{ "cells": [ { "cell_type": "markdown", "source": [ "# Deterministic Optimal Economic Growth Model\n", "\n", "**Randall Romero Aguilar, PhD**\n", "\n", "This demo is based on the original Matlab demo accompanying the Computational Economics and Finance 2001 textbook by Mario Miranda and Paul Fackler.\n", "\n", "Original (Matlab) CompEcon file: **demdoc02.m**\n", "\n", "Running this file requires the Python version of CompEcon. This can be installed with pip by running\n", "\n", " !pip install compecon --upgrade\n", "\n", "Last updated: 2021-Oct-01\n", "
" ], "metadata": { "collapsed": false } }, { "cell_type": "markdown", "source": [ "## About\n", "\n", "Social benefit maximizing social planner must decide how much society should consume and invest.\n", "\n", "* State\n", " - k capital stock\n", "* Control\n", " - q consumption rate\n", "* Parameters\n", " - 𝛼 capital share\n", " - 𝛿 capital depreciation rate\n", " - 𝜃 relative risk aversion\n", " - 𝜌 continuous discount rate\n", "\n", "\n", "## Preliminary tasks\n", "\n", "### Import relevant packages" ], "metadata": { "collapsed": false, "pycharm": { "name": "#%% md\n" } } }, { "cell_type": "code", "execution_count": 1, "outputs": [], "source": [ "import pandas as pd\n", "import matplotlib.pyplot as plt\n", "from compecon import BasisChebyshev, OCmodel" ], "metadata": { "collapsed": false, "pycharm": { "name": "#%%\n" } } }, { "cell_type": "markdown", "source": [ "### Model parameters" ], "metadata": { "collapsed": false } }, { "cell_type": "code", "execution_count": 2, "outputs": [], "source": [ "𝛼 = 0.4 # capital share\n", "𝛿 = 0.1 # capital depreciation rate\n", "𝜃 = 2.0 # relative risk aversion\n", "𝜌 = 0.05 # continuous discount rate" ], "metadata": { "collapsed": false, "pycharm": { "name": "#%%\n" } } }, { "cell_type": "markdown", "source": [ "### Approximation structure" ], "metadata": { "collapsed": false } }, { "cell_type": "code", "execution_count": 3, "outputs": [], "source": [ "n = 21 # number of basis functions\n", "kmin = 1 # minimum state\n", "kmax = 7 # maximum state\n", "basis = BasisChebyshev(n, kmin, kmax, labels=['Capital Stock']) # basis functions" ], "metadata": { "collapsed": false, "pycharm": { "name": "#%%\n" } } }, { "cell_type": "markdown", "source": [ "### Steady-state" ], "metadata": { "collapsed": false } }, { "cell_type": "code", "execution_count": 4, "outputs": [ { "data": { "text/plain": "Capital stock 5.127998\nRate of consumption 1.410200\nValue Function -14.182390\nShadow Price 0.502850\ndtype: float64" }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "kstar = ((𝛿+𝜌)/𝛼)**(1/(𝛼-1)) # capital stock\n", "qstar = kstar**𝛼 - 𝛿*kstar # consumption rate\n", "vstar = ((1/(1-𝜃))*qstar**(1-𝜃))/𝜌 # value\n", "lstar = qstar ** (-𝜃) # shadow price\n", "\n", "steadystate = pd.Series([kstar, qstar, vstar, lstar],\n", " index=['Capital stock', 'Rate of consumption', 'Value Function', 'Shadow Price'])\n", "\n", "steadystate" ], "metadata": { "collapsed": false, "pycharm": { "name": "#%%\n" } } }, { "cell_type": "markdown", "source": [ "## Solve HJB equation by collocation\n", "\n", "### Initial guess" ], "metadata": { "collapsed": false } }, { "cell_type": "code", "execution_count": 5, "outputs": [], "source": [ "k = basis.nodes\n", "basis.y = ((𝜌*k)**(1-𝜃))/(1-𝜃)" ], "metadata": { "collapsed": false, "pycharm": { "name": "#%%\n" } } }, { "cell_type": "markdown", "source": [ "### Define model and solve it." ], "metadata": { "collapsed": false } }, { "cell_type": "code", "execution_count": 6, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Solving optimal control model\n", "iter change time \n", "------------------------------\n", " 0 8.4e+00 0.0020\n", " 1 7.8e-01 0.0030\n", " 2 1.5e-01 0.0030\n", " 3 8.1e-03 0.0040\n", " 4 2.9e-05 0.0050\n", " 5 4.4e-10 0.0050\n", "Elapsed Time = 0.00 Seconds\n" ] } ], "source": [ "def control(k, Vk, 𝛼,𝛿,𝜃,𝜌):\n", " return Vk**(-1/𝜃)\n", "\n", "def reward(k, q, 𝛼,𝛿,𝜃,𝜌):\n", " return (1/(1-𝜃)) * q**(1-𝜃)\n", "\n", "def transition(k, q, 𝛼,𝛿,𝜃,𝜌):\n", " return k**𝛼 - 𝛿*k - q\n", "\n", "model = OCmodel(basis, control, reward, transition, rho=𝜌, params=[𝛼,𝛿,𝜃,𝜌])\n", "data = model.solve()" ], "metadata": { "collapsed": false, "pycharm": { "name": "#%%\n" } } }, { "cell_type": "markdown", "source": [ "## Plots\n", "\n", "### Optimal policy" ], "metadata": { "collapsed": false } }, { "cell_type": "code", "execution_count": 7, "outputs": [ { "data": { "text/plain": "
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IET0azpgTkYZhw4bht99+w+7duzFp0qSHjk1NTcXx48dhamqq1baSl5eHkpIS9a/lK1T0bus7W1cXvv32W0RFRaF///749NNPNYJ4aWnpI61M0qpVK3V7wbFjx9S977qcPHkS33zzDaytrXHixAm4uLgAKF8xozIV5+7fPbK6RCIRevTogR49eqhf85tvvsEPP/yAFStWqHvTK4Kbrhnh/Pz8Gt9fX6mpqWjVqpXWsbKyMnh7e1f79ar6/NbG57Y21dX3Q8VvdVJSUnSeP3ToEORyOR5//HHY2NgAKG9nOXbsGP744w/1EqBsYyGqfZwxJyINoaGhaNu2LaKjo7Fhw4ZKxymVSrz99ttQKBR48skntdpWVCoVjh49qnXdoUOHAJQ/lFmhvmckL168CACYMmWK1uz4iRMn1P9dk2XoKl4XAJYvX66zdxoo/wGgos/9ySefhLm5Odzd3eHu7o47d+7oXFM7Ojoa8fHxaNGihVbrkD4SExMRFhaG559/XuO4p6cn3n77bYjFYo2wVhHAMjMzNcYLgqD3b1QexZEjR7SOPcr3T5cuXQCUb+Cj65mIX3/9FUB5H74xqKvvh4oHfI8fP671PS4IAj744AO88cYbGscHDBgAW1tb/Pnnnzh06BBsbGzQr1+/GrwrInoYBnMi0mBqaoqlS5fCysoKy5Ytw4oVK7RmkJOSkjBr1iz8/fffaNGiBRYsWKDztZYuXaoR9E6fPo1NmzbB3t4eI0eOVB+v+DV8fczCAv/1uVeEvArR0dF499131R9XFqqr8vTTTyMwMBCxsbGYMmUKbt68qXE+Ozsbr776Ki5evAhXV1fMnj1bfW7ChAkAyledycjIUB9PS0tTf56fffbZGtXl7u6OnJwc/PPPP1rv/ZdffoFKpdJ4cLOiPWnr1q3q1hVBELBmzRqNFTrqypdffolr166pP7527RpWrVoFU1NTPPPMM+rjFTtaVvX906NHD8hkMkRFReGzzz7TCKV//vkntm/fDisrK6OaCa6L7wcfHx/07NkTt2/fxqpVqzR+SFmzZg0SExPRt29f9Ww5UN5nP2TIEMTGxuLChQsYMmSI1m/DiOjRsZWFiLT4+fnh+++/x4svvoivv/4amzdvRqdOnWBra4uUlBRcvnwZSqUS3bt3x4oVK2Btba3zdUpLSzFkyBD07NkThYWFOH36NCQSCT788EONVSwq2hK+++47XL9+HeHh4RpLHta2cePGYffu3diwYQOOHz+Oli1bIiUlBZcuXYK1tTVcXV2RmpqKjIwM9W6M1SEWi7Fu3TrMmjUL586dw9ChQ9GuXTt4enoiLy8PFy5cQElJCTw8PPDNN99o/LZhypQpOHfuHA4ePIgBAwaoHxQ8deoUioqKMHjwYPWMfHWJRCIsXrwYL7zwAmbNmoUOHTrAzc0NycnJuHTpEiwtLTF//nz1+DFjxmDLli04evQohgwZgjZt2iA2Nhbx8fEYNmwY9u/fX6M69GVhYYFRo0ahZ8+eAMp/m1FWVoa3335bo8Wl4iHlAwcOoKCgAKGhoRgzZozO979ixQpMnjwZX331FQ4cOIC2bdsiOTkZFy9ehLm5OT766COtFX8Mqa6+Hz744AOMHz8eX331FX777TfIZDLcvHkTcXFxcHV1xf/93/9pXRMeHo4dO3ZApVIZ1Q8vRI0JZ8yJSCc/Pz/8/PPPePPNN9G2bVtcunQJhw4dQmZmJvr164evvvoKGzdufOh63evXr0f//v1x+vRpxMTEICQkBNu3b9cK3f3798fEiRNhZmaGI0eO4MqVK3X63tq2bYtNmzYhODgYqampOHLkCAoLCzFmzBjs2bNHvdLEg7PK1WFnZ4dNmzbhgw8+QHBwMFJSUnDw4EFcvHgRrVu3xuuvv459+/ZprYIikUjw+eef4//+7//QqlUrnDx5EmfPnkXbtm2xdOlSrFq1SmP97erq06cPIiIi0Lt3b9y9excHDx5ESkoKRo4ciV27dmnMmHt6emL79u3o168fsrKycOTIEbi6umLz5s0a64vXlaVLl+KZZ57BlStXcP78eXTp0gUbNmzA+PHjNcZVrEtuZ2eHo0eP4ty5c5W+ZuvWrbF7926MGzcOCoUCBw8eRHJyMsLCwhAZGalziUZDqqvvB09PT+zcuRMTJ06EXC7HoUOHkJ2djaeeegqRkZE6e9bbt28PU1NTeHp6qtuCiKh2iQRdjXZERI8gNDQUiYmJOHHihN4bFRFVmDhxIk6fPo0ff/xRa010MpzffvsNc+bMwZw5czTar4io9nDGnIiIiHSqWMYzISEBn332GUxNTTF69GhDl0XUaLHHnIiIiHQ6cuQI/ve//6l3wp0yZUqNVgQiIv0wmBMREZFOPj4+cHR0REFBAUaMGIHXXnvN0CURNWrsMSciIiIiMgLsMSciIiIiMgJNspVFpVJBqeQvCoiIiIiobpmaSvQe2ySDuVIpICenyNBlEBEREVEj5+xsq/dYtrIQERERERkBBnMiIiIiIiPAYE5EREREZAQYzImIiIiIjACDORERERGREWAwJyIiIiIyAk1yuUQiIiIiotomL1MhLr0A0Sn5iE7Jx83MIhyY20fv6xnMiYiIiIiqSakScDurCFH3Qnh0Sj7i0gtRpqr5JpYM5kREREREDyEIAlLz5YhOyUfUvX+uphSgSKGs9BqphQnaueq/uRDAYE5EREREpCGvRIGrKQXqEB6Vko/MwtJKx1uYiNHG1QbtmtvCv7kt2jW3hYedBUQiUbXuy2BORERERE1WRV94VPJ/IfxudnGl4yUiwNfJGv5u5SHcv7kU3o5WMBFXL4TrYlTBfNGiRbhz5w42b95c5disrCysWLEChw4dQklJCfz9/fHaa6+hY8eOdV8oERERETU4KkHAnaxiRKXkqYN4VX3h7nYW8G9ui4B7QdzPxQYWppI6qc9ognlkZCQiIyMRFBRU5diCggKMHz8eaWlpmDJlCqRSKbZu3YrJkycjMjISMpmsHiomIiIiImOWli/XaEe5mpKPwtLK+8LtLEwQ4CZFu+Y28G9e/u9mVmb1Vq/Bg7lSqcTatWvxxRdf6H3NunXrcOvWLWzevBndunUDAAwdOhT9+/fH+vXrsWzZsroql4iIiIiMUIG8TP1wZsW/0wsq7ws3NxGjjYvNfy0pbrZwl1a/L7w2GTSYy+VyjBkzBrGxsQgPD8eJEyeqvEYQBOzevRshISHqUA4Azs7OmDdvHkxNTeuyZCIiIiIysNIyFeIyChGVnI/olDxEpeTjdlblfeFiEdDK0br8wcx7QdzX0QomEuPaa9PgwbygoAArV67E0KFDERoaWuU1CQkJSE1NxYwZMwCUB/WioiJYW1tj/PjxdV0yEREREdUjlSDgbnZx+Sz4vb7wa+kFUCgr7wt3k5qrV0fxd7NFGxdbWJnVTV94bTJoMLexscHvv/8OExP9y7hz5w4AwNHREUuXLsWOHTtQUFCAFi1aYOHChXqFeyIiIiIyTtlFpbiSnI8rKfm4kpSH6NR8FMirWC+8ecUKKeVh3NG6/vrCa5NBg7lYLIZYXL1fIeTl5QEAVq1aBRMTE7z11lsQi8WIiIjA7NmzERERgeDg4Lool4iIiIhqUWmZCtfSC3A5OR9RyXm4kpyPxNySSsebSUTwc7G9b6lCW3jaG7YvvDYZ/OHP6iotLW/iz8vLw2+//QY7OzsAQGhoKAYMGIDly5czmBMREREZGUEQkJhbUj4bnlzeFx6bVnlLigiAt6OVxlKFjzlZG11feG1qcMHcysoKADBw4EB1KAcAqVSK0NBQ7N69G4WFhbC2tjZUiURERERNXoG8DFHJ+biSUj4THpWcj+xiRaXjm1maIsDNFgFuUgS4lbek2Jg3uKj6SBrcu3V1dQUAODg4aJ1zcHDQeBiUiIiIiOpemUrAjYxCdTvKleR83M4qQmWPZ5pKRPeWKpSivZtxLFVoDBpcMG/dujXMzMxw/fp1rXMJCQkwNzfXGdqJiIiIqHakF8jVfeGXk8s37ikpU1U63tO+fPfM9vdmw1s728DMpPG2pNRUgwvmVlZWCA0NxcGDBxEXF4fWrVsDAOLj43Ho0CH0798fEonxL4dDRERE1BCUKJS4mlqAK+rZ8DykPWTjHhtzyb2+cKm6N7w+d89syIw+mMfHx+P8+fPo3LkzvLy8AABvvPEGTp8+jUmTJmHSpEkwNTXFpk2bYGFhgVdffdXAFRMRERE1TCpBwN2sYnVf+JXkfFxPL0BlS4ZLRICvkzXau0vVM+ItHCwhbuItKTVl9MH8zJkzWLhwIZYsWaIO5p6entixYwc++eQTREREQBAEdO3aFfPmzVOPISIiIqKHyylWICo5H5eT89Sb9+TLyyod72Jjpp4JD3CToo2rDSxN2alQW0SCIFS+bVIjpVAokZNTZOgyiIiIiOpNmUrA9fQCXErKv9eWkof4nMrXDLcwEaNtc1sENLdFgLsUAc1t4WJrXo8VNw7OzrZ6jzX6GXMiIiIiqr6solJcTip/OPNyUh6iq3hA08fBCv5utvdWSZHC18kaJmK2pNQnBnMiIiKiBq5MqUJcRiEuJ5W3pVxOynvoDpp2FibqlpT2blK0a24LWwvGQkPjV4CIiIiogamYDb90L4hHp+RDXslsuPjeA5od3KVo7yZFe3cpvBrRNvaNCYM5ERERkRH7bzY8D5futaYkVTEb3t5dig7u/+2gaW3GyNcQ8KtEREREZEQyCyt6w8tDeFWz4Y/dW66Qs+ENH4M5ERERkYGUKVW4ll6oEcQfNhtub2mKADdbdVtKu+a2sDLjcoWNBYM5ERERUT3JKCzFlYoQnpSH6NQCvWbDK4K4J2fDGzUGcyIiIqI6oDUbnpSHpDx5pePtLU3R3s1WHcTbunI2vKlhMCciIiKqBbnFClxOLn9A82JiHqIe0hsuEQGPOduogzhnwwlgMCciIiKqNkEQcCe7GJcSy4P4paQ83MqqfFfxZpam9wJ4eRBv19yWW9mTFgZzIiIioiqUKJSITs3XCOK5JWU6x4oAPOZcvm54xT8edpwNp6oxmNfQ+fNnceHCOUyf/ryhSyEiIqJall4gV7ekXErKQ0xaAZQqQedYazOJeqWU8rXDpbAxZ8Si6uN3TTX9/PMemJqawdnZBQAQFXUFf/99EC+++D8DV0ZEREQ1UaYScCO9EBeT8nApKReXkvKQ/JCHNN3tLNDBXYrAe0Hc18kaEjFnw+nRMZhX05AhI7B37y7s2rUG+fl5KCoqxOTJ0w1dFhEREempQF5W/pBmYh4uJuUhKjkfRQqlzrEmYhHautqg/X1B3MnGvJ4rpqaCwbwG7u8RE4slEInEBqyGiIiIKiMIAhJzS9QtKZeS8nAjoxC6m1LKlyy8fza8jasNLPiQJtUTkSAIlX1vNloKhRI5OZU/Of0wP/+8ByYmpnBxccWFC+fQo0cvtrIQEREZidIyFa6m5qtD+KWkPGQVKSod7+NopQ7hHdylaNHMkg9pUq1ydrbVeyxnzKtp+PBwAOUPfwKAv38A/P0DDFgRERFR05VdVIqL91pSLiXl4WpqPhRK3XOOFibi/x7S9LBDezdbSC1M67liospxxhxAXNw1RER8hQsXzkEQgC5duuK11xbi2WefRHDw43jvvY8MWC0REREB5W0pCTkl+DcxFxcT8/BvYi7uZBdXOt7V1vy/2XAPKVo728CED2lSPeOMeTWcPXsa8+bNRfPmzTF58nSYm5vjl19+xuuvz0FxcTFat5YZukQiIqImqUwl4FpagUYQr6wtRSICZC425f3h92bDm0st6rliokfTpIN5dnY23n13IWQyP6xa9SXMzcv/Bx40aBjGjBkJAGjd2s+QJRIRETUZhaVluJKUXx7Ek/JwJTkPxQrdW9pbmUruhXApOnrYwd+NO2lSw9ekg/nWrd8hNzcXy5e/rg7lAGBjYwOZrA3OnTvNGXMiIqI6kl4gV8+EX0zMw7X0AlSyhw+crM3Q0cMOHe8FcV9na7alUKPTpIP5wYO/o2PHzmjTpp3O846OjnBwcKznqoiIiBofQRBwO6v4XgjPxb+JeUjMLal0fCtHK/VseKCHFO5SbmlPjV+TDeaZmRlIT09DaOgArXMqlQo3b16HTNbGAJURERE1fBXLFlasmHIxMRe5JWU6x5pKRGjnaovAezPiHdylsLPkainU9BhVMF+0aBHu3LmDzZs3V+u6mJgYjB49Gs8//zxefvllva4pKSn/KV3XT99HjvyN7OwstrEQEVGTJM69Dat/v4F57C6IFIUQTK0h9xuFoo7PQWXnrfOa/JIyXErKU8+IR6Xko7SSZQttzU0Q6FG+iU9HDzu0bW4LcxNu1kdkNME8MjISkZGRCAoKqtZ1ZWVlWLhwIRSKyjcP0MXFxRUSiQT//nte43hKSjI+++wTAGAwJyKiJsfsziFIf30eUCogEspnuEWKAlhEbYNFTCTyBn+N0pahSMkrwb/39Yc/bDdNN6m5ejY80MMOrRytIGZbCpEWgwdzpVKJtWvX4osvvqjR9V9//TXi4uKqfZ2pqSkGDRqKX37ZhwULXkXPnr2RlpaKffv2oFkzB6SnpzGYExFRkyLOvQ3pr89DVKa9NrhIKAPKymCxfyamSVbgXEEzna8hAvCYs7X6Qc0O7lIuW0ikJ4MGc7lcjjFjxiA2Nhbh4eE4ceJEta6PjY3F2rVr8eKLL2LVqlXVvv8rr7wBExMTHD36D86dO4uAgPb46KNP8O2365GYGA9PzxbVfk0iIqKGyurfbwDlw38DLVKVYaRiD85hKgDA/N5umhUz4u3dpLAxN/i8H1GDZPBgXlBQgJUrV2Lo0KEIDQ3V+9qKFpbg4GCMHDmyWsE8JycLe/b8BACQyVojODgYvXv3VZ+/fv0amjVzwE8//fjQ1wkPH6vx8Z49O6q8d+/eIXByclF/fPToX8jISH/oNW3a+KNNG3/1xzExUYiJiXroNU5OzhrvKSMjDUePHq6yPr6ncnxP5fieyvE9/YfvqVxje09lAuDsF4QR0T