{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "notes"
    }
   },
   "source": [
    "# Calculations and Excercises_for: Long-Run Economic Growth Theory: Understanding The Solow Model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Setting up the Python/Jupyter environment"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/javascript": [
       "\n",
       "IPython.OutputArea.prototype._should_scroll = function(lines) {\n",
       "    return false;}"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%%javascript\n",
    "\n",
    "IPython.OutputArea.prototype._should_scroll = function(lines) {\n",
    "    return false;}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true,
    "jupyter": {
     "outputs_hidden": true
    }
   },
   "outputs": [],
   "source": [
    "# keep output cells from shifting to autoscroll: little scrolling\n",
    "# subwindows within the notebook are an annoyance..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/delong/anaconda3/lib/python3.6/site-packages/statsmodels/compat/pandas.py:56: FutureWarning: The pandas.core.datetools module is deprecated and will be removed in a future version. Please use the pandas.tseries module instead.\n",
      "  from pandas.core import datetools\n"
     ]
    }
   ],
   "source": [
    "# set up the environment by reading in every library we might need: \n",
    "# os... graphics... data manipulation... time... math... statistics...\n",
    "\n",
    "import sys\n",
    "import os\n",
    "from urllib.request import urlretrieve\n",
    "\n",
    "import matplotlib as mpl\n",
    "import matplotlib.pyplot as plt\n",
    "from IPython.display import Image\n",
    "\n",
    "import pandas as pd\n",
    "from pandas import DataFrame, Series\n",
    "from datetime import datetime\n",
    "\n",
    "import scipy as sp\n",
    "import numpy as np\n",
    "import math\n",
    "import random\n",
    "\n",
    "import seaborn as sns\n",
    "import statsmodels\n",
    "import statsmodels.api as sm\n",
    "import statsmodels.formula.api as smf\n",
    "\n",
    "# report library versions..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true,
    "jupyter": {
     "outputs_hidden": true
    }
   },
   "outputs": [],
   "source": [
    "%matplotlib inline \n",
    "\n",
    "# put graphs into the notebook itself..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true,
    "jupyter": {
     "outputs_hidden": true
    }
   },
   "outputs": [],
   "source": [
    "# graphics setup: seaborn-whitegrid and figure size...\n",
    "\n",
    "plt.style.use('seaborn-whitegrid')\n",
    "\n",
    "figure_size = plt.rcParams[\"figure.figsize\"]\n",
    "figure_size[0] = 12\n",
    "figure_size[1] = 10\n",
    "plt.rcParams[\"figure.figsize\"] = figure_size"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 4.3 Solving the Solow Growth Model\n",
    "\n",
    "## 4.3.1 Getting an Exploratory Sense of How the Model Behaves\n",
    "\n",
    "The two simulation runs presented above both made the hugely unrealistic assumptions of no labor force growth and no growth in the efficiency of labor. How does the model behave if we relax those unrealistic assumptions, and incorporate labor force and efficiency of labor growth? We can see the same way we saw above: assume various parameter values and initial conditions, and see what happens. Back when Robert Solow originally developed his model, computer time was so expensive that the only way to gain understanding was to solve the algebra and then think. Now, however, (as long as our programs run without bugs) we can directly see. Figure 4.14 presents the behavior of the model for the same parameter values as above, only with labor force growth at 1% per year and labor efficiency growth at 2% per year.\n",
    "\n",
    "This time the economy does not stagnate: there is no tendency for the economy's level of output or of output per worker or of the capital stock to head for some asymptote where they then stick. And there should not be. This model was built to understand the ongoing and—so far—fairly constant proportional growth that modern industrial economies have experienced since the Industrial Revolution. If our model predicted some eventual cessation of growth and subsequent stagnation, either we would have been doing it wrong, or it would be huge news. Indeed, there is no reason for output per worker to stagnate: labor is becoming more efficient and productive, and the other productive resource in the economy is capital, which is something labor can and does create. And with both efficiency and with both labor efficiency and the labor force increasing, there is no reason for output growth to approach any end. And with output increasing and savings a constant share of output, we would expect the capital stock to grow too.\n",
    "\n",
    "----\n",
    "\n",
    "&nbsp;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Figure 4.3.1: Solow Model Simulation: 2% Annual Efficiency of Labor Growth, 1% Annual Labor Force Growth**\n",
    "\n",
    "<img style=\"display:block; margin-left:auto; margin-right:auto;\" src=\"http://delong.typepad.com/.a/6a00e551f08003883401bb09ed6fd7970d-pi\" alt=\"Full model run\" title=\"full_model_run.png\" border=\"0\" width=\"600\" />\n",
    "\n",
    "α = 1/2, δ = 3%, s = 15%\n",
    "\n",
    "----\n",
    "\n",
    "&nbsp;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true,
    "jupyter": {
     "outputs_hidden": true
    }
   },
   "outputs": [],
   "source": [
    "# we are going to want to see what happens for lots of\n",
    "# different model parameter values and initial conditions,\n",
    "# so stuff our small simulation program inside a function, so \n",
    "# we can then invoke it with a single line...\n",
    "\n",
    "def sgm_200yr_run(L0, E0, K0, n=0, g=0, s=0.15, alpha=0.5, delta=0.03, T=200):\n",
    "\n",
    "    sg_df = pd.DataFrame(index=range(T),columns=['Labor', \n",
    "        'Efficiency',\n",
    "        'Capital',\n",
    "        'Output',\n",
    "        'Output_per_Worker',\n",
    "        'Capital_Output_Ratio'],\n",
    "        dtype='float')\n",
    "\n",
    "    sg_df.Labor[0] = L0\n",
    "    sg_df.Efficiency[0] = E0\n",
    "    sg_df.Capital[0] = K0\n",
    "    sg_df.Output[0] = (sg_df.Capital[0]**alpha * (sg_df.Labor[0] * sg_df.Efficiency[0])**(1-alpha))\n",
    "    sg_df.Output_per_Worker[0] = sg_df.Output[0]/sg_df.Labor[0]\n",
    "    sg_df.Capital_Output_Ratio[0] = sg_df.Capital[0]/sg_df.Output[0]\n",
    "\n",
    "    for i in range(T):\n",
    "        sg_df.Labor[i+1] = sg_df.Labor[i] + sg_df.Labor[i] * n\n",
    "        sg_df.Efficiency[i+1] = sg_df.Efficiency[i] + sg_df.Efficiency[i] * g\n",
    "        sg_df.Capital[i+1] = sg_df.Capital[i] - sg_df.Capital[i] * delta + sg_df.Output[i] * s \n",
    "        sg_df.Output[i+1] = (sg_df.Capital[i+1]**alpha * (sg_df.Labor[i+1] * sg_df.Efficiency[i+1])**(1-alpha))\n",
    "        sg_df.Output_per_Worker[i+1] = sg_df.Output[i+1]/sg_df.Labor[i+1]\n",
    "        sg_df.Capital_Output_Ratio[i+1] = sg_df.Capital[i+1]/sg_df.Output[i+1]\n",
    "\n",
    "        \n",
    "    fig = plt.figure(figsize=(12, 12))\n",
    "\n",
    "    ax1 = plt.subplot(3,2,1)\n",
    "    sg_df.Labor.plot(ax = ax1, title = \"Labor Force\")\n",
    "    plt.ylabel(\"Parameters\")\n",
    "\n",
    "    ax2 = plt.subplot(3,2,2)\n",
    "    sg_df.Efficiency.plot(ax = ax2, title = \"Efficiency of Labor\")\n",
    "\n",
    "    ax3 = plt.subplot(3,2,3)\n",
    "    sg_df.Capital.plot(ax = ax3, title = \"Capital Stock\")\n",
    "    plt.ylabel(\"Values\")\n",
    "\n",
    "    ax4 = plt.subplot(3,2,4)\n",
    "    sg_df.Output.plot(ax = ax4, title = \"Output\")\n",
    "\n",
    "    ax5 = plt.subplot(3,2,5)\n",
    "    sg_df.Output_per_Worker.plot(ax = ax5, title = \"Output per Worker\")\n",
    "    plt.xlabel(\"Years\")\n",
    "    plt.ylabel(\"Ratios\")\n",
    "\n",
    "    ax6 = plt.subplot(3,2,6)\n",
    "    sg_df.Capital_Output_Ratio.plot(ax = ax6, title = \"Capital-Output Ratio\")\n",
    "    plt.xlabel(\"Years\")\n",
    "\n",
