Homework 4 Question 1 (Value Function Iteration).ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Homework 4 Question 1 (Value Function Iteration)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "from IPython.display import display, Math, Latex\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import sympy as sy\n",
    "from operator import itemgetter\n",
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "import math\n",
    "from math import exp\n",
    "from matplotlib import cm\n",
    "from matplotlib.ticker import LinearLocator, FormatStrFormatter\n",
    "from plotly.offline import init_notebook_mode, iplot\n",
    "import plotly.graph_objs as go\n",
    "from math import log\n",
    "plt.style.use(\"ggplot\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [],
   "source": [
    "theta = 0.679\n",
    "beta = 0.988\n",
    "delta = 0.013\n",
    "h = 1\n",
    "#k = ((beta**(-1)-1+delta)/((1-theta)*h**theta))**(-1/theta)\n",
    "k = 1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1 a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 153,
   "metadata": {},
   "outputs": [],
   "source": [
    "def m(ki, kj):\n",
    "    c = ki**(1-theta)*h**theta+(1-delta)-kj\n",
    "    #print(c)\n",
    "    #Step 4 (consumption must be non negative)\n",
    "    if c >= 0:\n",
    "        return math.log(c)\n",
    "    else:\n",
    "        return -10000000"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 255,
   "metadata": {},
   "outputs": [],
   "source": [
    "k_min = 0.01\n",
    "k_max = 2\n",
    "p = 200\n",
    "\n",
    "#Step 1\n",
    "k = np.linspace(k_min, k_max, p) #The continuous variable k is discretized by defining a grid for the values of k\n",
    "\n",
    "#Step 2\n",
    "V = []\n",
    "V.append(np.zeros(p)) #Guess a solution\n",
    "V.append(np.zeros(p))\n",
    "k_dec = []\n",
    "k_dec.append(np.zeros(p))\n",
    "#ki_dec = []\n",
    "#ki_dec.append(np.zeros(p))\n",
    "kj_dec = []\n",
    "kj_dec.append(np.zeros(p))\n",
    "\n",
    "#Step 3\n",
    "#Define the return matrix M\n",
    "\n",
    "M = [0]*p\n",
    "for i in range(p):\n",
    "    M[i] = [0] * p\n",
    "\n",
    "for i in range(p):\n",
    "    for j in range(p):\n",
    "        M[i][j] = m(k[i], k[j])\n",
    "\n",
    "\n",
    "Chi = M + np.multiply(beta,V[-1])\n",
    "V.append(Chi.max(1))\n",
    "k_dec.append(Chi.argmax(1))\n",
    "#ki_dec.append()\n",
    "kj_dec.append(k[k_dec[-1]])\n",
    "\n",
    "while np.linalg.norm(V[-1] - V[-2]) > 0.01: #STEP 6: If ||Vs+1 − Vs|| < ε, stop and report success. Otherwise, go back to the previous step, STEP 5, replacing s = s + 1.\n",
    "    #STEP 5.1: Compute the matrix, χ\n",
    "    Chi = M + np.multiply(beta,V[-1])\n",
    "    \n",
    "    #STEP 5.2: Compute the updated value function Vs+1 as the maximum element in each row of χ\n",
    "    V.append(Chi.max(1))\n",
    "    k_dec.append(Chi.argmax(1))\n",
