labs/lab-2/lab 2 HW.ipynb

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   "cells": [
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "I highly recommend that you take a glance through [Frank Ramsey's](http://en.wikipedia.org/wiki/Frank_P._Ramsey) original paper, entitled [A Mathematical Theory of Saving](http://folk.uio.no/gasheim/zRam1928.pdf).  In particular the introduction where Ramsey states that the common practice amongst economists and decision theorists of discounting the future was \"ethicially indefensible and arises mearly from the weakness of the imagination.\"  Ramsey leaves little doubt that his paper was normative and not positive in character.  Finally, there is not a single citation at the end of Ramsey's paper: he simply signed his name!  Apparently, for this model at least, Ramsey owed no intellectual debts. "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%load_ext autoreload\n",
      "%autoreload 2"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 29
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# These libaries will be doing the bulk of the heavy lifting!\n",
      "import numpy as np\n",
      "import pandas as pd\n",
      "import sympy as sp\n",
      "from scipy import linalg\n",
      "\n",
      "# these models contain all of the code\n",
      "import ramsey\n",
      "import pwt\n",
      "\n",
      "# matplotlib is for graphics\n",
      "import matplotlib as mpl\n",
      "import matplotlib.pyplot as plt"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from sympy.interactive import printing\n",
      "printing.init_printing(use_latex=True)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 273
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# define symbolic variables\n",
      "k = sp.symbols('k')\n",
      "\n",
      "# define symbolic parameters\n",
      "alpha, sigma = sp.symbols('alpha,sigma')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 274
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# define symbolic expressions \n",
      "rho = (sigma - 1) / sigma\n",
      "f   = (alpha * k**rho + (1 - alpha))**(1 / rho)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 275
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Part a) (5 points)\n",
      "The code in the cell below will compute the derivative of $f$ with respect to $\\sigma$ and simplify it as much as possible. You job is to simplify it further! HINT: You may wish to make use of the following relationship:\n",
      "\n",
      "$$ \\alpha_k(k) = \\frac{kf'(k)}{f(k)} = \\frac{\\alpha k^{\\sigma-1}{\\sigma}}{\\alpha k^{\\sigma-1}{\\sigma} + (1 + \\alpha)} \\tag{1}$$"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# always check the docstring!\n",
      "sp.diff?"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 373
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# differentiate f with respect to sigma and simplify\n",
      "df_dsigma = sp.diff(f, sigma).simplify()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 374
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# can you simplify this result further?\n",
      "df_dsigma"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$$\\frac{\\left(\\frac{\\alpha k^{\\frac{\\sigma -1}{\\sigma}} \\left(1 + \\frac{- \\sigma + 1}{\\sigma}\\right) \\log{\\left (k \\right )}}{\\alpha k^{\\frac{\\sigma -1}{\\sigma}} - \\alpha + 1} - \\left(\\frac{\\sigma}{\\sigma -1} -1\\right) \\log{\\left (\\alpha k^{\\frac{\\sigma -1}{\\sigma}} - \\alpha + 1 \\right )}\\right) \\left(\\alpha k^{\\frac{\\sigma -1}{\\sigma}} - \\alpha + 1\\right)^{\\frac{\\sigma}{\\sigma -1}}}{\\sigma -1}$$"
       ],
       "metadata": {},
       "output_type": "pyout",
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       "prompt_number": 375,
       "text": [
        "                                                                              \n",
        "\u239b   \u03c3 - 1                                                        \u239e            \n",
        "\u239c   \u2500\u2500\u2500\u2500\u2500                                                        \u239f            \n",
        "\u239c     \u03c3   \u239b    -\u03c3 + 1\u239e                         \u239b   \u03c3 - 1        \u239e\u239f \u239b   \u03c3 - 1  \n",
        "\u239c\u03b1\u22c5k     \u22c5\u239c1 + \u2500\u2500\u2500\u2500\u2500\u2500\u239f\u22c5log(k)                  \u239c   \u2500\u2500\u2500\u2500\u2500        \u239f\u239f \u239c   \u2500\u2500\u2500\u2500\u2500  \n",
        "\u239c         \u239d      \u03c3   \u23a0          \u239b  \u03c3      \u239e    \u239c     \u03c3          \u239f\u239f \u239c     \u03c3    \n",
        "\u239c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 - \u239c\u2500\u2500\u2500\u2500\u2500 - 1\u239f\u22c5log\u239d\u03b1\u22c5k      - \u03b1 + 1\u23a0\u239f\u22c5\u239d\u03b1\u22c5k      -\n",
        "\u239c         \u03c3 - 1                 \u239d\u03c3 - 1    \u23a0                      \u239f            \n",
        "\u239c         \u2500\u2500\u2500\u2500\u2500                                                  \u239f            \n",
        "\u239c           \u03c3                                                    \u239f            \n",
        "\u239d      \u03b1\u22c5k      - \u03b1 + 1                                          \u23a0            \n",
        "\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "                                          \u03c3 - 1                               \n",
        "\n",
        "         \u03c3  \n",
        "       \u2500\u2500\u2500\u2500\u2500\n",
        "       \u03c3 - 1\n",
        "      \u239e     \n",
        "      \u239f     \n",
        "      \u239f     \n",
        " \u03b1 + 1\u23a0     \n",
        "            \n",
        "            \n",
        "            \n",
        "            \n",
        "\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "            "
       ]
      }
     ],
     "prompt_number": 375
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Part b) (5 points)\n",
      "\n",
      "The code in the cell below computes...\n",
      "\n",
      "$$\\lim_{\\sigma \\rightarrow 1}\\ \\frac{df}{d\\sigma}$$\n",
      "\n",
      "What is the sign of the resulting limit? Is is positive? Negative? Or indeterminate? What does this imply about the sign of a small shock to $\\sigma$ when the production function is Cobb-Douglas?"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# always read the docstring\n",
      "sp.limit?"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 366
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# limit as sigma -> 1\n",
      "sp.limit(e=df_dsigma, z=sigma, z0=1)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$$\\frac{1}{2} \\alpha \\left(- \\alpha + 1\\right) e^{\\alpha \\log{\\left (k \\right )}} \\log^{2}{\\left (k \\right )}$$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAM0AAAAfCAYAAABESklNAAAABHNCSVQICAgIfAhkiAAACKxJREFU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\nrgAAAABJRU5ErkJggg==\n",
       "prompt_number": 367,
       "text": [
        "            \u03b1\u22c5log(k)    2   \n",
        "\u03b1\u22c5(-\u03b1 + 1)\u22c5\u212f        \u22c5log (k)\n",
        "\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "             2              "
       ]
      }
     ],
     "prompt_number": 367
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Part c): (10 points)\n",
      "\n",
      "Determining the sign of $\\frac{df}{d \\sigma}$"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# create a numpy function from the symbolic expression for df_dsigma\n",
      "df_dsigma_num = sp.lambdify(args=(k, alpha, sigma), expr=df_dsigma, modules='numpy')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 361
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.figure(figsize=(8,6))\n",
      "kgrid = np.linspace(0, 10, 1000)\n",
      "\n",
      "# specify some numeric values for alpha and sigma (you may wish to change these!)\n",
      "tmp_alpha = 0.5\n",
      "tmp_sigma = 0.5\n",
      "\n",
      "plt.plot(kgrid, df_dsigma_num(kgrid, tmp_alpha, tmp_sigma), \n",
      "         label=r'$\\alpha=%g, \\sigma=%g$' %(tmp_alpha, tmp_sigma))\n",
      "\n",
      "plt.axhline(0, ls='dashed', color='k')\n",
      "\n",
      "# add axes label, title, legend, etc\n",
      "plt.xlabel('Capital per effective worker, $k$', fontsize=15, family='serif')\n",
      "plt.ylabel(r\"$\\frac{df}{d\\sigma}$\", fontsize=25, family='serif', rotation='horizontal')\n",
      "plt.title('The effect of a change in $\\sigma$ on $f(k)$', fontsize=20, family='serif')\n",
      "plt.legend(loc=0, frameon=False)\n",
      "\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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CXDJLV+giIjZYvx7CwqBuXdi5E267ze6KxNcp0EVEstHp0zB8OKxaBW+/DZ06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\nRU5ErkJggg==\n",
       "text": [
        "Figure(640x480)"
       ]
      }
     ],
     "prompt_number": 370
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$$\\frac{1}{2} \\alpha \\left(- \\alpha + 1\\right) e^{\\alpha \\log{\\left (k \\right )}} \\log^{2}{\\left (k \\right )}$$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAM0AAAAfCAYAAABESklNAAAABHNCSVQICAgIfAhkiAAACKxJREFU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\nrgAAAABJRU5ErkJggg==\n",
       "prompt_number": 292,
       "text": [
        "            \u03b1\u22c5log(k)    2   \n",
        "\u03b1\u22c5(-\u03b1 + 1)\u22c5\u212f        \u22c5log (k)\n",
        "\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "             2              "
       ]
      }
     ],
     "prompt_number": 292
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "kgrid = np.linspace(0, 10, 1000)\n",