    "    plt.suptitle('Solow Growth Model: Simulation Run', size = 20)\n",
    "\n",
    "    plt.show()\n",
    "    \n",
    "    print(n, \"is the labor force growth rate\")\n",
    "    print(g, \"is the efficiency of labor growth rate\")\n",
    "    print(delta, \"is the depreciation rate\")\n",
    "    print(s, \"is the savings rate\")\n",
    "    print(alpha, \"is the decreasing-returns-to-scale parameter\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
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H+fPPPzl8+LDpw/DNH8jzIr/P2yw1a9bMtq6LiwuQv7ZmTSNpNBo5efIka9aswc7OjvHj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3TainUKMiGEeNBs2HWG1Ixchj0eSA1fN3vHuS+lNvDvvfdekcc3b95k8uTJ5RZICCEqgiOnrnPk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\ne1i7LYd/rznAvqNFAHRvH8+41A5c0S5exV0anEqnm6+3ZhMXHUK39vFmx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/lLvT5nF9o/\ntG/f3mt+x+qLN+2zQfvtmvK2fTZov305ubTP/nF1us82xPj444+NRx55xDAMw9iyZYtx7733mpZl\nxYoVxuOPP24YhmEUFhYa11xzjbF8+XLjH//4h2mZDMMwysvLjZtuuumcZb/97W+Nb7/91jAMw5gz\nZ47xySefmBHtHPPnzzeWLVtm2nP20ksvGSNHjjRuvfVWwzAu/Bzl5uYaI0eONCoqKozi4uLq2/WZ\n6/bbbzd27dplGIZhvPnmm8af/vQnwzAMY/z48UZ+fn6dZvm5bBf6t/OG5+ysoqIi48YbbzROnjxp\nGEb9PmcX2j94y+9YffKmfbZhaL99OczeZxuG9tuXm0v77B9Xl/tsDaGh6kIgAwcOBKBHjx7s2LHD\ntCzDhw/ngQceAMAwDKxWKzt27OCLL77g9ttvZ9asWdjt9nrPtWfPHsrKypgyZQqTJ09m69at7Ny5\nk759+wIwaNAg1q5dW++5vm/79u0cOHCAcePGmfacJSUlsXDhwur7F3qOtm3bRs+ePbHZbERGRpKU\nlMSePXvqNdczzzxD586dAXC73QQHB+PxeMjMzGTu3LmMHz+eFStW1GmmH8t2oX87b3jOzlq4cCF3\n3HEHCQkJ9f6cXWj/4C2/Y/XJm/bZoP32pfKGfTZov325ubTP/nF1uc9WgQfsdnv1W4wAVqsVl8tl\nSpbw8HAiIiKw2+1Mnz6dGTNm0L17dx5++GFef/11WrZsyQsvvFDvuUJCQrj77rv5xz/+wf/+7//y\n4IMPYhgGAQEB1blLSkrqPdf3/f3vf2fatGkApj1nw4YNIzDwu5FpF3qO7Hb7OW/XhYeH1/kfqx/m\nSkhIAGDz5s0sXbqUu+66i9LSUu644w4WLFjAyy+/zBtvvFEvpe+H2S70b+cNzxlAfn4+69at4+ab\nbwao9+fsQvsHb/kdq0/etM8G7bcvlTfss0H77cvNpX32j6vLfbYKPBAREYHD4ai+7/F4zvslqE85\nOTlMnjyZm266iVGjRpGamkq3bt0ASE1NZdeuXfWeqU2bNtx4440EBATQpk0bYmJiyM/Pr17vcDiI\nioqq91xnFRcXc/jwYfr37w/gFc8ZcM7Y0rPP0Q9/3xwOR72MM/+hDz74gHnz5vHSSy8RGxtLaGgo\nkydPJjQ0lIiICPr372/KUdsL/dt5y3P20UcfMXLkSKxWK4Apz9kP9w/e/DtWV7xtnw3ab9eUt+6z\nQfvtmtI++6fV1T5bBR7o1asXa9asAWDr1q106NDBtCx5eXlMmTKFhx56iFtuuQWAu+++m23btgGw\nbt06unbtWu+5/n979xIS1RvGcfxn/r2RCKULwwrpsklSAg0zMSGwRVOziWoEQdoEQgMy0YwjgniZ\nXEkFSfsiiIIIoqWBaVcSpKCVjIIQEbYwb6eYnhbhgGiLRGfmnP/3s3sHzuF9n3PmN88MZ8559OiR\nBgYGJElfvnzR/Py8jh8/rjdv3kiSRkZGVF1dnfJ5rXj37p2OHTuWHGdCzSTp0KFDa2pUWVmp9+/f\ny3Ecff/+XZOTkyk/5548eaJ79+7p7t272rNnjyRpampKgUBAiURCP3/+1Pj4eFrqtt6xy4Sarcyn\noaEhOU51zdbLh0w9x7ZSJmW2RG5vRKZmtpS576lMzW0y+++2MrO5C43+fGMcGxvTxYsXZWaKxWJp\nm8udO3c0NzenoaEhDQ0NSZIikYhisZhycnJUUlKi3t7elM/r3Llz6ujoUCAQUFZWlmKxmHbs2KGu\nri4NDg5q3759OnXqVMrntSIej2v37t3JcXd3t3p7e9NaM0kKh8NrapSdna2WlhY1NzfLzNTe3q68\nvLyUzSmRSKi/v1+7du3SlStXJEk1NTUKBoPy+/06f/68cnJy5Pf7dfDgwZTNa8V6x66wsDCtNVsR\nj8eTH5yStH///pTWbL186OzsVF9fX0adY1stkzJbIrc3IlMzWyK3/xWZ/XdbmdlZZmZbNnMAAAAA\nm4pLaAAAAAAXoYEHAAAAXIQGHgAAAHARGngAAADARWjgAQAAABehgQf+UU9Pj4LB4KrXRkdHdfLk\nSU897RIAvILchtfQwAP/KBQK6ePHjxoeHpb059HM3d3disViqx7vDgDIDOQ2vIb7wAMb8PLlS0Wj\nUT179ky3bt3Sr1+/FI1GNTExoevXr8txHO3cuVM9PT0qKyvTq1evdPPmTTmOo7m5OYXDYTU1Nenq\n1auan5/X9PS0IpGIxsbG9Pr1a23btk1NTU1qa2tL91IBwBPIbXiKAdiQzs5OCwaD5vP5bGlpyRzH\nMZ/PZ58/fzYzs+fPn9ulS5fMzKytrc3i8biZmb148cL8fr+ZmYVCIYtGo2ZmNj09bWfOnDEzs6Wl\nJQuFQuY4TopXBQDeRW7DK/5L9xcIwK0ikYgaGxt1+/Zt5efn69OnT5qZmdHly5clSWYmx3EkSYOD\ngxoeHtbTp081MTGhxcXF5H6qqqokSaWlpcrOzlZzc7MaGxvV3t6u3Nzc1C8MADyK3IZX0MADG1RY\nWKiioiKVlZVJkhKJhMrLy/X48ePkeHZ2VmamQCCguro61dTUqLa2Vh0dHcn95OXlSZJyc3P18OFD\nvX37ViMjI7pw4YLu37+vvXv3pn5xAOBB5Da8gj+xApvkwIED+vr1q8bHxyVJDx480LVr1/Tt2zfN\nzMwoGAzqxIkTGh0dVSKRWLP9hw8f1NraqqNHjyocDqu8vFzxeDzVywCA/w1yG27FL/DAJsnPz9eN\nGzfU39+vHz9+qKioSAMDAyouLtbZs2d1+vRpbd++XUeOHNHCwoKWl5dXbX/48GFVVFTI5/OpoKBA\nFRUVqq+vT9NqAMD7yG24FXehAQAAAFyES2gAAAAAF6GBBwAAAFyEBh4AAABwERp4AAAAwEVo4AEA\nAAAXoYEHAAAAXIQGHgAAAHARGngAAADARX4D1T/awFaUJA0AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11d7e2f28>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.01 is the labor force growth rate\n",
      "0.02 is the efficiency of labor growth rate\n",
      "0.03 is the depreciation rate\n",
      "0.15 is the savings rate\n",
      "0.5 is the decreasing-returns-to-scale parameter\n"
     ]
    }
   ],
   "source": [
    "# Now let's start with a low initial capital stock, and with\n",
    "# growth in workers and in efficiency...\n",
    "\n",
    "sgm_200yr_run(L0 = 1000, E0 = 1, K0 = 1000, g = 0.02, n = 0.01,\n",
    "    s = 0.15)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "----\n",
    "\n",
    "&nbsp;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Only one economic variable plotted in Figure 4.3.1 seems to be approaching any sort of limit or asymptote: the capital-output ratio. Is that a special feature of the particular initial conditions we chose? Let's choose a different set of initial conditions and see. \n",
    "\n",
    "Figure 4.3.2 plots a simulation run starting with a very high initial capital stock. In its first few periods the simulated economy is behaving substantially differently. The capital stock is not rising but falling, as depreciation overwhelms gross investment. Output per worker is falling as well, as increased efficiency of labor cannot keep up with the reduction in the buildings, machines, and inventories the average worker has at his or her disposal. The capital-output ratio is falling very rapidly at the start.\n",
    "\n",
    "But by the end of the simulation run, the economy is at the same place in Figure 4.3.2 that it was in Figure 4.2.1. Whatever influence the initial conditions had on the state of the economy has been erased. That the labor force and the efficiency of labor are at the same levels and have the same growth rates is no surprise: that is compelled by the basic setup. But the capital stock, the level of output, the level of output per worker, and the capital-output ratio—all were very different in the first, initial years. And the capital-output ratio is approaching the same steady-state asymptote in Figure 4.3.2 that it had approached in Figure 4.3.1. \n",
    "\n",
    "----\n",
    "\n",
    "&nbsp;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Figure 4.3.2: Solow Simulation Run with High Initial Capital Stock**\n",
    "\n",
    "<img style=\"display:block; margin-left:auto; margin-right:auto;\" src=\"http://delong.typepad.com/.a/6a00e551f08003883401b7c94a26e7970b-pi\" alt=\"High Initial Capital Stock\" title=\"High_Initial_Capital_Stock.png\" border=\"0\" width=\"600\" />"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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H+fPPPzl8+LDpw/DNH8jzIr/P2yw1a9bMtq6LiwuQv7ZmTSNpNBo5efIka9aswc7OjvHj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Wbj448/pkmTJs7IJoQQZcKKjXFYCuwMD2+CXle2LoQSQoiKZNu+C5w4n0HnljUJCfZ3dZy7dtsC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\nqx8wdhQcPlrKJ6v2s2xjFsu2FvPN9hIGdo9l+IB4eneMrmmzGvv75Snl8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QsXYrfbmTBh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\nQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1210affd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.01 is the labor force growth rate\n",
      "0.02 is the efficiency of labor growth rate\n",
      "0.03 is the depreciation rate\n",
      "0.15 is the savings rate\n",
      "0.5 is the decreasing-returns-to-scale parameter\n"
     ]
    }
   ],
   "source": [
    "sgm_200yr_run(L0 = 1000, E0 = 1, K0 = 200000, g = 0.02, n = 0.01,\n",
    "    s = 0.15)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "----\n",
    "\n",
    "&nbsp;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4.3.2 Analyzing the Solow Model\n",
    "\n",
    "### 4.3.2.1 Balanced Growth\n",
    "\n",
    "Earlier, when we had assumed that labor force and efficiency were both constant, and thus that n and g were both equal to 0, our equilibrium condition was K/Y = s/δ. Since the saving-investment rate s and the depreciation rate δ were both constant, our equilibrium condition required that the capital-output ratio K/Y be constant as well. There was where the economy was in equilibrium, in balance, with a stable level of not only the capital-output ratio but of the capital stock and output as well.\n",