    "    kj_dec.append(k[k_dec[-1]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 256,
   "metadata": {},
   "outputs": [
    {
     "data": {
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THexyMAweRhh7SRaQe/cjFJw/VstnYJYkSXsUa7eyZdY0ii89m60iz5sBmzZmB7t1Jww7DgYfkwXkw3s5f6xWycAsSZJ2iFu3wptzibOnEee8BvNnsmrLluzgEX0IJ56WrSIPHkbodli+xUrNxMAsSVIbFmu3whvvDchsD8i9+xNOO5+DTngf6w7vTehycL7FSjkxMEuS1IbE2roV5Fl7Dshh6IhszKLzQQB0rKpifXV1jlVL+TIwS5LUiu0IyLNfI86e1qCALOm9DMySJLUiew/I/bKAPGQ4DBlmQJYayMAsSVILlgXkee/OIM+bCVtqsoMGZKlRGJglSWpBYnEbvP0GceYU4syp2TZv2wNyr76E959bN2IxjNDFgCw1BgOzJEllbMeT9GZOJc6aArOmwcb12cEj+hBOHUs4agQMHm5AlpqIgVmSpDITV60gzpwCs+pWkVevyA50PYww+mQ46ljCUSMJh3TNt1CpjTAwS5KUs7hhHcye9u4q8tJF2YHOXQhDR8LRxxKOHgmHHeGT9KQcGJglSWpmsaYG5k4nzppKnDUV3poPMUKHjtns8WnnEY46Nrtpr1DIu1ypzTMwS5LUxOK2bfDGnOxGvVlTYP5s2FYL7Spg4FDCuKsIRx8L/QcTKirzLlfSLgzMkiQ1gfjOEuKMycQZr8KsqbBpI4QAfQYQxl6crSAPPobQoWPepUqqh4FZkqRGEDeuh1lT60LyZFi+NDvQ9TDCCe8nHDMKjhrpXshSC2RgliRpH+wYs5jxahaQX58DsQgdDoCjRhDOvZRw9Cg4vKc36kktnIFZkqQGysYsXiVOnwyzt49ZFKDfIMIHrsgC8oChhAr/9Sq1Jv4TLUnSHsSNG7K9kKfXzSJXL8sOdOuejVkMG52NWRzYJd9CJTUpA7MkSXVijNljp1+bRJz+CsyfBdu2QccDYOgIwnmXEY4ZDd3dD1lqSwzMkqQ2LW5Yn80gbw/Ja1ZlB/r0J5z3QcLw42DAUY5ZSG2Y//RLktqUWCwSF8wjTtu+ijw7u1mv04HZ6vHw4wnDRvvYaUk7GJglSa1eXL+WOP1VmP4K1TMmU9y+itx3EOGiDxOGHw/9hxDatcu3UEllycAsSWp1YrEIO68ivzE3W0U+sAsdjhtDzeDh2SryQYfkXaqkFsDALElqFeLGDTDjVeLUl4mvTYJ1a7In6/UbTBiXZKvI/QZxcPfDqa6uzrtcSS2IgVmS1GLFpYuIU18iTn0J5s3IdrTo1DkLxyPqZpG7HJx3mZJaOAOzJKnFiLVbYc504rSXs5D8zpLsQK++hHMvI4w8MXtwiLPIkhqRgVmSVNbi2lXZLPLUl2DGZNi8CSoqsweGjL2UMPIEQrfueZcpqRUzMEuSykosFuHt17NZ5KkvwZtzswOHdCOcdAZh5AlZWO7QMd9CJbUZBmZJUu7ilhqYOYU45UXi1Jdhzcrshr0BQwmXXZuNWvTu59P1JOXCwCxJykVctza7YW/yRJjxKmypgQM6EYYdByNPJAw/zhv2JJWFegNzkiR9gNuBHkARGJ+m6Q+SJLkTGFp32iHA6jRNR+1ybUfgKaBD3Wf9Pk3Tf23E+iVJLUhctpg4eSJxykSYNyvbG7lrFeHUcwijToYhwwkVlXmXKUnv0ZAV5lrgpjRNX0mSpAswKUmSR9M0vXL7CUmSfBdYs5tra4Cz0zRdnyRJJfBMkiQPpmn6QqNUL0kqa7FYhDfmEKdMJE5+EZa8nR3o3Z/wgSQLyUcOcNRCUlmrNzCnaboEWFL39bokSWYCvYAZAEmSBCABzt7NtRFYX/dtZd3/YqNULkkqS9k88tQsJE95EdauhnbtstXjMy4kjDrJXS0ktSglzTAnSdIPGA1M3Onl04BlaZrO3cM17YBJwCDgv9M0nbiH824EbgRI05SqqqpSSttnFRUVzfZZrYH9Kp09K439Kl059Ky4djU1Lz9HzYtPUzN5ItRsJhzQiQ7HnUKHk06jw3FjKHQ+KNcatyuHfrU09qw09qt05d6zEGPDFnyTJOkMPAl8M03TCTu9/j/AvDRNv1vP9YcAfwA+k6bpa/V8XFy8eHGD6tpfVVVVPiK1BPardPasNPardHn1LK6sJk5+gfjK8zBnejaPfEg3wqiT351Hriy/eWR/xkpnz0pjv0qXV8969uwJUO9MWINWmOvmj+8G7tglLFcAlwPH1/ceaZquTpLkCeACoL7ALEkqQ/GdxcRXns9C8htzsheP6EO46MOE0WPgyIHOI0tqdRqyS0YAbgVmpml6yy6HxwKz0jRduIdrDwO21oXlA+rO//Z+1ixJaiYxRlj8FnHSc8RXn4eFb2YH+g4ifPA6wuhTCEf0zrVGSWpqDVlhPhW4DpiWJMnkute+lKbpA8BVwG93PjlJkp7Az9M0vQg4AvhV3RxzAUjTNP1jo1UvSWp0MUZ4c+67K8nvLM4eIjLwaMKV12ch2Zv2JLUhDZ5hbmbOMJcp+1U6e1Ya+1W6xuhZLG6DuTOJr9aF5FXV2c4WQ0cQjntfNpd88KGNVHG+/BkrnT0rjf0qXauYYZYktT47QvLLzxBfeS7b/q2iEoaNzh5HfeyJhAO75F2mJOXOwCxJbUgsboN520Py87BmFbRvDyNOIBz/fsKI4wkdD8i7TEkqKwZmSWrlYrGYheRJzxInPQdrVkJlXUg+4f2EkScQOnTMu0xJKlsGZklqhWKxCK/PIr78LHHSs7B6e0g+PgvJI05wJVmSGsjALEmtRBaSZ2fjFpOeg9Urspnk4ccTTjg1m0nu2CnvMiWpxTEwS1ILFmNk6/zZFB+5j/jy07CyGioq6kLyRwkjTyQcYEiWpP1hYJakFiguXUR88SniS0+xcumibAu4Y0ZnDxM59mRDsiQ1IgOzJLUQceVy4kvPEF98Ct6anz1MZMhwunzwb9gwZCSh80F5lyhJrZKBWZLKWFy3Ntvd4sUnYe6M7MV+gwnJ9dnNe4d2o1NVFRt9SIIkNRkDsySVmbh5I/HVidlK8szJsG0bHNGHcOk1hJNOJ3TvmXeJktSmGJglqQzE2q3w2ivEF54gTn0Jtm6Bbt0J515GOOl06N2PEOp9eqskqQkYmCUpJzFGeGMO8YW/EF96Gtavgy4HE94/lnDSGTBgKKFQyLtMSWrzDMyS1Mzi8qXEiU8QX3gSli2CyvaEUScTxpyZ7XRR4V/NklRO/FtZkppB3LCeOOkZ4vNPwLy6m/eGDCec/0HC8acSOh2Ya32SpD0zMEtSE8nmkidRfP4JmPoi1NZCj96Ey64ljDmT0K173iVKkhrAwCxJjWjHXPLzf8mevLd9LvmMC7ORi76DvHlPkloYA7MkNYK4emV2896zj8FS55IlqTXxb3BJ2kexditMfZnis4/Ba5OgWIRBRxP+1rlkSWpNDMySVKK48E3is38mvvAXWL8WDu6a3bz3vnMIPXrnXZ4kqZEZmCWpAeLG9cQXnyI+8xgsmAftKuDYkyi8f2w2ctGuXd4lSpKaiIFZkvYgFoswayrx2ceIrzwPtVuzJ+5deQPh5DMJXQ7Ku0RJUjMwMEvSLmL1smzk4rk/w8rl0Kkz4bRzCaeeC0cOcJcLSWpjDMySBMTaWpj6IsWnHoYZk7MXjx5F+PBHs90uKtvnW6AkKTcGZkltWly+lPj0I9l2cGtXw6FVhHFXEU4dS+h2WN7lSZLKgIFZUpsTa7fC5IkUn34kW00OBRh5AoXTz4fhxxEK3sAnSXqXgVlSmxHfWUx86pFsNnndGuh6GOHSawjvG0voWpV3eZKkMmVgltSqxdqtxFcnEp96CGZNhUIBRp6UrSYPG+VqsiSpXgZmSa1SXLWC+NRDxKcfgTWroFt3wmXXEk49h3BIt7zLkyS1IAZmSa1GjBFmT6P4lwdg8gsQIww/nsJZF8Gw0a4mS5L2iYFZUosXN20kPv848YkHYcnbcGAXwrmXEs64kHBYj7zLkyS1cAZmSS1WXLSA+Jc/EV94Amo2Q7/BhI99lnDC+wntO+RdniSplTAwS2pRspv4XiA+8QDMmQ4VlYQTTyOc9QFC/8F5lydJaoUMzJJahOwmvoeJTz+c3cRXdXj2FL5TxxI6H5R3eZKkVszALKmsxfmziH++nzjp2V1u4juOUCjkXZ4kqQ0wMEsqO7G2ljjpWeKf74c35sABBxLGXkI48yJv4pMkNTsDs6SyEdevZcOTD1D8412wegV070m45u8Jp5xN6HhA3uVJktooA7Ok3MVFbxEfv5/4/F9Yv3ULHDOKwt9+yrELSVJZMDBLykUsFmH6KxQfuw9mTIbK9oQxZ9L1Q9ex+sCD8y5PkqQdDMySmlXcUkN87nHiY/fBskVwSFfCB68jnHY+octBVFRVQXV13mVKkrSDgVlSs4jr1hKfeID4lz/BujXQdxDhhpsIx59KqPCvIklS+fLfUpKaVFy+lPjoPcRnH4MtW2DECRTOvxyGDCOEkHd5kiTVy8AsqUnEN+YSH55AfOV5KBQIY84gnPdBQs8j8y5NkqSSGJglNZoYI7w2ieLDf4DZ07L9k8//IOGccYRDuuVdniRJ+8TALGm/xdqtxIlPER/5Ayx+Cw6tIlzxd4TTziMc0Cnv8iRJ2i8GZkn7LNbUEJ9+mPjwH7IHjfTuR7j+nwgnnOaNfJKkVsN/o0kqWdy0kfiXP2Vbw61bA0OGUfjIZ2DYaG/kkyS1OgZmSQ0W168l/vl+4p//CJs2wPDjKFyUEAYfk3dpkiQ1GQOzpHrF1SuzreGefAhqNsNxp1C46ApC30F5lyZJUpOrNzAnSdIHuB3oARSB8Wma/iBJkjuBoXWnHQKsTtN0VEOubcT6JTWhWL0s2xrumcdg2zbCSacRLryC0Mut4SRJbUdDVphrgZvSNH0lSZIuwKQkSR5N0/TK7SckSfJdYE0J185olOolNYm4dCHxgd8TX3wSCIT3nU244EOE7kfkXZokSc2u3sCcpukSYEnd1+uSJJkJ9AJmACRJEoAEOLvUayWVl7h0EfGPvyO++DRUVhDOvCh72EjXqrxLkyQpNyXNMCdJ0g8YDUzc6eXTgGVpms7dh2t3Pn4jcCNAmqZUVTXPv6ArKiqa7bNaA/tVupbQs9olC9mQ3sbmpx6GyvZ0uvRqDrz0agqHdG32WlpCv8qNPSuN/SqdPSuN/SpdufeswYE5SZLOwN3A59I0XbvToauB3+7jtTukaToeGF/3bayurm5oafulqqqK5vqs1sB+la6cexaXLyX+6U7i83+BdhWEcy4mXHA5NQcdSk1tEXKou5z7Va7sWWnsV+nsWWnsV+ny6lnPnj0bdF6DAnOSJJVkgfeONE0n7PR6BXA5cHyp10rKT6xeRnzgLuJzf4ZQIJw9LptRPvjQvEuTJKnsNGSXjADcCsxM0/SWXQ6PBWalabpwH66V1MziiuXEB1Lis49BCIQzLiRc+CHCId3yLk2SpLLVkBXmU4HrgGlJkkyue+1LaZo+AFzFLuMYSZL0BH6epulF9VwrqZnEldXEB+8iPv0oBAinnU+48MPezCdJUgOEGGPeNexOXLx4cbN8kHNGpbFfpcuzZ3Hdmmz04okHIEJ4/1jCRVcQuh6WSz0N4c9Y6exZaexX6exZaexX6XKeYQ71neeT/qRWKG7amD2Z75F7YUtNto/yxVcRunXPuzRJklocA7PUisStW4h/eYD44F2wfh0c/z4Kl15LOKJ33qVJktRiGZilViBu20Z87s/E+38Hq6rhmFEUPngdod/gvEuTJKnFMzBLLViMEV55juI9v4ali6D/EAp/9znCUSPzLk2SpFbDwCy1UHHOdIq/