+q21cqYyZSYozpMWQGL0ZHDzu0cbWBqYT94US1waDB3MbGBr///jtMTKpfxrp163Dnzh18+eWXKCt7+B8iD1IoFEhKStB5Lj8/H5mZGXjssccqHVMZfcbL5XKNjzMy0qu8zt3dU+PjvLzcatcml8urfQ3A91SB76kc39N/9+V7Ksf3VK6hvSeFIEaaygapKhukqmyRrrKG8uZdjDIvKu9FqYKlUIyJ3byqXQcRPZxBg7lYLIZYXP2fsuPi4rBmzRq88847aN68ORISqveHlKmpqcYfkE5Ozur/vnnzOgDAx6eV1h+iVdFnvLm5ucbH99+7MlKpndbHVd3rwdc1Nzev9vsB+J4qu7cufE+6X5fv6T98T7rvrQvfk+7Xrel7aubqhfgSM9wtNsPdElOkyE0h6EjghbCELbT7yx8kmNlUuwYiqppIEITKHqKud6GhofDw8HjocolKpRJPP/00rK2t8d133wEAEhIS0K9fP7z00kt6LZeoUCiRk1Ok89yuXZFYsWIpvv56I/z9A2r2RoiIiAwoLV+OfxNzcT4hF/8m5uJGhu6/8wDA18kKnTzs0MnTDoPjl8Mh7oeHtrMIIhOU+I9HQZ8P66J0okbH2dlW77EN7umMiIgIxMTEYNu2bcjKygIA5OXlAQCKi4uRlZUFe3v7Gs3EA8CoUWMwatSYWquXiIioLgmCgIScElxIyMWFxFxcSMitdEdNiQho42qLTp526h017e/fyMdtFnBzF/CwFlGJKYo6zqzld0FEQAOcMZ84cSJOnz790Nc5ePAgPD0r/1Xfw2bMiYiIjJlKEHAjoxAXEvLUYTyzsFTn2IoVUzremxFv7yaFlZnkoa+vax1zoHymHBJT9TrmRKSfRj1jPn/+fPUMeYWMjAy88cYbCAsLQ3h4OJydq+71IyIiagjKVAKupRXgXHwOLiTk4t/EPOTLdc9oW5tJEOghVbemtHW1hVk1d9QsbRmKrGf+gNW/62B6NRISZTGUEkso2o5BUceZle78SUSPrsEF84AA7b7vioc/vby8EBwcXN8lERER1ZoypQoxaQU4H5+Lcwk5uJiYh8JSpc6xzSxNy9tSPO3Q2cMOjzlbQyJ+9B01VXbe5T3k7CMnqldGH8zj4+Nx/vx5dO7cGV5eXJqJiIgaF4VSheiUfJxPKH9Y82JiLooVKp1jm9uao5Onnfqfls0sIeLW9kSNhtEH8zNnzmDhwoVYsmQJgzkRETV4pWXlQfxcQg7Ox+fiUlIeSsp0B3F3Owt09rRDZ087dPGyh7sdt7YnasyM6uHP+sKHP4mIqL7Iy1S4kpxXPiMen4PLyfmQVxLEPe0t0MXTHp29ysN4c6lhg3hMTBTy8nIhldpp7FpKRPpr1A9/EhERGbMShRKXk/Pu9YjnIio5D6VK3XNgLZpZqmfDO3vawcXWXOc4Q4mJiUJSUgLc3T0ZzInqAYM5ERHRIyhWKHEpMQ/nE3JwPiEXV5LzUabSHcR9HKzUs+GdPe3gZGNcQZyIDIvBnIiIqBoKS8twMbGiNSUX0an5UFYSxFs5Wqlnwzt52sHR2qyeqyWihoTBnIiI6CGKFUr8m5iLs3dzcT4hB1dT8lFJZwpaO1uXz4Z72aOThxTNrBjEiUh/DOZERET3qegRPxufi7N3cxCVontGXARA5mJzr0e8fIt7u/u3tyciqiYGcyIiatJKy1S4kpKHc3dzcTY+B5eT86DQMSUuAtDG1Qad762a0tFDCqkFgzgR1R4GcyIialLKlCpEp5ZvcX/2bg4uJuVVunxha2drdPGyR1ev8h5xBnEiqksM5kRE1KgpVQJi08qD+Jm75VvcFyl0b3Hv42CFLl526NbCHp097WFvxSBORPWHwZyIiBoVlSAgLr1QPSN+ITEXBXLdQbxFM0t08bJDVy97dPayhxNXTdHg5OSs8W8iqlvc+ZOIiBo0QRBwM7OoPIjHl++umVtSpnOsu9S8vDWlhT26eNnD1cg29CGixoc7fxIRUaMlCALuZBffmxEvX8Iwq0ihc6yLjZk6hHf1soe7nWG3uCciehgGcyIiMnrJeSU4cycHZ+JzcC4+B+kFpTrHOViZoquXPbq0KA/iXvYWEIlE9VwtEVHNMJgTEZHRySlS4Oy9hzXP3M1GfE6JznF2FiYaM+LeDpYM4rUoIyMNcrkc5ubmcHJyMXQ5RI0egzkRERlcUakSFxJzy2fF72bjWnqhznE25hJ08ayYEbeDr5M1xAzidebo0cNISkqAu7snwsPHGrocokaPwZyIiOqdQqnCleR8nLmbjTN3c3A5WffumuYmYgS6S9GthT26tWyGNi42kIgZxImocdI7mJeWlmL16tXYt28fMjMzoVRqLz0lEokQHR1dqwUSEVHDpxIExKUV4vS9IP5vYi6KFdqb+khEQLvmtuVBvEUztHeXwtxEbICKiYjqn97BfNmyZdiyZQt8fX3RtWtXmJlxrVciItJNEATE55SoZ8TP3q18CUNfJyt0a9Hs3qY+drAx5y9ziahp0vtPvwMHDmDgwIFYvXp1XdZDREQNVEaBHGfic+71iecgJV+uc5yb1Fw9I961BTf1ISKqoHcwLywsxOOPP16XtRARUQNSIC9Tb3N/+m4ObmXq3rjN3rJ8CcNuLe0R1MIeHnZcwpCISBe9g3lAQACuXLmCMWPG1GU9RERkpMqUKlxOzsepO9k4fScbUSn50PG8JqxMJejkaXdvVtwejzlz5RQiIn3oHcznz5+PGTNmQCaTYciQIXBwcKjLuoiIyMAEQcDtrGKcupONU3eycT4+F0UK7Qf/TcQitL+3ckpQC3v4N7eFiYQPbBIRVZdIEAQd8x3ahgwZgqysLOTl5VX+Yg1kVRaFQomcHN2/ciUiasqyikpx+k6OelY8rZIdNls7W6N7y2YIammPjh52sDSV1HOlVB/27NnBdcyJHpGzs63eY/WeMQ8MDGRPIBFRI1OiUOLfxFycuhfG4yrZ2MfFxgxBLZuhe8vy1VMc+cBmk8AwTlS/9J4xb0w4Y05ETZVKEHAtrUAdxC8m5qJUqf3XgJWpBJ297ND9XhjnVvdERDVTJzPmFW7cuIGDBw8iKSkJpqamcHd3R58+fdCqVavqvpSWRYsW4c6dO9i8eXOVY48cOYK1a9ciKioKYrEYgYGBeOWVV9CxY8dHroOIqDFJySu51ydevoJKTrFCa4xYBPg3t1XPige42cKUfeJERPWqWjPmn376KTZs2ACVSnO3NrFYjClTpmDevHk1LiQyMhKLFi1CUFBQlcH89OnTmDRpElq3bo2nnnoKZWVl2LZtG9LS0rBt2zZ06NDhoddzxpyIGrOKZQwrZsXvZhfrHOdpb6GeEe/qZQ9bC27sQ0RU2+pkxjwyMhLr169HSEgIZs2aBV9fX6hUKty8eRPr1q3Dt99+i9atW+PJJ5+sVrFKpRJr167FF198ofc1H330Edzc3LBjxw5YWloCAMLDwzF06FCsXLkS3377bbVqICJqyMpUAqKS89Sz4lHJedDRnQKphUn5yiktm6F7S3t42FnWf7HUoPDhT6L6pXcw37JlC7p3746vvvpK43jHjh2xZs0aTJ48GVu2bKlWMJfL5RgzZgxiY2MRHh6OEydOVHlNbm4uYmJiMHXqVHUoBwAnJyd069YNx44d0/v+REQNVXJeCU7czsbJ29k4czcbBXLdyxgGekjvrZ7SDG1cbCARs0+ciMhY6R3Mb926hfnz51d6fuDAgfj000+rdXO5XI6CggKsXLkSQ4cORWhoaJXX2NjY4Ndff9UI5RWys7MhkXDJLiJqfEoUSpxLyMWJW1k4eTsbdyppT/F1slIH8c6eXMaQiKgh0TuYW1tbIz09vdLzaWlpMDc3r9bNbWxs8Pvvv8PERP++RolEAm9vb63jMTExOH/+PHr37l2tGoiIjJEgCLiRUYQTt8uD+L+VrJ5ib2mK7i3t0cO7GXq0bAYnm+r9OUxERMZD70Tcu3dvbNmyBYMHD0abNm00zl29ehVbtmxBSEhItW4uFoshFj/6U/+FhYXq2fznnnvukV+PiMgQcooVOH0nGydul++0ma5jcx+JWIQObrbo4e2AHt7N0MbVhtvdExE1EnoH87lz5+Lo0aN46qmn0Lt3b/j4+AAAbt68iWPHjsHW1havvPJKXdVZqeLiYsyaNQsxMTF4/vnnERQUVO81EBHVRMVDmxW94tEp+dC1TJa7nQV63psR79rCHjbmXD2FiKgx0vtPd3d3d0RGRmL58uX4+++/8ffffwMALC0t0b9/f7z++uvw8vKqs0J1ycvLw/PPP4/z58/jqaeewty5c+v1/kRE1aXPQ5sWJmJ0bWGPHi2boaePA7zsLbi5DxFRE1CtaRdPT0+sXLkSKpUK2dnZEAQBDg4OtdKOUl2ZmZmYPn06rl69iqeffhrvvfce/+IiIqOj70ObrZ2ty2fFvZsh0N0OZibc3IeIqKmp0e9DxWIxHB0da7sWvRUUFKhD+ZQpU7Bw4UKD1UJEdD9BEHA3uxjHb2fj+K0snI/PeehDmz29HdDduxmcrM0MUC0RERmTSoN527ZtsWzZMowYMQIA0KZNmypnpEUiEaKjo2u3Qh0WL16Mq1evYtKkSQzlRGRwJQolzsXn4vitLBy7lYXE3BKtMRKxCB3cpepZcT8XPrRJxq937xDI5fJqr7pGRDVTaTAPDw9HixYtND42RKtIfHw8zp8/j86dO8PLyws3btzA3r17YWtri7Zt22Lv3r1a14SFhdV7nUTUtNzNLsaxW1k4fisLFxJyIS9TaY1xtTVHsE8zBHs78KFNapCcnFwMXQJRk1Lp3xJLlizR+Pjjjz+u82J0OXPmDBYuXIglS5bAy8sLp0+fBgDk5+dXOlvOYE5Ete3+WfHjt7OQkKN7VryThxTBPg7o6eMAX0crPvtCRER6EwmCoGt1Li2TJk3CrFmz0LNnT53nDx06hOXLl2P//v21WmBdUCiUyMkpMnQZRGTk7mYXlwfxW1k4X8msuIuNGYJ9HBDs44BunBUnIqIHODvb6j220r9BiouLkZ2drf749OnTGDBgAFq2bKk1VqVS4Z9//kFCQkI1SyUiMh73r6By7Fbls+IdPaToxVlxagKOHv0LGRnpcHJyRu/efQ1dDlGj99BgHh4ejvz8fADlD3Z+9NFH+Oijj3SOFwQBvXr1qpsqiYjqCGfFiSqXkZGOpCROuhHVl0r/dnFwcMAnn3yCy5cvQxAErFmzBgMGDICfn5/WWLFYDAcHBwwbNqxOiyUielQKpQrnE3Jx9GYWjt3MRPxDZsWDvcvDuK8TZ8WJiKjuPXTap0+fPujTpw8AICkpCc888wwCAwPrpTAiotqSWViKY7eycPRmFk7dzkaRQnu3TRcbM/T0cUAvzooTEZGB6P03z/2rtGRlZSEpKQkSiQSenp6wtdW/qZ2IqK6pBAGxaQU4erM8jEen5GuNkYiADh526HUvjHNWnIiIDK1aU0Jnz57Fp59+ikuXLqFiMReJRIIePXpg3rx5kMlkdVIkEVFVikqVOH0nu7xF5VYWMgpLtcbYWZigp48DHm/lgB7ezSC1MDVApURERLrpHcxPnTqF6dOnw8rKCuPGjYO3tzeUSiVu376Nffv24dlnn8X27dsZzomo3iTkFOPYvVnxcwk5UCi1V399zMkavVs5oHcrBwS4SSERc1aciIiMk97B/LPPPoOHhwe2b98OBwcHjXOzZ8/G2LFjsWLFCnz11Ve1XiQREQCUKVW4mJSnDuO3srT3IzA3EaOrl706jDeXWhigUiIiourTO5jHxMTgf//7n1YoBwAnJyeMGzcOa9eurdXiiIhyihU4fisLx25m4cTtbOTLy7TGuNiYoXcrR/RuVf7gpoWpxACVEhERPRq9g7mjoyMyMzMrPS+Xy2FjY1MrRRFR0yUIAm5kFOHIzUwcu5mFy8l5UD3QoSICEOAmVc+Kt3a25oObRHWgTRt/uLt7Qiq1M3QpRE2C3sH8hRdewPvvv49OnTohNDRU49zFixexadMmvPbaa7VeIBE1fmVKFS4k5uLv65k4ciMTSXlyrTE25hL0aOmAx30d0NO7GZpZmRmgUqKmpU0bf0OXQNSkiISK5VWqsGjRIhw/fhzJyclo1aoVfH19YWpqivj4eFy+fBlmZmZaa5yLRCJ89913dVL4o1AolMjJ0e5NJaL6k19ShhO3s/DPjUwcu5WFArn22uLeDpbo5eOIx30dEOguhYlEbIBKiYiIas7ZWf9lxfUO5g/Okuvr0KFDNbquLjGYExlGYm4xjtwoD+PnE3KhfKBHRSICOnra4QlfRzzeyhFezSwNVCkREVHtqJNg3pgwmBPVD5Ug4GpKPv65kYl/bmThekah1hhrMwl6ejvgicccEOztADtLri1OZCxiYqKQl5cLqdSObS1ENVSdYM49p4moVpUolDhzNwf/3MjEkZtZyNSx0U9zW3M84euIJ3wd0dnLDqZsUSEySjExUUhKSoC7uyeDOVE90DuYl5aWYt26dTh27BjS09OhUqm0xohEIvz555+1WiARGb/MwlIcu1neonLyTjbkZdp/PrR1tVGHca6iQkREpE3vYP7hhx/ihx9+QPPmzeHh4QGxmDNcRE3Z7cwiHL6egX9uZOFKch4e7Ikzk4jQrUUzPOHrgN6tHOFia26QOomIiBoKvYP5H3/8geHDh+PTTz+ty3qIyEhV9Iv/dT0Tf1/PwO2sYq0x9pam6N3KAU/4OqJ7y2awMuNGP0RERPrSO5grlUp069atLmshIiNTplThXEIuDsdl4J8bmUgr0O4Xb9nMEn0eK29RCXCTQiJmiwoREVFN6B3MBw0ahD/++ANPP/10XdZDRAZWrFDixO1sHI7LwNGbWciXl2mNCXCzRchjTujzmCO8HawMUCUREVHjo3cwnz9/Pp577jk888wz6N+/PxwdHXU+vBUeHl6b9RFRPcgpUuCfm5n4+3omTul4eFMiFqGrlx1CHnPCE77sFyciIqoLegfzc+fOITo6GsXFxfj33391jhGJRAzmRA1Ecl4JDt/rF7+QkIsH9vqBhYkYwT4OCGntiF4+DpBacH1xIiKiuqR3MF+2bBmsrKzwxhtvwMfHBxIJH+oiakgEQcCNzCIcjsvA39czEZNWoDXGzsIET/g6IqS1E4Ja2MPClP+fEzVlTk7OGv8morql986fHTp0wBtvvIGJEyfWWTGLFi3CnTt3sHnz5irHxsfHY+nSpTh9+jQAICQkBAsWLICDg0OV13LnT2oqVIKAK8n5+CsuA4evZyAhp0RrjJvUXN0vHuhhBxM+vElERFRr6mTnTx8fH+Tn59eoIH1ERkYiMjISQUFBVY7Nzs7G5MmTUVpaihkzZkCpVCIiIgKxsbGIjIyEmZlZndVJZOyUKgH/Jubir7gM/BWXoXMllcecrBHymCNCHnOCzIWb/RARERkDvYP5nDlz8Oabb8Lf3x+PP/54rW0wpFQqsXbtWnzxxRd6X7Nx40akpKRg37598PX1BQAEBgZi6tSp2LNnD8aOHVsrtRE1FGVKFc7F5+LQvZnxrCKFxnkRgA7uUoS0dkLIY47wtLc0TKFERERUKb2DecVM9AsvvABzc3PY29tr9ZmLRCL8+eefet9cLpdjzJgxiI2NRXh4OE6cOKHXdfv370dQUJA6lANAcHAwfHx8sH//fgZzahJKy1Q4czcHB6+l458bmcgt0VzWUCICunjZI1TmhD6POcHJmr9JIqLqychIg1wuh7m5OZycXAxdDlGjp3cwLywshLe3N7y9vWvt5nK5HAUFBVi5ciWGDh2K0NDQKq/Jzc1FfHw8Bg0apHXO398fhw8frrX6iIxNiUKJk7ezcejehj+FpUqN8yZiEYJa2qNfa2c84esIeyuupEJENXf06GEkJSXA3d0T4eGc9CKqa3oHc30eyKwuGxsb/P777zAx0bsMpKamAgBcXV21zjk7O6OgoAD5+fmwtdW/0Z7ImBWVKnHsVhYOXcvAsVuZKFZorjFuJhGhp7cDQmVOeLyVI2wt9P//iYiIiIyHQf8GF4vF1e5VLywsBABYWmr3yJqbl296UlRUxGBODVqBvAxHbmbi0LUMnLitveGPhYkYvVo5ILS1E3q1coC1GcM4ERFRQ6f33+b9+vXTa9zBgwdrXIw+VCpVlWNq68FUovqUW6zA3zcy8VdcBk7dyYZCqbmSqbWZBL1bOSBU5oxg72ZcY5yIiKiR0TuYu7u7ax1TqVTIyMjAnTt34O3tjV69etVqcbpYW1sDKO9Pf1DFsYoxRMYur0SBw9cz8WdsOk7fzYHyge03bc1N8MRjjujX2glBLZvB3IQ/dBIRETVWtdJjfuXKFcyYMUOvNcgfVcUPCOnp6Vrn0tLSIJVKYWVlVed1ENVUgbwMf1/PxJ/X0nHydjbKHgjj9pamCHnMEaEyJ3T1soephGGciIioKaiVxtSAgABMmDABa9as0blaSm2SSqXw9PREVFSU1rno6GgEBATU6f2JaqKwtAz/3MjEn7EZOHE7S6tNpZmlKUJlTugnc0InT3vuvklERNQE1doTY05OTrh9+3ZtvdxDDRw4EJs2bcKNGzfUa5kfP34ct27dwvTp0+ulBqKqFCuUOHIjE3/EpuP4rSyUPhDG7SxMECpzQn+ZMzp7MYwTERE1dbUSzNPT07F9+3adfeiPKj4+HufPn0fnzp3h5eUFAJg5cyb27t2LKVOmYNq0aZDL5Vi/fj38/f0RFhZW6zUQ6atEUb604Z+x6ThyM0trNRWphQlCHnPEAD9ndPWyhwnbVIiIiOieR16VpbS0FFlZWVAqlXj33XdrrbAKZ86cwcKFC7FkyRJ1MHdwcMCWLVuwZMkSrF69GhYWFujfvz/mzZsHMzPubkj1S16mwolbWfgjNh1HbmqvM25jLkGfx5wwQOaMoJbsGSeihoObChHVL5EgCELVw4CJEyfqPC6RSODk5IThw4cjJCSkNmurMwqFEjk5RYYugxqwMqUKJ+9k4/eYdJ07cFqbSfCEryP6+zmjR8tmMONqKkRERE2Ss7P+e+voHcwbEwZzqgmVIOBCQi5+j0nHwWvpyC0p0zhvaSouD+MyZ/T0ceDShkRERFStYP5IPeYKhQLHjh2DRCJBz549YWLC3QepcREEAbFpBfj1ajr+iE1DWkGpxnlzEzEeb+WAAX7OCPZx4KY/REREVGN6J+nS0lJ88MEHSEhIwIYNG1BaWoqnn34aMTExAABfX1989913cHR0rLNiierLnawi/B6Tjl9j0nA3u1jjnEQsQo+WzTCorTP6+DrByoxhnIgapz17diApKQHu7p7sNyeqB3oH8y+++AI7duzAU089BQDYs2cPrl69ikmTJqFt27b4+OOPsWrVKixevLjOiiWqS6n5cvwRm47fY9JwNbVA63wnTzsMauOMfq2dYW9laoAKiYiIqDHTO5gfOHAAo0ePxgcffAAA+O2332Bra4t58+bBxMQE8fHxiIyMrLNCiepCTrECh66l47eYdFxIyMWDD1z4udhgUBtnDPBzRnOphUFqJCIioqZB72CekpKCjh07AgCKi4tx5swZhISEqPvK3dzckJeXVydFEtWmolIl/rmRid9i0nDidjaUKs043qKZJQa1ccbANi7wdrAyUJVERETU1OgdzJ2cnJCRkQEAOHLkCEpLSzWWR4yNjYWLi0utF0hUG8pUAk7dycaB6FT8fT0TJQ9s/ONsY4YBfs4Y3NYFbVxsIBJxF04iIiKqX3oH8+7du+O7776Dubk5tm7dCktLS/Tv3x95eXnYuXMnduzYgWeeeaYuayWqlooVVX6JTsNvMWnIKlJonJdamCC0tRMGt3VBRw87SMQM40RERGQ4egfzN998E6mpqVi6dCmsrKzwwQcfQCqV4ty5c1i6dCm6deuGl156qS5rJdJLSl4Jfr2ahl+upuFWpuZ69eYm5WuND27rgp7ezbgLJxERERkNvYO5VCrFt99+i6ysLNjY2MDMzAwA0LZtW/zwww8IDAyssyKJqlIgL8OhuAwciE7FuXjNhzhFALp42WFIO1eEtnaCjTnX2yciIiLjU+2E4uDgoPGxlZUVQzkZRJlShZN3svFLdBr+uZEJ+QN94z6OVhja1gWD27pwRRUiIiIyetUK5v/88w/27duHjIwMKJVKrfMikQjfffddrRVH9CBBEHA1tQC/RKfi95h0ZBdr9o07WJliUBsXDG3nAj8+xElE9Eh69w6BXC6Hubm5oUshahL0DuZbt25Vr2Hu6OiobmUhqg/JFX3j0am4naW5E6e5iRghjzliSDtXdG/ZDCZ8iJOIqFY4OXG1NaL6JBIE4cE9VXQaNGgQrKyssG7dOjg5OdV1XXVKoVAiJ6eo6oFkUMUKJQ5dy8C+qBSci8/VOCcC0KWFPYa2dUFf9o0TERGRkXJ2ttV7rN5pJjk5GW+++WaDD+Vk3ARBwL+Jedh3JQUHr2WgSKHZMtXK0QpD27licFsXuNryV6tERETUeOgdzFu0aKHeYIiotqXklWB/dCp+jkpFQk6JxrlmlqYY3NYFw9q5QuZizb5xIqJ6cvToX8jISIeTkzN69+5r6HKIGj29g/lzzz2HDz/8EIMGDULr1q3rsiZqIkoUShy+nol9V1Jw5m6OxhKHErEIj7dywHB/V/TycYAJ1xsnIqp3GRnpSEpKMHQZRE2G3sH83LlzsLa2RlhYGHx8fODg4KA1c8lVWagqgiDgSnI+9kWl4PeYdBSWaraqtHa2xnD/8lYVBys+YExERERNh97B/MiRIwCA5s2bo7i4GImJiXVWFDU+6QVy/BKdhp+jUrRWVbGzMMHgti4Y4d8cfq42BqqQiIiIyLD0DuaHDh2qyzqoESpTqnDkZhb2Xk7BidtZUN3XqyIRAT19HDAioDl6+zjAzIStKkRERNS0VXuNOaVSiStXriAxMRFmZmZwc3ODv79/XdRGDdSdrCL8dCUFP0elIqtIcwMgH0crjPB3xZB2rnCyZqsKERERUYVqBfO//voL7733HlJTU1Gx/LlIJIKLiwveffddhIaG1kmRZPxKFEocisvA3sspOJ+guea4jbkEg9q4YERAc7Rz5W6cRERERLroHczPnj2Ll19+GY6Ojpg7dy58fX0hCAJu3ryJbdu2Yc6cOdi0aRM6d+5cl/WSkYlNK8Deyyk4cDUVBXLNBzk7eUgR1t4N/WROsDCVGKhCIiIiooZB72D++eefw8PDAz/++CNsbTV3MBo3bhyeeuoprF27FuvWratWAfHx8Vi6dClOnz4NAAgJCcGCBQvg4ODw0OuuXLmC5cuX48KFCxCLxQgKCsK8efPQqlWrat2fqq9AXobfYtKw93IKrqYWaJxrZmmK4f6uGNm+ObwdrAxUIREREVHDo3cwv3TpEmbPnq0VygHAxsYGo0ePrnYoz87OxuTJk1FaWooZM2ZAqVQiIiICsbGxiIyMhJmZ7h7kmzdvYuLEibC0tMSLL74IAPj2228xbtw47N27F66urtWqg6omCAIuJeVhz+UU/BmbjpIylfqcCEBPn2YIa++Gx1s5wJRrjhMRNQpt2vjD3d0TUqmdoUshahKq/fBnZUQiERQKRdUD77Nx40akpKRg37598PX1BQAEBgZi6tSp2LNnD8aOHavzuu+++w5FRUXYunUr2rVrBwDo0aMHxowZg40bN2L+/PmP9mZILadYgf1RqdhzOVlrmcPmtuYYGdAcIwJc0VxqYaAKiYiorrRpw8UdiOqT3sE8MDAQP/74I8aNGwcrK80WhYKCAkRGRqJ9+/bVuvn+/fsRFBSkDuUAEBwcDB8fH+zfv7/SYJ6QkIBmzZqpQzkAdOjQAfb29rh27Vq1aiBtgiDgcnI+dl5Mwp+x6ShV/rfOoUQsQshjjghr3xxBLZpBIuaDnERERES1Qe9g/tJLL2HSpEkYPnw4JkyYAG9vbwBQP/yZmpqK9957T+8b5+bmIj4+HoMGDdI65+/vj8OHD1d6bcuWLXH8+HFkZWWpe9FzcnKQn58PFxcXvWsgTYWlZTgQnYZdl5IRl16oca5FM0uEt2+OYf6u3JGTiIiIqA7oHcy7du2Kzz//HIsXL8ayZcvUS94JggBnZ2esXLkSPXr00PvGqampAKCzH9zZ2RkFBQXIz8/X2dM+Y8YM/PXXX3j11VexYMECiEQiLFu2DKamppg4caLeNVC52LQC7LqYjF+vpqFI8d/KKhKxCH0fc8Lojm7o7GnHZQ6JiJqYmJgo5OXlQiq1Y1sLUT2oVo95v379EBISgqioKCQkJAAAPDw84O/vDxOT6rWrFxaWz8haWlpqnTM3NwcAFBUV6Qzm7u7ueP755/H+++8jLCwMACCRSLB69WqN9haqXIlCiT+vpWPnxWRcSc7XOOcmNceTHdwwIqA5NwEiImrCYmKikJSUAHd3TwZzonpQ7Yc/JRIJOnTogA4dOiAzMxP29vaQSKq/RrVKpapyjFise3WPzz77DGvXrkVQUBDGjh0LpVKJ77//Hq+88gpWr17NjY4e4nZWEXZdTMb+6FTklZSpj4sA9GrlgNGB7ujhzd5xIiIiovpWZTDfsmULfvjhB+zevVtrVvyjjz7CiRMn8Nxzz2HKlCnVurG1tTUAQC6Xa52rOFYx5n55eXmIiIhAQEAANm7cqP6hYNiwYRg9ejTefvtt9O7du9KlFpsihVKFv69nYufFJJyN19yV09HaDGHtmyO8fXO4cWUVIiIiIoOpNJgLgoD58+fjp59+gp2dHZKSktCiRQuNMZ6enhCLxVi6dCkuXbqEFStW6H1jd3d3AEB6errWubS0NEilUq3VXwDg9u3bKC0txfDhwzVm6k1NTTFixAh88sknuHnzJtq0aaN3LY1VeoEcuy8lY9elFGQWlmqc69bCHk8FuqGPryNMuO44ERERkcFVGswjIyPx008/Ydy4cZg/f7667/t+c+fOxYsvvoh3330Xe/fuxRNPPIHw8HC9biyVSuHp6YmoqCitc9HR0QgICNB5XcVMuFKp1DpX0R6jT5tMY1WxEdCOC0k4GJcBpeq/pQ6lFiYY7u+KJzu4cVdOIiIiIiPz0GDerVs3vPPOOw99AXNzc3z00UeIjY3F999/r3cwB4CBAwdi06ZNuHHjhnot8+PHj+PWrVuYPn26zmtat24NFxcX7N69GxMnTlT/wCCXy7Fnzx40a9YMrVu31ruGxqJEocTvsenYcSEJsWkFGufautpgbCd39Jc5w8K0+s8DEBEREVHdqzSYX79+Hf/73//0ehGxWIxBgwbh66+/rtbNZ86cib1792LKlCmYNm0a5HI51q9fD39/f/VqK/Hx8Th//jw6d+4MLy8vSCQSvPPOO5gzZw5Gjx6N0aNHQ6VSYefOnbh586Z62cSmIjmvBD/+m4y9l5ORe9/DnCZiEfr7OePpTu7wb27LpQ6JiIiIjFylwVwikVTrAcpmzZpVuopKZRwcHLBlyxYsWbIEq1evhoWFBfr374958+ap733mzBksXLgQS5YsgZeXFwBgwIAB2LBhA7788kusXLkSANCuXTt88803eOKJJ6pVQ0MkCALO3M1B5L9J+OdGJu7rVoGzjRlGdXDDkx3c4MilDomIiIgajEqDecuWLXHlyhW9X+jy5cvqBzqro1WrVli3bl2l50eNGoVRo0ZpHe/Zsyd69uxZ7fs1ZMUKJX6JTsUPF5JwK7NI41wnDynGdPJA38f4MCcREdUOJydnjX8TUd2qNJgPGzYMK1euxNSpU6vs2Y6Li8O+ffswYcKEWi+QgLR8OXb8m4Tdl5I11h43NxFjcFsXjOnoDj8XGwNWSEREjVHv3n0NXQJRkyISBEHQdaKwsBCjRo1Cbm4u3nzzTQwbNkxrIyGVSoVffvkFH3/8MVQqFfbs2QMXF5d6KfxRKBRK5OQUVT3QwKJT8rHtXAL+vKa5uoqb1BxjOrpjZEBz2Fk2nX56IiIioobG2Vl7F/vKVBrMAeDmzZt48cUXcefOHVhZWcHf3x/Ozs5QqVTIzMxEVFQUioqK4ObmhjVr1qBt27a18gbqmjEHc6VKwN/XM7DtXCIuJuVpnAt0l2JcFw888ZgTTLgzJxEREZHRq7VgDgClpaXYunUr9u/fj5iYGJSVlbdSmJqaomPHjhg4cCCefvrpBrXTpjEG8wJ5GX66koIfziciKe+/3VAlYhH6y5zwbGcP+LtJDVghERE1NRkZaZDL5TA3N4eTk/H/RpzIGNVqMH9QVlYWJBIJ7Ozsql2YsTCmYJ6YW4wfzifhpyspKCz9b9MkqYUJwtu7YWwnd7jaam/uREREVNf27NmBpKQEuLt7Ijx8rKHLIWqQqhPMK334szIODg7VvYR0iErOw+azCfgrLkNjucMWzSzxTGcPDPd3hSU3AyIiIiJqMqodzKnmBEHA8VvZ2HQmHucTcjXOdWthj3FdPBDs4wAxNwMiIiIianIYzOuBQqnCbzFp2HwmATfvW39cIhZhcBtnjOviCRmXOyQiIiJq0hjM61CBvAx7Lqdg+7kEpBWUqo9bm0kQ3t4Nz3bxYP84EREREQF4SDDfvn07evbsCW9v73osp3HIKJBj+/kk7LqUhAL5fw90Olqb4dnOHhjVwQ22FvyZiIiIiIj+U2k6XLZsGd566y11MO/Xrx/efPNN9OvXr75qa3BuZxZhy9kE/HI1FQrlf090ejtYYmJXLwxu6wIzE7EBKyQiIiIiY1VpMDczM8Off/6Jjh07wtLSEomJiUhKSkJSUtJDX9Dd3b3WizR2V1PzseHkXRy+nqlxvKOHFBO6euFxXz7QSUREREQPV+k65p988gkiIiIgqmagvHr1aq0UVpdqax3zfxNyseHUXZy4na0+JgLQ5zFHTOjqiUCPhrvWOxEREdcxJ3p0tbbB0OHDhxEbG4vS0lKsWbMGAwYMgJ+f30Nf8KWXXtK/UgN5lGAuCAJO38lBxKm7uHDfkocSsQhD27pgUpAXvB2saqtUIiIiImrA6mTnz9DQULz11luNose8JsFcJQg4ciMLG07dRXRKvvq4mUSEkQHNMSnIC25Si9oulYiIiIgasDoJ5hWUSiWuXLmCxMREmJmZoXnz5ggICKh2kYZUnWCuVAk4eC0d356Kx/WMQvVxS1Mxngp0x/guHnCy4ZKHRERERKStOsG8Wmv2/fXXX3jvvfeQmpqKijwvEong4uKCd999F6GhodWr1IiVKVX45Woavjsdj7vZxerjtuYmGNvJHc909oC9pakBKyQiIiKixkTvGfOzZ89iypQpcHR0xPjx4+Hr6wtBEHDz5k1s27YNGRkZ2LRpEzp37lzXNT+yh82YK5Qq7ItKxcZTd5GcJ1cfb2ZpinFdPDC6oztszLkGORERNX58+JPo0dXJjPnnn38ODw8P/Pjjj7C11bzBuHHj8NRTT2Ht2rVYt26d/pUakTKlCj9HpWLDA4Hc2cYME7t54cn2zWFhKjFghURERETUmOkdzC9duoTZs2drhXIAsLGxwejRoxtkKC9TqrA/OhUbTt5F0n2BvLmtOaZ298Jw/+bcFIiIiIiI6lyt9WSIRCIoFIraerk6V6YS8Mu9QJ6YW6I+7mprjmndvTAioDlMJQzkRERERFQ/9A7mgYGB+PHHHzFu3DhYWWmu011QUIDIyEi0b9++1gusC7klCoz59gwScv4L5C42ZpjavQVGBnCGnIiIiIjqn97B/KWXXsKkSZMwfPhwTJgwAd7e3gCgfvgzNTUV7733Xl3VWauSckvUodzZxgxTglogvD0DOREREREZjt7BvGvXrvj888+xePFiLFu2DCKRCED5TpjOzs5YuXIlevToUWeF1jYnazNMCfJCeAc3mDOQExEREZGBVavHvF+/fggJCUFUVBQSEhIAAB4eHvD394eJSc3a1ePj47F06VKcPn0aABASEoIFCxbAwcHhoddlZWVhxYoVOHToEEpKSuDv74/XXnsNHTt2rPKenvaW2D29G1dZISIiIiKjUe00LZFI0KFDB3To0OGRb56dnY3JkyejtLQUM2bMgFKpREREBGJjYxEZGQkzMzOd1xUUFGD8+PFIS0vDlClTIJVKsXXrVkyePBmRkZGQyWQPva+tuQmUDOVEREREZEQMulPOxo0bkZKSgn379sHX1xdA+UOmU6dOxZ49ezB2rO7NDNatW4dbt25h8+bN6NatGwBg6NCh6N+/P9avX49ly5bV23sgIiJqrHr3DoFcLoe5ubmhSyFqEgwazPfv34+goCB1KAeA4OBg+Pj4YP/+/TqDuSAI2L17N0JCQtShHACcnZ0xb948mJqa1kvtREREjZ2Tk4uhSyBqUgz21GNubi7i4+Ph7++vdc7f3x9XrlzReV1CQgJSU1MRHBwMoDyoFxYWAgDGjx9f6Sw7EREREZExM1gwT01NBQC4urpqnXN2dkZBQQHy8/O1zt25cwcA4OjoiKVLl6Jr167o3LkzBgwYgEOHDtVt0UREREREdaRGrSypqalISUlBq1atYG5uDhMTE4jF1cv4FbPclpaWWucqetmKiopga2urcS4vLw8AsGrVKpiYmOCtt96CWCxGREQEZs+ejYiICPVsOhEREdXc0aN/ISMjHU5Ozujdu6+hyyFq9KqVps+dO4dRo0YhJCQEzzzzDK5cuYLTp08jJCQEv/zyS7VurFKpqi5OR9gvLS0FUB7Qt2/fjlGjRiE8PBxbt26FVCrF8uXLq1UHERER6ZaRkY6kpARkZKQbuhSiJkHvYH7p0iVMnToVhYWFmDx5svq4nZ0dTExM8Prrr+Pvv//W+8bW1tYAALlcrnWu4ljFmPtZWVkBAAYOHAg7Ozv1calUitDQUERFRaln44mIiIiIGgq9g/mqVavg6emJvXv34rnnnoMgCACA9u3b46effoKvry++/vprvW/s7u4OAEhP1/4pPC0tDVKpVB3C71fRk65rAyIHBwcIgoCioiK96yAiIiIiMgZ6B/MLFy5g1KhRsLCwgEgk0jhnY2ODsWPHIi4uTu8bS6VSeHp6IioqSutcdHQ0AgICdF7XunVrmJmZ4fr161rnEhISYG5uXuWuoURERERExqZaPeaV7cQJlLef6NM3fr+BAwfixIkTuHHjhvrY8ePHcevWLQwdOlTnNVZWVggNDcXhw4c1fhCIj4/HoUOH0K9fP0gk3NWTiIiIiBoWvYN5YGAgfv75Z53nioqKEBkZifbt21fr5jNnzoSdnR2mTJmCb7/9Fl999RXmzJkDf39/hIWFASgP3Hv37kV8fLz6ujfeeAO2traYNGkS1q5di/Xr12P8+PGwsLDAq6++Wq0aiIiIiIiMgd7BfM6cOYiOjsaECROwZ88eiEQiXLp0CZs2bUJYWBgSEhLwwgsvVOvmDg4O2LJlC9q0aYPVq1fju+++Q//+/bF+/Xr17PyZM2cwb948nDlzRn2dp6cnduzYgW7duiEiIgJr165F27Zt8f3338PLy6taNRARERERGQORUPEUpx6OHTuGd999FwkJCRrHnZ2d8fbbb2PgwIG1XmBdUCiUyMnhA6JEREQPs2fPDiQlJcDd3RPh4dxZm6gmnJ1tqx50T7WCOQAIgoDo6GjcvXsXKpUKHh4eCAgIgIlJjfYqMggGcyIioqrFxEQhLy8XUqkd2rTxN3Q5RA1SnQTzhQsX4plnnkFgYKDO8ydPnkRERATWrVun980NhcGciIiIiOpDdYK53j3mu3fv1ngA80GnTp3CqVOn9L4xERERERH9p9IZ8/j4eAwfPhylpaUAyltYHly//EHt27fHjh07ar/KWsYZcyIiIiKqD7XWyrJz506cPXsWgiBgz5496Nq1q85VT8RiMRwcHPDss8+qd/Q0ZgzmREREVWOPOdGjq04wf+gTm0899RSeeuopAEBiYiJefPFF9OzZ89GqIyIiogYhJiZKvSoLgzlR3dN7KZXNmzdXOUapVHLXTSIiIiKiGqjWGodnz57Fb7/9hqKiIqhUKvVxpVKJwsJCnDt3DidPnqz1IomIiIiIGju9g/nOnTuxaNEiVLSki0Qi3N+ebmZmhpCQkFovkIiIiIioKdB7ucRNmzbBy8sLBw4cwE8//QRBEPD333/jn3/+wfTp01FWVoZx48bVZa1ERERERI2W3sH89u3bGDNmDHx8fCCTyWBtbY0zZ87AxcUFb7zxBnr16oVvvvmmLmslIiIiImq09A7mYrEYzZo1U3/csmVLxMTEqD/u27cvrl27VrvVERERERE1EXoH8xYtWmgEb29vb1y9elX9cVlZGQoLC2u3OiIiIiKiJkLvYD506FBs27YNK1euhFwuR69evXDq1Cns3r0bly5dwtatW+Hj41OXtRIREVE9cnJyhru7J5ycnA1dClGT8NCdP+9XVlaGBQsW4JdffsG5c+dgamqKqVOn4syZMxCJRJBIJPj888/Rt2/fuq75kXHnTyIiIiKqD9XZ+VPvYF4hIyMDTk5OAACFQoH9+/cjJycHvXr1QuvWratXqYEwmBMRERFRfajTYP4we/fuRVhYWG29XJ1hMCciIiKi+lBrwbysrAx//vknLl68CEEQ0K5dOwwbNgwSiURjXGJiIt555x0cP35c44FQY8VgTkREVLWMjDTI5XKYm5vDycnF0OUQNUjVCeaV7vyZmZmJ6dOnIzY2VmO3z3Xr1mHLli2ws7MDAHz33Xf47LPPUFxcjC5dujxi6URERGQsjh49jKSkBLi7eyI8fKyhyyFq9CpdlWXFihWIiYnBM888gx07dmDfvn14/fXXkZCQgPfffx+lpaWYPXs2Pv74Y5iZmeH999/H1q1b67N2IiIiIqJGo9IZ8xMnTmDgwIF499131cdat24NCwsLfPrpp/i///s/HDx4EP369cPixYvh6OhYLwUTERERETVGlc6YZ2ZmomfPnlrHn3jiCRQXF2Pv3r1YtGgR1qxZw1BORERERPSIKg3mcrkcNjY2Wscrjo0bNw4TJkyou8qIiIiIiJoQvXf+fNATTzxRKwXEx8fjpZdeQlBQEIKCgjBv3jxkZWVV6zViYmIQEBCAzz//vFZqIiIiIiKqb5X2mFd5oUmNL1XLzs7G5MmTUVpaihkzZkCpVCIiIgKxsbGIjIyEmZlZla9RVlaGhQsXQqFQPHI9RERERESG8tB0nZOTg6SkJI1jubm5AICsrCytcwDg7u6u9803btyIlJQU7Nu3D76+vgCAwMBATJ06FXv27MHYsVUvzfT1118jLi5O73sSERERERmjhwbzjz76CB999JHOc6+//rrWMZFIhOjoaL1vvn//fgQFBalDOQAEBwfDx8cH+/fvrzKYx8bGYu3atXjxxRexatUqve9LRERERGRsKg3mTz75ZJ3eODc3F/Hx8Rg0aJDWOX9/fxw+fPih11e0sAQHB2PkyJEM5kRERLWMmwoR1a9Kg/mSJUvq9MapqakAAFdXV61zzs7OKCgoQH5+PmxtdW9jum7dOty5cwdffvklysrK6rRWIiIiIqK6VuNVWR5VYWEhAMDS0lLrnLm5OQCgqKhI57VxcXFYs2YN5s+fj+bNm9ddkURERERE9cRgwVylUlU5RizWLk+pVGLhwoXo0qWLXg+HEhERERE1BI++5mENWVtbAyjfyOhBFccqxtwvIiICMTEx2LZtm3q987y8PABAcXExsrKyYG9vrzPUExERkf727NmBpKQEuLt7st+cqB4YLJhXLKuYnp6udS4tLQ1SqRRWVlZa544cOQKFQoExY8ZonYuIiEBERAQOHjwIT0/P2i+aiIiIiKiOGCyYS6VSeHp6IioqSutcdHQ0AgICdF43f/589Qx5hYyMDLzxxhsICwtDeHg4nJ2d66RmIiIiIqK6YrBgDgADBw7Epk2bcOPGDfVa5sePH8etW7cwffp0ndfoCuwJCQkAAC8vLwQHB9ddwUREREREdcSgwXzmzJnYu3cvpkyZgmnTpkEul2P9+vXw9/dHWFgYACA+Ph7nz59H586d4eXlZchyiYiIiIjqjEGfkHRwcMCWLVvQpk0brF69Gt999x369++P9evXw8zMDABw5swZzJs3D2fOnDFkqUREREREdUokCIJg6CLqm0KhRE6O7jXSiYiIqBxXZSF6dM7OujfL1IVrChIRERERGQEGcyIiIiIiI2DQhz+JiIjIePXuHQK5XA5zc3NDl0LUJDCYExERkU5OTi6GLoGoSWErCxERERGREWAwJyIiIiIyAmxlISIiIp2OHv0LGRnpcHJyRu/efQ1dDlGjx2BOREREOmVkpCMpKcHQZRA1GWxlISIiIiIyAgzmRERERERGgMGciIiIiMgIMJgTERERERkBBnMiIiIiIiPAYE5EREREZAQYzImIiIiIjADXMSciIiKd2rTxh7u7J6RSO0OXQtQkiARBEAxdRH1TKJTIySkydBlERERE1Mg5O9vqPZatLERERERERoDBnIiIiIjICLDHnIiIiHSKiYlCXl4upFI7tGnjb+hyiBo9zpgTERGRTjExUTh79iRiYqIMXQpRk8BgTkRERERkBBjMiYiIiIiMgMGDeXx8PF566SUEBQUhKCgI8+bNQ1ZWVpXXHTlyBOPGjUNgYCA6deqEKVOm4N9//637gomIiIiI6oBBH/7Mzs7G5MmTUVpaihkzZkCpVCIiIgKxsbGIjIyEmZmZzutOnz6NmTNnonXr1pg7dy7Kysqwbds2TJgwAdu2bUOHDh3q+Z0QERERET0agwbzjRs3IiUlBfv27YOvry8AIDAwEFOnTsWePXswduxYndd99NFHcHNzw44dO2BpaQkACA8Px9ChQ7Fy5Up8++239fYeiIiIiIhqg0FbWfbv34+goCB1KAeA4OBg+Pj4YP/+/Tqvyc3NRUxMDAYPHqwO5QDg5OSEbt264cKFC3VeNxERERFRbTPYjHlubi7i4+MxaNAgrXP+/v44fPiwzutsbGzw66+/aoTyCtnZ2ZBIJLVdKhERERFRnTNYME9NTQUAuLq6ap1zdnZGQUEB8vPzYWtrq3FOIpHA29tb65qYmBicP38evXv3rpN6iYiImhonJ2eNfxNR3TJYMC8sLAQAnTPf5ubmAICioiKtYF7Za82fPx8A8Nxzz9VilURERE1X7959DV0CUZNisB5zlUpV5RixuOryiouLMWvWLMTExOC5555DUFBQbZRHRERERFSvDBbMra2tAQByuVzrXMWxijGVycvLw7Rp03Dq1Ck89dRTmDt3bu0XSkRERERUDwzWyuLu7g4ASE9P1zqXlpYGqVQKKyurSq/PzMzE9OnTcfXqVTz99NN47733IBKJ6qxeIiKipiYjIw1yuRzm5uZwcnIxdDlEjZ7BgrlUKoWnpyeioqK0zkVHRyMgIKDSawsKCtShfMqUKVi4cGFdlkpERNQkHT16GElJCXB390R4uO69RYio9hh0HfOBAwfixIkTuHHjhvrY8ePHcevWLQwdOrTS6xYvXoyrV69i0qRJDOVERERE1CgYdOfPmTNnYu/evZgyZQqmTZsGuVyO9evXw9/fH2FhYQCA+Ph4nD9/Hp07d4aXlxdu3LiBvXv3wtbWFm3btsXevXu1XrfiWiIiIiKihsKgwdzBwQFbtmzBkiVLsHr1alhYWKB///6YN28ezMzMAABnzpzBwoULsWTJEnh5eeH06dMAgPz8/EpnyxnMiYiIiKihEQmCIBi6iPqmUCiRk1Nk6DKIiIiM2p49O9hjTvSInJ2r3pOngkF7zImIiIiIqByDORERERGREWAwJyIiIiIyAgzmRERERERGgA9/EhERERHVET78SURERETUwDCYExEREREZAQZzIiIiIiIjYNCdP4mIiMh4cYMhovrFGXMiIiIiIiPAYE5EREREZAQYzImIiIiIjACDORERERGREWAwJyIiojp1/vxZRER8begyiIwegzkRERHViZ9/3oPffvtF/XFU1BV8+eUqA1ZEZNy4XCIRERHpbdq0CSgrU2DTph+qHDtkyAjs3bsLu3atQX5+HoqKCjF58vR6qJKoYeKMOREREemlrKwMt2/fROvWMr2vEYlE6v8WiyUQiRg9iCrDGXMiIiLSqXfvEMjlcpibmwMAbt++hdLSUjz2mJ9e1x84sA+WlpZ4/vnZuHDhHHr06IXNmzfgxRf/V5dlEzVYDOZERESkk5OTi8bHcXGxAACZTL9gPnx4OIDyhz8BwN8/AP7+AbVXIFEjw98nERERkV4qgvn9rSz5+flYuPA1hIYGY+/eXTqv69y5K6ZPf75eaiRqyDhjTkRERHqJi7sGFxdXSKV2AICYmKt4++0FAAR8+WUE2rRpa9gCiRo4BnMiIiLS6ejRv5CRkQ4nJ2f07t0XcXHXEBjYEQCwe/eP+PzzFejSpRvefnuxOqwTUc0xmBMREZFOGRnpSEpKAAAkJSWioCAfnp4t8H//9xYOHfoDU6fOxJQpMzRWXiGimjN4MI+Pj8fSpUtx+vRpAEBISAgWLFgABweHOrmOiIiIqi8u7hoAYOfOHyAWi7F8+Wp069bDwFURNS4GDebZ2dmYPHkySktLMWPGDCiVSkRERCA2NhaRkZEwMzOr1euIiIioZioe/Bwx4kns3h2JGzeuM5gT1TKDBvONGzciJSUF+/btg6+vLwAgMDAQU6dOxZ49ezB27NhavY6IiIhqJi4uFvb29njttfmQy0vw5Zer4ebmjj59Qg1dGlGjYdDlEvfv34+goCB1uAaA4OBg+Pj4YP/+/bV+HREREdVMXNw1tG5dvn75vHlvoVOnLli8+G1ERV0xcGVEjYfBgnlubi7i4+Ph7++vdc7f3x9Xruj+H72m1xEREVHNFBcXIy0tVR3MTUxM8MEHy+Dm5o4FC15FUlKigSskahwMFsxTU1MBAK6urlrnnJ2dUVBQgPz8/Fq7joiIiGomLa387977d/y0tbXFsmWfAQDeeON/yMvLM0RpRI2KwXrMCwsLAQCWlpZa58zNzQEARUVFsLW1rZXriIiIqGZatvTG0aNntY67u3tg377fDVARUeNksGCuUqmqHCMWa0/o1/S6+5maSuDszOBORET0MDNnTjd0CURNisFaWaytrQEAcrlc61zFsYoxtXEdEREREZExM1gwd3d3