    "\n",
    "Now we have added more realism back into our model by allowing the labor force and labor efficiency to both increase over time, at their constant rates n and g. This should, one would think, change how the economy behaves—and it would change the equilibrium condition that we look at to understand in which directions the economic variables of interest are changing.\n",
    "\n",
    "What effect does this added realism—allowing n and g to take on values other than 0—have on our equilibrium condition that the capital-output ratio be stable?\n",
    "\n",
    "In an important sense: None! Our equilibrium condition is, in a sense, the same: that the capital-output ratio be constant. But this time, when the capital-output ratio is constant the economy's equilibrium is not one of stable and stagnant balance but rather one of _balanced growth_. Output per worker is then growing at the same rate as the capital stock per worker. Output is growing and the same rate as the capital stock. The former two per worker variables are in balance, and they are both growing at the same rate as the efficiency of labor. The latter two economy-wide aggregate variables are in balance, and they are growing at the same rate as the sum of labor efficiency growth and labor force growth.\n",
    "\n",
    "----\n",
    "\n",
    "&nbsp;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Box 4.3.1: Some Easy Mathematical Tools**\n",
    "\n",
    "This is a good place to introduce four mathematical rules of thumb to make life easier. They are all only approximations. But they are good enough for our purposes. They are:\n",
    "\n",
    "1. The growth-of-a-product rule: The growth rate of a product is equal to the sum of the growth rates of its components. Since total output Y is equal to output per worker Y/L times the number of workers L, the growth rate of total output Y will be equal to the growth rate of Y/L plus the growth rate of L.\n",
    "\n",
    "2. The growth-of-a-quotient rule: The proportional change of a quotient is equal to the difference between the proportional changes of its components. Since output per worker Y/L is equal to the quotient of output Y and the number of workers L, its growth rate will be the difference between their growth rates.\n",
    "\n",
    "3. The growth-of-a-power rule: The proportional change of a quantity raised to a power is equal to the proportional change in the quantity times the power to which it is raised. For example, suppose that we have a situation in which output Y is equal to the capital stock K raised to the power a: Y = Ka. Then the growth rate of Y will be equal to a times the growth rate of K.\n",
    "\n",
    "4. The rule of 12: A quantity growing at k percent per year doubles in 72/k years. A quantity shrinking at k percent per year halves itself in 72/k years.\n",
    "\n",
    "You may hear people say that a background in calculus is needed to understand intermediate macroeconomics. That is not true. These four mathematical rules of thumb contain 95 percent of what calculus is used for in intermediate macro  economics. (Of course, you do need calculus if you want to do more than just take them on faith, and instead have a deep understanding of just why these rules of thumb work.)\n",
    "\n",
    "----\n",
    "\n",
    "&nbsp;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4.3.2.2 The Balanced Growth Capital-Output Ratio\n",
    "\n",
    "But at what value will the economy’s capital-output ratio be constant? Here is where allowing n and g to take on values other than 0 matters. The capital-output ratio will be constant—and therefore we’ll be in balanced-growth equilibrium — when K/Y = s/(n + g + δ). Add up the economy’s labor-force growth rate, efficiency-of-labor growth rate, and depreciation rate; divide the saving-investment rate by that sum; and that is your balanced-growth equilibrium capital-output ratio.\n",
    "\n",
    "Why is s/(n + g + δ) the capital-output ratio in equilibrium? Think of it this way: Suppose the economy is in balanced growth. How much is it investing? There must be investment equal to δK to replace depreciated capital. There must be investment equal to nK to provide the extra workers in the labor force, which is expanding at rate n, with the extra capital they will need. And, since the efficiency of labor is growing at rate g, there must be investment equal to gK in order for the capital stock to keep up with increasing efficiency of labor.\n",
    "\n",
    "Adding these three parts of investment requirements together and setting the sum equal to the gross investment sY actually going on gets us to:\n",
    "\n",
    "(4.3.1)&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;\n",
    "$ (n + g + δ)K = sY   $\n",
    "\n",
    "This is a condition for capital and output to be in balance—for savings at that capital-output ratio to be such so to equal the investment requirements for capital and output to grow at the same rate. Thus the economy’s investment requirements for balanced growth equal the actual flow of investment when the capital-ouput ratio is:\n",
    "\n",
    "(4.3.2)&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;\n",
    "$ \\left(\\frac{K}{Y}\\right)_* = \\frac{s}{n+g+δ}  $\n",
    "\n",
    "Where we add the star (\\*) to denote that this is an _equilibrium condition_: this is not the current capital-output ratio, but rather the equilibrium capital-output ratio: the one toward which the economy is heading and at which it will rest.\n",
    "\n",
    "This, equation (4.3.2) is thus the balanced-growth equilibrium condition. \n",
    "\n",
    "When it is attained, what the capital-output ratio K/Y will be is constant because s, n, g, and δ are all constant. So when there is balanced growth—when output per worker Y/L and capital per worker K/L are growing at the same rate—the capital-output ratio K/Y will be constant. If the capital-output ratio K/Y is lower than s/(n + g + &delta;), then depreciation (&delta;K) plus the amount (n + g)K that capital needs to grow to keep up with growing output will be less than investment (sY), so the capital-output ratio will grow. It will keep growing until K/Y reaches s/(n + g + &delta;). If the capital-output ratio K/Y is greater than s/(n + g + &delta;), then depreciation (&delta;K) plus the amount (n + g)K that capital needs to grow to keep up with growing output will be greater than investment (sY), so the capital-output ratio will shrink. It will keep shrinking until K/Y falls to s/(n + g + &delta;). \n",
    "\n",
    "----\n",
    "\n",
    "&nbsp;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4.3.2.3 Some Algebra\n",
    "\n",
    "To see more formally that K/Y = s/(n + g + δ) is the balanced-growth equilibrium condition requires a short march through algebra—simple algebra, we promise. Start with the production function in its per worker form:\n",
    "\n",
    "(4.3.3)&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;\n",
    "$ \\frac{Y}{L} = \\left(\\frac{K}{L}\\right)^α \\left(E\\right)^{1-α} $\n",
    "\n",
    "Break the capital-labor ratio down into the capital-output ratio times output per worker:\n",
    "\n",
    "(4.3.4)&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;\n",
    "$ \\frac{Y}{L} = \\left(\\frac{K}{Y}\\frac{Y}{L}\\right)^α \\left(E\\right)^{1-α} $\n",
    "\n",
    "Regroup:\n",
    "\n",
    "(4.3.5)&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;\n",
    "$ \\frac{Y}{L} = \\left(\\frac{Y}{L}\\right)^α\\left(\\frac{K}{Y}\\right)^α \\left(E\\right)^{1-α} $\n",
    "\n",
    "Collect terms:\n",
    "\n",
    "(4.3.6)&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;\n",
    "$ \\left(\\frac{Y}{L}\\right)^{1-α} = \\left(\\frac{K}{Y}\\right)^α \\left(E\\right)^{1-α} $\n",
    "\n",
    "And clean up:\n",
    "\n",
    "(4.3.7)&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;\n",
    "$ \\left(\\frac{Y}{L}\\right) = \\left(\\frac{K}{Y}\\right)^{\\frac{α}{1-α}} \\left(E\\right) $\n",