vw3emANH9KHwyS/BqJMJod57FyRJUgkMzFILE5cupHj3r2DyRDikG+GjnyWcciah0C7v0iRJapUMzFILEdeuJt7/O+JTD0H7DoTLriWMvZTQoUPepUmS1KoZmKUyF2tqiI/dS3zo7myLuNMvyLaIO+iQvEuTJKlNMDBLZSoWtxGff4J4z69h9QoYNYbCh/6W0MMt4iRJak4GZqkMxTnTKd75M3jrdeg3mMLHv0AYMizvsiRJapMMzFIZiSuWE+/+JfGlp+HQKsINNxFOPI1QKORdmiRJbZaBWSoDsaaG+PDdxIcmAGQzyufSNT1JAAAgAElEQVR/yBv6JEkqAwZmKUcxRuJLTxN//0tYVZ2tJn/oo4Ruh+VdmiRJqmNglnISF8yj+LufwbyZcOQACjfc5JyyJEllyMAsNbO4bi3xD7cTn3kUOh9E+NtPE049xwePSJJUpgzMUjOJxSLx2ceId/8KNm0gnHNJNqvc6cC8S5MkSXthYJaaQXxrPsU7fgKvz4bBx1C45hOE3v3yLkuSJDWAgVlqQnHjBtb+/HaKD0yAzl0IH/sc4ZSzCCHkXZokSWogA7PUBGKMxIlPEu/6BZvWrSGceSHhsmsJnTrnXZokSSqRgVlqZHHxWxR/81OYPQ36Dabr125hzcFVeZclSZL2kYFZaiRx6xbiA3cRH7wbOnQkXPtJwmnnUtn9cKiuzrs8SZK0jwzMUiOIc6ZT/N8fwdJFhDFnEpLrCV0OzrssSZLUCAzM0n6IG9cT7/4V8amHoVt3Cp/9N8Lw4/IuS5IkNSIDs7QPYozwyvMUfzse1q4mnHcZ4ZJrCB065l2aJElqZAZmqURx1QqKv/kJTJ6YPdL6M18h9B2Ud1mSJKmJGJilBorFIvHJh4gTfgXFbYQPf5Qw9lJCOx9pLUlSa2ZglhogLl9K8Vc/zLaKO/pYCtd9inBYj7zLkiRJzcDALO1FLBaJTz1E/P0voVAgfOQzhFPH+qQ+SZLaEAOztAdxxTvZqvLMKXDMKAp/+xlCt8PyLkuSJDUzA7O0ixgj8emHieltAITrPkk47XxXlSVJaqMMzNJO4orlFG//IcyYDEeNpPDRfyR06553WZIkKUcGZom6VeVnHiWmt0KMhL/5BOH0CwiFQt6lSZKknBmY1ebFdWuyWeUpL8KQ4dmqsjtgSJKkOgZmtWlx+qsUb/s+bFhHuOLvCGMvcVVZkiS9h4FZbVLcuoU44XbiY/fBEX0ofPbfCH36512WJEkqQwZmtTlx0QKKP/sOLFpAOOsD2RP72nfIuyxJklSmDMxqM2KMxMf/RPz9bXBAJwr/+DXCiBPyLkuSJJU5A7PahLh2FcXb/h+8NglGnEDho58hHHRo3mVJkqQWwMCsVi++NoniL74PmzcRrvl7wpkX+RASSZLUYAZmtVpx2zbivb8mPng39OpL4aZvEnodmXdZkiSphTEwq1WKK6uzG/vmzSCcdh7hqo97Y58kSdonBma1OnHaJIq/uAW21hJuuInCyWfkXZIkSWrBDMxqNWJtLfHeO4gP3Q29+1H4+y8SevTOuyxJktTCGZjVKsS1qyj+9D9hznTC6RcQrrzeEQxJktQoDMxq8eL8WRR/8i3YuJ5w/ecpjDkz75IkSVIrYmBWixVjJD71MPG346FrFYWb/4vQ28dbS5KkxmVgVosUt24h/uanxGceheHHUbjhJsKBXfIuS5IktUIGZrU4ccVyiv/zH7BgHuEDCeGSqwmFdnmXJUmSWql6A3OSJH2A24EeQBEYn6bpD5IkuRMYWnfaIcDqNE1H7eb6XwDjgHfSNB3eaJWrTYqzpmY399VupfCpLxFGjcm7JEmS1Mo1ZIW5FrgpTdNXkiTpAkxKkuTRNE2v3H5CkiTfBdbs4fpfAj8iC93SPokxEh+5h3j3r6BHLwqfvNkt4yRJUrMo1HdCmqZL0jR9pe7rdcBMoNf240mSBCABfruH658CVjZKtWqT4pYa4s++Q/z9bTB6DIUv/ZdhWZIkNZuSZpiTJOkHjAYm7vTyacCyNE3n7k8hSZLcCNwIkKYpVVVV+/N2DVZRUdFsn9UaNHe/tq1czurvfY3a+bPofO0n6HT5dYQQmu3zG4M/Y6WxX6WzZ6WxX6WzZ6WxX6Ur9541ODAnSdIZuBv4XJqma3c6dDV7WF0uRZqm44Hxdd/G6urq/X3LBqmqqqK5Pqs1aM5+xQXzKf7o32HTBgqf/BKbRp3MphUrmuWzG5M/Y6WxX6WzZ6WxX6WzZ6WxX6XLq2c9e/Zs0HkNCsxJklSSheU70jSdsNPrFcDlwPH7UKO0R3HSsxR/8T3ofDCFf/m2+ytLkqTcNGSXjADcCsxM0/SWXQ6PBWalabqwKYpT2xNjJP7pTuK9v4GBR2U39x10aN5lSZKkNqwhK8ynAtcB05IkmVz32pfSNH0AuIpdxjGSJOkJ/DxN04vqvv8tcCZQlSTJQuBf0zS9tZHqVysSt24l/vL/EV98kjDmLMLffopQ2T7vsiRJUhsXYox517A7cfHixc3yQc4Zlaap+hU3rKf442/CnOmEy64lXHRFi7u5b0/8GSuN/SqdPSuN/SqdPSuN/SpdzjPM9QYOn/Sn3MUV71D8wddh+RLCDTdROPmMvEuSJEnawcCsXMUF8yn+8BuwdQuFz32DMNSHQUqSpPJiYFZu4rRJFH/6bTiwC4XP/x9CzyPzLkmSJOmvGJiVi+LTjxB//WPo3Y/CZ75GOKRr3iVJkiTtloFZzSrGSHzgLuI9v4bhx1H4+y8SOnbKuyxJkqQ9MjCr2cRikfj724iP3ksYcybhI/9IqPBHUJIklTfTippF3LaNePuPiM/9mXD2OMKVNxAKhbzLkiRJqpeBWU0ubt1Ccfx/weSJhEuuIYy7stXssSxJklo/A7OaVNy0keJ/fxNmTyNcfSOFs8flXZIkSVJJDMxqMnH9Worf/zdY+Abh+s9TGHNm3iVJkiSVzMCsJhHXraF4y1