      "plt.plot(kgrid, sp.lambdify((k, alpha, sigma), alpha_k * sp.log(k) - sp.log(f), modules='numpy')(kgrid, 0.5, 1.5))\n",
      "plt.axhline(0, ls='dashed', color='k')\n",
      "plt.ylim(-0.5, 0.1)\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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0AcAghD4AGITQBwCDEPoAYBBCHwAMQugDgEEIfQAwSNChX1dXp9TUVLndbqWlpam+vr7F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\nvgTthgoVegAAAABJRU5ErkJggg==\n",
       "text": [
        "Figure(480x320)"
       ]
      }
     ],
     "prompt_number": 300
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.plot(kgrid, sp.lambdify((k, alpha, sigma), f, modules='numpy')(kgrid, 0.5, 0.5))\n",
      "plt.plot(kgrid, kgrid, 'k--')\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "Figure(480x320)"
       ]
      }
     ],
     "prompt_number": 288
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# compute marginal product\n",
      "mpk = f.diff(k)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 318
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "mpk"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$$\\frac{\\alpha k^{\\frac{\\sigma -1}{\\sigma}} \\left(\\alpha k^{\\frac{\\sigma -1}{\\sigma}} - \\alpha + 1\\right)^{\\frac{\\sigma}{\\sigma -1}}}{k \\left(\\alpha k^{\\frac{\\sigma -1}{\\sigma}} - \\alpha + 1\\right)}$$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAIkAAAAvCAYAAADXYek6AAAABHNCSVQICAgIfAhkiAAABF1JREFU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\n",
       "prompt_number": 319,
       "text": [
        "                             \u03c3  \n",
        "                           \u2500\u2500\u2500\u2500\u2500\n",
        "                           \u03c3 - 1\n",
        "   \u03c3 - 1 \u239b   \u03c3 - 1        \u239e     \n",
        "   \u2500\u2500\u2500\u2500\u2500 \u239c   \u2500\u2500\u2500\u2500\u2500        \u239f     \n",
        "     \u03c3   \u239c     \u03c3          \u239f     \n",
        "\u03b1\u22c5k     \u22c5\u239d\u03b1\u22c5k      - \u03b1 + 1\u23a0     \n",
        "\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "        \u239b   \u03c3 - 1        \u239e      \n",
        "        \u239c   \u2500\u2500\u2500\u2500\u2500        \u239f      \n",
        "        \u239c     \u03c3          \u239f      \n",
        "      k\u22c5\u239d\u03b1\u22c5k      - \u03b1 + 1\u23a0      "
       ]
      }
     ],
     "prompt_number": 319
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "sp.limit(mpk, sigma, 1)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$$\\frac{\\alpha e^{\\alpha \\log{\\left (k \\right )}}}{k}$$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAADEAAAAjCAYAAAA9guKMAAAABHNCSVQICAgIfAhkiAAAAo1JREFU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\nLXY6BuKoaLX14pbjePo/Jycn58/8AmJ/gTpBir47AAAAAElFTkSuQmCC\n",
       "prompt_number": 320,
       "text": [
        "   \u03b1\u22c5log(k)\n",
        "\u03b1\u22c5\u212f        \n",
        "\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "     k     "
       ]
      }
     ],
     "prompt_number": 320
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "mpk.diff(sigma)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "latex": [
        "$$- \\frac{\\alpha^{2} k^{2 \\frac{\\sigma -1}{\\sigma}} \\left(\\frac{1}{\\sigma} - \\frac{\\sigma -1}{\\sigma^{2}}\\right) \\left(\\alpha k^{\\frac{\\sigma -1}{\\sigma}} - \\alpha + 1\\right)^{\\frac{\\sigma}{\\sigma -1}} \\log{\\left (k \\right )}}{k \\left(\\alpha k^{\\frac{\\sigma -1}{\\sigma}} - \\alpha + 1\\right)^{2}} + \\frac{\\alpha k^{\\frac{\\sigma -1}{\\sigma}} \\left(\\frac{1}{\\sigma} - \\frac{\\sigma -1}{\\sigma^{2}}\\right) \\left(\\alpha k^{\\frac{\\sigma -1}{\\sigma}} - \\alpha + 1\\right)^{\\frac{\\sigma}{\\sigma -1}} \\log{\\left (k \\right )}}{k \\left(\\alpha k^{\\frac{\\sigma -1}{\\sigma}} - \\alpha + 1\\right)} + \\frac{\\alpha k^{\\frac{\\sigma -1}{\\sigma}} \\left(\\frac{\\alpha k^{\\frac{\\sigma -1}{\\sigma}} \\sigma \\left(\\frac{1}{\\sigma} - \\frac{\\sigma -1}{\\sigma^{2}}\\right) \\log{\\left (k \\right )}}{\\left(\\sigma -1\\right) \\left(\\alpha k^{\\frac{\\sigma -1}{\\sigma}} - \\alpha + 1\\right)} + \\left(- \\frac{\\sigma}{\\left(\\sigma -1\\right)^{2}} + \\frac{1}{\\sigma -1}\\right) \\log{\\left (\\alpha k^{\\frac{\\sigma -1}{\\sigma}} - \\alpha + 1 \\right )}\\right) \\left(\\alpha k^{\\frac{\\sigma -1}{\\sigma}} - \\alpha + 1\\right)^{\\frac{\\sigma}{\\sigma -1}}}{k \\left(\\alpha k^{\\frac{\\sigma -1}{\\sigma}} - \\alpha + 1\\right)}$$"
       ],
       "metadata": {},
       "output_type": "pyout",
       "png": 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       "prompt_number": 321,
       "text": [
        "                                                                              \n",
        "                                                                              \n",
        "                                                \u03c3                             \n",
        "                                              \u2500\u2500\u2500\u2500\u2500                           \n",
        "                                              \u03c3 - 1                           \n",
        "      2\u22c5(\u03c3 - 1)             \u239b   \u03c3 - 1        \u239e                  \u03c3 - 1         \n",
        "      \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500             \u239c   \u2500\u2500\u2500\u2500\u2500        \u239f                  \u2500\u2500\u2500\u2500\u2500         \n",
        "   2      \u03c3     \u239b1   \u03c3 - 1\u239e \u239c     \u03c3          \u239f                    \u03c3   \u239b1   \u03c3 -\n",
        "  \u03b1 \u22c5k         \u22c5\u239c\u2500 - \u2500\u2500\u2500\u2500\u2500\u239f\u22c5\u239d\u03b1\u22c5k      - \u03b1 + 1\u23a0     \u22c5log(k)   \u03b1\u22c5k     \u22c5\u239c\u2500 - \u2500\u2500\u2500\n",
        "                \u239c\u03c3      2 \u239f                                           \u239c\u03c3      \n",
        "                \u239d      \u03c3  \u23a0                                           \u239d      \u03c3\n",
        "- \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 + \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "                                       2                                      \n",
        "                     \u239b   \u03c3 - 1        \u239e                                       \n",
        "                     \u239c   \u2500\u2500\u2500\u2500\u2500        \u239f                                       \n",
        "                     \u239c     \u03c3          \u239f                                      k\n",
        "                   k\u22c5\u239d\u03b1\u22c5k      - \u03b1 + 1\u23a0                                       \n",
        "\n",
        "                                              \u239b   \u03c3 - 1                       \n",
        "                                              \u239c   \u2500\u2500\u2500\u2500\u2500                       \n",
        "                        \u03c3                     \u239c     \u03c3     \u239b1   \u03c3 - 1\u239e         \n",
        "                      \u2500\u2500\u2500\u2500\u2500             \u03c3 - 1 \u239c\u03b1\u22c5k     \u22c5\u03c3\u22c5\u239c\u2500 - \u2500\u2500\u2500\u2500\u2500\u239f\u22c5log(k)  \n",
        "                      \u03c3 - 1             \u2500\u2500\u2500\u2500\u2500 \u239c           \u239c\u03c3      2 \u239f         \n",
        "    \u239b   \u03c3 - 1        \u239e                    \u03c3   \u239c           \u239d      \u03c3  \u23a0         \n",
        "    \u239c   \u2500\u2500\u2500\u2500\u2500        \u239f               \u03b1\u22c5k     \u22c5\u239c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 +\n",
        " 1\u239e \u239c     \u03c3          \u239f                        \u239c          \u239b   \u03c3 - 1        \u239e   \n",
        "\u2500\u2500\u239f\u22c5\u239d\u03b1\u22c5k      - \u03b1 + 1\u23a0     \u22c5log(k)            \u239c          \u239c   \u2500\u2500\u2500\u2500\u2500        \u239f   \n",
        "2 \u239f                                           \u239c          \u239c     \u03c3          \u239f   \n",
        "  \u23a0                                           \u239d  (\u03c3 - 1)\u22c5\u239d\u03b1\u22c5k      - \u03b1 + 1\u23a0   \n",
        "\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 + \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        " \u239b   \u03c3 - 1        \u239e                                                           \n",
        " \u239c   \u2500\u2500\u2500\u2500\u2500        \u239f                                                           \n",
        " \u239c     \u03c3          \u239f                                                           \n",
        "\u22c5\u239d\u03b1\u22c5k      - \u03b1 + 1\u23a0                                                           \n",
        "                                                                              \n",
        "\n",
        "                                           \u239e                     \u03c3  \n",
        "                                           \u239f                   \u2500\u2500\u2500\u2500\u2500\n",
        "                                           \u239f                   \u03c3 - 1\n",
        "                         \u239b   \u03c3 - 1        \u239e\u239f \u239b   \u03c3 - 1        \u239e     \n",
        "                         \u239c   \u2500\u2500\u2500\u2500\u2500        \u239f\u239f \u239c   \u2500\u2500\u2500\u2500\u2500        \u239f     \n",
        " \u239b     \u03c3         1  \u239e    \u239c     \u03c3          \u239f\u239f \u239c     \u03c3          \u239f     \n",