    "\n",
    "This tells us that _if the capital-output ratio K/L is constant, then the proportional growth rate of output per worker is the same as the proportional growth rate of E_. And the proportional growth rate of labor efficiency E is the constant g. \n",
    "\n",
    "Recall  that the labor force is growing at a constant proportional rate n. With output per worker growing at rate g and the number of workers growing at rate n, total output is growing at the constant rate n + g. Thus for the capital-output ratio K/Y to be constant, the capital stock also has to be growing at rate n + g. \n",
    "\n",
    "This means that the annual change in the capital stock must be: (n + g)K. Add in investment necessary to compensate for depreciation, and that is why we have:\n",
    "\n",
    "(4.3.2)&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;\n",
    "$ \\frac{K}{Y} = \\frac{s}{n+g+δ}  $\n",
    "\n",
    "as our balanced-growth equilibrium condition.\n",
    "\n",
    "----\n",
    "\n",
    "&nbsp;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4.3.2.4 From Algebra Back to Economics\n",
    "\n",
    "In economic terms, the balanced-growth equilibrium capital-output ratio is equal to the share of production that is saved and invested for the future—the economy’s saving-investment rate s—divided by the sum of three things:\n",
    "\n",
    "* The growth rate of the labor force n.\n",
    "* The growth rate of the efficiency of labor g.\n",
    "* The depreciation rate δ at which capital breaks down and wears out.\n",
    "\n",
    "We’ll sometimes call s/(n + g + δ) the “equilibrium” capital-output ratio, and we’ll sometimes call it the “balanced-growth” capital-output ratio. To be always saying “balanced-growth equilibrium” capital-output ratio is too much of a mouthful.\n",
    "\n",
    "How do we know K/Y = s/(n + g + δ) gives us balanced growth, where capital per worker K/L and output per worker Y/L grow at the same rate? Suppose the current capital-output ratio is lower than s/(n + g + δ). Then (n + g + δ)K would be less than the economy’s total investment which is equal to sY, the saving rate s times the level of output Y. Thus saving and investment will more than provide new workers with the capital they need to be fully productive, more than cover the increase in output due to the increase in labor efficiency, and more than com  pensate for the wearing out of capital through depreciation. The capital stock would grow faster than n + g. Since n + g is the rate at which output grows, the capital-output ratio would rise.\n",
    "\n",
    "Suppose instead the current capital-output ratio were above s/(n + g + δ). Then sY will be less then the economy’s total investment sY will be insufficient to keep the capital stock growing at rate n + g. And since n + g is the rate at which output grows, the capital-output ratio will fall.\n",
    "\n",
    "Thus a capital-output ratio greater than s/(n + g + δ) makes the capital-output ratio fall. And a capital-output ratio less than s/(n + g + δ) makes the capital- output ratio rise. So a capital-output ratio equal to s/(n + g + δ) is indeed the balanced-growth equilibrium condition.\n",
    "\n",
    "We have now solved our Solow growth model.\n",
    "\n",
    "It delivers one equilibrium condition: telling us that the stable capital-output ratio will be s/(n + g + δ), and that the economy will evolve over time to reduce the gap between the current capital-output ratio K/Y and its equilibrium balanced-growth value.\n",
    "\n",
    "It consists of five behavioral relationships:\n",
    "\n",
    "* A production function.\n",
    "* A rate of labor-force growth: n.\n",
    "* A rate of growth in the efficiency of labor: g.\n",
    "* A rate of depreciation of capital: δ.\n",
    "* The saving-investment rate: s.\n",
    "\n",
    "“Bob Solow got the Nobel Prize for that?!” you may ask. Ah, but what he got the Nobel Prize for was taking a complicated subject and making a useful model of it that was very simple indeed. The model is simple to write down. But it is powerful. And now we get to use it to generate  insights.\n",
    "\n",
    "----\n",
    "\n",
    "&nbsp;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4.3.3 Understanding the Solow Model\n",
    "\n",
    "### 4.3.3.1 Deriving the Balanced Growth Path for Output per Worker\n",
    "\n",
    "Along what path for output per worker will the balanced-growth equilibrium condition be satisfied? Y/L is, after all, our best simple proxy for the economy’s overall level of prosperity: for material standards of living and for the possession by the economy of the resources needed to diminish poverty. Let’s calculate the level of output per worker Y/L along the balanced-growth path.\n",
    "\n",
    "Begin with the capital-output ratio version of the production function that we just calculated above:\n",
    "\n",
    "(4.3.7)&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;\n",
    "$ \\left(\\frac{Y}{L}\\right) = \\left(\\frac{K}{Y}\\right)^{\\frac{α}{1-α}} \\left(E\\right) $\n",
    "\n",
    "Since the economy is on its balanced-growth path, it satisfies the equilibrium con  dition K/Y = s/(n + g + δ). Substitute that in:\n",
    "\n",
    "(4.3.8)&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;\n",
    "$ \\left(\\frac{Y}{L}\\right) = \\left(\\frac{s}{n+g+δ}\\right)^{\\frac{α}{1-α}} \\left(E\\right) $\n",
    "\n",
    "s, n, g, δ, and α are all constants, and so [s/(n + g + δ)]<sup>(α/(1-α))</sup>;is a constant as well. This tells us that along the balanced-growth path, output per worker is simply a constant multiple of the efficiency of labor, with the multiple equal to:\n",
    "\n",
    "(4.3.9)&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;\n",
    "$ \\left(\\frac{s}{n+g+δ}\\right)^{\\frac{α}{1-α}}  $\n",
    "\n",
    "Over time, the efficiency of labor grows. Each year it is g percent higher than the last year. Since along the balanced-growth path output per worker Y/L is just a constant multiple of the efficiency of labor, it too must be growing at the same proportional rate g.\n",
    "\n",
    "Now it is time to introduce time subscripts, for we want to pay attention to where the economy is now, where it was whence, and where it will be when. So rewrite (4.3.8) as:\n",
    "\n",
    "(4.3.8')&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;\n",
    "$ \\left(\\frac{Y_t}{L_t}\\right) = \\left(\\frac{s}{n+g+δ}\\right)^{\\frac{α}{1-α}} \\left(E_t\\right) $\n",
    "\n",
    "Paying attention to the equations for how labor efficiency and the labor force grow over time, $ E_t = E_0(1 + g)^t  $ and $ L_t = L_0(1 + n)^t  $, we can plug in and solve for what Y/L and Y will be at any time t—as long as the economy is on its balanced-growth path.\n",
    "\n",
    "----\n",
    "\n",
    "&nbsp;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Box 4.3.2: Along the Balanced-Growth Path, Output per Worker Is a Constant Multiple of the Efficiency of Labor**\n",
    "\n",
    "Along its balanced-growth path, the level of output per worker is a constant multiple of the efficiency of labor. What that multiple is depends on all the parameters of the growth model: the saving rate s, the labor-force growth rate n, the efficiency-of-labor growth rate g, the depreciation rate δ, and the diminishing-returns-to-investment parameter α. The equation is:\n",
    "\n",
    "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;\n",
    "$ \\frac{Y_t}{L_t} = \\left(\\frac{s}{n+g+\\delta}\\right)^\\left(\\frac{\\alpha}{1-\\alpha}\\right)E_t  $\n",
    "\n",
    "with:\n",
    "\n",
    "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;\n",
    "$ E_t = E_0{(1 + g)^t}  $\n",
    "\n",
    "----\n",
    "\n",
    "&nbsp;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Figure 4.3.3: Output per Worker and the Efficiency of Labor on the Balanced Growth Path**\n",
    "\n",
    "<img style=\"display:block; margin-left:auto; margin-right:auto;\" src=\"http://delong.typepad.com/.a/6a00e551f08003883401b7c94d7d3a970b-pi\" alt=\"Output per Worker a Constant Multiple\" title=\"Output_per_Worker_a_Constant_Multiple.png\" border=\"0\" width=\"600\" />\n",