dh6SIKn/wSYeSJeZckSZK0TwzManRx7SqK3/0qLF9K4TNfIRwzOu+SJEmS9pmBWY0qrl5J8btfgZXLKfzj1whHjcy7JEmSpP1iYFajiSurs7C8ZiWFz/4rYcjwvEuSJEnabwZmNYq4YjnF734Z1q2h8LmvEwYdnXdJkiRJjcLArP0WV7xD8b++BBs3UPinbxAGDM27JEmSpEZjYNZ+iatWZGMYmzZQ+Pw3CP0G512SJElSo/LZxNpnce3qbOu4dWsofPbfMCxLkqTWyMCsfRLXr83C8srlFD7zNccwJElSq2VgVsnixvUUv/evsGwxhU9/hTBkWN4lSZIkNRkDs0pS3LSB4g++DosWUPjkzYSjj827JEmSpCZlYFaDxZoaVv/7P8Obcync+M+EESfkXZIkSVKTc5cMNUjcto3i+P+kOHMK4frPE447Je+SJEmSmoUrzKpXjJH4vz+CqS/R5cYvUDj5jLxLkiRJajYGZtUr/uF/ic/+mXDxVXS64IN5lyNJktSsDMzaq+Kf7yc++HvC6ecTLr4673IkSZKanYFZe1R88SninT+H0WMIf/MJQgh5lyRJktTsDMzarThjMvEX34fBx1D4+BcIhXZ5lyRJkpQLA7P+Slwwn+KP/wN69KLwqS8TKtvnXZIkSVJuDMx6j7hqBcUf/R848EAKn/s3QqfOeZckSZKUKwOzdog1myn+6N9h0yYKn/kq4ZBueZckSZKUOwOzAIjFIsVffA/efj2bWe7dP++SJEmSyoKBWQDEe++AV54nXPF3hGNPzLscSZKksmFgFsXnHic+cBfhtPMIYy/JuxxJkqSyYmBu4+LcGcTbfwRHjSRc417LkiRJuzIwt2Fx+VKKP/6/0K07hU/8f4SKirxLkiRJKjsG5jYq1tRkYblYzHbEOLBL3iVJkiSVJQNzGxRjJP76v2HRAgofv4nQo1feJUmSJJUtA3MbFJ94kPjCE4SLryYMPz7vciRJksqagbmNifNnEe/8OYw4gfCBJO9yJEmSyp6BuQ2Ja1dT/Mm3oWsVhes/Tyj4xy9JklQfE1MbEbdtozj+v2DDOgqf+BfCgZ3zLkmSJKlFMDC3EfEP/wuzpxGu/SThyAF5lyNJktRiGJjbgPjK88SHJxDOuIDC+87OuxxJkqQWxcDcysUV71D85f+DfoMJV34873IkSZJaHANzKxaL2yj+/BaIRQo3/jOhsjLvkiRJklocA3MrFv90F8ybQfibfyAc1iPvciRJklokA3MrFefNIN7/O8KYMymMOTPvciRJklqsivpOSJKkD3A70AMoAuPTNP1BkiR3AkPrTjsEWJ2m6ajdXH8B8AOgHfDzNE2/1VjFa/fixg3ZKEZVd8I1n8i7HEmSpBatISvMtcBNaZoeDYwBPpUkyTFpml6ZpumoupB8NzBh1wuTJGkH/DdwIXAMcHWSJMc0XvnaVYyR+Osfw6pqCjfcRDigU94lSZIktWj1BuY0TZekafpK3dfrgJlAr+3HkyQJQAL8djeXnwTMS9P09TRNtwC/Ay5tjMK1e/H5x4kvPU245BrCgKH1XyBJkqS9qnckY2dJkvQDRgMTd3r5NGBZmqZzd3NJL+Dtnb5fCJy8h/e+EbgRIE1TqqqqSiltn1VUVDTbZzW12iULWfnb8VQOP45Dr/17Qrt2jf4ZralfzcWelcZ+lc6elcZ+lc6elcZ+la7ce9bgwJwkSWey0YvPpWm6dqdDV7P71WWAsJvX4u5OTNN0PDB++znV1dUNLW2/VFVV0Vyf1ZTitm0U/+srUGjHtus+zYpVq5rkc1pLv5qTPSuN/SqdPSuN/SqdPSuN/SpdXj3r2bNng85rUGBOkqSSLCzfkabphJ1erwAuB47fw6ULgT47fd8bWNygylSS+PAEeGMO4cYvErqW73+hSZIktTQN2SUjALcCM9M0vWWXw2OBWWmaLtzD5S8Bg5Mk6Q8sAq4CrtmPerUbceGbxPt+Szjh/RROfH/e5UiSJLUqDdkl41TgOuDsJEkm1/3vorpjV7HLOEaSJD2TJHkAIE3TWuDTwMNkNwumaZpOb7TqRaytpXjbD6DTgW4hJ0mS1ARCjLsdKc5bXLy4eSY3WvqcUfGPdxLvvYPCP/wL4bj3NfnntfR+5cGelcZ+lc6elcZ+lc6elcZ+lS7nGebd3XP3Hj7prwWLi98i/vFOwomnNUtYliRJaosMzC1ULBYp3v4jOOAAwtU35l2OJElSq2VgbqHikw/B/FmE5AZCl4PzLkeSJKnVMjC3QHHlcuKEX8Exowhjzsy7HEmSpFbNwNwCFX/zUygWKVz7SUKod05dkiRJ+8HA3MLEyRNhyouES64mHNYj73IkSZJaPQNzCxJraij+7mfQ80jCOZfkXY4kSVKbYGBuQeIDd8GKdyhc8wlCRYOeai5JkqT9ZGBuIeLSRcRHJhDGnEkYOjzvciRJktoMA3MLEGOk+NvxUNme8OGP5V2OJElSm2JgbgmmvAgzXs1u9Dv40LyrkSRJalMMzGUu1m6leNcvoEdvwpkfyLscSZKkNsfAXObi43+Cd5ZQSK73Rj9JkqQcGJjLWFy3hvjHO2H4cYQRx+ddjiRJUptkYC5j8b7fQM0mClf8Xd6lSJIktVkG5jIVl7xNfPJhwhkXEHoemXc5kiRJbZaBuUwVJ/wvdOhAuPjqvEuRJElq0wzMZSjOmwmTXyCcfzmhy8F5lyNJktSmGZjLTIyR4t2/hIMPJZx7ad7lSJIktXkG5nIz5UWYN5Nw8dWEDh3zrkaSJKnNMzCXkVjcRnHC7XB4L8KpY/MuR5IkSRiYy0p88SlY8jaFD17rQ0okSZLKhIG5TMRt24j3/w5694fRp+RdjiRJkuoYmMtEnPhE9gjsS68mFPxjkSRJKhcmszIQa2uzR2AfORCOPTnvciRJkrQTA3MZiM8/DsuXUrjkGkIIeZcjSZKknRiYcxZra4l/SqHfYBh5Qt7lSJIkaRcG5pzFiU/CincoXHyVq8uSJEllyMCco1gsEh+6O9sZY4Sry5IkSeXIwJynKS/C0oWECz/k6rIkSVKZMjDnJMZI8cHfw2E9CMefmnc5kiRJ2gMDc15mT4M35hDO+yChXbu8q5EkSdIeGJhzUnzwbjjoEMKp5+RdiiRJkvbCwJyD+NbrMONVwthLCZXt8y5HkiRJe2FgzkF87D7o0JFwxvl5lyJJkqR6GJibWVy7ivjSU4RTziZ06px3OZIkSaqHgbmZxScfhtpawjnj8i5FkiRJDWBgbkaxdivxyQdh+PGEHr3zLkeSJEkNYGBuRvHlZ2DNKgrnXJx3KZIkSWogA3MziTESH7sfevSGYaPzLkeSJEkNZGBuLq/PhgXzCOeM8zHYkiRJLYiBuZnEJx+CDgcQxpyVdymSJEkqgYG5GcSN64mTniGcfAah4wF5lyNJkqQSGJibQZz4JGzZQjjdB5VIkiS1NAbmJhZjzMYx+g4i9B2YdzmSJEkqkYG5qb0xBxYtIJx+Xt6VSJIkaR8YmJtYfOph6NCRcNLpeZciSZKkfWBgbkJx00biS08TTjqd0LFT3uVIkiRpH1TUd0KSJH2A24EeQBEYn6bpD+qOfQb4NFAL/ClN0y/u5vrPAh8HAvCzNE2/33jll7f40tOwpYZwmuMYkiRJLVVDVphrgZvSND0aGAN8KkmSY5IkOQu4FBiZpukw4Du7XpgkyXCysHwScCwwLkmSwY1WfZmLL/wle7JfvzbzW5YkSWp16g3MaZouSdP0lbqv1wEzgV7APwDfStO0pu7YO7u5/GjghTRNN6ZpWgs8CXywsYovZ7F6GcydQRhzpk/2kyRJasFCjLHBJydJ0g94Chhe9+u9wAXAZuALaZq+tMv5R9edcwqwCfgz8HKapp/ZzXvfCNwIkKbp8Vu2bNmH307pKioqqK2tbfT3XX/XbWz4zc+o+undtOt+RKO/f16aql+tmT0rjf0qnT0rjf0qnT0rjf0qXV49a9++PWRjw3vV4MCcJElnshXib6ZpOiFJkteAx4HPAicCdwID0jSNu1x3PfApYD0wA9iUpuk/1fNxcfHixQ2qa39VVVVRXV3dqO8ZY6T41U/CwYfS7p//b6O+d96aol+tnT0rjf0qnT0rjf0qnT0rjf0qXV4969mzJzQgMNd70x9AkiSVwN3AHWmaTqh7eSEwoS4gv5gkSRGoApbvfG2aprcCt9a9z/+tu651e3MuLFtEOL9NTJ9IkiS1avXOMCdJEsgC78w0TW/Z6dA9wNl15wwB2gN/9Z8GSZJ0r/v1SOBy4Lf7X3Z5iy88ARWVhOPfl3cpkiRJ2k8NWWE+FbgOmJYkyeS6174E/AL4Rd1oxhbgI2maxiRJegI/T9P0orpz706SpBuwFfhUmqarGve3UF5ibW229/KxJxE6dc67HEmSJO2negNzmqbPsOfZjmt3c/5i4KKdvj9tn6triWa8CuvWEE45K+9KJEmS1Ah80l8jiy8/C50OhGGj8y5FkiRJjcDA3IhibS1xyovZOEZFZd7lSJIkqREYmBvT7GmwcT3hOG/2kyRJai0MzI0ovvIcdOgIx4zKuxRJkiQ1EgNzI4nFbcRXXyCMOIHQvkPe5UiSJKmRGJgby9yZsG4NOI4hSZLUqhiYG0l89XmobE8YcXzepUiSJKkRGZgbQSwWia88D8NGEzoekHc5kiRJakQG5sbw5lxYVe3uGJIkSa2QgbkRxMkToV07wrEn5l2KJEmSGpmBuRHE1ybBwKMInTrnXYokSZIamYF5P8XVK+HtNwjDvdlPkiSpNTIw76c4/VUAwrDjcq5EkiRJTcHAvL9emwQHd4U+/fOuRJIkSU3AwLwf4rZtxBmTCcNHE0LIuxxJkiQ1AQPz/nhjDmxcD8OcX5YkSWqtDMz7IU5/BUKBcMyovEuRJElSEzEw74c4bRIMHEo40O3kJEmSWisD8z6Ka1fDgnnujiFJktTKGZj3UZxRt53cCOeXJUmSWjMD876aORU6d4E+A/KuRJIkSU3IwLyP4tzpMHgYoWALJUmSWjPT3j6IK6th+VLCkOF5lyJJkqQmZmDeB3HudADCkGE5VyJJkqSmZmDeF3NegwMOhN798q5EkiRJTczAvA/inOkw6GhCoV3epUiSJKmJGZhLFNeugqULHceQJElqIwzMpZo7A8Ab/iRJktoIA3OJ4pzp0L4DHDkw71IkSZLUDAzMJYpzXoOBRxEqKvIuRZIkSc3AwFyCuGEdLFrgOIYkSVIbYmAuxdwZEKM3/EmSJLUhBuYSxLkzoKIC+g/JuxRJkiQ1EwNzCeKbc6HPAEJl+7xLkSRJUjMxMDdQLBbhrfmEvoPyLkWSJEnNyMDcUO8shs2boK/byUmSJLUlBuYGigvmAxD6ucIsSZLUlhiYG2rBPKhsD0ccmXclkiRJakYG5gaKC+ZBn/6Edu3yLkWSJEnNyMDcALFYhAWvE5xfliRJanMMzA2xbDHUbIK+g/OuRJIkSc3MwNwAccE8AFeYJUmS2iADc0MsmAft28MRffKuRJIkSc3MwNwA2Q1/A7zhT5IkqQ0yMNcjFrfBW6/7hD9JkqQ2ysBcn2WLoWazT/iTJElqowzM9Xj3hj9XmCVJktoiA3N9FsyH9h2gR++8K5EkSVIOKuo7IUmSPsDtQA+gCIxP0/QHdcc+A3waqAX+lKbpF3dz/T8BNwARmAZ8LE3TzY32O2hicfFbcEQfb/iTJElqoxqywlwL3JSm6dHAGOBTSZIckyTJWcClwMg0TYcB39n1wiRJegH/CJyQpulwoB1wVaNV3xyWLiQc4eqyJElSW1XvCnOapkuAJXVfr0uSZCbQC/g48K00TWvqjr2zl884IEmSrUAnYHFjFN4cYs1mWFntOIYkSVIbFmKMDT45SZJ+wFPA8Lpf7wUuADYDX0jT9KXdXPNZ4JvAJuCRNE3/Zg/vfSNwI0Capsdv2bKlpN/IvqqoqKC2tna3x7a+PpuVN32Mg