        " \u239c- \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 + \u2500\u2500\u2500\u2500\u2500\u239f\u22c5log\u239d\u03b1\u22c5k      - \u03b1 + 1\u23a0\u239f\u22c5\u239d\u03b1\u22c5k      - \u03b1 + 1\u23a0     \n",
        " \u239c         2   \u03c3 - 1\u239f                      \u239f                        \n",
        " \u239d  (\u03c3 - 1)         \u23a0                      \u239f                        \n",
        "                                           \u239f                        \n",
        "                                           \u23a0                        \n",
        "\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
        "      \u239b   \u03c3 - 1        \u239e                                            \n",
        "      \u239c   \u2500\u2500\u2500\u2500\u2500        \u239f                                            \n",
        "      \u239c     \u03c3          \u239f                                            \n",
        "    k\u22c5\u239d\u03b1\u22c5k      - \u03b1 + 1\u23a0                                            \n",
        "                                                                    "
       ]
      }
     ],
     "prompt_number": 321
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "dmpk_dsigma = mpk.diff(sigma)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 331
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "dmpk_dsigma_num = sp.lambdify((k, alpha, sigma), dmpk_dsigma, modules='numpy')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 332
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.figure(figsize=(8,6))\n",
      "kgrid = np.linspace(0, 10, 1000)\n",
      "\n",
      "plt.plot(kgrid, dmpk_dsigma_num(kgrid, 0.9, 0.9))\n",
      "plt.axhline(0, ls='dashed', color='k')\n",
      "#plt.ylim(-0.5, 0.1)\n",
      "plt.xlabel('Capital per effective worker, $k$', fontsize=15, family='serif')\n",
      "plt.ylabel(r\"$\\frac{df'}{d\\sigma}$\", fontsize=25, family='serif', rotation='horizontal')\n",
      "plt.title('The effect of a change in $\\sigma$ on MPK with $\\sigma<1$', fontsize=20, family='serif')\n",
      "          \n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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AHz4MnD8PtG8P+PgA06cDXboADg7K1FaqFI6KisK4ceP0vrZjxw40adIEzz77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\nAABJRU5ErkJggg==\n",
       "text": [
        "Figure(640x480)"
       ]
      }
     ],
     "prompt_number": 360
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "cs = plt.contour(X, Y, numeric_tmp(X, Y, 15, 1.0, 0.5, 0.5, 0.5), 30)\n",
      "plt.clabel(cs)\n",
      "\n",
      "plt.xlabel('x', fontsize=15, family='serif')\n",
      "plt.ylabel('y', fontsize=15, family='serif', rotation='horizontal')\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Part a) (25 points)\n",
      "\n",
      "Copy the code for the following Python functions from the `lab-2.ipynb`:\n",
      "\n",
      "* `ces_output`\n",
      "* `marginal_product_capital`\n",
      "* `equation_motion_capital`\n",
      "* `consumption_euler_equation`\n",
      "* `crra_utility`\n",
      "* `ramsey_jacobian`\n",
      "* `analytic_k_star`\n",
      "* `analytic_c_star`\n",
      "\n",
      "Define a Python dictionary called `baseline_params` containing the model parameters with the following values:\n",
      "\n",
      "* $\\alpha$ = 0.5\n",
      "* $\\delta$ = 0.04\n",
      "* $\\rho$   = 0.04\n",
      "* $\\sigma$ = 1.0\n",
      "* $\\theta$ = 2.5\n",
      "* $n$ = 0.01\n",
      "* $g$ = 0.015\n",
      "* $A0$ = 1.0\n",
      "* $L0$ = 1.0\n",
      "\n",
      "Create an instance of the `ramsey.Model` class called `model` using the functions and parameters defined above and then add the steady state functions to the `model` object using the code from the lab.  Finally compute the steady state values. If you have done everything correctly, then you should get the following...\n",
      "\n",
      "    {c_star: 3.07831598008, k_star: 18.1077410593}"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def ces_output(t, k, params):\n",
      "    \"\"\"\n",
      "    Constant elasticity of substitution (CES) production function.\n",
      "\n",
      "    Arguments:\n",
      "\n",
      "        t:      (array) Time.\n",
      "        k:      (array) Capital (per person/effective person).\n",
      "        params: (dict) Dictionary of parameter values.\n",
      "       \n",
      "    Returns:\n",
      "\n",
      "        y: (array-like) Output (per person/ effective person)\n",
      "\n",
      "    \"\"\"\n",
      "    # extract params\n",
      "    alpha = params['alpha']\n",
      "    sigma = params['sigma']\n",
      "    gamma = (sigma - 1) / sigma\n",
      "    \n",
      "    # nest Cobb-Douglas as special case\n",
      "    if gamma == 0:\n",
      "        y = k**alpha\n",
      "    else:\n",
      "        y = (alpha * k**gamma + (1 - alpha))**(1 / gamma)\n",
      "    \n",
      "    return y\n",
      "\n",
      "def marginal_product_capital(t, k, params):\n",
      "    \"\"\"\n",
      "    Marginal product of capital for CES production function.\n",
      "\n",
      "    Arguments:\n",
      "\n",
      "        t:      (array-like) Time.\n",
      "        k:      (array-like) Capital (per person/effective person).\n",
      "        params: (dict) Dictionary of parameter values.\n",
      "       \n",
      "    Returns:\n",
      "\n",
      "        mpk: (array-like) Derivative of output with respect to capital, k.\n",
      "\n",
      "    \"\"\"\n",
      "    # extract params\n",
      "    alpha = params['alpha']\n",
      "    sigma = params['sigma']\n",
      "    gamma = (sigma - 1) / sigma\n",
      "    \n",
      "    # nest Cobb-Douglas as special case\n",
      "    if gamma == 0:\n",
      "        mpk = alpha * k**(alpha - 1)\n",
      "    else:\n",
      "        mpk = alpha * k**(gamma - 1) * (alpha * k**gamma + (1 - alpha))**((1 / gamma) - 1)\n",
      "    \n",
      "    return mpk\n",
      "\n",
      "def equation_motion_capital(t, vec, params):\n",
      "    \"\"\"\n",
      "    Equation of motion for capital (per person/ effective person).\n",
      "\n",
      "    Arguments:\n",
      "\n",
      "        t:      (array-like) Time.\n",
      "        vec:    (array-like) Vector of endogenous variables [k, c] where k is \n",
      "                capital (per person/effective person) and c is consumption \n",
      "                (per person/effective person).\n",
      "        params: (dict) Dictionary of parameter values.\n",
      "       \n",
      "    Returns:\n",
      "\n",
      "        k_dot: (array-like) Rate of change in the stock of captial \n",
      "               (per person/effective person).\n",
      "\n",
      "    \"\"\"\n",
      "    # extract params\n",
      "    n     = params['n']\n",
      "    g     = params['g']\n",
      "    delta = params['delta']\n",
      "    \n",
      "    # unpack the vector of endogenous variables\n",
      "    k, c = vec\n",
      "    \n",
      "    # formula for the equation of motion for capital \n",
      "    k_dot = ces_output(t, k, params) - (n + g + delta) * k - c\n",
      "    \n",
      "    return k_dot\n",
      "\n",
      "def consumption_euler_equation(t, vec, params):\n",
      "    \"\"\"\n",
      "    Equation of motion for consumption (per person/ effective person).\n",
      "\n",
      "    Arguments:\n",
      "\n",
      "        t:      (array-like) Time.\n",
      "        vec:    (array-like) Vector of endogenous variables [k, c] where k is \n",
      "                capital (per person/effective person) and c is consumption \n",
      "                (per person/effective person).\n",
      "        params: (dict) Dictionary of parameter values.\n",
      "       \n",
      "    Returns:\n",
      "\n",
      "        c_dot: (array-like) Rate of change in consumption (per person/effective \n",
      "               person).\n",
      "\n",
      "    \"\"\"\n",
      "    # extract params\n",
      "    g     = params['g']\n",
      "    delta = params['delta']\n",
      "    rho   = params['rho']\n",
      "    theta = params['theta']\n",
      "    \n",
      "    # unpack the vector of endogenous variables\n",
      "    k, c = vec\n",
      "    \n",
      "    # marginal product of capital\n",
      "    mpk = marginal_product_capital(t, k, params)\n",
      "\n",
      "    # formula for the equation of motion for consumption\n",
      "    c_dot = ((mpk - delta - rho - theta * g) / theta) * c\n",
      "    \n",
      "    return c_dot\n",
      "\n",
      "def crra_utility(c, params):\n",
      "    \"\"\"\n",
      "    The optimal growth model assumes that the representative individual has CRRA utility.      \n",
      "    utility. Individual utility is a function of consumption per effective person, c. The \n",
      "    parameter, 0 < theta, plays a dual role: \n",
      "        \n",
      "        1) theta is the agent's coefficient of relative risk aversion\n",
      "        2) 1 / theta is the agent's elasticity of inter-temporal substitution\n",
      "    \n",
      "    N.B.: If theta = 1, then CRRA utility is equivalent to log utility! \n",
      "    \n",
      "    Arguments:\n",
      "    \n",
      "        c:      (array) Consumption per effective person\n",
      "        \n",
      "        params: (dict) Dictionary of model parameters.\n",
      "        \n",
      "    Returns: \n",
      "    \n",
      "        utility: (array) An array of values respresenting utility from consumption per \n",
      "                 effective worker.\n",
      "        \n",
      "    \"\"\"\n",