BwCkp6drnUtLS4NUKoWVlVWtXUdEREREZMwMFsylUik8PT0RFRWldS46OhoBAQG1eh0RERERkTEz6DrmAwcOxIkTJ3Djxg31sePHj+PWrVsYOnRorV9HRERERGSsRIIgCIa6eVZWFoYPHw6JRIJp06ZBLpdj/fr1aNGiBb7//nuYmZkhPj4e58+fR+fOneHl5aX3dUREREREDYlBgzkA3Lx5E0uWLMHZs2dhYWGBPn36YN68eXBwcAAA7Nq1CwsXLsSSJUswatQova8jIiIiImpIDB7MDWXRokW4c+cONm/ebOhSSA9HjhzB2rVrERUVBbFYjMDAQLzyyivo2LGjoUsjPZw4cQKrV69GTEwMbGxsMHjwYLzyyitcQamBiYmJwejRo/H888/j5ZdfNnQ5pIfRo0fj8uXLWscHDRqE1atXG6Aiqo6srCysWLEChw4dQklJCfz9/fHaa6/x7z4jl5CQgH79+j10zKZNm9C9e3et4wZbx9yQIiMjERkZiaCgIEOXQno4ffo0Zs6cidatW2Pu3LkoKyvDtm3bMGHCBGzbtg0dOnQwdIn0ECdPnsS0adPg7++P119/HcnJydi0aROuXLmCrVu3VrnvABmHsrIyLFy4EAqFwtClkJ4EQcCNGzfQv39/DBw4UOOch4eHgaoifRUUFGD8+PFIS0vDlClTIJVKsXXrVkyePBmRkZGQyWSGLpEq4eDggGXLlmkdl8vleP/99+Ho6Ig2bdrovLZJBXOlUom1a9fiiy++MHQpVA0fffQR3NzcsGPHDvWOr+Hh4Rg6dChWrlyJb7/91sAV0sMsW7YMbm5u2LJlCywsLAAAbm5uWLx4MY4cOYI+ffoYuELSx9dff424uDhDl0HVkJCQgKKiIvTr1w9hYWGGLoeqad26dbh16xY2b96Mbt26AQCGDh2K/v37Y/369TqDHxkHKysrnf/PffjhhygrK8Onn34KOzs7ndc2makquVyOJ598Ep9//jnCwsLg6upq6JJID7m5uYiJicHgwYPVoRwAnJyc0K1bN1y4cMGA1VFV5HI5mjVrhrFjx6pDOQD1b6tiY2MNVRpVQ2xsLNauXYsXX3zR0KVQNVy/fh0A4Ovra+BKqLoEQcDu3bsREhKiDuUA4OzsjHnz5qFr164GrI5qIjY2Flu2bMGTTz750K9fk5kxl8vlKCgowMqVKzF06FCEhoYauiTSg42NDX799VeNUF4hOzsbEonEAFWRvszNzREREaF1/OrVqwD+2zCMjFdFC0twcDBGjhyJVatWGbok0lPFbzgqgnlRURE34GsgEhISkJqaihkzZgAoD+pFRUWwtrbG+PHjDVwd1cTKlSthYWGBV1555aHjmsyMuY2NDX7//Xeuc97ASCQSeHt7a/2GIyYmBufPn0enTp0MVBnVRGJiInbt2oUPP/wQMpkMAwYMMHRJVIV169bhzp07WLx4saFLoWqKi4uDtbU1lixZgk6dOqFTp07o378/9u/fb+jSqAp37twBADg6OmLp0qXo2rUrOnfujAEDBuDQoUMGro6qKyYmBn/99ReeeeYZuLi4PHRsk5kxF4vFfMiskSgsLMT8+fMBAM8995yBqyF95eTkqH9TZWlpiUWLFsHc3NzAVdHDxMXFYc2aNXjnnXfQvHlzJCQkGLokqobr16+jsLAQ+fn5WLZsGfLy8rBp0ya8+uqrUCgUCA8PN3SJVIm8vDwAwKpVq2BiYoK33noLYrEYERERmD17NiIiIhAcHGzgKklf27dvh0QiwYQJE6oc22SCOTUOxcXFmDVrFmJiYvD8889zZZ0GRCQSYeXKlSgtLcXmzZsxdepUrFixAoMHDzZ0aaSDUqnEwoUL0aVLF4wdO9bQ5VANjB07FiqVSqP1YdiwYRg+fDg++eQTjBgxgu2ARqq0tBRAeUD/7bff1A8KhoaGYsCAAVi+fDmDeQNRUlKCn376CaGhoXqthsQpZGow8vLyMG3aNJw6dQpPPfUU5s6da+iSqBrs7OwwdOhQhIeHY+vWrXB3d8fHH39s6LKoEhEREYiJicFrr72GrKwsZGVlqWfxiouLkZWVBZVKZeAq6WGeffZZrX5kCwsLhIWFISMjQ/1wKBmfimcBBg4cqLF6h1QqRWhoKKKiolBYWGio8qgaTp06haKiIr0noRjMqUHIzMzEpEmTcP78eTz99NP48MMPIRKJDF0W1ZCFhQVCQkKQnJyMrKwsQ5dDOhw5cgQKhQJjxoxBz5490bNnTzz55JMAykN7z549kZSUZOAqqSYqdsguKioycCVUmYrnqnTtZu7g4KB+GJSM399//w1TU1OEhIToNZ6tLGT0CgoKMH36dFy9ehVTpkzBwoULDV0S6enGjRuYOXMmpk+frjVzV1hYCJFIBDMzMwNVRw8zf/589Qx5hYyMDLzxxhsICwtDeHg4nJ2dDVQdVSU1NRXTpk3DkCFD8NJLL2mcu3XrFgDA09PTEKWRHlq3bg0zMzOdv9VISEiAubm5ztBOxuf8+fNo3749bGxs9BrPGXMyeosXL8bVq1cxadIkhvIGpmXLlsjPz8f333+v7pkEyldn+f3339GtWze9/7Ci+hUQEIDg4GCNfzp37gwA8PLyQnBwMB/eNWKurq7Iz89HZGQkCgoK1MeTk5Oxa9cudO/enT9YGTErKyuEhobi8OHDGht7xcfH49ChQ+jXrx+fD2gAFAoFrl+/jnbt2ul9DWfMyajduHEDe/fuha2tLdq2bYu9e/dqjeGOdsbLxMQEixYtwrx58zBx4kSMHDkS2dnZ2Lp1K0QiEd5++21Dl0jUaL3zzjuYPXs2nnnmGYwZMwaFhYXYunUrTExM8O677xq6PKrCG2+8gdOnT2PSpEmYNGkSTE1NsWnTJlhYWODVV181dHmkh+TkZCgUCri5uel9DYM5GbXTp08DAPLz8yudLWcwN25hYWEwNTXF+vXrsWTJElhZWaFHjx6YO3cufHx8DF0eUaPVv39/rFmzBl9//TU+/fRTWFhYICgoCK+++ip3A20APD09sWPHDnzyySeIiIiAIAjo2rUr5s2bBy8vL0OXR3rIyckBgGr9ZlgkCIJQR/UQEREREZGe2GNORERERGQEGMyJiIiIiIwAgzkRERERkRFgMCciIiIiMgIM5kRERERERoDBnIiIiIjICDCYExEREREZAQZzIqI6VlBQgA0bNmDUqFHo0qULOnbsiNGjR+OHH36ASqWq03tPnDgRoaGhWvVkZWVV+7UWLFgAPz8/vcb+8ssvmDhxIrp164YOHTpg4MCB+OCDD5CWlqY1VqVSISEhodr16OPUqVPw8/PDrl276uT1iYhqE4M5EVEdunnzJp566imsWLECfn5+ePXVVzFnzhyYm5vjnXfewbx581CX+7y98MILePPNN9UfX7lyBUOGDEFcXFyd3XPlypWYO3curKysMHv2bLz55pt4/PHH8eOPPyIsLAx3795Vjy0oKMDYsWOxe/fuOquHiKihMDF0AUREjZVcLseLL76InJwc/Pjjj2jTpo363LRp0/Dee+9h27Zt6NChAyZNmlQnNfTq1Uvj42vXrumcta4tycnJWLduHSZOnIhFixZpnBs+fDjGjx+PFStW4LPPPgNQvmX15cuX0adPnzqriYiooeCMORFRHdm2bRtu3bqFhQsXaoTyCvPnz4ednR2+//57A1RXNy5evAilUqn1AwEAdOrUCR06dMC///5b/4URETUADOZERHVk//79sLKywrBhw3Set7CwwI4dO7Bnzx71MUEQsH37dowePRqdOnVC+/btMXjwYHzzzTcaLS+hoaF46623EBkZiX79+qFjx4545plncPLkSY173N9j/vnnn2PhwoUAgEmTJmn0np84cQIzZsxA9+7d4e/vj8cffxzvvPMO8vLyqvWera2tAQC7d+9GaWmp1vlNmzbh8OHDAMr7v/v16wcA+OKLL+Dn56fuNS8uLsby5csRGhqKgIAAhIaG4tNPP0VxcbHG65WWluLzzz/HwIED0aFDBwwaNAjffPMNlEplpTXu378fbdu2xZw5cx46joiovrGVhYioDgiCgKtXr6Jz584wNTWtdJy3t7fGx5999hm++uorPPnkkxg7diwKCwuxZ88eLF++HM7OznjyySfVY48fP46ffvoJEydOhLOzM7Zv344ZM2Zgw4YNCAoK0rrXgAEDkJ6ejh9++AEvvPAC2rdvDwA4evQoZs6cic6dO2POnDkQiUQ4duwYfvjhBygUCixZskTv9929e3d4enrit99+w7lz5zBw4ED06tUL3bp1g52dHczMzNRjfX19sXDhQixZsgQDBgzAgAED4ODggNLSUkydOhX//vsvRo0ahYCAAFy6dAnr1q3DuXPnsGnTJvXndPbs2fjnn38wYsQITJ06FZcuXcLy5cuRmZmp/iHkfkeOHMH8+fPxxBNPYPny5ZBIJHq/NyKiOicQEVGty8zMFGQymTB37ly9ryktLRU6d+6sdU1+fr4QEBAgPP/88+pjffv2FWQymfDHH39o3LNr167C2LFj1ccmTJgg9O3bV/3xzp07BZlMJpw8eVJ9bPr06ULfvn0FuVyucd+xY8cKnTp1Un88f/58QSaTVfk+bt68KYSHhwsymUz9T9u2bYWJEycKR44c0RgbHx8vyGQyYfXq1epj27ZtE2QymfDtt99qjF23bp0gk8mErVu3CoIgCIcPHxZkMpmwdu1ajXGvvfaa4O/vL+Tk5AgnT54UZDKZsHPnTuH8+fNCYGCgMHnyZKGkpKTK90FEVN/YykJEVAfE4vI/XqvTKmFqaorjx49j8eLFGsezs7NhY2ODoqIijeOtWrVC//791R87ODggLCwMFy9eRGZmpt73/frrr7Fz506N2ezK7qkPHx8f7Nq1C5s2bcKkSZPg6+sLpVKJU6dOYfr06fjmm28eev2hQ4dgY2OD8ePHaxyfNGkSbGxscPDgQQDA4cOHIRaLMWHCBI1x8+fPx969e2FjY6M+FhcXh+effx4eHh5Yu3YtzM3Nq/2+iIjqGltZiIjqgJ2dHUxNTau9XripqSkOHz6MgwcP4tatW7hz5w5yc3MBQGtZxccee0zr+pYtW0IQBCQmJsLR0VGve0okEsTHx2PVqlW4fv067t69i9TU1GrV/SCRSITu3buje/fuAICkpCTs3LkTX3/9NVatWoWwsDC4urrqvDYhIQFeXl5aLUBmZmbw8vJCYmIiAKjf4/0BHACcnZ3h7OyscWzDhg0Qi8UoKSlBeno6WrRo8Ujvj4ioLnDGnIioDohEInTq1AlXrlxBWVlZpeNWrlyJV199Fenp6RAEAW+88QbmzJmDhIQEdOrUCfPmzcPvv/8ONzc3rWt19a5XzNBXp3f6+++/x5gxY3Dy5El4e3tjxowZ2LFjB0aMGKH3a1TYvHkz1q9fr3Xc3d0dL7/8MubMmYOysrKHrszy4A8g91OpVOr3rVQqIRKJ9KrLz88PmzdvhkqlwnvvvafXNURE9Y3BnIiojgwYMABFRUX45ZdfdJ4vKSnBjz/+iOPHj8Pe3h5nz57Fzz//jBdffBHbtm3Dm2++idGjR8PDwwM5OTla19+/UU+FO3fuQCKRwNPTU68a5XI5Pv74Y3Tv3h0///wzPvjgA0yaNAmBgYE12h30zz//xJo1ayptgZHJZADKV6SpjIeHB+Lj46FQKDSOl5aWIiEhQf1Diru7OzIyMlBYWKgxLioqCq+99hquX7+uPjZlyhR07doVU6ZMwdGjR/Hzzz9X+70REdU1BnMiojry9NNPw8PDA0uXLsW1a9c0zimVSvzf//0fMjIyMHPmTJiamqrD94MtKjt27EBxcbHWzPvly5c1Zp4zMjLw008/oUePHrCzs9NZU0Xvu0qlAlD+w0FxcTG8vb1hYvJfd+PVq1dx+vRpAHjojP+DRowYgaKiInz88cfqe1RQqVSIjIyEVCpFt27dAPw3s3//2NDQUBQUFGDr1q0a12/btg2FhYUICQkBAPTp00f9mvfbvn07Dhw4ACcnJ636XnzxRbi5uWHJkiXVXgqSiKiusceciKiOmJub44svvsC0adMwevRojBgxAu3bt0dOTg5+/fVXXL16FYMHD8bUqVMBlG/AY2NjgyVLliApKQlSqRSnTp3CL7/8AnNzc62ZYTMzM8ycOROTJ0+GhYUFtm3bBpVKhXnz5lVak4ODA4Dy8JqRkYERI0YgMDAQu3btgo2NDXx8fBAXF4fIyEh1iC8sLKw06D9o1KhROHLkCH744QdcuHABgwcPRvPmzZGZmYkDBw4gNjYWy5cvh5WVFQDA3t4eYrEYhw4dgru7OwYOHIgxY8Zg9+7d+Pjjj3Ht2jUEBATgypUr2LVrFwIDAzFmzBgA5QG+V69e+PjjjxEXF4f27dvjwoUL2LNnD2bPng17e3ut+qysrLBgwQL873//w6effqr1oC0RkSGJhIc18xER0SNLTU3Fxo0b8c8//yApKQmCIMDPzw9jx47FqFGjNPqkz507h08//RQxMTEwMzODj48PJk2ahEuXLmHTpk34559/4OTkhNDQUHh4eGDYsGH48ssvkZ+fj65du+K1117T2GV04sSJSExMxKFDhwAACoUCb7zxBv766y+Ym5vjyJEjyMrKwpIlS3Dq1CmUlpaqX9fX1xcvv/wyVq9ejUGDBmHBggXYvXs3YmNjH/p+BUHA3r17sXfvXsTExCA/Px92dnbo0qULZsyYgQ4dOmiM/+abbxAREYGSkhJ888036N69OwoKCrBmzRocOHAAGRkZaN68OYYNG4ZZs2ZptMGUlJTgyy+/xL59+5CRkYEWLVpg3LhxePbZZyEWi3Hq1ClMmjQJS5YswahRo9TXTZ8+HceOHcP27dvRqVOnR/r6EhHVFgZzIqIGqCKYb9682dClEBFRLWGPORERERGREWAwJyIiIiIyAgzmRERERERGgD3mRERERERGgDPmRERERERGgMGciIiIiMgIMJgTERERERkBBnMiIiIiIiPAYE5EREREZAQYzImIiIiIjMD/A6PVaLqhnrxUAAAAAElFTkSuQmCC\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots()\n", "data['control'].plot(ax=ax)\n", "ax.set(title='Optimal Consumption Policy',\n", " xlabel='Capital Stock',\n", " ylabel='Rate of Consumption',\n", " xlim=[kmin, kmax])\n", "ax.set_ylim(bottom=0)\n", "ax.hlines(qstar, 0, kstar, colors=['gray'], linestyles=['--'])\n", "ax.vlines(kstar, 0, qstar, colors=['gray'], linestyles=['--'])\n", "ax.annotate('$q^*$', (kmin, qstar))\n", "ax.annotate('$k^*$', (kstar, 0))\n", "ax.plot(kstar, qstar, '.', ms=20);" ], "metadata": { "collapsed": false, "pycharm": { "name": "#%%\n" } } }, { "cell_type": "markdown", "source": [ "### Value function" ], "metadata": { "collapsed": false } }, { "cell_type": "code", "execution_count": 8, "outputs": [ { "data": { "text/plain": "
", "image/png": 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\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots()\n", "data['value'].plot(ax=ax)\n", "ax.set(title='Value Function',\n", " xlabel='Capital Stock',\n", " ylabel='Lifetime Utility',\n", " xlim=[kmin, kmax])\n", "\n", "lb = ax.get_ylim()[0]\n", "ax.vlines(kstar, lb , vstar, colors=['gray'], linestyles=['--'])\n", "ax.annotate('$k^*$', (kstar, lb))\n", "ax.plot(kstar, vstar, '.', ms=20);" ], "metadata": { "collapsed": false, "pycharm": { "name": "#%%\n" } } }, { "cell_type": "markdown", "source": [ "### Shadow price" ], "metadata": { "collapsed": false } }, { "cell_type": "code", "execution_count": 9, "outputs": [ { "data": { "text/plain": "
", "image/png": 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\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "data['shadow'] = model.Value(data.index, 1)\n", "\n", "fig, ax = plt.subplots()\n", "data['shadow'].plot(ax=ax)\n", "ax.set(title='Shadow Price Function',\n", " xlabel='Capital Stock',\n", " ylabel='Shadow Price',\n", " xlim=[kmin, kmax])\n", "\n", "ax.set_ylim(bottom=0)\n", "ax.hlines(lstar, 0, kstar, colors=['gray'], linestyles=['--'])\n", "ax.vlines(kstar, 0 , lstar, colors=['gray'], linestyles=['--'])\n", "ax.annotate('$\\lambda^*$', (kmin, lstar))\n", "ax.annotate('$k^*$', (kstar, 0))\n", "ax.plot(kstar, lstar, '.', ms=20);" ], "metadata": { "collapsed": false, "pycharm": { "name": "#%%\n" } } }, { "cell_type": "markdown", "source": [ "### Residual" ], "metadata": { "collapsed": false } }, { "cell_type": "code", "execution_count": 10, "outputs": [ { "data": { "text/plain": "
", "image/png": 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\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots()\n", "data['resid'].plot(ax=ax)\n", "ax.set(title='HJB Equation Residual',\n", " xlabel='Capital Stock',\n", " ylabel='Residual',\n", " xlim=[kmin, kmax]);" ], "metadata": { "collapsed": false, "pycharm": { "name": "#%%\n" } } }, { "cell_type": "markdown", "source": [ "## Simulate the model" ], "metadata": { "collapsed": false } }, { "cell_type": "markdown", "source": [ "### Initial state and time horizon" ], "metadata": { "collapsed": false } }, { "cell_type": "code", "execution_count": 11, "outputs": [], "source": [ "k0 = kmin # initial capital stock\n", "T = 50 # time horizon" ], "metadata": { "collapsed": false, "pycharm": { "name": "#%%\n" } } }, { "cell_type": "markdown", "source": [ "### Simulation and plot" ], "metadata": { "collapsed": false } }, { "cell_type": "code", "execution_count": 12, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "PARAMETER xnames NO LONGER VALID. SET labels= AT OBJECT CREATION\n" ] }, { "data": { "text/plain": "
", "image/png": 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\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots()\n", "model.simulate([k0], T).plot(ax=ax)\n", "ax.set(title='Simulated Capital Stock and Rate of Consumption',\n", " xlabel='Time',\n", " ylabel='Quantity',\n", " xlim=[0, T])\n", "\n", "ax.axhline(kstar, ls='--', c='C0')\n", "ax.axhline(qstar, ls='--', c='C1')\n", "\n", "ax.annotate('$k^*$', (0, kstar), color='C0', va='top')\n", "ax.annotate('$q^*$', (0, qstar), color='C1', va='bottom')\n", "\n", "ax.annotate('\\nCapital Stock', (T, kstar), color='C0', ha='right', va='top')\n", "ax.annotate('\\nRate of consumption', (T, qstar), color='C1', ha='right', va='top')\n", "\n", "ax.legend([]);" ], "metadata": { "collapsed": false, "pycharm": { "name": "#%%\n" } } } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 2 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython2", "version": "2.7.6" } }, "nbformat": 4, "nbformat_minor": 0 }