7/4TTqeclaz1FPu9tYv7Z49K439Kp09K439Kp09K439Kl1ePWvfvj1AqO+8BgfmJEk6A08C30zTdEKSJK8BjwOfBU4E7gQGpGkad7rmUOBu4EpgNXAX8Ps0TX9dz8fFxYubZyG6qqqK6urq3R4rTnyS+PPvUvi3HxJ69W2Wesrd3vql3bNnpbFfpbNnpbFfpbNnpbFfpcurZz179oQGBOYG7ZKRJEklWfC9I03TCXUvLwQmpGka0zR9keyGwKpdLh0LvJGm6fI0TbcCE4D3Ney3UAaWLoJQgO5H5F2JJEmSctKQXTICcCswM03TW3Y6dA9wNvBEkiRDgPbArv9p8BYwJkmSTmQjGecALzdG4c1i2SKo6k6obJ93JZIkScpJvYEZOBW4DpiWJMnkute+BPwC+EXdaMYW4CNpmsYkSXoCP0/T9KI0TScmSfJ74BWy3TZeBcY3+u+iicQlC73hT5IkqY1ryC4Zz7Dn2Y5rd3P+YuCinb7/V+Bf97XAvMRiEd5ZRDh6ZN6lSJIkKUc+6W9PVlXDli2uMEuSJLVxBuY9WbIQgGBgliRJatMMzHsQl2aBmR698i1EkiRJuTIw78myRdCpM3Q5OO9KJEmSlCMD8x7EJQvhiN6EUO9e1pIkSWrFDMx7snQR4XDHMSRJkto6A/NuxE0bYc1Kd8iQJEmSgXm3lv7/7d19sFxlfcDx7yUvrTGEBK4C4VVapGAHQano0IqU1gLTknHq/BreBiqUglARwTJSKw7UFmGGl6lF3gsob79CQDoKAkW0teILFIYi1aECJRDB3JsLiaFJk2z/OGfhZHPv3t287O7d/X5mdrJ7nnPOPvvLs+f+9jnPec6LAAztaA+zJEnSoDNhHkft5XKGjO3tYZYkSRp0JszjWfIiTJsGb9uh2zWRJElSl5kwj+flF2F4B4amT3rncEmSJPU5E+Zx1JYthW2Hu10NSZIk9QAT5vGMjTI0d7tu10KSJEk9wIS5QW3dumJKubnbdrsqkiRJ6gEmzI1WvApr18I8e5glSZJkwryhsVEAh2RIkiQJMGHe0LIiYXZIhiRJksCEeQO1sZHiiT3MkiRJwoR5Q2OjMLQVzJnb7ZpIkiSpB5gwNxobgTlzGZo2rds1kSRJUg8wYW5QGxtx/LIkSZLeYMLcaMw5mCVJkvQmE+ZGYyMMOQezJEmSSibMFbX/Ww0rlsM29jBLkiSpYMJcVd60xLv8SZIkqc6Eucq7/EmSJKmBCXNFbcy7/EmSJGl9JsxV3uVPkiRJDUyYq8ZGYMZMmPXWbtdEkiRJPcKEuaqcg3loaKjbNZEkSVKPMGGuqI2NOEOGJEmS1mPCXLVshCHnYJYkSVKFCXOpVqvBq6P2MEuSJGk9Jsx1K38Jq1d7lz9JkiStx4S5rj6lnD3MkiRJqjBhrvMuf5IkSRqHCXOp9sZNSxySIUmSpDeZMNctM2GWJEnShkyY614dhdlbMzRjZrdrIkmSpB5iwlyqLRtxhgxJkiRtYHq3K9ArhrYdNmGWJEnSBkyYS1sdfUq3qyBJkqQe5JAMSZIkqQkTZkmSJKkJE2ZJkiSpCRNmSZIkqQkTZkmSJKkJE2ZJkiSpiUmnlYuIXYCbgB2AdcDVmXl5WfYXwOnAGuDrmfmXDdvuBdxeWbQH8LnMvGzzVF+SJEnaslqZh3kNcFZmPhYRWwOPRsQDwPbAAmDfzFwVEW9v3DAzfwLsBxAR04AXgbs2W+0lSZKkLWzShDkzlwBLyufLI+JpYCfgz4ALM3NVWfbKJLs6FPjvzHx+06osSZIkdU5bd/qLiN2B/YHvAxcDvxMRXwD+Fzg7M3/YZPOFwK0bWU9JkiSpK4ZqtVpLK0bEbODbwBcyc1FE/CfwEHAG8FsUY5X3yMwNdhgRM4GXgHdl5ssT7P9k4GSAzHzv6tWrN+LjtG/69OmsWbOmI+/VD4xX+4xZe4xX+4xZe4xX+4xZe4xX+7oVs5kzZwIMTbZeSz3METEDuBO4OTMXlYsXA4vKBPkHEbEOGAZ+Mc4uDgcemyhZBsjMq4Gry5e1pUuXtlK1TTY8PEyn3qsfGK/2GbP2GK/2GbP2GK/2GbP2GK/2dStm8+fPb2m9SaeVi4gh4Drg6cy8pFJ0N/C75TrvBGYCE33So3A4hiRJkqagVnqYDwKOA56MiMfLZecC1wPXl0MzVgPHZ2YtIuYD12bmEQARMQv4feDPN3vtJUmSpC2slVky/o2Jx3YcO876LwFHVF6vBLbb2ApKkiRJ3eSd/iRJkqQmTJglSZKkJkyYJUmSpCZanoe5w+hGK0gAAAmMSURBVHqyUpIkSeo7k87D3Ks9zEOdekTEo518v6n+MF7GzHj13sOYGS9j1lsP4zXlYjapXk2YJUmSpJ5gwixJkiQ1YcL85u241Rrj1T5j1h7j1T5j1h7j1T5j1h7j1b6ejlmvXvQnSZIk9QR7mCVJkqQmTJglSZKkJqZ3uwJbUkQcBlwOTAOuzcwLG8p/BbgJeC8wAvxJZj5Xln0GOBFYC3wiM7/Zwap3RQvx+hRwErAG+AXwscx8vixbCzxZrvo/mXlkxyreJS3E6wTgYuDFctGXMvPasux44LPl8r/JzBs7UukuayFmlwKHlC9nAW/PzLll2SC2seuBPwReyczfHKd8iCKeRwArgRMy87GybODaWAvxOgY4p3y5Ajg1M58oy54DllMc89dk5gEdqXSXtRCzDwFfA54tFy3KzPPLsqbf537UQrw+DRxTvpwO7A28LTNHB7GNRcQuFHnWDsA64OrMvLxhnSlxHOvbHuaImAb8A3A4sA9wVETs07DaicCyzPx14FLgi+W2+wALgXcBhwFXlPvrWy3G6z+AAzJzX+AO4KJK2euZuV/5GIREppV4AdxeiUs9Wd4WOA84EHgfcF5EzOtQ1bumlZhl5pn1eAF/DyyqFA9UGyvdQHEMmsjhwJ7l42TgyzC4bYzJ4/UscHB5DLuADS8yOqRsX32fyFTcQPOYAfxr5btXT5ZbPQb2mxtoEq/MvLhyDPsM8O3MHK2sMmhtbA1wVmbuDbwfOG2cdjIljmN9mzBTBPeZzPxZZq4GbgMWNKyzAKj/WrkDOLT8pbMAuC0zV2Xms8Az5f762aTxysxvZebK8uUjwM4drmMvaaV9TeQPgAcyczQzlwEPMPkfrH7QbsyOAm7tSM16VGZ+BxhtssoC4KbMrGXmI8DciNiRAW1jk8UrM/+9jAd4DANaamMT2ZRj4JTVZrw8hmUuqfcWZ+Zy4Glgp4bVpsRxrJ+HZOwEvFB5vZjiV8q462Tmmoh4FdiuXP5Iw7aN/8H9ppV4VZ0I3Ft5/asR8SOKX5MXZubdm7+KPaXVeP1xRHwQ+ClwZma+MMG2/d6+oI02FhG7Ae8AHqosHrQ21oqJ2tKgtrF2NB7DasD9EVEDrsrMnp7iqsM+EBFPAC8BZ2fmU7T/N2OgRMQsiuTu9MrigW5jEbE7sD/w/YaiKXEc6+ce5vFuddg4h95E67Sybb9p+TNHxLHAARTjc+t2LU8xHQ1cFhG/tvmr2FNaidc/A7uXp38f5M2zGYPYvqC9z70QuCMz11aWDVoba4XHsI0QEYdQJMznVBYflJnvoTg9fFr5Q1fwGLBbZr6bYphU/Yeqbay5PwK+2zAcY2DbWETMBu4EPpmZrzUUT4njWD8nzIuBXSqvd6b4dTzuOhExHdiG4lRLK9v2m5Y+c0T8HvBXwJGZuaq+PDNfKv/9GfAwxa/IfjZpvDJzpBKjayguLm1p2z7VzudeSMOpzAFsY62YKKaD2sYmFRH7AtcCCzJzpL680r5eAe6i/4fhtSQzX8vMFeXzbwAzImIY29hkmh3DBqqNRcQMimT55sxcNM4qU+I41s9DMn4I7BkR76CYpWAhRc9U1T3A8cD3gI8CD2VmLSLuAW6JiEuA+RQD0X/QsZp3x6Txioj9gauAw8ovfH35PGBlZq4qD6QHsf4Fgf2olXjtmJlLypdHUozdAvgm8LeVixc+THFxSL9r5TtJROwFzKP4XtaXDWIba8U9wOkRcRvF6fBXM3NJRAxqG2sqInaluJD0uMz8aWX5W4GtMnN5+fzDwPldqmZPiYgdgJfLv43vo+hoGwHGaOH7PIgiYhvgYODYyrKBbGPldWHXAU9n5iUTrDYljmN9mzCXY5JPp0hOpgHXZ+ZTEXE+8KPMvIfiP/ErEfEMRc/ywnLbpyIigR9TjJc8reHUcN9pMV4XA7OBf4oIeHNqr72BqyJiHcXB9MLM/HFXPkiHtBivT0TEkRRtaBQ4odx2NCIuoEggAc5vOG3Xl1qMGRQXytyWmdVTbwPXxgAi4lbgQ8BwRCymuGJ8BkBmXgl8g2IqpmcopmP607JsINtYC/H6HMV1KleUx7D61F7bA3eVy6YDt2TmfR3/AF3QQsw+CpwaEWuA14GF5Xdz3O9zFz5CR7UQL4CPAPdn5i8rmw5qGzsIOA54MiIeL5edC+wKU+s45q2xJUmSpCb6eQyzJEmStMlMmCVJkqQmTJglSZKkJkyYJUmSpCZMmCVJkqQmTJglaQuJiHsj4vgm5VdGxF+3uK+HI+KkCco+HxFf3dh6NnnPYyLi/k3YfsI6S9JU0rfzMEvSlhARzwEnZeaDk62bmYdXtjuh3O63K+WnbIk6bi6ZeTNwc/11RNSAPTPzme7VSpI6zx5mSZIkqQl7mCVpI9V7jYFHgBMpbhf88cy8tyx/GPgq8F3gSmBGRKyguMPc3Ii4AVicmZ8tb//6FYpbw04vtzklMxe3WacZwE3ATIq7Ju4HXE5xt8TXgTuBT2Xm6nL9GnAG8ElgDvCPwDmZua7aKx4R3ynf4olymxOB+zdHnSWp19nDLEmb5kDgJ8AwcBFwXUQMVVfIzKeBU4DvZebszJw7zn62okhWd6O4bezrwJfaqUhEvAW4G1gFRJkUrwXOLOv3AeBQ4OMNm34EOAB4D7AA+FjjvjPzg+XTd5ef4fbNUWdJmgrsYZakTfN8Zl4DEBE3AlcA2wM/b2cnmTlC0ftLua8vAN9qYxdzgPuAJ4AzMrNW7vfRyjrPRcRVwMHAZZXlX8zMUWA0Ii6j6Jm+tgN1lqQpwYRZkjbNG4lxZq6MCIDZ7e4kImYBlwKHAfPKxVtHxLTMXNvCLt4PzACOqifL5X7fCVxC0YM8i+K4/2jDti9Unj8PzO9QnSVpSnBIhiR1Rm2S8rOAvYADM3MOUB8CMTTxJuu5H/g74F8iYvvK8i8D/0Uxu8Uc4Nxx9rlL5fmuwEstvuem1lmSpgQTZknqjJeBnSNi5gTlW1OMAR6LiG2B89p9g8y8CLiFImkeruz3NWBFRPwGcOo4m346IuZFxC4UFwDe3uQz7LE56yxJU4EJsyR1xkPAU8DPI2LpOOWXAW8BllLMunHfxrxJZl5AceHfg2USezZwNLAcuIbxk+GvUQzTeBz4OnDdBLv/PHBjRIxFMfZks9RZknrdUK022VlCSVK/8mYkkjQ5e5glSZKkJkyYJUmSpCYckiFJkiQ1YQ+zJEmS1IQJsyRJktSECbMkSZLUhAmzJEmS1IQJsyRJktTE/wMpx+fATIGZ5gAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x22ec40fea58>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def plot1A():\n",
    "    plt.plot(k, V[-1], label='Value function')\n",
    "    plt.legend()\n",
    "    plt.rcParams[\"figure.figsize\"] = (12,8)\n",
    "    plt.xlabel('Initial kapital')\n",
    "    \n",
    "plot1A()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}