      "    # extract the params\n",
      "    theta = params['theta']\n",
      "    \n",
      "    if theta == 1:\n",
      "        utility = np.log(c)\n",
      "    else:\n",
      "        utility = (c**(1 - theta) - 1) / (1 - theta)\n",
      "    \n",
      "    return utility\n",
      "\n",
      "def ramsey_jacobian(t, vec, params):\n",
      "    \"\"\"\n",
      "    The Jacobian for the optimal growth model is computed using symbolic \n",
      "    differentiation and then evaluated numerically.\n",
      "\n",
      "    Arguments:\n",
      "\n",
      "        t:      (array-like) Time.\n",
      "        vec:    (array-like) Vector of endogenous variables [k, c] where k is \n",
      "                capital (per person/effective person) and c is consumption \n",
      "                (per person/effective person).\n",
      "        params: (dict) Dictionary of parameter values.\n",
      "       \n",
      "    Returns:\n",
      "\n",
      "       jac: (array-like) Jacobian matrix of partial derivatives.\n",
      "\n",
      "    \"\"\"\n",
      "    # declare two symbolic variables\n",
      "    k, c = sp.symbols('k,c')\n",
      "    \n",
      "    # represent the system of equations as a SymPy matrix\n",
      "    k_dot = lambda k, c: equation_motion_capital(t, [k, c], params)\n",
      "    c_dot = lambda k, c: consumption_euler_equation(t, [k, c], params)\n",
      "    F     = sp.Matrix([k_dot(k, c), c_dot(k, c)])\n",
      "\n",
      "    # now computing the Jacobian is trivial!\n",
      "    symbolic_jacobian  = F.jacobian([k, c])\n",
      "        \n",
      "    # lambdify the function in order to evaluate it numerically\n",
      "    numeric_jacobian   = sp.lambdify(args=[k, c], expr=symbolic_jacobian, modules='numpy') \n",
      "    \n",
      "    # output num_jac evaluated at vec\n",
      "    evaluated_jacobian = np.array(numeric_jacobian(vec[0], vec[1]))\n",
      "    \n",
      "    return evaluated_jacobian\n",
      "\n",
      "def analytic_k_star(params): \n",
      "    \"\"\"Steady-state level of capital (per person/effective person).\"\"\"\n",
      "    # extract params\n",
      "    n     = params['n']\n",
      "    g     = params['g']\n",
      "    alpha = params['alpha']\n",
      "    delta = params['delta']\n",
      "    rho   = params['rho']\n",
      "    theta = params['theta']\n",
      "    sigma = params['sigma']\n",
      "    gamma = (sigma - 1) / sigma\n",
      "    \n",
      "    # nest Cobb-Douglas as special case\n",
      "    if gamma == 0:\n",
      "        k_star = (alpha / (delta + rho + theta * g))**(1 / (1 - alpha))\n",
      "    else:\n",
      "        k_star = (1 - alpha)**(1 / gamma) * ((alpha / (delta + rho + theta * g))**(gamma / (gamma - 1)) - alpha)**(-1 / gamma)\n",
      "    \n",
      "    return k_star\n",
      "\n",
      "def analytic_c_star(params): \n",
      "    \"\"\"Steady-state level of consumption (per person/effective person).\"\"\"\n",
      "    # extract params\n",
      "    n     = params['n']\n",
      "    g     = params['g']\n",
      "    delta = params['delta']\n",
      "    \n",
      "    # compute k_star\n",
      "    k_star = analytic_k_star(params)\n",
      "    \n",
      "    # compute c_star\n",
      "    c_star = ces_output(0, k_star, params) - (n + g + delta) * k_star\n",
      "    \n",
      "    return c_star"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 381
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# start by defining a dictionary of parameter values\n",
      "baseline_params = {'alpha':0.5, 'n':0.01, 'g':0.015, 'rho':0.04, 'theta':2.5, \n",
      "                   'delta':0.04, 'sigma':1.0, 'A0':1.0, 'L0':1.0}"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 412
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# we create an instance of the optimgal growth model as follows...\n",
      "model = ramsey.Model(output=ces_output,                \n",
      "                     mpk=marginal_product_capital, \n",
      "                     k_dot=equation_motion_capital, \n",
      "                     c_dot=consumption_euler_equation,\n",
      "                     utility=crra_utility,\n",
      "                     jacobian=ramsey_jacobian, \n",
      "                     params=baseline_params)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 413
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# create a dictionary containing the steady state expressions\n",
      "steady_state_funcs = {'k_star':analytic_k_star, 'c_star':analytic_c_star}\n",
      "\n",
      "# pass it as an arg to the set_functions method\n",
      "model.steady_state.set_functions(func_dict=steady_state_funcs)\n",
      "\n",
      "# compute the steady state values!\n",
      "model.steady_state.set_values()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 414
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# display the values as follows\n",
      "model.steady_state.values"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 415,
       "text": [
        "{c_star: 3.07831598008, k_star: 18.1077410593}"
       ]
      }
     ],
     "prompt_number": 415
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Part b) (5 Points)\n",
      "\n",
      "Plot a phase diagram for the model using the `plot_phase_diagram` method."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.figure(figsize=(8,6))\n",
      "model.plot_phase_diagram(gridmax=100, arrows=True)\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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V6Mc/Fi5ciD179qBp06bIz8/H7bffjubNm5dvIRwSv2EcEiciur6lS5eif//+\n8PPzK/M8fvvtN+zcuRPZ2dlo37497rzzznKs0Dn+WlcVwsAmIipeUlISRo8ejWeffRajRo0q0zyM\nRiO6d++OnTt3AgA6dOiAtWvXIjQ0tDxLdcATpxARUbURHR2NGjVqYMCAAWWex9q1a9GkSRPb9fbt\n2yMuLq48yitWiU+cQkREpHc5OTnIzs5GeHi4w23Jycn48ssvi3xsly5dMGzYMJw4cQJhYWG26aGh\noThy5EiF1FsYA5uIiKqNzZs3o1evXkhOTkZCQgImTpyI1NRUKIqCxo0b45133rnuPDIzM+2OnPLy\n8kJ2dnZFlg2AgU1ERJVIqVc+wSZpNcr0uLi4OJw7dw5XrlzBXXfdhdjYWCiKUqp5REVF4dy5c7br\nubm5Tnvs5Y2BTURElaasQVteNm7ciLvvvhvjx4/HmjVrEBAQYLutpEPiLVu2xMqVK23T09LS0LFj\nxwqtG2BgExFRNXH58mWYzWZMnDgRR44cQUJCAi5cuGA7JKukQ+LNmzfH3r17AQAigv379+N///tf\nhdYOMLCJiKiaSEhIwJAhQwAA3bp1w8aNGzF48OBSz8fT0xOTJ0/G1KlTISKYNm1apZwNlMdhVyE8\nDpuIqOricdhEREQ6wMAmIiLSAQY2ERGRDjCwiYiIdICBTUREpAMMbCIiIh1gYBMREekAA5uIiEgH\nGNhEREQ6wMAmIiLSAZ5LnIiIqBR+++037Ny5E9nZ2Wjfvr3tx0MqGgObiIiqlbZt22LevHlo27Zt\nqR9rNBrx8ssvY+fOnQCADh06oFevXggNDS3vMh1wSJyIiKqVN998E82aNSvTY9euXYsmTZrYrrdv\n3x5xcXHlVVqx2MMml9iyZQsURUG3bt1cXQoRVTN33HGHw7Tk5GR8+eWXRT6mS5cuGDZsGE6cOIGw\nsDDb9NDQUBw5cqRC6rwWA5sqXXx8PPr164fx48czsImqGeX0h+Uyn7L+lHBGRgZmz56NmJgYvPvu\nu9i0aRMMBgMaN26Md95557qPz8zMtPvtay8vL2RnZ5epltJiYFOl2r59O2JjY2EymVxdChG5QFmD\ntjzk5uZi6NChWLBgARo2bIh+/frBYDCUah5RUVE4d+6c3TzDw8PLu1SnGNhUafbs2YMBAwbgypUr\nri6FiKqhtWvXonnz5mjYsCEAwN/f33ZbSYfEW7ZsiZUrV9qmp6WloWPHjhVXdCEMbBfQNA1bt25F\njx49XF2hvBELAAAgAElEQVRKpUlKSkLfvn3tho4+//xz/P7772Wan4hgzJgxePzxx8urRCKq4s6c\nOYOmTZvarm/YsAEdO3aEv79/iYfEmzdvjr179wKwfA7t378f//vf/yqs5sIUEZFKeabrUBQFblJK\nhdu2bRv69OmDzMxMeHt7l9t8ldMfunS4qTjr16/HkCFDkJeXV67zrS5thohuXFZWFt544w3bvjNR\nUVFlOrRr8eLFSExMhIigc+fOGDhwYHmX6hQD2wXeeecdvPLKK9i0aVO59rLdObABYP78+XjssceQ\nm5sLAJgwYQI+++yzMs1r4sSJmD59erVpM0REPA7bBVauXAlFUbBhwwZXl1KpRo0ahf/+97/w9fV1\ndSlERLrDwK5kZrMZv//+O0QEK1ascHU5lW7cuHF49913XV0GEZHucKezSpaYmAhPT0/k5eVh7969\nMJlM8PCoXm/DM888A0VRULNmTVeXQkSkG9UrKdxAfHw8jEYjAMDT0xP79u1Dhw4dXFxV5Xv66add\nXQIRka5wSLySrVy50randEFBATZu3OjiioiISA8Y2JVIRLBt2zbb9fz8/Gq5HZuIiEqPgV2JLl++\nbHdKTlVV7U5xR0REVBQGdiUKDg5GTk4OtmzZAsCyx3hiYqKLqyIiIj1gYBMREekAA5uIiEgHGNhE\nREQ6wMAmIiLSAQY2ERGRDjCwiYiIdICBTUREpAMMbCIiIh1gYBMREekAA5uIiEgHGNhEREQ6wMAm\nIiLSAQY2ERGRDjCwiYiIdICBTUREpAMMbCIiIh1gYBMREekAA5uIiEgHGNhEREQ6wMAmIiLSAQY2\nERGRDjCwiYiIdICBTUREpAMMbNKVvXv3ombNmpg+fToAIDAwEGPHjnVxVUREFY+BTboSHh6O7Oxs\n2/Xs7GwEBQW5sCIiosrBwCZdqVu3LkJDQ23XAwIC0K9fPxdWRERUORjYpDu9e/e2Xc7NzUX37t1d\nWA0RUeVgYJfBxo0b8dlnn7m6jGpr0KBBqFGjBgCgYcOGCA4OdnFFREQVj4FdSlu2bMFtt92G+fPn\nu7qUaqtnz54wm80AgP79+7u4GiKiyuHh6gL05Pfff8ftt9+OgoICV5dSrUVFRcHHxweapmHAgAGu\nLoeIqFKwh11C+/btw6233oorV664upRqT1EU9OjRA/n5+ejZs6eryyEiqhTsYZfAiRMn0Lt3b2Rl\nZdmm7dixA4qiuLCq6m3QoEHYt28fwsPDXV0KEVGlYGCXgJeXF7y8vKAoCkTENr3w4UWlNXz48PIo\nrdq69957ERMT4+oyiIgqjSKFE8iFrg1Dd3P06FF07twZGRkZAIDOnTtj+/btLq7KnnL6Q0jdSa4u\ng4iIKgC3YZdQ06ZNsWXLFp5Vi4iIXIKBXQotWrTApk2b4O/v7+pSiIiomuE27FJq3bo1Nm3ahAMH\nDri6FCIiqka4DbsK4TZsIqKqi0PiREREOsDAJiIi0gEGNhERkQ4wsImIiHSAgU1ERKQDDGwiIiId\nYGATERHpAAObiIhIBxjYREREOsDAJiIi0gEGNhERkQ4wsImIiHSAgU1ERKQDDGwiIiIdYGATERHp\nAAObiIhIBxjYREREOsDAJiIi0gEGNhERkQ4wsImIiHSAgU1ERKQDDGwiIiIdYGATERHpAAObiIhI\nBxjYREREOsDAJiIi0gEGNhERkQ4wsImIiHSAgU1ERKQDDGwiIiIdYGATERHpAAObiIhIBxjYRERE\nOsDAJiIi0gEGNhERkQ54uLoAItIfEUFOLpCTC+TmCvLygbx8QW4ebJfz8oDcPOttlmkmE2A2Ayaz\n5b/ZLLbLJhNg1qy3C0QARQEUKFAUQFX/vl7oTy102WAAvDwBT08FXp6Alxfg5anA09My3TJNgaeH\n9TbA10eBny/g52v/38sLUBTF1YuZyA4Dm6gayssTZFwSXLho+cu4BMv/i4LLWYKsbCAzW5CV7fxy\n9hXA2wvw9wN8vBX4+FjCz8cb8PEufNl6G+DtpcDDA/AwWMLVYAA8DAp8Pa2XC/9XoCgKRCzBbf3T\nCl22TdMs/80aYDRaviRkZgEFRqDAqMFo/PtyAWA0CQoKrLdZlkNOLnAl1/oFxPLfZILTIPfzBQJq\nKAgKUBAYAATWUBAYoCAoAAgMUP6+DgQFXr0cWMOyDPgFgG4UA5uoCjCbBecuCNLPCtLP/f2/0OVz\nGYILGdZwFhhNQGiI8vcfUDPYcrlmsILgIAV1awMBNVQE1FAQWMMSUgE1gAB/S0DV8Ac8PKpuAJlM\nltECa4Bfybn6P/sKcDnL8qUgM0uQmS1ISwcys7W/rwOXMy3TM7MsX3BECi9j++VdM6TQ5WDYTffz\nZdDTVQxsIjeXny84lS44cUrDiVOCv9KuXj59xhLKFy4KQoIU1KmtoE6tq/8bNVDQuZ2KWqF/h8Lf\n4eDvxyAojofH319QapTPMsrNtXxRsvzBMrqRcXVacqpmf9vfIx8KgNphytW/UAXhtZxfD6upVOkv\nUQQoIiKuLgKAbfiLyk45/SGk7iRXl0GlZDIJTpwSHEvRcDTF8j/lpPZ3MFs+uOuFK4ior6BhPdX2\nv2E9BfXrWMK5VqgCT09+WFc1V3IEZ89f/TtzTnD2QqHrhW7LuCQICgDCa6kIr6WgXvjff3Wsl1XU\nq6Ogbm0Fvr5sK3rEHjZRJTCbBcmpgoNHNRxN0XD0uOBYqoZjqZaecp1aCppEqmjSSEGTRio63uyB\niPqWcK5TW4HBwA/Y6sjfT0FUhIKoiOvf12y2fLk7