    "\n",
    "\n",
    "\n",
    "----\n",
    "\n",
    "&nbsp;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4.3.3.2 Interpreting the Balanced Growth Path for Output per Worker\n",
    "\n",
    "We now see how capital intensity and technological and organizational progress drive economic growth. Capital intensity—the economy’s capital-output ratio—determines what is the multiple of the current efficiency of labor E that balanced-growth path output per worker Y/L is. Things that increase capital intensity—raise the capital-output ratio—make balanced-growth output per worker a higher multiple of the efficiency of labor. Thus they make the economy richer. Things that reduce capital intensity make balanced-growth output per worker a lower multiple of the efficiency of labor, and so make the economy poorer.\n",
    "\n",
    "Suppose that α is 1/2, so that α/(l—α) is 1, and that s is equal to three times n + g + δ, so that the balanced-growth capital-output ratio is 3. Then balanced-growth output per worker is simply equal to three times the efficiency of labor. If we consider another economy with twice the saving rate s, its balanced-growth capital-output ratio is 6, and its balanced-growth level of output per worker is twice as great a multiple of the level of the efficiency of labor.\n",
    "\n",
    "The higher is the parameter α—that is, the slower diminishing returns to investment set in—the stronger is the effect of changes in the economy’s balanced-growth capital intensity on the level of output per worker, and the more important are thrift and investment incentives and other factors that influence s relative to those that influence the efficiency of labor.\n",
    "\n",
    "* Suppose that the balanced-growth capital-output ratio is 4. Then if α is 1/3, α/(1—α) is 1/2, and the balanced-growth path level of output per worker is twice the level of the efficiency of labor, as you then multiply the efficiency of labor by the square root of the capital-output ratio. Most economists think that 1/3 is a reasonable parameter value for the United States today.\n",
    "\n",
    "* By contrast, if α is 1/2, α/(l—α) is equal to 1, and again with a balanced-growth capital-output ratio of 4, the level of output per worker is fully four times the level of the efficiency of labor, as you then multiply the efficiency of labor by the capital-output ratio.. Most economists think that 1/2 is a reasonable parameter value for the United States a century ago or for relatively poor countries today.\n",
    "\n",
    "* But some economists—for example, Paul Romer, currently of the World Bank—believe that the evidence points at still higher values of α. If α = 2/3, and again with a balanced-growth capital-output ratio of 4, the level of output per worker is fully sixteen times the level of the efficiency of labor, as you then multiply the efficiency of labor by the square of the capital-output ratio.\n",
    "\n",
    "Note—this is important-that changes in the economy’s capital intensity shift the balanced-growth path up or down to a different multiple of the efficiency of labor, but the growth rate of Y/L along the balanced-growth path is simply the rate of growth g of the efficiency of labor E. The material standard of living grows at the same rate as labor efficiency. \n",
    "\n",
    "To change the very long run growth rate of the economy you need to change how fast the efficiency of labor grows. Changes in the economy that merely alter the capital-output ratio will not do it. They can have a large effect on the level. \n",
    "\n",
    "This is what tells us that technology, organization, worker skills, education—all those things that increase the efficiency of labor and keep on increasing it—are likely to be ultimately more important to growth in output per worker than saving and investment. The U.S. economy experienced a large increase in its capital-output ratio in the late nineteenth century. It may be experiencing a similar increase now, as we invest more and more in computers. But the Gilded Age industrialization came to an end, and the information technology revolution will run its course. Aside from these episodes, it is growth in the efficiency of labor E that sustains and accounts for the lion’s share of long-run economic growth.\n",
    "\n",
    "----\n",
    "\n",
    "&nbsp;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Box 4.3.3: Calculating Balanced Growth Path Output per Worker: An Example**\n",
    "\n",
    "To see how to use the expression for output per worker when the economy is on its balanced-growth path, let’s work through an example. \n",
    "\n",
    "Suppose that the economy’s labor-force growth rate n is 1 percent per year, the efficiency-of-labor growth rate g is 2 percent per year, and the depreciation rate δ is 3 percent per year. Suppose further that the diminishing-returns-to-investment parameter α is 1/2, and the economy’s saving-investment rate s is 18 percent.\n",
    "\n",
    "Then the balanced-growth equilibrium capital-output ratio s/(n + g + δ) equals 3, and α/(l—α) equals 1. Substituting these values into equation (4.3.8) above:\n",
    "\n",
    "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;\n",
    "$ \\frac{Y_t}{L_t} = \\left(\\frac{0.18}{0.06}\\right)^\\left(\\frac{0.5}{1-0.5}\\right)E_t  $\n",
    "\n",
    "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;\n",
    "$ \\frac{Y_t}{L_t} = \\left(3\\right)^\\left(1\\right)E_t  $\n",
    "\n",
    "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;\n",
    "$ \\frac{Y_t}{L_t} = 3(E_t)  $\n",
    "\n",
    "For these parameter values, balanced-growth output per worker is simply three times the efficiency of labor, whatever the value of the efficiency of labor is. When the efficiency of labor is 10,000 per year, balanced-growth output per worker is 30,000 per year. When the efficiency of labor rises to 20,000 per year, balanced- growth output per worker rises to 60,000 per year.\n",
    "\n",
    "Over time, because balanced-growth output per worker is a constant multiple of the efficiency of labor, its growth rate is the same as g, the growth rate of the efficiency of labor: 2 percent per year.\n",
    "\n",
    "----\n",
    "\n",
    "&nbsp;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The implications of the balanced-growth capital-output ratio for the balanced-growth level of output per worker, and how that level changes over time, can be seen in an alternative, diagrammatic way. Take a look at Figure 4.3.4. As before, draw the production-function curve that shows output per worker Y/L as a function of capital per worker K/L for the current level of the efficiency of labor Et. In addition, as before, draw the line that shows where the capital-output ratio is equal to its balanced-growth equilibrium value, K/Y = s/(n + g + δ). This line starts at the bottom left origin point (0, 0) and climbs toward the upper right. Because K/L is on the horizontal axis and Y/L is on the vertical axis, the slope of the line is not K/Y but instead Y/K or (n + g δ)/s\n",
    "\n",
    "Look once again at where the curves cross. That point shows the current level of output per worker along the balanced-growth path. Output per worker is given by the production function for the current levels of capital per worker and the efficiency of labor. And the capital-output ratio is at its balanced-growth path level. Anything that increases the balanced-growth capital-output ratio will lower Y/K. Thus rotating the equilibrium line clockwise raising the balanced-growth path level of output per worker. Anything that decreases the balanced-growth capital output ratio rotates the equilibrium line counterclockwise. It thus lowers the level of output per worker for a given value of the efficiency of labor E.\n",
    "\n",
    "----\n",
    "\n",
    "&nbsp;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Figure 4.3.4: Balanced Growth Path Output per Worker: Graphically**\n",
    "\n",
