoDkCSQVM3wAAzRFI6mD6BgBogkBSDdM3AEBjBJJqmL4BABojkNTE9A0A\nYEIgqYzpGwBAQSCpjOkbAEBBIKmP6RsAQAjhrnYB5kpNTd25c+eJEyf8/PwGDBjwwgsvdO/eXe2i\nrGZiZMDOk+WT1h79aly42rUAgDocoIdkNBrj4uLeeOONH374oWvXrhcvXkxJSYmOjv7pp5/ULs2a\nmL4BgItzgED6+9///v33399///27d+9OSUnZunXr//7v/1ZXV8+cObO2tlbt6qyG6RsAuDgHCKSV\nK1e6u7svXLhQq9UqLU8//fT9999fXFx84sQJdWuzLqZvAODKZA+khoaGwsLCsLCw2267rXF7UFCQ\nEOLMmTMq1WUrTN8AwGXJPqjBaDTOmzev+fiFnJwcIYTBYFChJltSRoE/uCxrQmSAQa9VuxwAsB/Z\ne0ju7u5PPvnksGHDGjfu2bPnxx9/DAkJCQkJUasw22H6BgCuSfZAau67776Li4vz8vKaP3++RqNp\nfeGw6xISEuxTnlUwfQMAK0pISDCdDNWupTVuDQ0NatdgroqKinfeeWfDhg3+/v4fffTR4MGDW18+\nLCzs+PHj9qnN6vJLqx9clvXVuPCoYJ3atQBwHjKfGB2mh5SZmfnwww9v2LBhzJgxaWlpt0wjR2ea\nvoFR4ABchOyDGhRfffXVokWLevbsmZycfO+996pdjp1MjAwoKK1+cFnWxMEB8TFBapcDALblAD2k\nzMzMRYsWDR48ePPmza6TRor4mKDtU+7ecbKM+0kAnJ7sgWQ0GhctWtSpU6cVK1b4+vqqXY4KTNOB\nk0kAnJvsl+xycnIKCgr69OmzdOnS5p9OmjSpV69e9q/Kzgx67fYpd8/bmhe0YM/2KXfzfBIApyR7\nIP36669CiFOnTq1atar5p2PHjnWFQBLXxzgYDmgfXJZFJgFwSo407LutZB7daLF5GXkrfyqKjw6a\nGBmgdi0AHI/MJ0bZe0hoIj4maHhIl0lrjxaUVjP0DoAzkX1QA5qLCtZtn3I3wxwAOBkCySEpwxx2\nnCx78FOmvAPgJAgkR6UMB48K1gUt2MNsDgCcAIHkwAx6bXxMkDI1OJkEwNERSA4vPiYoPjrowWVZ\n3FIC4NAYZecMJkYGRAXrlFcoMfQOgIOih+QklGEOK38qmrT2qNq1AIAlCCTnoWSSQadlmAMAR0Qg\nORWDXjshMoBhDgAcEYHkbBoPvWOYAwAHQiA5J+VFSszmAMCBEEhOS7mllF9WHbRgD7EEQH4EkjMz\n6LVfjQtXJhkilgBIjkByfga9dnvc3aZYWnmgSO2KAKAFBJKrUGIpPjpIefPsjpNlalcEADdgpgbX\noszpkHygaNLaowadNj4mKCpYp3ZRACAEPSQXpIwL3z7l7qhg3YOfHpy09ihPLAGQAYHkopRYypsz\n1KDTKk8sEUsA1EUguTRTb0kIwYO0ANRFIOGGWGJ0OAC1EEj4D1Ms8dASAFUQSLgBDy0BUAuBhBaY\nHlpKPlCk9JZ4bgmArfEcEm5qYmTAxMiA/NLq5ANFD3560KDXThwcMCEywKDXql0aACdEIOEWlHtL\nEyID8suqkg+cC1qwx6DXxkcHTYwMULs0AE7FraGhQe0abCUsLOz48eNqV+Fs8kurd5ws23myfMfJ\nsqhg3fDgLiQT4EBkPjESSLCQkkzJB4ryy6qjgnUTIm9nFiJAfjKfGAkktJdyk2nHyTKSCZCfzCdG\nAglWoyTTyp+KhBATBwcMD+lCMgGykfnESCDB+vJLq+dtzVt5oEgZmEcyAfKQ+cRIIMFWTMMflGRS\nRkAoP6hdGuC6ZD4xEkiwB1M45ZdWKbeaCCdAFTKfGAkk2FuTcDLotFHBOi7rAfYh84mRQIKaCCfA\nzmQ+MRJIkAXhBNiBzCdGAgkyahJOQgjltpPyA5PpARaT+cRIIEF2+aXV+WVV+aXVSj7tOFlu0GsN\nOq1B783ICKCtZD4xMrkqZGfQaw16rQgWpknzGkdU8oGqB08eJKIAJ0AgwfE0iaj80mohhHKJT5lb\nT1nMNLjcoPPmKh8gPwIJDk8Jm4n6gJt1oXacLFcWM/WilF/pSAFSIZDghFq8yieEUN57q9yLEkIo\n1/qEEEoyKd0p068A7IxAgksw9aKEEI1f4GTqSwkhlO5Ufll1fmm1qTslCCrAXhhlBzSl5JPpop8Q\nQhl9rgSVEMKUVQadNlDpjRFXcBAynxgJJKANGmeVEML8uGJgBSQh84mRQAKspvW4EtevHBp0WiFE\n49Bq9BG5BduS+cTIPSTAagymaAkW4sabVYomiVVQWp1fVp1fVq0MsjA/twTRBWdEIAH20ySxbuZm\nuSWESD7wn+gyLdYoov5zqVA0CjDRqO/VeGFAQgQSIB0zc0tczyQhRH5ZlenXghsvGIobA0zcGEuN\n+2GmX5uEmSDPYBcOE0jbtm1LS0vLycnx9fUNDQ2NjY0NDAxUuyhAZYYmyXGrAFO0GGPiepKZemNK\nmIlmeSZajTRTi2gp2MT1bBPEG5pxjEENCxYsSElJ8fLyioiIqKioyM3N9fLyJb04EAAAD6xJREFU\nSkxMHDZsWCtryXzvDnBcjZOpSaSJ66kmrseYaBRsNzb+/yqipYS73t5CzolGUdd8ddEo85p/BJlP\njA4QSPv27Rs/fnyfPn1WrlzZs2dPIURGRsarr77arVu3jIwMrfamR5vM+x2ASfOEa95ecMMyjX5u\nlHbNProh8xTN86lxzokbI7DJAoF6bfOBKg5H5hOjA1yyW79+vRBi1qxZShoJIWJiYkaPHp2enr57\n9+6RI0eqWp3zS0hImDp1qtpVODb2Yetu6B41Dowbr0C2czc2z6fG4dfiAgUtRRpsxwF6SMOHD79w\n4UJWVlbjzlB6evrMmTPHjx8/Z86cm60o8x8CDoTd2H7sQ6tgN1qFzLuxg9oF3EJtbe358+d79uzZ\n5NJccHCwEOLMmTMq1QUAsDLZA6mioqK+vr5z585N2pWWS5cuqVEUAMD6ZL+HVFtbK4Rwd29ap9Ki\nfNqKsLAwGxXmUtiN7cc+tAp2o3OTPZA0Go1oKXiUFuXTm5H2OikAoDnZL9l5e3sLIaqqqpq0Ky3K\npwAAJyB7IPn6+nbq1On06dNGo7Fxe35+vhAiIMDhnwkAAChkDyQhRHh4eE1NzZEjRxo3ZmVlCSEi\nIiJUKgoAYGUOEEjR0dFCiCVLlphaioqKVq9erdFoRowYoV5dAABrcoAHY2trax977LGcnJz+/fuP\nGTOmuLg4PT29pKRk8uTJs2bNUrs6AIB1OEAgCSFKSkrefvvtbdu2KXeSfHx8XnrppdjY2NZH2QEA\nHIhjBBIAwOk5wD0kAIArIJAAAFIgkAAAUiCQAABSkH0uu5vZtm1bWlpaTk6Or69vaGhobGxsYGBg\n66ts2bJl+/btTRq7du365ptv2qxMh3fp0qXHH3/8+eeff+6559SuRXZt2lccjeZLTU3duXPniRMn\n/Pz8BgwY8MILL3Tv3l3toiRlwb6S6lB0yEBasGBBSkqKl5dXRERERUXFunXrNm3alJiYOGzYsFbW\nSk9Pz8zM9PHxadzYo0cPGxfr2JKSks6ePXvlyhW1C3EAbdpXHI3mMBqNU6dO/f777319ffv373/u\n3LmUlJR169Z98cUXgwcPVrs6uVi8r+Q6FBsczd69e0NDQ0eNGnXmzBml5dtvvw0PD3/ggQeqqqpa\nWXHkyJF/+ctf7FKjY6urq8vLy9uxY8eMGTNCQ0NDQ0OXL1+udlEyqqurs3hfcTSaY/Xq1cr1D9P/\n2uvWrQsNDb3//vtramrUrU02Fu8rqQ5Fx+shrV+/Xggxa9asnj17Ki0xMTGjR49OT0/fvXv3yJEj\nW1zr6tWrZ86ciYqKsludjis3N3fs2LFqV+EAcnNzhRAW7CuORjOtXLnS3d194cKFphdGP/300xkZ\nGf/+979PnDjRv39/dcuTimX7SrZD0fECad++fRqNZvjw4Y0bR44cmZ6evnfv3psF0okTJxoaGvr1\n62eXGh1bQEDAxx9/rPz866+/JiUlqVuPtJTJ5i3YVxyN5mhoaCgsLAwLC7vtttsatwcFBf373/8+\nc+YMgWRi8b6S7VB0sECqra09f/58r169TH8FKIKDg4UQZ86cudmKysv6br/99iVLlhw+fNjb2zss\nLOy//uu//P39bV2zw/H19Y2JiVF+bv6uXpj4+voKISzYVxyN5jAajfPmzWt+Tz4nJ0cIYTAYVKhJ\nVhbvK9kORQc73VRUVNTX13fu3LlJu9Jy6dKlm62o7PcZM2Zcu3bNYDCcPn16+/bt33zzzUcffTR0\n6FCb1gw0wdFoDnd39yeffLJJ4549e3788ceQkJCQkBBVqpKTxftKtkPRwZ5DUt5c3vxPUaWl+ZvO\nTY4fP+7m5vbCCy/89NNP//rXv37++ecZM2ZUVFS8+eably9ftmnNQBMcjZb57rvv4uLivLy85s+f\nz8TKrTNzX8l2KDpYD0nZs82DR2lpZb9/+OGHtbW1prGMGo1mypQpubm5mzdvzsjIaP7HBWA7HI1t\nVVFR8c4772zYsMHf3/+jjz66++671a5IXm3aV7Idig7WQ/L29hZCVFVVNWlXWpRPW9StW7fmI+uV\nV/9lZ2dbuUqgVRyNbZKZmfnwww9v2LBhzJgxaWlpPIHUirbuK9kORQfrIfn6+nbq1On06dNGo7Fx\nfyg/P19cH/XUovr6ejc3Nzc3tyZbE0JcvHjRVuUCLeFoNN9XX321aNGinj17Jicn33vvvWqXIzUL\n9pVsh6KD9ZCEEOHh4TU1NUeOHGncmJWVJYSIiIhocZX8/Pzw8PCZM2c2aVdu6HF3FPbE0Wi+zMzM\nRYsWDR48ePPmzaRR6yzYVxIeio4XSEp3csmSJaaWoqKi1atXazSaESNGKC2lpaUZGRkZGRnKvaXA\nwEC9Xp+ZmXns2DHTWuXl5V988YW7u/sf//hH+/4L4Fo4Gi1jNBoXLVrUqVOnFStWKH+z42bM3Ffy\nH4oOdslOCDFu3Li1a9fu37//iSeeGDNmTHFxcXp6elVV1eTJk00XQ7Ozs6dNmyaE2L9/f+fOnd3c\n3ObOnTtt2rRx48Y9++yzYWFhSoZduHBh+vTpv/vd71T9B8HJcTRaJicnp6CgoE+fPkuXLm3+6aRJ\nk3r16mX/quRk5r6S/1B0vEDy8PBITk5+++23t23bply48/Hxee2112JjY1tZKyYmZtmyZe+9996X\nX34phHBzc+vTp88nn3zCH6SwP45Gc/z6669CiFOnTq1atar5p2PHjiWQTCzeV7Idim4NDQ2qfHH7\n1dbW5ufn+/j4BAQENLkp14ry8vKioqI+ffo0md0WsD+ORkhCkkPRgQMJAOBMHG9QAwDAKRFIAAAp\nEEgAACkQSAAAKRBIAAApEEgAACkQSAAAKRBIAAApEEgAACkQSAAAKRBIAAApON5s34Blzp49m5WV\ndfjw4d9++83b2zswMHDIkCEjR440f2Zeq8jOzt63b1///v3vuuuu1pfcvHlzRUXFk08+6e3t3f7v\nte7WAFtgclW4hOTk5Hfffbeurq5Je2ho6Pz58++8804bfW9aWlpxcfHjjz+u1+uVljVr1sydO/eF\nF16YPXt26+tGR0cXFBTs2rWrW7du7a/EulsDbIEeEpxcTU3Na6+9tnXrVk9Pz8mTJw8aNGjgwIHV\n1dWHDh36/PPPjxw5Mnny5G+++aZv3762+PbVq1dnZWXdd999pkDq0KGDp6enRqOxxdcBDo1AgpP7\n5ptvtm7dqtPpli1b1vgqWa9evaKjo1955ZXMzMxXX301LS3NPvU888wzzzzzjH2+C3AsDGqAM6us\nrFy2bJkQYvHixc3v2Wg0moULF3p4eGRnZ584caL56uXl5QUFBWVlZa1/S01Nzblz59p/9fvatWun\nT5+uqam55ZLmFGb+1gBJ0EOCM1u7dm15eXlYWNjw4cNbXECn0/3tb387e/bslStXTI1lZWXLli3b\nuHFjRUWF0tKnT5/Y2Nhx48Ypv3722WerVq1auHBhx44d33///UOHDl27dq1jx45jxoz5n//5n44d\nOwohXnzxxaNHj5aWlgohnn/+eXd392eeeebll19OTU394IMPnn322SlTppi+cePGjV9//fXx48fr\n6uq0Wm10dPTrr7/evNpbFtamrQGyIZDgzI4cOSKEePTRR1tZ5s9//nPjX69evRobG3vkyJFOnToN\nGzasd+/eubm5+/fvj4+P79Sp05gxY4QQlZWVxcXF+/btW716dbdu3WJiYgoLC3/++ed//OMfly9f\n/vDDD4UQ3t7enTp1unTpUm1tbceOHb28vLy8vIQQVVVVxcXFly9fNn3j/PnzV61apdFoBgwYEBIS\nkp2dnZ6efujQocYZaWZh5m8NkBCBBGeWn58vhOjdu7f5q2zZsuXIkSMPPPDA8uXLTUMPPv30048+\n+mj79u2m874Q4rPPPpsyZcq0adM6dOgghPjll1+eeeaZjIyM8+fP33bbbUosPfvss1lZWZ988km/\nfv1a/Lq9e/euWrXKx8dn+fLl99xzj9L4888/x8XFlZeXt7Uw87cGSIh7SHBmSiD16NHD/FXOnTsX\nHh4+YcKExgPhhg4dKoQoKChovGS/fv2mT5+upJEQ4s4774yIiKivrz916pT5X5eYmCiEeOmll0z5\nIYQYNGjQa6+9ZkFh5m8NkBCBBGem1WqFEJcuXTJ/lVdeeSU1NXXYsGHKr0aj8cSJE8uXL2++5LBh\nw5o8VBsSEiKEaFNf5NChQ0KIP/3pT03aH3vsMQ8Pj7YWZv7WAAlxyQ7OLDAwsKysrLCwsJVlSkpK\nSkpK/Pz8TB2pqqqqLVu27Nu379ixY/n5+deuXWvxbN69e/d2lnfhwoWqqiovL6/mm/L09OzRo0eT\nPlnrhbV1a4BsCCQ4sz59+vzyyy+//fZbK8u88847aWlpcXFx06dPF0L89ttvsbGxpaWlPXv2jIyM\nfOihh0JCQm677bYmYx+EEO2fc0gZKe7u3vL/hk0enr1lYW3aGiAhAgnObOjQoZs3b05NTX311Vc7\nd+7cfIH6+vqsrCwhxJAhQ5SWmTNnlpaWzpgxo/Gw7OzsbFuUd9ttt3l7e1+5cuXixYtdu3Zt/JHR\naCwqKmrccsvC2rQ1QELcQ4Ize/TRR4OCgqqqqhISElpcYM2aNYWFhX5+fsp0dmVlZXl5eV5eXrGx\nsY0XO3nypI0qHDhwoBAiNTW1SfvWrVurqqpMv5pZmJlbA+REIMGZaTSaGTNmCCG+/vrrN998s7a2\ntvGnmzdvXrJkiRBi7ty5yvAHjUbj5uZWU1NTUlJiWuzMmTPKYk1WN4dyAe3q1as3WyAuLk4IsWLF\nioMHD5oaCwoK3n333Sb/EHMKM3NrgJy4ZAcnN3r06IULF7799tsbN278/vvv77jjjoEDB5aXlx86\ndOjw4cNCiGeffdb0dJGfn99dd92VlZU1bty4Rx55RKvVnjx5MjMzc+DAgcXFxXl5ee+9996sWbPM\n//bevXvv379/2rRpISEho0ePbjKlghDiD3/4w1NPPfXPf/5zwoQJw4YN69evX25u7u7du3U6nV6v\nVyZ6ML8wM7cGyIkeEpzfk08+uW7duiFDhtTV1e3atWvZsmVr1qw5fPhwcHDwF198MXfu3MYLL126\ndOjQocXFxUlJSZ988snu3btjY2NTUlJGjBhRXV2dlJTUpjnrXnzxxbvuuuvy5cs//vhjXl5ei8ss\nWLDgr3/9q7+///fff5+YmLh169a+fft+8803nTp1sqAwM7cGSIj3IcGF1NfXFxQUZGdnd+vWLSgo\nqEuXLjdbsqSkpLCwsFu3bgEBAabG7Ozs7t27+/n52ai80tLSoqKi4OBg5fphOwszZ2uAVAgkAIAU\nuGQHAJACgQQAkAKBBACQwv8B/CK4eOZa44cAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(q,P);\n",
    "ylabel('Precio');\n",
    "xlabel('Cantidad');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Incluso podríamos usar interpolación lineal para evaluar puntos de la función de demanda fuera de los encontrados en la tabla que caracteriza la demanda:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "pi =\n",
      "\n",
      "    0.3560\n"
     ]
    }
   ],
   "source": [
    "pi = interp1(q,P,1.456)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Matlab",
   "language": "matlab",
   "name": "matlab"
  },
  "language_info": {
   "file_extension": ".m",
   "help_links": [
    {
     "text": "MetaKernel Magics",
     "url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md"
    }
   ],
   "mimetype": "text/x-octave",
   "name": "matlab",
   "version": "0.9.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}