e96yGeT0WUFauuD4CcGWXWakpQvSzlj+/P1g\nCfBwy5c+W6jXUdGgroKG9Sy9dlVlu3Mn7GFXIexhu15+vuDIcQ1JRwQHDmtIOqLhwBENR49rCK+l\noEVTFc2iVDSNtAa0iqgIBd7e/GCkyiEiyLgInErXLAFuC3INp05bN79YtsE3qKsgor5lNCeivmL7\nEmmdVsOf7bYyMbCrEAZ25RERnDot2HdAw94/Nez904w/kjSknBRENlAQ3UxFTHPV8r+ZipuaqvD3\n44cb6UduruDk6av7S1j+rPtRWP77+AARhTbTRNS3jgioaByhomYI95UoTwzsKoSBXTFMJstQ9t4/\nNezdfzWgVVVBu1Yqbm5p+Wsdbek9s7dM1YGI4EIG7EI89aQg5aSG5FRB8gkNmgY0jlALhfjf/xup\niGzAbemlxcCuQhjYN07E0pPYsceMnQkadu41I2G/hnrhCtq1MljCuZWKtjEq6tRW2HsgKsbFS4Lj\nJzQkn7D+13D8hCXMT5yyHNnQ+JowbxqlolmUZe93rl/2GNhVCAO79LKvCLb9bsaOBM0S0ns1qCrQ\nuZ2KTu0M6HSzio43GxAUyA8OovJkNv+9U9xff4d5qiXYj6ZoOJKsocAINI20jFo1a6xY/kepaNZY\nRVjN6jnUzsCuQhjY13f+gmDzTjM27TRj0w4zDhzW0K6Viq4dDOjUzoDO7VQ0qMdv9kSudvGSZQfO\nI8ctAX7k+NXrIrga4FEKmjVWbddrhlTddZeBXYUwsB2dPqPhty2WgI7fruHkaQ1dOxjQs7MBvboY\n0LGtCh+fqruCE1U11m3ntjA/ruFI8tUw9/IEWjS17PDZoqlqu9yogf4Pj2RgVyEMbMsQ98ZtZqzb\nZMav8WakndHQu4sBvbtaQrptjMqzQRFVUSKWk8scPKrh4FFB0hHt78sazl0QNGusokUTFS2aKrZA\nb95YhZ9OjuBgYFch1TGwzWbBrr0afo03Y90mE/b8oeGWtgYM6GVA/54GdGij6v5bNRHduOwrgsPH\nNCQdvRriSUcsJzCq8/c5EqwhHt1MRcvm7je8zsCuQqpLYF+6LFizwYTl68xYFWdCvToqBvSyhHTP\nzgYe70xEJWYyWc4GdzXELSc7OnBYQ0ANBS2bq2jVQkWrm1S0vMlyfoXyOsd8aTGwq5CqHNiHj2lY\nvs6EZb+asTvRjF5dDBjS3wOD+xnQsL7q6vKIqIqxHuL55yEN+w9q2H9Iw5+HLIEeXktBy5ssIW4N\n8xZNK35/GAZ2FVKVAltEsOcPDT8tN+GXlSZcyQWG9LeE9K3dDbrZ5kREVYv1dwGsAW4N82OpGiLq\nKWjVQrX1yttEG9A0qvx+RY2BXYXoPbBFBDsTLCH90woTPDyAkYM9cNdgD3Roo/JQKyJyWwUFlj3V\n9x+0BPkfBy1/p88IopupaBOtok2M5X/raANqhZb+84y/1kUuJSLYsUfD90tN+HmFCX6+wD/u8MDi\nr3zQJoYhTUT64OWloOVNBrS8yWA3PfuKYP9BDYlJGhIPaPhlZQESkzT4+SpIS/Av1XMwsMkljh7X\n8O0vJsz/xQhVAe4b7oFV3/ogpjlDmoiqjhr+Crp0MKBLh6tBLiL461TpR5QZ2FRpzl8Q/LDMhG9+\nNiI5VXDvMA9897kPbmnLkCai6kNRFEQ04JA4uRmzWbD6NzP+7zsjfttqRuytHvj3c14Y0MsAT0+G\nNBFRSTGwqUKkntTw1QIjvlpoQr06Csbd74m5//VBYABDmoioLBjYVG6MRsGyX8348lsjdu414/7h\nnljxjQ/axBiu/2AiIioWA5tu2LkLgtnzjZg5z4iohgoeG+WJX/7Phz9OT0RUjhjYVGYJf5jxyf+M\nWLzGhLtiPbBing/atmRvmoioIjCwqVRMJsGiVWZ88r8CpPwlmPCwJ45s9kdYGU4CQEREJcfAphLJ\nzRXM/dGE92cWoE4tBRMf88LwgQb+VCURUSVhYFOxLl0WzJhrxKdfGdGxrYp5//VB904c9iYiqmwM\nbHIq/ayGj2YZ8b+FRgzp74FfF/qgVQsGNRGRqzCwyc7Z8xqmfW7E198bMWqEJxLW+CGiAX++kojI\n1RjYBMBy2tD3Zxbg/xYY8cCdntgf54d6dRjURETugoFdzWVcFHzwRQFmzTfinqEe2PerHxrUY1AT\nEbkbBnY1lZcn+PQrI96bUYA7B3lgzxo/NOLQNxGR22JgVzOaJvj2FxNem1aADm1UbF7sh5uaMqiJ\niNwdA7sa+XWjCS+9WQBfH+C7z3l4FhGRnjCwq4GjxzU893o+Dh3T8O4r3hgRa+DvTxMR6QzHQquw\nKzmCV9/NR5chOejV2YA/f/PDXYM9GNZERDpUKT3shIQErF+/HpGRkRg5cmRlPGW1JiL4abkZk6bk\no2dnA/at80P9uvxuRkSkZ5U2JJ6VlYW8vLzKerpq69BRDU++ko/zGYL5n/mgVxdupyYiqgoqJLDj\n4uKQkpKCdevW4eOPP0a7du1w7Ngx9q4ryGOPPYaDBw8BxpNotW8x2t3cCLvjv+EPcxARVSGKiEh5\nzjA5ORmTJ0/GvHnzkJ+fD29v75IVoigo51KqjfYdeiNhT7ztelhYGKZOnYonnnjChVUREVF5Kvce\n9k8//YR//OMfAFDisLaaPHmy7XKfPn3Qp0+fcqys6sm+InhtWgH2H9Lspp8/fx6//PILA5uIqAop\n98A+f/48IiIiAACHDx9GYGAg6tSpU6LHFg5sKt6mHWY89GweenY2oGNbFVu3Xr0tLCwMI0aMcF1x\nRERU7sp91+HHH38cK1aswPLly5GWllbisKaSyc8XvPRGPu55PA/Tp3hj7n990LRpJMLCwgBYwnrA\ngAHsXRMRVTHlvg27rLgN+/r27jfjwWfy0SxKwaz3fFAr9OpOZTNnzsSTCz7GjPsmMqyJiKogBrYO\nmM2C92cY8eGsAnz4ujceHOn85CfK6Q8hdSe5oEIiIqpoPDWpm0s/q+HBp/ORXyD4fTV/UYuIqLri\np78bWxdvQvvbc9G1g4q4H30Z1kRE1Rh72G7IZBJM+agAXy004ZtPvNGvJ98mIqLqjkngZs6c03DP\n43nw9FCwZ40vwmuxV01ERBwSdys7E8zoOCgXvTobsGaBD8OaiIhs2MN2E18vNOLltwow+z1vDB/E\nt4WIiOwxGVzMaBRMfL0Av8absPEXX0Q3Y6+aiIgcMbBd6EKGYMSjuQisoWDnSj8EBfLXtYiIyDl2\n51zk6HENXYfmoEt7A5bM8WFYExFRsRjYLrB5hxk9hufihce9MO01b6gqw5qIiIrHIfFK9t0vRjz3\negHmf+qN2/pw8RMRUckwMSrR+zMK8NnXRqz/wQetow2uLoeIiHSEgV0JRAT/fKsAy341YcsSXzSo\nxy0RRERUOgzsCmYyCR5/OR9/HNSwaZEfQmtyezUREZUeA7sC5eUJHngqD1nZwPoffFHDn2FNRERl\nw7HZCpKTIxj6cB5UFVg214dhTUREN4SBXQGsYV07TMHCmT7w9mZYExHRjWFgl7OcHMEdD+ehbriC\nuf/1hsHAsCYiohvHwC5H1rCuX0fBnOkMayIiKj8M7HKSkyMY8lAeGtRV8PXHDGsiIipfDOxyUFAg\nGPlYHuqFK/jqI4Y1ERGVPwb2DTKbBQ89mw8PA9izJiKiCsPjsG+AiOCpV/Nx+qyGVfN94enJsCYi\noorBwL4Br00rwK69GuJ+9IWvL8OaiIgqDgO7jD77qgA/rzBh02I/BAYwrImIqGIxsMtg+a8mvP2p\nEVuW+KJWKMOaiIgqHgO7lPYkmjFmYh6Wz/NFVAT32SMiosrBxCmFv05pGDomD7Pe80Hn9vw9ayIi\nqjwM7BLKzBIMHp2HieM8MSKWAxNERFS5GNgloGmCh57NQ9cOKp4f7+nqcoiIqBpiV7EE3vqvEWfP\nC77/wgeKwp3MiIio8jGwr2P5rybMmm/ErpW+8PJiWLuKpmnIyclBjRo1XF0KEZFLcEi8GIeOanjk\n+Xz8OMsHdcO5qFxpzZo1iIyMxJEjR1xdChGRSzCFinAlRzDi0Ty89U8vdL2Fe4S7Wm5uLi5fvoxu\n3bohJSXF1eUQEVU6BnYRnnktHx3aqHj0fm41cBd+fn7IyMhA165dcfLkSVeXQ0RUqZhGTsz/2YjN\nO83YvcaPO5mVExGB2Wwu8+Otj9U0DefOnUPXrl2xa9cu1KlTp7xKJCJya+xhX+PwMQ0TX8/HD7N8\nUMPfEtYrVqzA/fff7+LK9G3IkCHw9PQs89/dd9+NzMxMAJbwTk9Pxz//+U8XvyoiosrDHnYheXmC\nu8fn4Y2XvNG25dXt1osWLcLSpUuhaRpUld9xymLt2rUAgCtXrpTp8UuWLMHjjz+OzMxMqKqK2rVr\n4+233y7PEomI3BoDu5B/vVOAplEKxj9ov1jWrVuH3NxcHDhwAK1atXJRdfpm3bTg5+dXpsd7e3vb\n5hMWFoZt27ahXr165VYfEZG7Y3fxbxu2mvDDMhNmTbM/OUpGRgZOnz4Nb29vxMfHu7BCysnJQUhI\nCLZu3YqIiAhXl0NEVKkY2LCcJ3zMxHzMfs8boTXtdzLbsmULfHx8kJubi5UrV7qoQvL29kZAQAC2\nbNmCJk2auLocIqJKxyFxAM9Pzkf/ngYM7u+4ONatW4esrCwAlvAWEe457gIDBw5ESkoKAgMDXV0K\nEZFLVPvAXrHOhPWbzUhc73zb6po1ayAiAID8/HwkJyezh+cCBoOBYU1E1Vq1HhK/dFnw2Ev5mDPd\nBwE1HHvN2dnZSE5Otl1XVZXbsYmIyCWqdWD/8+18DL3NgN5dnZ96dNeuXQAs208VRUFBQQHWr19f\nmSUSEREBqMaBvWWnGct+NeOdf3kXeZ927dph9uzZCAkJgYhg1qxZmDRpUiVWSUREZKGIdQOtiymK\ngsoqpaBA0O62XEye5IV/3HH9zfgPPPAAvvvuu0qrr6yU0x9C6rrnFwovLy8YjUa3X4ZERO6qWvaw\n35thROMIBSOH8Fe4iIhIH6rdXuLJqRqmf1mAPfxhDyIi0pFq18N+YWo+nh/vhYgG1e6lExGRjlWr\nHvb6TSYk7Nfw3ec+ri6FiIioVKpNN9NkEjz3egE+fN0bPj4cCiciIn2pNoE96xsjaoUquHMQdzQj\nIiL9qRZD4hkXBVM+MmLd9z7c0YyIiHSpWvSwp31egOEDDWgTw941ERHpU5XvYZ9M0/B/C4xIXOf8\nxz2IiIj0oMr3sKd+XIBx93uift0q/1KJiKgKq9I97ENHNSxaZcLhzf6uLoWIiOiGVOlu57/fL8Ck\n8V4ICeaOZkREpG9VNrD/SDIjfrsZz4z1dHUpREREN6zKBvZb/zXi+cc84efH3jUREelflQzsQ0c1\nxG0x44mH2LsmIqKqoUoG9tufFuCZsZ4IqMHeNRERVQ1Vbi/x5FQNK9aZcGwb9wwnIqKqo8r1sN+b\nUYAnHvJEUCB710REVHVUqR72+QuC75eacDCeZzUjIqKqpUr1sGfNN2LEIA+E16pSL4uIiKjq9LDz\n8wWfzzFizXc+ri6FiIio3FWZruj3S01odZOK1tH8RS4iIqp6qkRgiwg+mmXExMd43LW72bt3L159\n9VUYjUYAwKuvvoo9e/a4uCoiIv2pEoEdv11DfoHg9j7sXbub7du347333rNdnzZtGrZs2eLCioiI\n9KlKBPasb4x4fLQnVJWHcrmb3r17w9vb23bd19cXvXv3dmFFRET6pPvAPn9BsDLOhNEjORzujlq0\naAFFufpFStM0tGrVyoUVERHpk+4De84PRgy73cOtf0JTRPDnn3+6ugyXUBQFXbp0sV2/5ZZboKq6\nb3ZERJVO15+cIoLZ3xoxfpR7966PHDmC1q1bY968ea4uxSViY2Ph4+MDLy8vxMbGurocIiJd0nVg\n/7bFDG8vBV1vce+XoWkaPD098fjjj+P77793dTmVrnfv3vD09ISPjw/69Onj6nKIiHTJvZPuOr7+\n3oRH7/ew20bqrry9vZGbm4sxY8Zg8eLFri6nUrVt2xZGoxF5eXlo3769q8shItIl3Z7pLPuKYNmv\nJnz4esWfN1zTNADA6tWry/T45ORk23HIubm5uP/++/Hzzz9j0KBB5VajOzMYDGjfvj2MRiM8Pd17\n8wURkbvSbWAvXm1C944G1A6r+EGC7t27Y+HCheUWsPn5+fjPf/5TbQIbAB599FHblxYiIio9RUTE\n1UUAlr2JS1PK7fflYsw9Hrh3uPv32A4ePIhOnTohKysLqqqiVq1a2LVrFxo2bFiuz6Oc/hBSd1K5\nzpOIiNyDLrdhnz6jYedeM4bdrq8BAkVREBISgm3btpV7WBMRUdWmy8D+bpEJdw70gK+v++9sZpWT\nk4Pg4GBs27YNUVFRri6HiIh0RpeBvXCJCfffqZ/edUBAAMLDw7F582Y0a9bM1eUQEZEO6Sf1/pZ6\nUkPKXxr6dNPPD33Ur18fJ0+e1MXhZ0RE5J5018NetMqEobd5wMNDX+HHsCYiohuhu8D+eYUJI2J1\nNzBARER0Q3QV2OlnNew/pKF/T/0MhxMREZUHXQX24tVmDOrrAW9vDi8TEVH1oqvA/mWlCXcN5nA4\nERFVP7oJ7MwswbbdZgzsy+FwIiKqfnQT2Os3m9G1gwH+fhwOJyKi6kc3gb0qzoRBt7J3TURE1ZMu\nAltEsCrOssMZERFRdaSLwP7zkAaDAbipKYfDiYioetJFYK/+zYxBtxp4tjAiIqq2dBHYazaYcXtv\nDocTEVH15faBXVAg2L7HjN5ducMZERFVX24f2L/v09A0UkVIMIfDiYio+nL7wN6wzayrn9IkIiKq\nCG4f2Bu3mdGHw+FERFTNuXVgG42W05H27MzAJiKi6s2tA3t3oobGESpqhnD7NRERVW9uHdjx27l3\nOBEREeDmgb1ttxldO7h1iURERJXCrdNw514Nnduzh01EROS2gX0yTYPRCEQ25PZrIiIitw3sHQka\nOrdTef5wIiIiuHNg7zFzOJyIiOhvbhvYO/ea0elmty2PiIioUrllIooIEvZr6NCGPWwiIiLATQM7\n5S9BQA0FoTW5/ZqIiAhw08De96eGtjFuWRoREZFLuGUqJiZpaBPtlqURERG5hFum4r4DZvawiYiI\nCnHLVNx3QEPbltzhjIiIyMrtAjsrW5CWLmgWxR3OiIiIrNwusJOOaGjRVIWHBwObiIjIyu0C+3Cy\nhuaN3a4sIiIil3K7ZDySrKF5Y/auiYiICnO7wD6cLGjGHjYREZEdt0vGI8c5JE5ERHQtt0pGEcHh\nZA3NotyqLCIiIpdzq2Q8c07g5QnUDOE2bCIiosLcKrCPHBcOhxMRETnhVul4+JiG5k3cqiQiIiK3\n4FbpeCxVQ5NGblUSERGRW3CrdPwrTRBRn9uviYiIruVmga2hYT0GNhER0bXcLLAFDeq6VUlERERu\nwa3S8VS6oEFd9rCJiIiu5VaBXcMP8PNjYBMREV3LrQK7YT23KoeIiMhtuFVCcjiciIjIObcK7PoM\nbCIiIqfcKrDDajKwiYiInHGrwA7lj34QERE55VaBzR42ERGRc24V2OxhExEROcfAJiIi0gEGNhER\nkQ64VWBzGzYREZFzbhXYQYGuroCIiMg9uVVgKwp72ERERM64VWATERGRcwxsIiIiHWBgExER6QAD\nm4iISAcY2ERERDrAwCYiItIBBjYREZEOMLCJiIh0gIFNRESkAwxsIiIiHWBgExER6QADm4iISAcY\n2ERERDrAwCYiItIBBjYREZEOMLCrkq1HXV0BERFVEAZ2VbL1mKsrICKiCsLAJiIi0gEGNhERkQ54\nuLoAq969e0NRFFeXoXvKR1yGRER68Prrr2Py5Mklvr8iIlJx5RAREVF54JA4ERGRDjCwiYiIdICB\nTUREpAMMbCIiIh1gYBMREekAA1vHfvjhB/Tq1ctuWkJCAj744AP89NNPLqqKiIgqAgNbx1q3bo2u\nXbs6TM/KykJeXp4LKiIiooriNidOodLbtm0bunXrZjetXbt2OHbsGEaOHOmiqoiIqCKwh61jO3fu\nRLt27bB48WJ06NDBNp1hTURU9TCwdezAgQPYvHkzhg8fjs2bN7u6HCIiqkAMbJ3Kzs4GACxatAgb\nNmyAr6+viysiIqKKxG3YOrVr1y4MGTIEAwYMwKJFi6BpGm699VZXl0VERBWEPWydOnjwIPr27YtG\njdHXrbgAAAGkSURBVBrh3LlzqFGjhqtLIiKiCsRf6yIiItIB9rCJiIh0gIFNRESkAwxsIiIiHWBg\nExEROTFq1Ch4eXlh1apVri4FAHc6IyIicionJwchISE4c+YMgoODXV0Oe9hERETObN26FU2aNHGL\nsAYY2ERERE5t2rQJ3bt3d3UZNjzTGRERkRObN2/Ggw8+CACYO3cu0tLSEB0djeHDh7ukHvawiYiI\nrmE0GrFjxw507doV8+fPxx133IENGzZg165dLquJPWwiIqJr7NmzB15eXliyZAkefPBB1KxZE++9\n9x6aNWvmsprYwyYiIrrGpk2b0LNnTzRv3hw///wzAKBt27bw8/NzWU0MbCIiomts3rwZd911F4YP\nH47ly5fjp59+gtlsxtGjR11WEwObiIioEBHBli1bbHuIe3l5QUTw22+/wcvLy2V1MbCJiIgKOXv2\nLOrXr48mTZoAAMaMGYOlS5ciLS0NERERLquLZzojIiLSAfawiYiIdICBTUREpAMMbCIiIh1gYBMR\nEekAA5uIiEgHGNhEREQ6wMAmIiLSAQY2ERGRDvw/LJbjZgVrlrUAAAAASUVORK5CYII=\n",
       "text": [
        "Figure(640x480)"
       ]
      }
     ],
     "prompt_number": 420
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Part c) (15 points)\n",
      "\n",
      "Plot the phase diagram following a 5% decrease in the value of $\\sigma$. Clearly explain why each of the $\\dot{c}=0$ and the $\\dot{k}=0$ shifts."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.figure(figsize=(8,6))\n",