    "<img style=\"display:block; margin-left:auto; margin-right:auto;\" src=\"http://delong.typepad.com/.a/6a00e551f08003883401b8d2d47336970c-pi\" alt=\"Equilibrium Is Where the Curves Cross\" title=\"Equilibrium_Is_Where_the_Curves_Cross.png\" border=\"0\" width=\"600\" />"
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O7+fMmTN4enrm+e/Qze8z57cBf12q8a/c3d3Nn0GZMmVYtGgRM2fOZNWqVfz666/8+uuv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\npJxUokVEREREykklWkRERESknP4/b4wXM4pwUA0AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x121bf2080>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "\n",
    "delta = 0.035\n",
    "n = 0.01\n",
    "g = 0.015\n",
    "s = 0.30\n",
    "alpha = 0.5\n",
    "E = 1\n",
    "\n",
    "output_per_worker = np.zeros((201, 3))\n",
    "\n",
    "for i in range(201):\n",
    "    lowestkoverl = 0\n",
    "    output_per_worker[i, 0] = lowestkoverl + i/4\n",
    "    output_per_worker[i, 1] = (output_per_worker[i, 0] ** alpha) * E**(1-alpha)\n",
    "    output_per_worker[i, 2] = (delta+n+g)/s * output_per_worker[i, 0]\n",
    "output_per_worker_df = DataFrame(data = output_per_worker, \n",
    "    columns = [\"Capital_per_Worker\", \"Output_per_Worker\", \n",
    "        \"Equilibrium Condition\"])\n",
    "\n",
    "output_per_worker_df.set_index('Capital_per_Worker').plot()\n",
    "plt.xlabel(\"Capital per Worker\")\n",
    "plt.ylabel(\"Output per Worker\")\n",
    "plt.ylim(0, )\n",
    "\n",
    "plt.title(\"Equilibrium Is Where the Curves Cross\", size = 20)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Over time the efficiency of labor increases. As the efficiency of labor increases, the production-function curve in Figure 4.3.5 will shift up and out to the right. Over time, therefore, the balanced-growth path equilibrium levels of output per worker and capital per worker levels will rise as the economy climbs up and to the right along the constant balanced-growth equilibrium line.\n",
    "\n",
    "----\n",
    "\n",
    "&nbsp;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Figure 4.3.6: Balanced Growth Path Output per Worker: Graphically: For E = 1/2, E =1, and E = 2**\n",
    "\n",
    "<img style=\"display:block; margin-left:auto; margin-right:auto;\" src=\"http://delong.typepad.com/.a/6a00e551f08003883401b7c94d7f7a970b-pi\" alt=\"Where the curves cross\" title=\"where_the_curves_cross.png\" border=\"0\" width=\"600\" height=\"505\" />"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x11da61f28>"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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zevVqFAoFCxYsYP78+SiVSrS0tFi0aFGF7bzzzjtMnTqVPXv2YGFhUeb1du3a\nsXr1ajp2/OeDz7hx45g5cyb79u0jJyeHefPmoa0t3VIIIYQQTzYNZVXnF9SC6OhoHB0dazuMagkK\nCiIlJYV33323tkN56tTlfiEeHekXojzSL0R5pF+I8qjbL2ROtBBCCCGEEGqS780fkWHDhtV2CEII\nIYQQ4hGRkWghhBBCCCHUJEm0EEIIIYQQapIkWgghhBBCCDVJEi2EEEIIIYSaHmkSferUKdV6ynFx\ncQwbNozhw4czd+7cMptu1CXx8fG8++67+Pj4MHToUAICAsrs+He//fv3k5SUpPa5qltPHb6+vsTE\nxACQl5eHo6MjX331lep1Hx8fzp8/X6W2SrYnfxh5eXlMnTqVoqIifHx8eO211/Dx8VH9O3HiRIV1\ni4qK+PDDDxkyZAg+Pj7ExcWVKbNhwwYGDBigau/q1aukpKQwb968h4pbCCGEEP8djyyJXrduHbNn\nz1YlVIsXL2by5Mls2bIFpVJJSEjIozr1I5WTk4Ofnx9jx45l8+bNfP/993Tu3Bl/f/8H1tu0aVOl\niXZN1lOHu7s7UVFRQPEaid27d+fQoUMA5ObmkpCQgK2t7SON4d82bNjA888/r9qhccmSJaW2Wbe3\nt6+w7oEDB8jLy2Pr1q34+/vz0UcflSlz5syZUm1aW1vTuHFjDAwMiIyMfGTXJYQQQoinxyNLolu2\nbMnnn3+u+vns2bM4OzsD0LNnT44cOfKoTv1IHTx4ECcnJzp37qw6NnDgQNLS0oiPj2fGjBmEhoYC\nEBoayowZMzh48CDnz59n+vTpxMbGMmjQIN5++20GDhzIp59+ClBpvby8PNX5goOD8fPzw9fXl5de\neol9+/YBEBkZybBhw3j99df54IMPyM/PJzg4mBEjRjBs2DCOHj1a7jW5ubmpkuhDhw7h7e1NZmYm\nmZmZnDhxAmdnZzQ0NAgLC8Pb25vXX3+dCRMmkJGRQUREBN7e3gwfPpwff/xR1WZQUBATJkwgLy9P\nrbiUSiU///wzPXr0eOB9iIqKKjU67ePjQ0hICNHR0aq6Xbp04cyZM2Xqnj17li+//JJhw4axdu1a\n1fEXXniBTZs2PfC8QgghhHh6FBUpOX8mkaUfqT+4+8jWie7bty83btxQ/axUKtHQ0ADAwMCAzMzM\nKrUTHR1d4Wt/pERwISv24QK9j61hK/o0dqnw9fDwcLS0tMrEpa+vz8GDB0lNTeXy5csYGBhw+fJl\nUlNTMTI41qgCAAAgAElEQVQywsLCgpEjR3Lx4kXi4uKYOHEi+vr6BAQE0KJFi0rrnT59WnWua9eu\nkZSUxIwZM8jMzGTOnDmYmJgwbdo05s6dS/369dm2bRufffYZWlpaKJVKpkyZApT/fhYVFXHu3Dmi\noqI4dOgQvXv3xtramm+//Zbr16/TvHlzoqKimD59OnPnzqVhw4bs3buXgIAA7O3tSU9PV4345ubm\nsnjxYuLi4vDz8yMmJoapU6dWOa7ExEQ0NDRU00syMzOZMGECurq6qngnTZqEsbExkydPLnMt165d\nw8zMTNVeYWEhkZGRaGlpqcrY29vj5eWFvr4+y5cvR1NTEwcHB4qKioiIiHhgnxNPNrl3ojzSL0R5\npF/8t93LKiD+6j2uX75HXk7JFGMTtdp4bJutlHw1D3D37l2MjY2rVO9B2y+eO3mN2LyEh47t35o0\naYJjl4rPmZCQQExMTJm4MjMz6d27N2fPnqVNmzY4OjqSlZXFX3/9haOjI0ZGRnTs2BFdXV06depE\nr169gOJRYD09PRo1avTAeq1bt1adKy4uDj09PZycnABYsWIFFhYWZGRk8M033wDF007Mzc2xtLSk\noKCg0m0su3Tpwt27d7G0tKRbt24olUoOHjzIzZs3mT59OkVFRTRs2BAvLy8A6tWrx/Lly2nXrh0d\nOnRQta+rq0t8fDw6Ojo4OTmRmpqqVlzHjx/H0tJSddzIyIhPPvmk1PVHR0ejVCpZsWJFqbqjRo3C\nysqKpk2bqupra2urvgGB4g9z7dq1w8jICICXXnqJ9PR0VXk9PT3s7e1L9VdRN8g2vqI80i9EeaRf\n/DcV5Bdy4czfnIi4TuylFAAKgVSUtO7YRO32HlsS3aFDByIiInBxcSE0NJRu3bo9dJs+XQbh02VQ\nDURXdZ6enqxZs4aYmBjs7OwA2L59Ow0aNKBFixYoFAqSk5MBOHfunKqehoYGSqUSgCtXrpCdnY1C\noSAmJoZBgwYRGRlZab1/O3v2LAApKSlkZWVhbm6Oubk5gYGBGBkZERISgr6+PomJiVVKCN3d3Vm7\ndi0DBgwAij+8BAYGAmBiYoJSqSQrK4tbt25hZmZGZGQkVlZWAGXaDwwMZNasWQQFBTFkyBC14mrU\nqBEZGRmVxtu1a1c2b95c5nhBQQF//PEH/fv35+TJk7Rr167U61lZWbzwwgvs2bMHfX19IiIiGDSo\nuA8plUq0tbUlgRZCCCGeIkk3MzgRcZ2Y6BvkZOcDoGuix/n0e9zV0mTca5151tlS7W8nHlsSPX36\ndObMmcPy5cuxtramb9++j+vUNcrAwIA1a9awaNEi0tPTKSwsxMbGhuXLlwPg7e3NzJkz2bVrlyrJ\nhOIpBNOmTWP+/Pno6OgwadIkUlJS6NevH7a2tpXW+/rrrzEx+edrhpSUFHx9fcnMzGTu3LloaWkx\na9Ys3nrrLZRKJQYGBixdupTExMQqXZebmxuzZ89m6dKlACgUCoyMjGjfvj1QnMwvWLCAd999Fw0N\nDerXr8/ixYu5dOlSue3Nnj0bb29vXF1d1YrL0tKS27dvU1BQgLZ2cfecPn069erVU5Xp2LFjhSMI\nXl5ehIWFMXToUJRKJYsWLQJg165d3Lt3jyFDhvDee+8xcuRIFAoFrq6uqm8FLl68SJcuXar0fgkh\nhBDiyZWbU8CZEwmciLjOzfh0AAyMdHF0t+LojTSOxaVh3kifJb7OWDevX61zaCjLG+Z8QjyNX7fc\nuHGD999/n23btlW7jeDgYK5evaqaT/y0Wbt2LdbW1qqpI/d7VP1i6dKleHh40LVr1xpvWzx6T+Pf\nC/HwpF+I8ki/eDoplUoSrqdzIvw6Z04mkJ9XiIYGtLE1w96lJUUGOnz8bTQpd3Jw7mDOe8MdMKyn\no6qvbr94bCPRovYFBARw5cqVMsfXrVuHnp5eLURUPl9fX2bNmoWnp+djm1qRnJxMVlaWJNBCCCFE\nHZN9L4+Y6BucCL/Orb+LF64waViPLs4t6eLcAiNjPXaHxbJ+8zGKipSM7N+eQX3aoqmp8VDnlST6\nMbOwsHioUWiAV199tVr1AgICHuq8j4uenh6ffPLJYz2nqampbLYihBBC1BFKpZK4K6mciLjOuZhE\nCguK0NTSoEPnpti7tMS6rSkamhpk5xaw7LtoQk8kYGKoy1QfR+zamNZIDJJECyGEEEKIOiErM5dT\nx+I5EXGd2yl3AWhkaoC9iyWdu1pgYPTPkrjxSZks3niM+KRM2ls1ZPrIrjSqX6+iptUmSbQQQggh\nhHhiFRUpufpXMsfD4/jrbBJFRUq0tTWxc7TA3qUlLa0bqvYiKfHnqQRWbj1Bdm4hL/W05o0XOqKt\nVbNTRCWJFkIIIYQQT5w7admcjLzOyWPx3EnLBqBJU2Psu7XkGYfm1NNXlKlTUFjEN7+c5efQq+gp\ntJjm05UeXZo/kvgkiRZCCCGEEE+EwsIiLp1L4njEda5cuIVSCQpdLRy6tcTexZJmLeqXGXUukXon\nmyWbojh/7TYtmhjyga8zLZoYPbJYJYmuhvj4eJYuXUp6ejr5+fnY2toyZcoUDA0NK6yzf/9+7Ozs\naNJEvR1xqltPHb6+vvj7+2NnZ0deXh6urq688847jB07FgAfHx9mzpypWjP6QTw8PNi7d2+pbbrV\nlZeXx6xZs1iyZAm+vr5kZ2eXWie6V69elS5Bc+rUKZYtW6bakCUoKAgrKytcXV2rHZcQQgghHo3b\nKXc5EXGdU8fiycrMBaB5SxPsXVrSyb45Ct0Hp6wxl5P5eHM06Vm59OjSnHcHd6FeJXUeliTRasrJ\nycHPz48FCxbQuXNnAHbu3Im/vz9r166tsN6mTZsICAhQOxmubj11uLu7ExUVhZ2dHdHR0XTv3p1D\nhw4xduxYcnNzSUhIwNbW9pGd/34bNmzg+eefVy1vt2TJkjLbfj/IunXr+Pnnn0sl3t7e3owePRpn\nZ2e0tLQeTeBCCCGEqLKC/EIunP6b4xHXuXa5eBtuvXo6OHdvhb1LS5o0M660DaVSyY4/LrN5zzk0\nNDR465VneKF7qwpHq2uSJNFqOnjwIE5OTqoEGmDgwIEEBQURHx/PF198Qf/+/enZsyehoaHs2bOH\nfv36cf78eaZPn87HH3/MlClTMDU1JSkpiZ49e/Lee+8xY8aMB9bbsmULCkXx3J/g4GAOHDjA3bt3\nSUtLY/z48fTt25fIyEg+/fRTtLS0aNGiBfPmzWPXrl3s2LGDoqIiJk6cWO5IrJubG4GBgYwePZpD\nhw7h7e3NsmXLyMzM5OzZszg7O6OhoUFYWBifffYZurq6mJiYsGjRIs6fP8+yZcvQ0dFh8ODBqjaD\ngoIICwtj+fLlnDx5sspxKZVKfv75Z3bu3PnA+xAVFcWKFStKHRs1ahSenp60bNmSzz//nGnTpqle\n09bWpkOHDhw8eBBPT0/1b7wQQgghakRyUibHw+OIibpB9r3ibbgtWzfCwaUltnZN0dGp2mBXVnY+\nnwUdJ+Ls3zSqr8d0Hyfat2r4KEMvpU4n0bHfbCT1yNEabbORmyut3vCt8PX4+HhatmxZ5riFhQU3\nb94st07v3r1p3749AQEB6OjokJCQwPr16zEyMmL48OGcPXu20nolCXSJ7OxsvvnmG27fvo23tzce\nHh7MmTOHLVu20KhRIz777DN27tyJtrY2xsbGrF69usJr6tChA1evXkWpVHLs2DHef/99XF1dOXLk\nCBcvXqRHjx4olUrmzJlDUFAQTZo0YePGjaxevZrevXuTm5vL9u3bAVi5ciWbN2/m/PnzrFixAk1N\nTbXiunbtGoaGhujo/LOD0P3bfo8ePZo+ffqopmrcr2/fvty4caPMcRsbGyIjIyWJFkIIIR6zgvxC\nzsckEh0ex/WrtwHQN1Tg2rs1Dt1a0si04imx5Ym9eYfFG46RmHoXuzaNmfp6V0yMqj+VtDrqdBJd\nG5o0aUJMTEyZ43FxcTRr1qzUsYp2VLe1tcXExAQAOzs7YmNjq1Tv35ycnNDU1KRx48YYGxtz69Yt\nbt26xeTJk4HiaSdubm5YWlrSqlWrB7alqamJra0toaGhmJqaolAo6NmzJwcPHuTChQuMHDmStLQ0\nDA0NVdNKnJycWL58Ob