      "model.plot_phase_diagram(gridmax=100, param='sigma', arrows=True, shock=0.95, reset=True)\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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3RpYFVm+w4PpNAa1GaWH711IGB97XR8uWdhVjOLuQuAKGc3URQlj9cDLkAenn\nBUKCJHRsq0FwPQl6PT/EyPloNBKmTlSOgRvy/h6AmJNrvQvcaBTYFm9BHX+pqBfIr5ZyP1R+DGci\nG+TkCmRcEEi/ICMjUyDXIPD8EyVH6dQNkDDyfr6tyHVIkgRvL8DbS0JoSOnrCQHU8pFw6YrAsZMy\nrt0QyDUAjUIlPDbWrfoKdhH8FCEqg8Ui8J8VJuQagAb1JTQIkZTZrILZGiC6nYeHhB6RxbvNTSYl\noK25kCVj/VYLAutIqBsgIbCO8lPHH9Bq+f5iOFONJ4TAtetALV9lgM3ttFoJj4x2g78fR7MSlZeb\nmwR/P+t/qxsgYUg/LS5fFbhyTSDpsHLWQt0ACeNGlmxpl3YoyVUxnKlGupUtcDpVxpk0ZdSqRgM8\nPEqHoLol3/y2joQlItu5uUlKb1T94stLO6U2+YiM2D8sqBcooV6ApPwOVFrdd36pdgUMZxfCubVt\nsynOjKTDMpo11qB5Ywn9erJlTKQWpb0Pw8OUMxsuXVHOgjiTJvDnARmtm0vo29P1ooyTkKgAJyGp\nGhaLsHrsymAQ8PDgKFIiV7Z1hxkpZwTqBUoIqqu0toPqKiPIneGLuOt93aAaSwiBrEsCJ07LOH5K\nIKiuhFFWRk57ean/jUlElXNvdy3CWouilvbeZBkXLwvc11uL8DD1z77HcCanZzAIxO224MRpGVoN\n0LqFBvf306JhfYYwUU3l5iYhJEhCSFDx5aX10P76uxnGAiC4roTgehKCAiWHfpFnOJPTc3NTLiow\nIUaHugGSU3RZEZFjlPb50KWjBuczBbIuK+dpX7yiXLd74lg3q5cDrWoMZ3IKQgikn1e6qu+ce9rN\nTULve9TfTUVE6hVUV4Ogun//XwiB6zcAv1rW19/xpwUBtYH6QZoqGVDKcHYhrji39qUrMpKPyDh0\nXIaHu4TRQ7VWT3ciIrInSZJQp7b1vwkhIARw8KiMTXEWmExASJCE0GAJ/XrZZ95xhrMLcaW5tU+n\nyvh9lwXZOQLh7TR4ZLQO9QJ5gQgicjxJknBvdy0ApccuJ1fgQpbA9ZvWJ0oxm5Vrc5enhc1wJlXy\n8gT699KiaSOJpzwRkar5eEto1bz0z6lrNwS++T8zzGYgNERC/SAJocEatG5ReoOD4UwOlZcnrF4U\nPiSIrWQicg31AjWYPkWP7BylhX0+S0ZCkoXhTOoihMDpVIG9SRZkZCoXenfF6feIiG7n6yOhdQup\nzFAuxHBwLtUcAAAgAElEQVSmamMwCBw4JGP/IQs83CV0Dddg9FANg5mI6A4MZxei9rm1dyZYkJcH\njBmqQ/1gno9MRFQahrMLUftI7YH32ucUAyIiV8dRN2RXFovAqbOy1b8xmImIbMOWM9mF2SyQdETG\nrgQL/GtJaNJQgk7HMCYiqgiGM1WKySSw/6CM+H0WBNWVMHqIDg1D2SFDRFQZDGeqlD8PyLiQJWP8\nSB3PTSYishOGswtxxNzavbppIEm86AQRkT2xqeNC4grSq+y+ZVlYvQ4qB3kREdkfw5nKJITA4eMW\nfLrchPTz1i9STkRE9sVubSpVarpyOTSNBhh6nw6NGvC7HBFRdWA4Uwm5BoH1W8zIvCRwX28twlpr\n2H1NRFSNGM5UgrseaNxAg5ghnPeaiMgRGM4uxF5za+t0EqK6cAQ2EZGj8CCiC6nIaVQmEwd5ERGp\nDcO5hjIaBTbFmbH8v2arp0gREZHjsFu7hhFC4GiKMgq7WSMNJsToONiLiEhlGM41SHaOMgr7+k1g\n9FAdGvPUqFKZTAK5BsCQV/x3Xr6AyQyYzYDFApgtykU/lN/KDwBoNIBWq/xopMJ/S8pyDaDXA54e\nEjw98NePVOy3hwcneCGqyRjONcilKwLB9SSMHa6tMVeMMpsFLl0RyLwkkHlR4OJlgWs3/v65fhO4\ndl3g+k3l/zduCeTkAkIA3l6Al6dU7LenhwQ3HaDTATpt4W9J+a1TgleSAIushLf812+LLP7+twUo\nMClBn5ePv35E0e98I2A0Ktv3qyWhlo/y28/3r59aQC0fCX61JNT2AwLrSKgbIBX7rdfXjOeXyFUx\nnF3I3ebWbt5Eg+ZNXKe1LIRA1iWB1HSBs2kyUjMEUtNlZGQqQZx5SeDqdYGA2hJC6kkICZIQXFdC\nHX8JdWpLaBSqQR1/oI6/hNr+ynL/WkoI6/WObbnKstJSv3lL4Ga2wM1b+Ou3wM3sv5cfPSlw5Rpw\n+arAlWsCl68qj9nLE6gb8FdY15YQVFdCaLCE+sEa1A8q/Lfyd62WQU6kNgxnFxJXUP0XvqgOl68K\nHD8l49hJGcdPKT9nzsk4d17A11tC00YSmjTQoGkjCREdtHhgoBLEIfUk1At0zutKazQSfH0AXx8J\nDcp5W1lWwvz2wL54ReBClox9yRZcuChwIUvgfJbSUxAUqAR1/SAJDUI0aNxAQpOGGjRpqOzXgDrs\nYieqbgxnF2QwCJxNlxHW2rnOVc7JFUg+IiPpiAXJR2UcTVGC2CIDbVto0KaFBm1bahDd3Q3NmygB\n4u3F0LiTRiOhtj9Q219Cq+Zlr1tQoPQ+XLiohHVGpoxzGQLx+0xITRdIzZBhNKJYWCvhLaFZYw1a\nNtXArxafAyJ7Yzi7mNOpMn7ZZEaHNhqEtXZ0NaW7eUsgIdGC/QdlJB5WAjkjUyCstQadwjToFKbF\nw6N0aNtSg3qBEltuVUSvl9CogYRGZTTPb2ULnMuQlbBOVw4f7Em04HSqwKlUGV6eElo2ldCymRLW\nrZpp0LKphBZNNfDx5vNGVBGSUMlJrpIk1djzbaXMxRAh0yt8+//9739IS8vA9xfPosHZRujbOwQv\nvzjBjhVWjhACKacFdu+3IH6fBbv3yzibJiOigwaRnbToFKZB5/ZKy9gZu6BrMiGU4/snzwqcPCPj\n5NnCH4HTqTL8/ZTgbt1cg3atNGjXUvkdGsIvXERlYcvZBaSczEB8wjXk1ctG+1bZyDx/GXv2tMA9\n99zjkHqEEDh2UuD3nWb8vsuCXQkW+HhL6N5Fix5dNXj6ETeEt+O83a5Akv46Xh0M3Nu9+GEUWRY4\nnymQckbGidPK+fVrN5twNEVGXr4oFtbtWmkQ1kqDhqEMbSKA4ewStFqgQYiEwAB/uOkkuLl5IiEh\noVrDOS1DxpYdFsT+ofx4uAP9e2nx4HAdPn3XHaEhrjNKnGyj0UhoGCqhYagG/XsX/9vVawJHTyrj\nCo6myNgYa8LRkzKycwTattSgQxsNwttpEB6mRXg7Dfz9GNhUszCcXYCHu4SQIA0APwBAXl4eunXr\nVqXbtFgEEhJlrN9qxrotFlzIkjGgjw79e2kxf6YezRozjKl0AXUk9L5Hi973FG9tX7+htLAPHpOR\nfNSCH34x49AxGYF1JIS3U8YjFAZ200YSNBqGNrkmhrMLqFevHjIzM+Hp6Ym8vDy0b9++SlrNuQaB\n37ZZsG6LGb/+bkFQXQnDB2jx+XvuuCdCw/NlqdJq+0vo2U2Lnt20ANwAKF8ET6cKJB9VAnv5KhOS\nj8q4cUugY1sNwttpEdFBg67hSvc4D5eQK+CAMBUoz4CwC1kyguuVbDHs2bMHCQkJ6Natm12DOS9P\nYOM2C35ca8bGbWZ066TFyMFaDL1PhyYN2Tomx7l2XSD5qHLa3YFDyjnc5zIEOrbTIDJci67hGnQN\n16J1c060Qs6H4awCtoSzEAJ7DsjYlWDBpIfcEFCn6j5sTCalhbzqFzM2/G5Gl45aPPSADqPu16Fu\nAD/kSL2ycwQSD8vYm2TBvmQZ+w5akHVJoHN7Jai7dlR+t2jKLnFSN4azCtwtnM1mgQ1blZmdxo/U\nVdngmCMnLFi+yoxvfzKjeWMJj4x2Q8wQLYLqsoVMzuv6DYEDh/4O633JMq7fFOjWSYvuXTTo3lWL\nezprUdufYU3qwXBWgbLCOTtH4L+/mFHLFxg5WFfmBQ3uNre2NTduCvzwsxnL/2vChYsCj43R4fEH\n3dCqOQOZXNflqwJ/7rdg934L/jygtLQbhCin+3XvqkVUhHL8mt3h5CgMZxUoK5x/+tWMOv7KOaR3\nO/9zbnY85vr2sGmbB49a8OkKE35cZ8aAPjo8MU6HAX20/DCiGslsFjh8XMbu/fJfgW3BxctK6zqq\niwbdu2gRFaFFndp8f1D14GhtlRs5WGu3Y2Mmk8DPv1nw7+UFOJUqMOVRNxzb7oXgemwlU82m00no\n1F6LTu21mDpRGSV+5arAnweU1vXiL0zYm5SPRqEa9L5Hgz5/nQbWoD7fO1Q1GM4qZ49gzs4RWPqd\nCf9aYkKzxhKen6THyMFannJCVIbAAAnDBugwbIDyMWk2CyQdkbHjTwt+XGfGi28a4eMtoU+UFr27\nKWHdqjlnOCP7YDi7sMtXBT75qgCffW1Cv546/LLcAxEdnetKVURqodNJyojvcC1eeUY5g+L4KYGd\neyyI223B/A8LkG8Eet+jUSZY6aZFeBiPW1PFMJxVQpYF9ibJ6Bpe+TdzxgUZ7//HhG9/MmHsMB3i\n13qhZTN2vxHZkyRJaNtSQtuWynzxgDKN7c4EC3b8acEX3yiDLHtGatGvp/ITHqbhKVxkEw4IUwEp\nczH+t/8l5BqUU6XKGpFdlp8yMrBjSV18/X8mPDnODa884/bXtJ5E5AiXrwps323Btj8siP3DjEtX\nBe6N0qJvDy369dKiXSsNu8HJKracHcxkEkW/J8ToKnTJxGvXBRZ9VoAl3/njkRjgaBwHeRGpQd0A\nCWOG6TBmmA6AOy5kyYiLVy4O8+GXJuTkAn17aNH3r5Z1i6Y8Zk0KtpwdyGhUzjGe1OdjmOu9Uu7u\n7Px8gY++NGHRZwUYPVSHN17So2EoQ5nIWZzLkP9qVSs/ANCvp9Kyvq+3lu/nGozh7ECb48woMAHD\n239k89zagDIQ5f/WWzDrHSM6ttVg0ZvuPKZM5OSEEDh1VihBvcuC33eZUS9QwsB7dRh4rxb3dtfC\n24ut6pqC4exAZrOAVgtosv6fzeG8L9mCaXOMyM4B/t9cPfr14pEJIldksSjzhG/ebsGWHRbsTbIg\nspMWA+9Vfjq35+AyV8ZwVgFbLnxx/YbA7AVG/LLJgvmv6jFpnI6naBDVIDm5yuAyJazNuHxV4L7e\nysx+A/qwC9zVMJxVoKxwFkLghzVmTJ9XgFH3a/Hua+6lXviiInNrE5FzSj8vY8sOJay37vy7C3xQ\ntBbR3bXw9OSXd2fGcK4mRqOARgOrs3KVFs6nzsqY+poRl68KfPG+O+6JKHsCkfLMrU1ErkOWlS7w\nTXEWbIozI/GwjN73aDGknxb399OhWWO2qp0Nn7FqYDIJfL9GecPYQpaVmb26DzdgcF8t9v3meddg\nJqKaS6OR0KWjFq+/qMf2n7yQttcbjz/ohn3JMno8kIc2vXPxylwjtu4ww2h03UaQK6mW0USJiYn4\n/fff0aRJE4wZM6Y6NqkaFovA/9aZ4VdLQmSnu38XSk2X8cQrRuTnC/zxixcv3UhE5ebvJ2HscB3G\nDtcVtao3xlrw1qICHEmREd1diyH9dbi/rxaNGvAzRo2q7VnJzs5Gfn5+dW1OFYQQ+GWTcu7iiEFl\nX/JRCIEvvzMh8n4DBkdrsfNnTwYzEVVaYav6jZf1iF/nhdPx3njoAR127rGgy2AD2vc1YOZ8I+Li\nzUWTIpHjVUnLOTY2Fqmpqdi6dSv+9a9/oXPnzjh9+nSNajULIbApzoIbNwUeHWN9ZPXTTz+NlJQU\n4IfhqNd6MyxSI+xc2wphrdmFTURVIzBAwsMxbng4xg0Wi8C+ZBm//m7GjHkFOJMmY3C0Dg8M1GJw\nX12pg0+p6tl9QNiZM2cwd+5cfP311zAajXB3d7etEBcbECbLAlt3WNAnSgsPD+sv8OjoaGyPNwDn\nHgLayAjQf4j5897A1KlTK7RNjtYmosq4kCVj/VYL1m42Y8efynnVDwzUYvgADiqrbnYP5/fffx9t\n27bF8OHDy1eIJGHOnDlF/4+OjkZ0dLQ9S1MVWRZo2ekTnLk4DEhaA9SfAQC47777sGXLFgdXR0Q1\nXa5BaWCs3WzG+q0W1AuUMHyAFg8M1KFbZ06AUtXs3q195coVNGrUCACQkpKCWrVqITg42Kbbzp07\n197lqNLNWwKPPJ+PKzndgavRAF4CAAQGBiImJsahtRERAYC3l4QRg3UYMVgZVJaQKGPtZjOemmHE\nlWsCw+5Tgvq+3lp4cVpRu6uSbu1Vq1ahY8eO8PHxsbn162rd2qU5flLGyCfycF9vHW6mT8Fvv63H\nlYOvIbDjexgwYAC+//57R5dIRFSmM+dkrNtixtrNyrSi90ZpMWKQEuR1AxjU9sBJSOzEYBDQ6VDm\ntZjXbTbjyelGLJitx5MPKxdn/+yzz/DsSAP+87NXhY81ExE5yo2bAhtjzfj5Nws2bTcjvJ0GMUN0\nGDVYx9O0KoHhbAdms8DX/zMjrLXG6mQhQgi8928TPl1hwv8t8UBUl+Lr2DK3NhGR2uXnC2zdacFP\nv5qxbosZjRtoMOp+HWKG6NC2JYO6PHhJIzvYGGuBlyfQrXPJF5/ZLPDsbCP2JctI2OCJ+sFV9wLl\naG0iciQPDwnDBugwbIAOZrPAzj0WrNlowcBxefD2QlFQdw3XlDnvA3H6zkrbf9CCtPMyRt2vK/Fi\ny84RGD4xH+kXBLb/VLXBDABxBelVev9ERLbS6ST07anDx2+7I22fF775xAMA8Mjz+WjU1YAX3zBi\n2x9mmM3O2WNa1RjOlZB+XkbsLgseesAN7u7Fg/lClow+o/LQKFTCupUe8PXht0QiqpkkSUJkJy0W\nvO6O4zu9sOkHTwTVlTBjXgGCw3PxxLR8/Pq7GQUFDOpCDOdKOH5KxgMDdQi8Y3TimXMyeo3Mw9jh\nOny+0B06HYOZiAhQgrpdKw3+8ZIe+zd5Yf8mL3Roq8E7HxUguFMuJr3MoAYYzpUy4F4dWrcovguP\nnZRxb0weXp2qx+sv6nlchYioDI0baDDtaT3+WOuF5C1eCA/7O6gffzkfG7bWzKBmONtR0mEL+o3N\nwzuv6TF1opujyyEicioNQzV4ebIS1Ae3eqFzew0WfKIE9cSXalZQ81QqO/lzvwUjJuXjPwvcMXpo\n+QbB2+tUKo7WJiJXlHFBxupfzfjfOjOOnpQxfIAOY4fpMKCPtsR4H1fBcLaDvUkWDH00Hys+dMeQ\n/uU/O43nORMR2eZ8pozVG8z433ozjqTIGHafEtQD73WtoGa3to1kWWDtJjNycot/gUg+YsGwx/Lx\n5QcVC2YiIrJdaIgGLz6lx86fvXA41guR4Rq8/58ChHRWRn1v2e4ap2cxnG20408LbtwS8PL8e9nR\nFBmDJ+Tj3++444FBDGYioupUP1iDF55UgvrgVi+Etdbg9fcK0KCLAS/8w4j4vRbIsnMGNcPZBhkX\nZOxLViYaKbxM2ulUGQPG5WHRm3qMHc5gJiJypAb1NZg+RY+9G72wc40n6gVKeGpGPpreY8Cst41I\nOmxxqkOnPOZ8FwUFAl98Y0L/3jq0a6V8l7l0RUbPEXl45Wn7jMrmMWciIvsTQuDQMRk//GzGql/M\n8HAHxo90w7gROrRqru62qbqrU4EtOywIDdEUBXNOrsDQR/MxboROdadLxRk5fScRUSFJktCxnTIz\n2Zk/vbD8Xx64el3g3tF56DLIgA8+K0D6ednRZVrFcL6LRqEShvRTriJlMgk8+Ew+OrTRYN6regdX\nVhLn1iYisk6SJER10eKj+e7I2O+F99/Q48RpGZ0GGtBnlAH/WWHC5avq6b1lON9Fh7ZaeHgoXe7P\nzjYCAL54350zfxEROSmtVkL/3jos/cADmYneeHWqHrsSLGjZMxfDHsvDf38xwWBwbFAznG300Zcm\nJCTJ+PELD7i5MZiJiFyBXi9h+EAdvv+PBzL2e2PcCB2WrTIjtIsyz/fvO82wWKo/qBnONtgcZ8bC\nT034ZbkHfLwZzERErsjHW8Ijo92w6QdPHI3zQsd2Gsx8uwCNIg14dZ4RyUcs1VYLw/kuUk7LeOQF\nI/77uQeaNOTuIiKqCUKClAty7N/khS2rPOHmBjzweD469jfg/U8LkHGhageSMW3usH23BSfPKDv9\n5i2BBx7Pw/yZevSJ0jq4sruL1nNebSIie2vXSoN3Z7vj7B4v/Psdd5xKlRE+wIB+Y/Ow7AcTbt6y\nf7c3w/k2WZdkJCRaEBKkDACbNC0f0T20eOZRdZ0yVRpe9IKIqOpoNBL6RGmxZJEHzu/3xvOT3LBu\nixmNInPx4DP5WLvJflfNYjj/RQiBdVss6N9LCx9vCR9/ZcK5DIGP5rk7ujQiIlIZDw8JMUN0WLPM\nE2f/9Eb/Xlos+qwAoRG5eOEfRuxLrtyMZAznvyQekqGRgM4dNEhItOCdj0z43xIPl7rKCRER2V+d\n2hKeedQNO3/2wp4NXgisI+GhKflo3zcPC/9dgPOZ5T8+zXAGkJcnEPuHBUP6a3H9BvDgM/n44n13\nNGvM3UNERLZr1liDOdP1OBXvhc8XuuPkWRnt+xkwaHwevv/J9vOnObc2gBs3BVLOyIjspMGDz+Sj\nfpAGH82vvu5szq1NROS6DAaBXzaZsfJ/ZiQkWRBzvw4TH3RD73tKH2jMpiEAfz8J3Tpr8e1qM46d\nFFj4D/VNzWkLzq1NRKQ+Xl4Sxo9yw2/fe+JwrBdaNdNgyixjmbdhOP/lXIaMV+Ya8e0n7vDwcM7j\nzJxbm4hI3eoHazDzOT0Ob/Mscz2GMwBZFpj4Uj5mTNGjU3v1n89MRETO7W7XZ2A4A/hwqQkWCzBj\nqnOcz0xERK5N5+gCHOVsmoyA2hKuXBN49+MC7NngBa3WObuziYjItdTIlrPRKLB6gxk5uTKemWnE\nrOf0aN6kRu4KIiJSoRqZSPH7LGjWWIOtO2VcvS4w7WnX6M7m3NpERK6hxnVr5+QKJCTKiBmiQ6+R\nefj1Ww/odK7RnV1dc2ubTCZYLBZ4eHhUy/aIiGqaGtdy/mOvBR3baTDvXwV4dLQOXTpydHZ5rVq1\nCh06dIDBYHB0KURELqlGhXNBgcChYzJ0WmBbvAVzZzjnZCOOlpeXh1OnTmHSpEkOm9WNiMiV1ahw\n1uslPDtRh9kLCrDwH3r4eLtGd7YjeHh4YP369Vi6dKmjSyEicjk1KpwB4IefLXDXAw+PqnGH20tl\nNpthMpls/jGbzZAkCQaDAS+//DKSk5Md/RCIiFxKjQrnm7cE3ni/AB+/7V5sdpbIyEhkZGQ4sDL7\nqMjc2gkJCXBzc4Ner7f557nnnkNeXh4ApYv71VdftfdDISKq0WpUOM/7VwGG9tcWGwR29epV7Nu3\nD3v27HFgZfZRkbm1r169CgDIycmx+efjjz+Gp6cyL6ynpyfee+89uz4OIqKarsb07aamy1jxowlH\n47yKLU9KSgIA7Nu3D6NHj3ZEaarg7e1t87ru7u4QQsDLywuLFi1CREREFVZGRFTzuHw45+cLbNxm\nwc8bzXj+cTcE1S3eWXDgwAFIkoRdu3Y5qELnlJ+fj5iYGEydOtXRpRARuRyXD+d9yTLOZcj4Lc6C\nk394lfj7rl27IITA4cOHHVCdc/Lw8ECzZs2wcuXKu15ZhYiIys+ljzmbzQJ7Ei3YFGfBrOfcUMu3\nZJAcOHAAgDKw6dKlS9VdolMaP348Dh06BB8fH0eXQkTkklw6nJOPysjOEThyQsazE0vOn20wGJCV\nlQVAOY5aePzZWVXX3Npubm7w8irZC0FERPbhsuEshMDufRbE/mHBm9P08PAo2Wo+dOhQUcjk5eUV\ntaKdVXXNrU1ERFXLZcP52nXg0hWB1HSBiWOtH1o/ePAg8vPzi/6/e/fu6iqPiIioVC4bzgF1JBw8\nJuPVqW7Q660PWhoyZAg+//xzAMBTTz2FN998szpLJCIissplw/ngUQv2JMp46uHSr9UcGhqKSZMm\nAQDGjh2Lrl27Vld5REREpXLZcH73YxOmTXaDpydP9SEiIufikuF88oyM33eZMdXKCG1XVpG5tYmI\nSH1cMpw//sqEpx9xg69PzWo1V2RubSIiUh+XmyHshzUmfPuTCYdjeR4uERE5J5dqOWddkrHqFzPu\n76tFaIhLPTQiIqpBXKrlvC/Zgj2JFqxd4enoUoiIiCrMZZqXZrPAj2staBSqQbfO2rvfgIiISKVc\nJpyPn5KRkGTBjCk1a4T27aprbm0iIqpaLhPOv++y4Op1gVH3u1RPfblwbm0iItfgMuF8LkPGk+Pd\n4OZWs06fIiIi1+MSzUyjUeDb1RbsXseBYERE5PxcouX8829mdGirQfMmLvFwiIiohnOJNFv6nRmT\nH3aJTgAiIiLnD+fUdBlJRywYOZjhzLm1iYhcg1OHsxACiz4rwJihOnh4cCAY59YmInINTh3OGRdk\n/LTBggmj2WomIiLX4dThvH6rBQICPSM5IxgREbkOpw1nIQT+b70ZDw7XQaNhlzYREbkOpw3nzIsy\nDhyS8fQjNXe6TiIick1OG84/rrOgTm0J7duwS7sQ59YmInINThvOh47JGDeCA8Fux7m1iaimCA8P\nR3JysqPLqDJOmW5CCGzZYcFv33O6TiKimmj+/Plo2bJlpe5j27ZtSEhIQE5ODiIiIjBq1Cg7VVd5\nThnO+w/K8PQA2rbkQLDKWLt2LT755BMAwD/+8Q889thjaN26tYOrIiIq27FjxzB//nzcunULjzzy\nSIXuw2QyYdasWUhISAAAdOnSBX369EFAQIA9S60wp+zW/vk3M0YO1kGSGM6VsWTJEmzduhUAsGjR\noqIXKRGRmrVt2xY+Pj4YMGBAhe9j8+bNaN68edH/IyIiEBsba4/y7MIpW85rNlrw1WJ3R5fh9Hr1\n6oXNmzfDZDLB3d0dnTt3dnRJRER3ZTAYkJOTg6CgoBJ/O3PmDJYuXVrqbaOiojBixAikpaUhMDCw\naHlAQABOnjxZJfVWhNOF8/FTFly/KdCts1M2+qtUnDG9XIPCIiIi4OnpCZPJBKPRiDZt2lRhdURE\n9rFr1y706dMHZ86cQWJiIqZNm4Zz585BkiQ0a9YMCxYsuOt93Lp1Cx4eHkX/1+v1yMnJqcqyy8Xp\nEm7hpyb07Kpx6MQjQggcO3bMYdsvTXnn1u7UqRPy8/MBAE2bNoVO53Tf1YioBoqNjcXly5eRm5uL\n0aNH48SJE+U+zNm0aVMIIYr+n5eXhzp16ti71Apzqk9jIQR27rHgnzP0Dq0jLS0NYWFh2LJlC/r3\n7+/QWiqjXr168PLyQkFBAbp16+bocojIScTFmxEXbymxPLqHFtE9SsaKtfVLW9cW27dvx4MPPohn\nnnkGmzZtgq+vb9HfbO3WDgsLw6+//lq0/MKFC4iMjKxQPVXBqcI5NU0g44LAiEGOnXhElmVIkoTR\no0fj6NGjqF+/vkPrqYz27dsjPj4ePXr0cHQpROQkonvoyhWs5V2/LDdv3oTFYsG0adNw8uRJJCYm\n4urVq0WnQdnard2qVSskJSUBUBp+hw8fxldffVVivdzcXDzwwANYvXo1/P39i5bPnDkTPXr0wMiR\nI+3yuO7kVN3a/7fBjDYtNPDxdnzZXl5eRU+a2Wx2dDkV1rt3b8iyzMFgROQUEhMTMWzYMABAjx49\nsH37djRu3Ljc9+Pm5oa5c+di3rx5mDdvHhYuXFjsGHQhb29vtGjRolgwA4BWq0WfPn0q9iBs4FQt\n503bzRjQp2pazQkJCTAajTatm5GRgYKCApjNZhw7dgyvvvoq/vWvf1VJXVWta9eukCQJHTt2dHQp\nRER3FR0djejoaACo8DnOhUaOHGm15btixQoEBwfj8OHDePbZZ+Hl5VX0t6+++gqhoaE4dOhQlR6j\ndppwlmUZyUdkvDfb/qdQ+fj44LXXXqvQbQ0GA5YsWYIPPvgAWq1ju9srMrd29+7dMXbs2GIvPiKi\nmmr16tXw9fXF4MGD8e233yI+Ph5RUVEAgDVr1sDf3x89e/bE+vXrq7QOx/cP2+h0KuDuLqFLuP1L\nzs7OhhDC5p8zZ87Ax8cHgNK9/fXXXzs8mIGKza0dEhKC//73v1VQDRGR89m1axeio6NhNBqh1Wqx\nffv2oslKdu3ahd69eyM+Ph7du3dHVlZWldXhNOG8ZYcFA3prVTMrmBACnp6emDhxIkaPHu3ocoiI\nyA5iYmKwceNGLFu2DAsWLEBgYCDOnj0LABgyZAiSkpKQnp6O8+fPlzgObU+SuP1ELweSJAlllfLQ\nM0cF9yYAAA61SURBVPkY0l+LiQ86/vrNZ8+eRbNmzdChQwfs27cPen3lTu2SMhdDhEy3U3VEROTs\nnKLlLITA9j8tuLe747uOAWX0XsOGDbFhw4ZKBzMREdGdnGJAWMppAb0b0LiBOrq069WrVzRVHBER\nkb05Rcv5l01mdO+iUVUYqqmWQnHG8k3fSURE6uQc4bzZjLDW6ujSVrPyzq1NRETqpPpwlmUZR47L\nGD6Q4UxERDWD6sM56bCALIBOYaovlYiIyC5Un3hbdirzaavxGC8REVFVUH047zkgo0sH1ZdJRERk\nN6pPvdR0gf69ebzZFhWZW5uIiNRH1ec5m80CKWdkDOij6jJVoyJzaxMR1UTbtm1DQkICcnJyEBER\nUXQ9aLVQdeodOSGjYX0JfrV4vJmIiP4WHh6Or7/+GuHh4eW+rclkwqxZs5CQkAAA6NKlC/r06YOA\ngAB7l1lhqu7WTkiS0a0zu7SJiKi4t99+Gy1btqzQbTdv3lx0pSkAiIiIQGxsrL1KswtVt5wTEi3o\n1knV3x+IiMgBhg8fXmLZmTNnsHTp0lJvExUVhREjRiAtLQ2BgYFFywMCAnDy5MkqqbOi1B3OSTKe\nfsTxV6EiIiL1uHbtGpYsWYJ27drhvffew86dO6HVatGsWTMsWLDgrre/desWPDw8iv6v1+uRk5NT\nlSWXm2rD2WCQcfykjA5teLzZVnHGdA4KI6IqF2dMtzpdcLS+odXPIGvrl7bu3eTl5eGBBx7ADz/8\ngIYNG6J///7Qast3+LNp06a4fPlysfsMCgoqdy1VSbXhHL9PRkBtCR4e7Na2VVwBw5mIql60e/mC\ntbzrl2Xz5s1o1aoVGjZU7s/b27vob7Z2a4eFheHXX38tWn7hwgVERkaWWD83NxcPPPAAVq9eDX9/\n/6LlM2fORI8ePTBy5Eh7PCSrVBvOu/db0LwJW81ERPS3ixcvokWLFkX/j4uLQ2RkJLy9vW3u1m7V\nqhWSkpIAAEIIHD58GF999VWJ9by9vdGiRYtiwQwAWq0Wffr0qeQjKZtqwznpiIyw1mw1ExHR38aP\nH4/58+fj559/BqB0Ud/eeraFm5sb5s6di3nz5kEIgYULFxYdg16xYgWCg4Nx+PBhPPvss/Dy8iq6\n3VdffYXQ0FAcOnQIderUsd+DskK14XzitIwh/fSOLoOIiFTE19cX77//fqXvZ+TIkSW6pVevXg1f\nX18MHjwY3377LeLj4xEVFQUAWLNmDfz9/dGzZ0+sX7++0tu/G9U2TdMyBHpEqrY8IiJyMbt27UJ0\ndDSMRiO0Wi22b99edD70rl270Lt3b8THx6N79+7Iysqq0lpUmX6XrsiQJKB1cx5zLg/OrU1EVHEx\nMTHYuHEjli1bhgULFiAwMBBnz54FAAwZMgRJSUlIT0/H+fPnSxyHtjdJCCGqdAs2kiQJhaVs+8OM\nOR8UYMcar7vcyjVImYshQqY7ugwiIlIJVbacT5wWaNNClaURERFVOVUm4InTMlo1U2VpREREVU6V\nCZhyhuFMREQ1lyoTkOFMREQ1meoSMDdXRmq6QNNGjq7E+cQZS851S0REzkd14Zx0VIZ/LcDdXXWl\nqZ61ieiJiMj5qC4BDx6RERqsurKIiIiqjepS8NgpGU0acvIRIiKquVQXzqdSBVo0UV1ZRERE1UZ1\nKZiRKaMFR2oTEVEZwsPDkZyc7OgyqozqrkqVnw90C2c4VwTn1iaimmL+/Plo2bJlpe5j27ZtSEhI\nQE5ODiIiIjBq1Cg7VVd5qgpnIQQyMgVaNWc4V0S0+/9v7/5imrz3OI5/GrAHaeGswOAwJ0QQEmcM\nsRxyhIVGtnhh1NlEXLJEL7abXbnEeMGlDVviNHM3u5shZssyk4UJM8ZlhEAJXefwBJwx+xOUpIzD\njnAkWymwUutzLky66VgmtfT5Wd+vu+dpnuf5cPXh+/ylnAHkvu+++05vvvmmotGoDh06lNY+EomE\nOjo6NDIyIklqbGyUz+dTaWlpJqOmzagWnL1taf16ye3ihjAAwMq2bNkit9utXbt2pb2Pvr6+1Ocg\nJcnr9WpgYCAT8TLCqMk5MmWpeoNR/y8AAAyzuLioWCymioqKP/w2MTGhM2fO/Om2O3bs0P79+zU5\nOamysrLU+tLSUo2Pj69J3nQYVc6T/7FU/SxTMwDgz4VCIfl8Pk1MTGhsbExHjx5VJBKRw+FQTU2N\nTpw48Zf7iEajKigoSC07nU7FYrG1jL0qRo2pkam7qn7WqEgAAMMMDAxodnZWCwsLOnDggH744Qc5\nHKsb7DZt2iTLslLLS0tLKikpyXTUtBk1OYf/nVTVBibndAXjP3JTGIA153gmMxOmNe1Oa7uhoSG9\n/PLLev311/XFF1+oqKgo9dvDntbeunWrLl26lFo/PT2tpqamtPKsBaPK+b8zlv7JY1RpCy5TzgDW\nXrqlmgm//PKLksmkjh49qvHxcY2Njen27dupx6Ae9rR2fX29rl69Kunek0LXr19XV1fXmmZfDaPK\n+X9zlqqeoZwBACsbGxvT3r17JUktLS0aGhrSnj17Vr2fdevWKRAIqLOzU5Zl6eTJk/ddg7abw/r9\nSXcbORwOlW+bV0/XerU05dkdJ6scP52WVXnskfcTmA8rUNSSgUQA8GQaGhrShQsX5Pf71d/fr9de\ne01VVVU6d+6campqUtemu7q69O6776qjo0OnT5/WkSNH9N5772Ush1FjanReqqnmmjMAwB6bN29W\nNBpVa2ur8vPzFY/HdfbsWcXjcS0vL8vr9aqsrEwzMzPKz8/XwsKCJGn37t0ZzWFUOSfuSBVPU84A\nAHu43e7UW8IikYhcLpeuXbum9vZ2+Xw+JRIJFRYWqry8XHNzc6qsrJQkFRcXZzSHUeX8TIVj1bfD\n4ze8WxsAHs3o6Kja2tokSR6PR1NTUzp48KC6u7vV39+vpaUleTweeTwenT9/XslkUuFwWM3NzRnN\nYdQ153/tWdDli4V2R8m6TF1zBgDkBqMm539wShsAALPKmevNAAAYVs6ev1POAABQzgAAGMaocl5c\nMuLetMdWMP6j3REAABlgVDn/vZjJ+VEElylnAMgFRpVzWQnlDACAUeX8dKndCQAAsJ9R5VxealQc\nAABsYdQnI3nOGQCQDYODgxoZGVEsFpPX6019D9oURpVzeZndCR5vvFsbwJOioaFBH374oRoaGla9\nbSKRUEdHh0ZGRiRJjY2N8vl8qQ9emMCo88hOp1FxHjs7/0Y5A3gyvPXWW6qrq0tr276+PtXW1qaW\nvV6vBgYGMhUtI4yanAEAeBj79u37w7qJiQmdOXPmT7fZsWOH9u/fr8nJSZWV/XaqtrS0VOPj42uS\nM12UMwDgsTI3N6f3339fzz33nN5++20NDw8rLy9PNTU1OnHixF9uH41GVVBQkFp2Op2KxWJrGXnV\nKGcAwKo4fjqdkf2k86ncpaUlvfTSSzp37pw2btyoF198UXl5eavax6ZNmzQ7O3vfPisqKladZS1R\nzgCAVbHz+/N9fX2qr6/Xxo337rFxuVyp3x72tPbWrVt16dKl1Prp6Wk1NTWtXeg0UM45JBj/kZvC\nAOS0W7duafPmzanlYDCopqYmuVyuhz6tXV9fr6tXr0qSLMvS9evX1dXVtWaZ08Ht0TmEd2sDyHWv\nvPKKfv75Z/X29qq3t1cej+e+6flhrFu3ToFAQJ2dners7NTJkydVUFCgYDCoY8eOaXh4WMePH1ck\nEpFlWfr44491+fJlDQ4O6ptvvtEbb7yhO3fu6Nixe2cQjhw5kvG/k8kZAPDYKCoq0qlTpx55P36/\nX36//751dXV1ikajam1tVTAYVDwe19mzZ+VwOLS8vCyv16tYLKaZmRnl5+drYWFBkrR79+5HzvMg\nJmcAACS53e7Ui0gikYhcLpeuXbum9vZ2+Xw+JRIJFRYWqry8XHNzc6qsrJQkFRcXZzwL5QwAgKTR\n0VG1tbVJkjwej6ampnTw4EF1d3erv79fS0tL8ng88ng8On/+vJLJpMLhsJqbmzOexWFZlpXxvabB\n4XDIkChZ5/jpdEbufgzMhxUoaslAIgCAnZiccwjv1gaA3EA55xAeowKA3EA5AwBgGMoZAADDUM4A\nABiGcgYAwDCUcw4Jxnl9JwDkAso5h/BubQDIDZSzCcI37E4AADAI5WyC8E27EwAADEI5AwBgGMoZ\nAADDGPPhi507d2poaMjuGAAAZMXx48cVCARW/M2YcgYAAPdwWhsAAMNQzgAAGIZyBgDAMJQzAACG\noZwBADAM5WyTTz75RD6f7751Y2Njeuedd9Td3W1TKgCACShnm2zbtk3Nzc1/WD8/P69ff/3VhkQA\nAFPk2x3gSfXVV1+ppaXlvnXbt2/XzZs31d7eblMqAIAJmJxtMjIyou3bt6u3t1eNjY2p9RQzAIBy\ntsm3336rUCgkv9+vUChkdxwAgEEoZxvEYjFJUk9Pj4LBoNavX29zIgCASbjmbIMrV65o79692rVr\nl3p6enT37l298MILdscCABiCydkG33//vdra2lRdXa3Z2Vm53W67IwEADMJXqQAAMAyTMwAAhqGc\nAQAwDOUMAMAKDh06JKfTqc8//zzrx+aaMwAAK1hcXJTH49GtW7f01FNPZfXYTM4AAKwgHA6rtrY2\n68UsUc4AAKxoeHhYzz//vC3H5iUkAACsIBQK6fDhw5KkDz74QNPT09qyZYv8fv+aH5vJGQCAByQS\nCX399ddqbm7WRx99pH379ikYDOrKlStZOT6TMwAADxgdHZXT6dRnn32mw4cPq6SkRKdOnVJdXV1W\njs/kDADAA4aHh9Xa2qr6+np9+umnkqSGhgYVFhZm5fiUMwAADwiFQjpw4ID8fr8uXryo7u5uJZNJ\n3bhxIyvHp5wBAPgdy7L05Zdfpu7UdjqdsixLg4ODcjqdWclAOQMA8DszMzPasGGDamtrJUmvvvqq\nLly4oOnpaVVVVWUlA28IAwDAMEzOAAAYhnIGAMAwlDMAAIahnAEAMAzlDACAYShnAAAMQzkDAGAY\nyhkAAMNQzgAAGOb/zrtmps5u3QsAAAAASUVORK5CYII=\n",
       "text": [
        "Figure(640x480)"
       ]
      }
     ],
     "prompt_number": 422
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\n",
      "model.solve_linearization("
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.figure(figsize=(8,6))\n",
      "\n",
      "k_star = model.steady_state.values['k_star']\n",
      "kgrid = np.linspace(0, 2.0 * k_star, 1000)\n",
      "\n",
      "# specify some numeric values for alpha and sigma \n",
      "tmp_alpha = model.params['alpha']\n",
      "tmp_sigma = model.params['sigma']\n",
      "\n",
      "plt.plot(kgrid, df_dsigma_num(kgrid, tmp_alpha, tmp_sigma), \n",
      "         label=r'$\\alpha=%g, \\sigma=%g$' %(tmp_alpha, tmp_sigma))\n",
      "\n",
      "plt.axhline(0, ls='dashed', color='k')\n",
      "\n",
      "# add axes label, title, legend, etc\n",
      "plt.xlabel('Capital per effective worker, $k$', fontsize=15, family='serif')\n",
      "plt.ylabel(r\"$\\frac{df}{d\\sigma}$\", fontsize=25, family='serif', rotation='horizontal')\n",
      "plt.title('The effect of a change in $\\sigma$ on $f(k)$', fontsize=20, family='serif')\n",
      "plt.legend(loc=0, frameon=False)\n",
      "\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "ename": "ZeroDivisionError",
       "evalue": "float division by zero",
       "output_type": "pyerr",
       "traceback": [
        "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m\n\u001b[0;31mZeroDivisionError\u001b[0m                         Traceback (most recent call last)",
        "\u001b[0;32m<ipython-input-424-38d65052a851>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m      8\u001b[0m \u001b[0mtmp_sigma\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mmodel\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mparams\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m'sigma'\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      9\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 10\u001b[0;31m plt.plot(kgrid, df_dsigma_num(kgrid, tmp_alpha, tmp_sigma), \n\u001b[0m\u001b[1;32m     11\u001b[0m          label=r'$\\alpha=%g, \\sigma=%g$' %(tmp_alpha, tmp_sigma))\n\u001b[1;32m     12\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
        "\u001b[0;32m/Users/clarissasweet/Library/Enthought/Canopy_32bit/User/lib/python2.7/site-packages/numpy/__init__.pyc\u001b[0m in \u001b[0;36m<lambda>\u001b[0;34m(k, alpha, sigma)\u001b[0m\n",
        "\u001b[0;31mZeroDivisionError\u001b[0m: float division by zero"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "text": [
        "Figure(640x480)"
       ]
      }
     ],
     "prompt_number": 424
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.figure(figsize=(8,6))\n",
      "\n",
      "# specify some numeric values for alpha and sigma (you may wish to change these!)\n",
      "tmp_alpha = model.params['alpha']\n",
      "tmp_sigma = model.params['sigma']\n",
      "\n",
      "plt.plot(kgrid, dmpk_dsigma_num(kgrid, tmp_alpha, tmp_sigma),\n",
      "         label=r'$\\alpha=%g, \\sigma=%g$' %(tmp_alpha, tmp_sigma))\n",
      "plt.axhline(0, ls='dashed', color='k')\n",
      "plt.xlabel('Capital per effective worker, $k$', fontsize=15, family='serif')\n",
      "plt.ylabel(r\"$\\frac{df'}{d\\sigma}$\", fontsize=25, family='serif', rotation='horizontal')\n",
      "plt.title(r'The effect of a change in $\\sigma$ on MPK', fontsize=20, family='serif')\n",
      "plt.legend(loc=0, frameon=False)\n",
      "          \n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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p06aYNGkSoqOjS9OURVJSeEyfiIiosBJPvW/evImEhATZ0D98+DA6d+4MAJg1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\n/wM1+QsBhvlsvQAAAABJRU5ErkJggg==\n",
       "text": [
        "Figure(640x480)"
       ]
      }
     ],
     "prompt_number": 409
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "dmpk_dsigma_num(1, tmp_alpha, tmp_sigma)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "png": "iVBORw0KGgoAAAANSUhEUgAAABsAAAASCAYAAACq26WdAAAABHNCSVQICAgIfAhkiAAAAR1JREFU\nOI3t1CtLBFEYh/Gf7i4ia9CkwY1WQSxGwaqfwGaw2aw2m8Gu38GsxWwRRIuXNZgEL4igYV28hNmB\nwzCzc2YFk2+Zmf95n/PMHM4c/rCGMs/T2ME9XtHALp4j5qrE1tDGepBt4wjDJaLK7Co6aAbZDL6x\nViKrzJ7hOCe/xUGJLIpNP7GOWdzkAG0s9hFFs6lsUrJZ3nKAd0xgpEAWzaayqWAwD4DxAlk0m8o6\nvetXDtDoM1aJTWVX+CiYrIkungrGo9lU1sWlZH2zNYYHyTbOq2g2/OHO0co01zCHiwLRwOym5GgZ\nDbKF3lstZXpbmb4qLJJluMZGkO3hJNM3j08cVmXrwf0LlrGF/V7WxEpG9og7nA7A/tfv6wdiPFQV\nohcVCQAAAABJRU5ErkJggg==\n",
       "prompt_number": 411,
       "text": [
        "0.0"
       ]
      }
     ],
     "prompt_number": 411
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def savings_rate(k):\n",
      "    \n",
      "    c = consumption_policy_func(k)\n",
      "    y = model.output(0, k, model.params)\n",
      "    \n",
      "    s = 1 - (c / y)\n",
      "    \n",
      "    return s"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 260
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "kgrid = np.linspace(kmin, kmax, 1000)\n",
      "plt.plot(kgrid, model.get_capitals_share(kgrid))\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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t8vYiIpbx+oVXIf+5/19hYSEVFRXk5+cTFxdXb5+DBw96PjQ3NxebzUa3bt14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\nsB1e6QavAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0xa84fc10>"
       ]
      }
     ],
     "prompt_number": 265
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "savings_rate(k_star)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 269,
       "text": [
        "0.35802484338211749"
       ]
      }
     ],
     "prompt_number": 269
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "k_star"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 271,
       "text": [
        "19.30052917806588"
       ]
      }
     ],
     "prompt_number": 271
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "kgrid = np.linspace(kmin, kmax, 1000)\n",
      "plt.plot(kgrid, savings_rate(kgrid))\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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6U1LkMs9jx8qBBvfdJ4chU9tksVhgsVgcj1966aWmj7ZsqBOhprP42LFj1+0s\nPnLkiKj+uWdyx44dYtSoUUIIISoqKsT58+eFEEKcOXNG6PV6cfz4cSGEEHFxceL9998XQgjx3nvv\niccee8xpnR5UV3m5EAkJQvj4CJGVpXQaai3nzgmRnCzElClC3HGHEAMGCLFggRBffMHBBO1Zc46b\nDX7CYrGIoKAg4evrK1asWCGEEOKtt94Sb731lhBCiCVLloj+/fsLg8Egpk2bJr788kshhBBHjx4V\noaGhIjQ0VAwfPlysXbvWsc+vvvpKxMXFiZCQEDFp0iRRWFjotC9EN7ZtmxB33inE9OlyRAi1P0VF\nQvztb0IMHy5E165CjB4txKpVQnz3ndLJqLU057jJCWUaU1oKLFggOwGXLZOzkzn9v+26cEGuSLtj\nh1ymvLxcTvB6+GFg+HB28moRF52jRsvJAZ56CnB1lSNG7rtP6UTUGEIA33wjFxv86CNg1y45bDgq\nSh78DQYWdq1jIaAmqa6Wy1IsWACEhQGvvsobgqtRSQmQmXn14N+hAzBihFzSYfhweaMiohosBNQs\nVVVyobC//U0uIbBgAZe2VlJZmWzusVjkPSeKioD775cH/shIucQDz/rpRlgI6KaUlQGrVgGvvw7c\ney/wzDNyHgIPOi3r/PmrB36LRa7iOXgwYDbLbehQ4JZblM1IbQcLATlFZSWwdq2cd6DTyb6ERx9l\nx6Oz/PADsHevXA7EYgG+/lo2zZnN8szfZJJ/70TNwUJATlVdLZsm/v53YPduOQHpscfkUgRca75x\nLl8GvvxSHvT37pXbjz/K5T+GDpUH/7AwHvjJeVgIqMWcPAls2gS89x7w00/AxInypuMmE2el1qiu\nBo4cAfbvl5vVKmd2e3nJg/7QobLJLTCQhZRaDgsBtYovv5Tr0XzwgbxD1ejRcujiAw8A3bsrna51\nXLggO3Hz8q4e+A8ckN9/4EC5DRokCyUX16XWxEJArc5muzqZac8eeXPy8HDZ1j1kCNCnT9vubK45\n4BcUyLb8ggK52WzyuxqNVw/8RiOHcpLyWAhIUZcvyzPj7Gx5B6t9+2RzidEoN4NBzlPw91fP4ndC\nyKauY8eAb7+V29GjV//8/nu5Ln///nLiVv/+cvP35x25SJ1YCEhVhJAH0rw8uR08CBw+LNvRO3cG\n/PzkWXXv3le3Xr1k88ptt13d3Nwa/zsvX5ajnn76qe5WUiLz/Pe/tbdOnWSOu+4CfH1r/+nlxaGb\n1LawEFC3N/3FAAAI6klEQVSbUFMgDh8Gjh+XP3//vexv+P57OaqmrEyOrz9/Xi6DodPJTulrtw4d\ngIsXZfON3S7/BOQdtLp1k9vtt1/9uXt3eeOea7fevTksltoXFgJqd4SQB/jKSrmm/rVbdbU8W9fp\n5Fl9p06yaBBpGQsBEZHGNee4ydHMREQax0JARKRxLARERBrHQkBEpHEsBEREGsdCQESkcSwEREQa\nx0JARKRxLARERBrHQkBEpHEsBEREGsdCQESkcSwEREQax0JARKRxDRaC7OxsBAcHw9/fHytXrqzz\nempqKkJDQ2EwGBAVFQWr1ep4zcfHByEhITAajQgLC3M8HxcXB6PRCKPRiH79+sFoNDrp6xARUZOJ\nBhgMBpGVlSVsNpsIDAwUxcXFtV4vLy93/GyxWMSwYcMcj318fERJSUm9+587d6545ZVXrvtaI+Ip\n7tNPP1U6QqMwp3Mxp3Mxp/M057hZ7xVBaWkpACA8PBze3t6IjIxEbm5urfd0vuY+f6WlpdDpdL8s\nNPUVISQnJ2PixIlNLF/qYbFYlI7QKMzpXMzpXMyprHoLgdVqRVBQkOOxXq9HTk5OnfelpKTAx8cH\n8fHxWL16teN5FxcXDB8+HDExMdi2bVudz+3atQs9e/aEr6/vzXwHIiK6CU65w2tsbCxiY2OxefNm\nxMbGIi8vDwCwZ88e9O7dG4WFhYiOjkZYWBh69erl+NymTZswadIkZ0QgIqLmqq/d6Ny5c8JgMDge\nP/3002L79u31tjX16NFDVFZW1nn+mWeeEatXr3Y8vnTpkujZs6c4derUDffl6+srAHDjxo0bt0Zu\nvr6+9R6jr6feKwIPDw8AcuSQl5cXMjIysHDhwlrvOXr0KO666y64uLggLS0NgwYNgru7OyorK3Hl\nyhV07doVxcXF2LlzJ5555hnH5zIzMxEcHIxf//rXN/z9R44cqS8eERE5QYNNQ8uXL0dCQgIuXbqE\nWbNmwdPTE0lJSQCAhIQEbN26FRs2bICbmxuMRiOWLl0KADh9+jTGjh0LAOjevTvmzp2Lvn37Ova7\nefPmNt1JTETUXrgIUc+wHiIiavdUObO4oUlsSomPj0fPnj0xYMAAx3NlZWUYM2YMvLy8EBMTg/Ly\ncgUTSidOnMADDzyA/v37w2w2Y+PGjQDUldVut8NkMsFgMGDIkCF4/fXXVZfxWleuXIHRaER0dDQA\ndea83gRONeasqKjA1KlTERAQAL1ej9zcXNXlPHTokGPSq9FohIeHB9544w2Ul5erKicArFmzBvfe\ney8GDRqEP/7xjwCa/t9dlYVg9uzZSEpKQmZmJhITE3H27FmlIwEApk2bhg8//LDWc2+++Sa8vLxw\n+PBh9OnTB2+99ZZC6a5yc3PD66+/joKCAmzZsgUvvPACysrKVJVVp9Ph008/xYEDB5CVlYW1a9fi\n8OHDqsp4rRUrVkCv18PFxQWAOv+7u7i4wGKxIC8vD/v27QOgzpwLFy6El5cX8vPzkZ+fj6CgINXl\nDAwMRF5eHvLy8vDFF1/g1ltvRWxsLFatWqWqnD/++CNeffVVZGRkwGq1oqioCDt37mzy36fqCkFj\nJrEpZdiwYejWrVut5/bt24fp06ejU6dOiI+PV0XWXr16wWAwAAA8PT3Rv39/WK1W1WW99dZbAQDl\n5eW4fPkyOnXqpLqMAHDy5EmkpaXhiSeecEyQVGNOAHUmcKoxZ2ZmJp5//nnodDq4urrCw8NDlTlr\nZGZmws/PD3379lVdTnd3dwghUFpaiqqqKlRWVuL2229ves4mjzNqYRkZGSIuLs7x+M033xQvvPCC\ngolqO3bsmLj77rsdj728vERVVZUQQoiKigrh5eWlVLTrOnz4sOjXr58oKytTXdYrV66IkJAQ0bFj\nR7Fy5UohhDr/Pn/729+K/fv3C4vFIh5++GEhhDpz9uvXT4SEhIgxY8aI1NRUIYT6cp44cUIEBgaK\nqVOnirCwMPGXv/xFVFZWqi7ntaZNmyYSExOFEOr7+xRCiLS0NOHm5ia6dOkinn/+eSFE03Oq7oqg\nrREq7msvKyvDhAkT8Prrr6NLly6qy9qhQwccPHgQR44cwapVq5CXl6e6jNu3b0ePHj1gNBprZVNb\nTkBO4Dx48CAWL16MOXPm4PTp06rLabfbUVRUhHHjxsFisaCgoADJycmqy1nj4sWL+OCDDzB+/HgA\n6vvvXlxcjBkzZuDrr7+GzWbD3r17sX379ibnVF0hGDx4ML755hvH44KCAgwZMkTBRPUbPHgwCgsL\nAQCFhYUYPHiwwomkS5cuYdy4cZg8eTLGjBkDQL1ZfXx8MHr0aOTm5qou42effYZt27ahX79+mDhx\nIj755BNMnjxZdTkBoHfv3gCA4OBgPPLII/jggw9Ul9PPzw+BgYGIjo6Gu7s7Jk6ciA8//FB1OWuk\np6dj0KBBuOOOOwCo79/Qvn37MGTIEPj5+aF79+4YP348du3a1eScqisE105is9lsyMjIgMlkUjjV\njZlMJqxbtw5VVVVYt26dKoqWEALTp0/H3Xff7RhFAKgr69mzZ3Hu3DkAQElJCT766COMGTNGVRkB\n4NVXX8WJEydw7NgxvP/++xg+fDjeffdd1eWsrKxEWVkZADgmcI4cOVJ1OQHA398fubm5qK6uxo4d\nOxAREaHKnIBcBufa+U5qyzls2DB8/vnn+PHHH3HhwgWkp6cjMjKy6TlbqNnqplgsFhEUFCR8fX3F\nihUrlI7jEBcXJ3r37i1uueUW0adPH7Fu3Tpx/vx58cgjj4i+ffuKMWPGiLKyMqVjil27dgkXFxcR\nGhoqDAaDMBgMIj09XVVZ8/PzhdFoFCEhISIyMlKsX79eCCFUlfGXLBaLiI6OFkKoL+e3334rQkND\nRWhoqBg+fLhYu3atKnMKIcShQ4eEyWQSoaGhYu7cuaK8vFyVOcvLy0X37t3F+fPnHc+pMefbb78t\nwsPDxT333CNeeOEFceXKlSbn5IQyIiKNU13TEBERtS4WAiIijWMhICLSOBYCIiKNYyEgItI4FgIi\nIo1jISAi0jgWAiIijfv/2+OCVOCtjlkAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0xa733130>"
       ]
      }
     ],
     "prompt_number": 270
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "kgrid = np.linspace(kmin, kmax, 1000)\n",
      "plt.plot(kgrid, consumption_policy_func(kgrid))\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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za9Ysc/DgQTNo0CATHR1tEhMTTX5+vtMxzWeffWaioqJMly5dTFxcnImLizML\nFixwVdasrCwTHx9vOnfubAYMGGBee+01Y4xxVcaf8/v9ZuDAgcYY9+Xctm2b6dKli+nSpYvp16+f\neeWVV1yZ0xhjNm3aZHr27Gm6dOlixowZYwoKClyZs6CgwDRp0sQcPHjw2F9zY85XX33V9OnTx3Tv\n3t1MmDDBlJaWVjqnNs6IiHhExLx0FBHxOhW2iIhHqLBFRDxChS0i4hEqbBERj1Bhi4h4hApbRMQj\nVNgiIh7x/1iawLdw/coOAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0xa857fb0>"
       ]
      }
     ],
     "prompt_number": 272
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "kgrid = np.linspace(kmin, kmax, 1000)\n",
      "plt.plot(savings_rate(kgrid), model.get_capitals_share(kgrid))\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0xa857eb0>"
       ]
      }
     ],
     "prompt_number": 268
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "model.get_capitals_share(kgrid)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}