179y7T/tGjR9HS0kJLS4vU1FS14kpLS6Nx48aljpU3neNBI9EVMTU1JTw8\n/IHvhRBCCCFqTkpSJtHh14mJileNOlu3a4xDN0tsOpqjpa3+snMhx64T+MMp8gqK8PZsy4h+7dF6\nyN0Hq6NOJ9Gt3vB94Kjxo+Dp6cmaNWuIiYnBzs4OgO3bt9OgQQNatGiBQqEgOTkZgHPnzqnqaWho\nqJLjK1eukJ2djUKhICYmhkGDBhEZGVlpvX8rGb1OSUkhKysLc3NzzM3NCQwMxMjIiJCQEPT19UlM\nTKzS1tnu7u6sXbuWAQMGAODo6EhgYCAAJiYmKJVKsrKyuHXrFmZmZkRGRmJlZQVQpv3AwEBmzZpF\nUFAQQ4YMUSuuRo0akZGRUWm8Xbt2rXAkuiIZGRk0bPj4vuYRQggh/osKCgq5EPM30eFxxF1JBYpH\nnd36tMGhW0saNjaoVrt5+YV8+eNp9oXHYaCnzfSRTjh3NK/J0NVSp5Po2mBgYMCaNWtYtGgR6enp\nFBYWYmNjw/Lly4HiB9hmzpzJrl27VEkmgL29PdOmTWP+/Pno6OgwadIkUlJS6NevH7a2tpXW+/rr\nr1Wj11CcPPv6+pKZmcncuXPR0tJi1qxZvPXWWyiVSgwMDFi6dCmJiYlVui43Nzdmz57N0qVLAVAo\nFBgZGalW5NDQ0GDBggW8++67aGhoUL9+fRYvXsylS5fKbW/27Nl4e3vj6uqqVlyWlpbcvn2bgoIC\ntLWLu+f90zk6duxY6eoc5Tl16hTu7u5q1xNCCCFE5VKTszgeXrzCxr27eQBYtWmMo6sltp2qN+pc\nIun2PT7aGMnlG3ewblafD0Y5Yd6oesl4TdFQVmXuQC2Jjo6uVrL0JLtx4wbvv/8+27Ztq3YbwcHB\nXL16lSlTptRgZE+OtWvXYm1tjZeXV7mvV6dfFBQU8MYbb7BhwwZZneMp9TT+vRAPT/qFKI/0i5pT\nWFDEhTN/E300TrXChr6Bgs5OLao117k8UeeT+OS7aLKy8/Fybsm4V+3QreLDh+pQt1/ISPR/SEBA\nAFeuXClzfN26dejp6dVCROXz9fVl1qxZeHp6VmkqSlVs3bqVcePGSQIthBBC1IDbKXf/f9T5Onez\nikedLVs3Kh51fsYcbe2H//9tYZGSoN8usHX/X+hoa/Lu4C4852L50O3WFEmiHzMLC4uHGoUGePXV\nV6tVLyAg4KHO+7jo6enxySef1GibI0aMqNH2hBBCiP+awsIiLv7/qHPspeJR53r6OnTrZY1DN0sa\nmz38qHOJO1m5LPsumpN/JdOkoT4zfJ1oY2FSecXHSJJoIYQQQghRobTUexyPiONkZDx3/383wZbW\nDXHsZkl7u6Zo1/DUiotxt/loUxQp6dl0bd8E/+EOGOorKq/4mEkSLYQQQgghSiksLOLSuSSij8Zx\n5a9kUBbvJujSoxUO3SwxNTeq8XMqlUr2HLnGVz+dpqhIic/z7XnNoy2atbB8XVVIEi2EEEIIIQBI\nv32PExHXORF5nayM4lHnFlYNcHC1pEPnZlXeTVBdObkFfPHDKQ4ev4GxgYKprzvSpZ3ZIzlXTZEk\nWgghhBDiP6yoSMml88Wjzpcv3AIl6Opp49y9FQ7dWmLW1PiRnj8hOYtFGyK5/ncmNpYNmO7jhGmD\nepVXrGWSRFdDfHw8S5cuJT09nfz8fGxtbZkyZQqGhhVPqN+/fz92dnaqHf+qqrr11OHr64u/vz92\ndnbk5eXh6urKO++8w9ixYwHw8fFh5syZqjWjH8TDw4O9e/eiq1v9rTfz8vKYNWsWS5YswdfXl+zs\n7FLrRPfq1avCJWjy8/OZOXMmCQkJ5OXl8c477+Dp6UlQUBBWVla4urpWOy4hhBDiaZKVkcOJyOsc\nD7/OnbRsAJpbNsCxmyUduzRFR/Ho08SwmJus+P4E2bkFvNC9FaNf7ITOQ6wn/ThJEq2mnJwc/Pz8\nWLBgAZ07dwZg586d+Pv7s3bt2grrbdq0iYCAALWT4erWU4e7uztRUVHY2dkRHR1N9+7dOXToEGPH\njiU3N5eEhARsbW0f2fnvt2HDBp5//nnV8nblbftdkZ9//hkTExM+/vhj0tPTeeWVV/D09MTb25vR\no0fj7Owsy9wJIYT4z1IqlcRdTSUqLI4LpxMpKlKio9DC0dUSRzdLzJvVfyxxFBQWsXH3OX48dAVd\nhRZTRjjSy8HisZy7pkgSraaDBw/i5OSkSqABBg4cSFBQEPHx8XzxxRf079+fnj17Ehoayp49e+jX\nrx/nz59n+vTpfPzxx0yZMgVTU1OSkpLo2bMn7733HjNmzHhgvS1btqBQFD+ZGhwczIEDB7h79y5p\naWmMHz+evn37EhkZyaeffoqWlhYtWrRg3rx57Nq1ix07dlBUVMTEiRPLHYl1c3MjMDCQ0aNHc+jQ\nIby9vVm2bBmZmZmcPXsWZ2dnNDQ0CAsL47PPPkNXVxcTExMWLVrE+fPnWbZsGTo6OgwePFjVZlBQ\nEGFhYSxfvpyTJ09WOS6lUsnPP//Mzp07H3gfoqKiWLFiRaljo0aNol+/fvTt21fVVknCrK2tTYcO\nHTh48CCenp7VuPNCCCFE3ZWTnU9M1A2ij14jOSkLAFNzI7q6WWHn2BxdPZ3HFsvtjByWbo7i7NVU\nmpsa8sEoJyzNH+2UkUehTifR+3ed49ypmzXaZofOzfB6sUOFr8fHx9OyZcsyxy0sLLh5s/xYevfu\nTfv27QkICEBHR4eEhATWr1+PkZERw4cP5+zZs5XWK0mgS2RnZ/PNN99w+/ZtvL298fDwYM6cOWzZ\nsoVGjRrx2WefsXPnTrS1tTE2Nmb16tUVX3OHDly9ehWlUsmxY8d4//33cXV15ciRI1y8eJEePXqg\nVCqZM2cOQUFBNGnShI0bN7J69Wp69+5Nbm4u27dvB2DlypVs3ryZ8+fPs2LFCjQ1NdWK69q1axga\nGqKj888v8/3bfo8ePZo+ffqwefPmCq8pKyuLiRMnMnnyZNUxGxsbIiMjJYkWQgjxn5F4I52oI3Gc\nOZFAfl4hmloadLJvjqObJS1bNURD4/GufHH6SgpLN0eRnpmLe+dmTBzcBf3HmMDXpDqdRNeGJk2a\nEBMTU+Z4XFwczZo1K3Wsoh3VbW1tMTEpXjDczs6O2NjYKtX7NycnJzQ1NWncuDHGxsbcunWLW7du\nqZLGnJwc3NzcsLS0pFWrVg9sS1NTE1tbW0JDQzE1NUWhUNCzZ08OHjzIhQsXGDlyJGlpaRgaGqqm\nlTg5ObF8+XJ69+5dpv2jR4+ipaWFlpYWqampasWVlpZG48aNSx0rbzpHRSPRnp6eJCYmMn78eIYP\nH86LL76oet3U1JTw8PDK3lohhBCiTsvPL+TcyZtEHblGwvV0AEwa1sOhmyX2zi0xMKr+c0vVpVQq\n2XnwMhv3nEcDGPtyJ17qYf3Yk/iaVKeTaK8XOzxw1PhR8PT0ZM2aNcTExGBnZwfA9u3badCgAS1a\ntEChUJCcnAzAuXPnVPU0NDRUyfGVK1fIzs5GoVAQExPDoEGDiIyMrLTev5WMXqekpJCVlYW5uTnm\n5uYEBgZiZGRESEgI+vr6JCYmVmnrbHd3d9auXcuAAQMAcHR0JDAwEAATExOUSiVZWVncunULMzMz\nIiMjsbKyAijTfmBgILNmzSIoKIghQ4aoFVejRo3IyMioNN6uXbuWOxKdkpLC6NGj+fDDD8tMXcnI\nyKBhw4aVti2EEELURanJWUQfjePUsXiy7+WDBrRtb4ajmxVtbM1qbb3lu9n5rNh6gqOnE2lorMs0\nHyc6WjeqlVhqUp1OomuDgYEBa9asYdGiRaSnp1NYWIiNjQ3Lly8HwNvbm5kzZ7Jr1y5Vkglgb2/P\ntGnTmD9/Pjo6OkyaNImUlBT69euHra1tpfW+/vpr1eg1FCeLvr6+ZGZmMnfuXLS0tJg1axZvvfUW\nSqUSAwMDli5dSmJiYpWuy83NjdmzZ7N06VIAFAoFRkZGqhU5NDQ0WLBgAe+++y4aGhrUr1+fxYsX\nc+nSpXLbmz17Nt7e3ri6uqoVl6WlJbdv36agoABt7eLuef90jo4dO1a4OseaNWvIyMggMDBQ9SFg\n3bp16OnpcerUKdzd3av0fgghhBB1QVFhEX+dSyLqyDWu/lW8Fbe+oQJ3zzY4drPEpKF+rcYXe/MO\nizceIzHlLs+0bsxUH0caGOnVakw1RUNZlbkDtSQ6OrrCZKmuunHjBu+//z7btm2rdhvBwcFcvXqV\nKVOm1GBkT461a9dibW2Nl5dXua9Xp18UFBTwxhtvsGHDBlmd4yn1NP69EA9P+oUoz9PQLzLv5HA8\nPI7jEdfJvJMDFG/F3dXVCls7c7S1a///db9HxfPFD6fIyy9kUJ82+DzfHi2tJ3f5OnX7hYxE/4cE\nBARw5cqVMsdLRmqfFL6+vsyaNQtPT88qTUWpiq1btzJu3DhJoIUQQtRZSqWS2EspRB+N48KZv1EW\nKVHoauPkboWjq+Uj3xSlqvILCln34xn2Hr2Gvp42U0Y44/pM09oOq8ZJEv2YWVhYPNQoNMCrr75a\nrXoBAQEPdd7HRU9Pj08++aRG2xwxYkSNtieEEEI8Ltn38jh1LJ7oo3GkJt8FoEkzY7q6WfKMgwUK\n3Scnnbt1+x4fbTrGpfh0rJoa88EoJ5o1rngzurrsyXnXhRBCCCGEys34dKLCrnHmZAIF+UVoaWti\n52iBo5slFpYNnriVLY5fuMWy76LIvJePR9cWvDPIDr3HsOthbXl6r0wIIYQQoo4pKCjk/KlEIsOu\nkRCXBkCDRvo4ulrSxakF+oaPf3m6yhQVKdm6/yJB+y+ipanJBO/OPOdi+cQl+TVNkmghhBBCiFp2\nJy2b6PA4jofHcS8rT7U8nVP3VrRuZ4pGLS1PV5mMu3l8siWa4xduYdagHjN8nWjbokFth/VYSBIt\nhBBCCFELlEol166kcuzPWC6eTUJZpESvng6uvVvT1c2SBo0MajvEB/rrehofbTpGclo2jrZm+I9w\nxEhfUXnFp4Qk0UIIIYQQj1FuTgEx0TeICoslOSkLAPNmxjh1b0Un+2boPOHziJVKJb+Gx/HlztMU\nFhUxop8tgz3b1dpmLrXlyb5LQgghhBBPiZSkTKKOxHHyWDx5uQVoamnQyb45Tu5WWFg9eQ8Klicn\nr4DVO2L4PSoeI30FU153xMHGrLbDqhWSRAshhBBCPCJFRUounUsi8s9YYi8V7yhoZKyHW5/WOLi0\nxND4ydmnoTI3k7NYvPEY1xIzaNfShOkjnTBrULs7ItYmSaKFEEIIIWrYvaxcjkdcJ/poHHfSsgGw\nbN0IJ3crbDqZP9E795Xn6OlEPvv+OPdyCujvZsXYlzuh8wTsilibJIkWQgghhKghCdfTiQqL5czJ\nmxQWFKGj0MLR1RInd6snZkdBdRQWFrF573l2/HEZXYUW/sMd6O3YorbDeiJIEi2EEEII8RAK8gs5\nd+omkWHXuHk9HYCGjQ1w6m5F564t0KunU8sRVk9aRg5Lv43izJVUmpsa8IGvM5Z18IPAoyJJtBBC\nCCFENdxJu0fU0ThOhF/n3t3itZ3bdWiCU3crrNs+uWs7V8XZq6ks3XyM2xm5uNk1ZdIQe/T16uaH\ngUdFkmghhBBCiCpSKpVcu5zKsbBYLp75G6US6unr4NanNY6uVjRoVLcftFMqlfwUepVvfjkLwJiX\nOvJyz9Z1YuWQx02SaCGEEEKISuTnFRATnUDkn7Ek/50JQFOL+ji5t6KjfTN0dOr+Q3b3cvJZufUk\nYTE3aWCky/SRTnS0blTbYT2xJIkWQgghhKhA+u17HAu7xomI6+Rk56OpWby2s3OPVjRvafLUjNDG\nJWaweGMkCcl36WjdiOk+XWlQh5bfqw2SRAshhBBC/ItSqSTuaiqRh/+ZsmFgqKCnVzscXS0xqv90\nJZcHo+NZ9cMpcvMKebV3G0b2b1/nluCrDZJECyGEEEIA+fmFnDmeQOThWJISM4DiKRsuPVrRoUsz\ntJ+ydZHzCwpZ//NZdofFUk9Xmw98nXCza1bbYdUZkkQLIYQQ4j/tTlo2UUeucTw8jux7+WhoatCx\nSzOcu7eqM9txqys5LZslm45x8XoaluZGfDDKmeamhrUdVp0iSbQQQggh/nOUSiXxsbeJOBzLhTN/\noyxSom+goPuzbenqaomxSb3aDvGROXHxFh9/G03mvTx6O1owflBn9HQlJVSXvGNCCCGE+M8oyC8k\n/uo9og+F8ndC8ZSNJs2McenRik72zdF+ClbZqEhRkZLtIX/x3b4LaGlq4jfIjn6uVk/lSPvjIEm0\nEEIIIZ56GXeyiToSx/Gjcdy7m4eGBrS3a4pzj1a0bNXwqU8kM+/lsXzLcaLOJ2HaoB4zRjrRrmWD\n2g6rTpMkWgghhBBPJaVSyY24NCIPx3I+JpGiIiX19HVo3cGQF151oX6Dur0xSlVdjk9n8aZj3Lp9\nDwcbM/xHOGJsoKjtsOo8SaKFEEII8VQpKCjk3MmbRP4Zy834OwCYNTXCuXsrnnFoTszpU/+JBFqp\nVPJbRBxrd56moLCI4c/ZMNjLBq06vB35k0SSaCGEEEI8Fe5m5RJ9NI6osGtkZeaioQG2z5jj3L0V\nlq0bPfVTNv4tJ6+ANcExhByLx0hfB/8RzjjaNqntsJ4qkkQLIYQQok67lZhBRGgsMcdvUFhQhK6e\nNt16WePcvRUmDZ/+Eef73UzJ4qONx4i9mUGbFiZ8MNIJs//g+/CoSRIthBBCiDpHWaTk8sVbhB+6\nSuylFAAaNNLHpYc1nZ1aoKv330xxws8k8lnQce7mFPC8qxVvvtIJnadsk5gnxX+zhwkhhBCiTsrL\nLXY28jMAACAASURBVCAm+gYRoVdJTb4LgGXrRnTraU3bDk3Q/I/O9y0sLOLbXy/ww++XUOho8d4w\nezy6tqztsJ5qkkQLIYQQ4omXkZ5N5J/FuwrmZOejpaVJ564WuPS0xrx5/doOr1alZeaw7NtoYi6n\n0LSxAR/4OtGq2X/7PXkcJIkWQgghxBMr4Xoa4Yeuci4msXhXQUMFPb3a0dXNEkNjvdoOr9adi01l\nyaYobmfk0K2TOZOHOmBQT6e2w/pPkCRaCCGEEE+UosIiLpz5m/DQq9y4lgaAmbkRLj2tecbh6d5V\nsKqUSiW7Dl/l611nUfJ/7N1neJTnnfb/74x670IghBBCSKJJQo0mejG494bBefbY3X92s9lkYzuQ\n5MmxR5JjcUs22WyeOFuyAdtxi724xJjem7pEkRAqIIQA9T6SRjP3/4UwiZPYFEu6Vc7PuzBCczqM\nRudc93X/LvjKXdO5f8nUMTWBxGwq0SIiIjIsdNvs5B+vJudIFa3NNgDiEsPJXDSFmLhQFcRrurrt\n/PztQg4X1RLo58FzT6UxKzbU7Fhjjkq0iIiImKqpoZPsQ1UUZFdj73Xg5u5C2vzJZGTFEBrua3a8\nYaX6Shubt+RQU9fB9Jhgvr0+nWBtazGFSrSIiIgMOcMwOF/RyImDlZSduQoG+Ad4smjlNObMnYSX\nt46l/lMHC2r4+duFdPc6uG9xLBvunI6ri9XsWGOWSrSIiIgMGYfDyenCWo7vr+BKbRsAEyYFMnfR\nFBJnj8dFpfDP2Puc/PrDU3x0uAovD1c2rk9nQdIEs2ONeSrRIiIiMui6bXbyjl0g+3AV7a3dWCww\nPWk8mYumEDU52Ox4w1ZDi43nt+Zw9kIzkyL82LQhnYnhfmbHElSiRUREZBC1NHVx4mAlBdnV9Pb0\n73fOzIohI2sKQSE6ivqLFJXV8+JrubR19rI4ZSJfezgJTw9Vt+FC/xIiIiIy4C5VN3NsfyUlxbUY\nBvgFeJK1Yhqp86Lx1BzjL+R0Gvxu7zle/6QEq9XC//fAbNbOn6zpJMOMSrSIiIgMCMNpUHbmKscO\nVFBd2QTAuAn+zFs8hRnJkbi4ar/zjXR09fKTN/LJOXOV0ABPNm5IJz5a212GI5VoERER+VLsvX0U\n5dZw/EAlTQ2dAMQmhDFvcazmO9+CipoWNm/J4WpTF8nTwnjmyVQCfD3MjiWfQyVaREREbktHew85\nR6rIPXIeW5cdFxcryRlRzF0cS3iEbn67FbtOXOCX7xVj73Py2Mp4HlsVj4tVHz6GM5VoERERuSX1\nV9o5fqCS4vwaHH1OvLzdyFoRR/qCyfjq4I9b0mN38Kv3itmVXY2vlxvfeTqDtMRxZseSm6ASLSIi\nIjdkGAbnyxs5dqCC8pI6AIJDfchcNIWktIm4a2rELbvS2MnmLTlUXmpl6sQANm7IYFywJpaMFHrF\ni4iIyOf6S4ejRE0OYt6SWKbNiMCqLQe3Jfv0FX7yRj6dNjur50bzN/fNwt3NxexYcgtUokVEROTP\ndNvs5B+/QPahKtr+6HCUuYtjmRgdZHa8EcvhNHj9kxLe2XMOd1cr//hoCisyJpkdS26DSrSIiIhc\n197azfGDleQdu0BvTx9u7i5kZMWQqcNRvrSW9h5efj2XonMNjA/xYeOGdKZEBpgdS26TSrSIiIhQ\nf7WdY/srKM6rwekw8PHzYOHyqaTOi8bL293seCNe6fkmnt+aQ2NrN5kzIvjG43Pw1aEzI5pKtIiI\nyBhWXdXE0X3llJ2+CkBImA/zlsQyO3Uirtqj+6UZhsFHh6v47w9OYRgGG+6czgNLpmov+SigEi0i\nIjLGfHqy4JF95dScbwYgclIgC5ZN1c2CA8jW08e/v13IwcJLBPp68OxTqcyeGmZ2LBkgKtEiIiJj\nRF+fg5N5lzi2v4KGug4A4qaPY/7SWCbFBOtkwQF08Wo7m7dkc/FqB4mTg/n2+jRCArzMjiUDSCVa\nRERklOu22ck7doEThyrpaOvB6mIhKT2KeUt0suBgOFR4iZ+/XYCtx8E9i6bwlbtm4OpiNTuWDDCV\naBERkVGqrdXGiYNV1ydtuHu4Mm9JLJlZMfgHalV0oPU5nPzPR6f54GAlXh4uPPdUGlnJkWbHkkGi\nEi0iIjLK1F9t59i+Corz+ydt+Pp5kLUijtR50XhqIsSgaGy18cLWXErONxE1zpdNGzKIGqdV/tFM\nJVpERGSU0KQNcxSdq+fl1/Jo6ehhUXIkX3skGS8dgz7q6V9YRERkBPuLkzaig1iwNJb4GRFYNGlj\n0DidBu/uO8dr20uwWCz8zX2zuGthjG7QHCNUokVEREYgR5+T4rwaju4rp7G+E4Bp1yZtRGnSxqDr\nsNn56Rv5nDh9hZAATzauTydhcrDZsWQIqUSLiIiMIL09feQfv8CxA5W0t3ZjdbGQfG3SRpgmbQyJ\nykutPL8lh8uNncyeGsqz69II9PMwO5YMMZVoERGREcDW1Uv2oSqyD1dh67Lj5u5C5qIpzFs8RZM2\nhtDu7Gp++W4RvX1OHl4ex5N3JOKiLTNjkkq0iIjIMNbWauP4gUryjl3A3uvAy9uNxaumkb4wBm8f\nd7PjjRm9dgf/se0kO45fwMfTlW+vTydjRoTZscREKtEiIiLDUGN9B0f3VVCUexGnw8AvwJOld8Qz\nZ2407pr8MKSuNHby/NYcKmpamRIZwKYN6USE+JgdS0ymn0IREZFh5HJNK0f2nuNM8WUwIDjUhwXL\npjIrNRJXV42pG2q5JVf58et5dNjsrMyYxN8+MBsPjQsUVKJFRERMZxgGFyobObKnnIqz9QBERPqz\ncHkcCbPGY9We2yHncBq8sbOUt3aV4eZq5R8eSWZVZrTZsWQYUYkWERExieE0KCu5ypE95dRc6J/x\nHB0bwoJlU4mND9OYOpO0dvTw8ut5FJbVMy7Ym00b0omdGGh2LBlmVKJFRESGmNPh5FRhLUf3llN3\npR3on/G8YPlUojRr2FRnLzTx/NZcGlpspE8fxz89Pgdfb93AKX9OJVpERGSI2O0OCrMvcmx/OS1N\nNixWC7NSI1mwdCrh4/3NjjemGYbBx0fP81/vn8TpNHhqTSIPLYvTVhr5XCrRIiIig6ynu4+8Y+c5\ndqCSzvYeXFytpM2fzLwlsQSFeJsdb8zr7unjF78rYn9+Df4+7jy7LpXkaeFmx5JhTiVaRERkkHTb\n7GQfruLEwUpsXXbcPVyZv3QqcxdPwVcn3A0LNXXtbN6SQ/WVduKjg9i4Pp1QHV4jN2FIS7Tdbmfj\nxo1cunQJq9XKD3/4Q2JjY4cygoiIyKDr7Ojh+MFKco+cp6e7D08vNxavjidj4WS8tL922DhSXMvP\n3izA1tPHXQtj+D93z8TN1Wp2LBkhhrREHzhwgL6+Pt58802OHDnCT3/6U37+858PZQQREZFB097a\nzdH9FeQf7z9d0MfXnYV3JpI2fzIenrr4O1w4nAb//cEpth2owNPdhWfXpbIoZaLZsWSEGdKf6JiY\nGBwOB06nk46ODlxd9YYiIiIjX0tTF0f3lVNw4iIOhxP/AE+Wr00kZe4k3HQwx7DS1NbNlj31VNf3\nMjHcl00b0pkUoZs65dYNaYv19vbm0qVLrFmzhubmZl555ZWhfHoREZEB1VjfweE95ZzMq8HpNAgK\n8WbBsqkkpUXhom0Bw87JigZefDWXlvZeFiZN4B8eScbb083sWDJCWQzDMIbqyTZv3oy7uzvf+ta3\nuHz5Mhs2bODDDz/Ew+Mv31yRl5c3VNFERERuWluLnYrTHdRW28AAX39XYmf4MiHaSyPRhiHDMDha\n0sHuolYswKqUADLjfXWYjfyZ1NTUm/7aIV2J9vf3x82t/xNfQEAAfX19OByOL/w7t/IfI2NDXl6e\nXhfyZ/S6kL9koF8Xl6pbOLy7jLOnrx3NPcGfrJVxJMwcj0XleVjqtNn56Zv5HD/VSrC/J99en4at\n6bzeL+TP3Ori7ZCW6KeffprvfOc7PPHEE9jtdr75zW/i7a35mCIiMrxdqGzk8O5zVJztL8+R0UFk\nrYgjLjFcq5nDWFVtK5u35HC5oZPZU0N5Zl0qQX6e5DWdNzuajAJDWqJ9fHz42c9+NpRPKSIiclsM\nw6DqXAMHd5VRXdkEwOSpIWStmMbkqSEqz8Pc3tyL/OJ3RfTaHTy0LI51dyTg4qJ96jJwNB5DRETk\njxiGQcXZeg7uLKPmQjMAUxPDyVoeR1RMsMnp5EbsfQ7+c9spth87j4+nK8+uy2DuzPFmx5JRSCVa\nRESE/vJcXlrHwZ1lXKpuASB+xjiyVk5jQlSgyenkZtQ1dbF5aw7lF1uYPN6fTU+nMyHU1+xYMkqp\nRIuIyJhmGAZlZ65yaFcZtRdbAUiYFcGildOIiAwwOZ3crLzSq/z49Tzau+wsS4viqw/OxtNdNUcG\nj15dIiIyJhmGQdnpqxzcVcblmlawwPSk8WStmMa4CTp8Y6RwOg3e2nWWN3adxdXFytceTmJVZrT2\nrMugU4kWEZExxXAalJ66wsFdZVytbQMLzEieQNbKaYRH+JkdT25BW2cvP/5tHvmldYQHe7NpfTpT\ntfVGhohKtIiIjAmG06Dk5GUO7iqj7nI7FgvMTIkka0UcYSrPI05ZdTPPb82hvtlGWuI4/umJOfh5\nu5sdS8YQlWgRERnVnE6DkqJaDu4+R/2V/vI8KzWSrBXTCA3XTWcjjWEYfHLsPP+x7RQOp5N1dyTw\n8PJpOilShpxKtIiIjEpOp8Gl812c2LOfhqsdWKwWktImsnBFHCFhKs8jUXdvH//vd0Xsy6vBz9ud\nZ9elkhIfbnYsGaNUokVEZFRxOpycKqzl0K4yGus7sVgtJKdHsXBFHMGhPmbHk9tUW9/B5i05nL/c\nxrRJgXx7fTrhQTr1WMyjEi0iIqOC0+HkZMElDu06R1NDJ1arhahYb+57dC5BISrPI9mxk7X89M0C\nurr7uHNBDH91zwzcXF3MjiVjnEq0iIiMaE6nwemCSxzYWdZfnl0spM6LZsGyqVRUlahAj2AOh5Ot\nH5fw3v5yPNxd+NYTc1iSGmV2LBFAJVpEREYow2lwpqiWAzvLaKjrwGq1MGfuJLJWxBHw6WX+KnMz\nyu1rbuvmhVdzOV3ZSGSYD5s2ZBA9XvO7ZfhQiRYRkRGlf87zZQ7sKKPuSjsWq4WUjEksXBFHUIj2\nyI4GpysbeWFrDs3tPcyfPZ5/fDQFb083s2OJfIZKtIiIjAifnjC4f8dZrta2YbFAUtpEslZO0w2D\no4RhGLx/sIL/+egMAH91zwzuXRSr0wdlWFKJFhGRYc0wDM6V1HFgx9nrx3PPmhPJolXTNKpuFOnq\ntvOztwo4WnyZYH8PnnsqnRlTQsyOJfK5VKJFRGRYMgyDirP17N9xltrqluvHcy9aOU0nDI4yFy63\nsXlLNpfqO5kZG8Jz69II8vc0O5bIF1KJFhGRYcUwDKrONbB/x1lqzjcDkDh7PItWTWOcbiwbdfbn\nXeTff1dET6+DB5dO5ak1ibi4WM2OJXJDKtEiIjJsnK9oYP8nZ6mubAIgfsY4Fq+OJyIywORkMtDs\nfQ7+6/1TfHz0PN6ernzn6XTmzZpgdiyRm6YSLSIipquuamL/J2c5X94AQFxiOItXxzMhKtDkZDIY\n6pq7eGFrDmXVLUwe78+mDelM0P52GWFUokVExDQ1F5rZ/8lZKsvqAYhNCGPJ6ngiJwWZnEwGS/7Z\nOl5+LY/2rl6Wpk7k7x5KwtNddURGHr1qRURkyF2tbWPf9lLKzlwFICYulCWr44mKCTY5mQwWp9Pg\n7T1l/HZHKS5WK3/3UBJ3zI3W+DoZsVSiRURkyDTWd7D/k7OcLqwFYNKUYJbekUB0rEaZjWbtXb38\n+PU88krrCAvyYuP6dKbpaoOMcCrRIiIy6Fqbuzi48xyFuRcxnAbjJwawdE0CsfFhWokc5covtrB5\nSzZ1zTbmJITzrSdS8fdxNzuWyJemEi0iIoOmo72Hw3vOkXf0Ag6Hk9Bxviy9I4GEWREqz6OcYRjs\nPHGBV947icPp5InVCTy6YhpWq/7dZXRQiRYRkQFn6+rl6P4Ksg9VYe91EBjszZLV05g5Z6JK1BjQ\n3dvHL98tZm/uRfy83XjmyUzmJISbHUtkQKlEi4jIgOnt6ePEoUqO7qugp7sPP39PVt49nZSMSbi4\n6gCNsaC2oYPNv8nh/OU24qIC2bg+nfBgb7NjiQw4lWgREfnS+uwOco+e5/Decro6evHydmPl3dNJ\nWzAZNzcXs+PJEDl+6jL/+kY+Xd19rJk/mb++dyZurvr3l9FJJVpERG6bw+GkMPsih3aV0dbajYen\nK4tXxzN3UQwenm5mx5Mh4nA4eXV7Ce/uK8fdzYVvPj6HZWlRZscSGVQq0SIicsucToPTBZfYv+Ms\nzY1duLpZmb80lvlLp+KtyQtjSnN7Ny+9msfJigbGh/rwnaczmDze3+xYIoNOJVpERG6aYRicPXWF\n/Z+cpe5KO1YXC+kLJrNwRRx+/p5mx5MhdqaqkRe25tDU1sO8WeP5x0dT8PHSFQgZG1SiRUTkplSd\na2DPxyXUVrdgsUBSehSLV00jUDeNjTmGYfDBoUr+58PTGMBX7prB/UtiNbZQxhSVaBER+UKXa1rY\n8/tSKsvqAZieNJ4lq+MJHedncjIxQ1e3nX97u5AjRbUE+nnw3FNpzIoNNTuWyJBTiRYRkb+oqaGT\nfdtLrx/RPWVaKMvWJjIhKtDkZGKW6itt/MtvcrhU38GMKSE891QawdrGI2OUSrSIiHxGR1s3B3eV\nkX+8GqfTYEJUAMvWJjJlWpjZ0cREB/Jr+Pd3CunudXD/kqmsX5uIq4tmf8vYpRItIiIAdNvsHN1f\nwYmDldh7HQSH+rBsbQKJs8drr+sYZu9z8usPTvHRkSq8PFzZuCGdBbMnmB1LxHQq0SIiY1yf3UHO\n0fMc3n0OW5cdX38PVt0zneSMSbhopXFMq2+28cKrOZy90Ex0hB+bns4gMszX7Fgiw4JKtIjIGOV0\nGhTn1nBg51lam214eLqybG0CmVkxuLnr18NYV1hWx0uv5dHW2cuSORP5+4eS8PTQ60LkU/ppEBEZ\nYwzDoOz0VfZuL6X+SjsurlbmLYllwTIdlCL9H67e2VvG65+U4mK18NUHZ7Nm3mRt6RH5EyrRIiJj\nSHVlI7t/X0LN+WYsFkjOiGLxqngCgrzMjibDQEdXLz/+bT65JVcJDfRi4/o04qODzY4lMiypRIuI\njAH1V9rZ8/sSys5cBSB+ZgTL1iYQplnPck15TQvPb8nhalMXydPCeObJVAJ8PcyOJTJsqUSLiIxi\n7W3dHNhxloIT1RgGTJoSzPI7E4marNVF+YOdJy7wynvF2PucPLYynsdWxeNi1fYNkS+iEi0iMgr1\ndPdxdH85xw/0j6sLHefLirumE5cYrr2tcl2P3cGv3itmV3Y1vl5ufOfpDNISx5kdS2REUIkWERlF\nHA4nBSeqObDjLJ0dvfj6ebD63hkkp0dh1bg6+SNXGjvZ/JscKmtbmToxgI0bMhgX7G12LBFT2Nva\nbvnvqESLiIwChmFw9tQV9vy+hMb6Ttw9XFhyRzxzF03BXWPJ5E9kn77CT97Ip9NmZ/XcaP7mvlm4\nu7mYHUtkyDjtdtpLz9JcUEhLYRGdFZV4fv87t/Q99M4qIjLCXTzfxO4Pz3DxfDMWq4W0+dEsWhWP\nr59uCpPPcjicvL6jlHf2nMPd1co/PprCioxJZscSGXSGYWC7VEvLtdLceuo0zu5uACyurvjPnEHv\nLX5PlWgRkRGqsb6DvR+XUlJ8GeifuLH8zkRCw3WinPy5lvYeXnotl+LyBsaH+LDp6XRiJgSYHUtk\n0PR1dtJafLJ/tbmgkJ66+uuPeU2cSGBKEoHJSQTMmI6Llxd5eXm39P1VokVERpjOjh4O7iwj79gF\nnE6DyOggVt6VyKQpIWZHk2GqpKqJF17NobG1m8wZEXzj8Tn4ermZHUtkQBlOJx0Vlf2rzQWFtJWe\nBacTABcfH0LmzyMwJZmglCQ8wsK+9POpRIuIjBD23j6OH6ziyN5yenv6CA71YdnaBBJnj9fEDfmL\nDMPgw8OV/PqD0xiGwYY7p/PAkqlYNb5ORonepmZaCguv7W0upu/TGwStVvziphKYkkxgSjJ+cVOx\nuAzsvn+VaBGRYc7pNCjOvci+7Wdpb+vG28edZWtnkjo3GhdXTdyQv8zW08fP3y7kUOElAn09ePap\nVGZP/fKrbyJmctrttJWUXl9t7qw6f/0x9+BgwlcsIyglmYCk2bj5De5hUirRIiLDWFV5A7veP82V\n2jZcXa0sXD6V+Uun4qlL8fIFLl5tZ/OWbC5e7SBxcjDfXp9GSICOdpeRxzAMui9fpqWgf7W59eQf\n3RDo5kZgctL11WbvSVFDelVOJVpEZBhqrO9g14dnKDvdf0z37NSJLF2TQECQipB8sUOFl/i3twro\n7nVwz6IpfOWuGbhqRriMIH1dNlpPnuwvzvkF9Fytu/6Y18TIa/uak/GfOQMXD/OmEKlEi4gMI12d\nvRzcVUbukfM4nQaTpgSz6p4ZTIgKNDuaDHP2Pie/+eg0HxyqxMvDheeeSiMrOdLsWCI3ZDiddFad\nv77a3F5SiuFwAODi7U3IvMzrq82e4eEmp/0DlWgRkWHA0eck5+h5Du4so9tmJyjEmxV3TSdhVoRu\nGpQbamy18cLWXErONxE1zo9NG9KJGje4+0FFvozellZaCguv7W0uwt7a2v+AxYLv1Nj+1eY5KfhN\nixvwGwIHikq0iIiJPj1pcPdHJTQ1dOLp5cbKe6aTvmAyrq7D8xeHDC9F5+p56bVcWjt6WZQSydce\nTsZLp1TKMOO022k/W3Z9i0ZnZdX1x9yCAglftoTAlBQCk2fj5u9vXtBboJ8yERGTXK5pYecHZ7hQ\n0YjVaiEjK4ZFK6fh7eNudjQZAZxOg3f3neO17SVYrRb+9v5Z3LkgRlcuZNjoaWikOT+f5tx8WotP\n4rDZgP4TAgNmz7q22pyMd3T0iHzdqkSLiAyxtlYb+z4upSivBgyYNmMcK+6arpMG5aZ12Oz89I18\nTpy+QkiAJxvXp5MwOdjsWDLGXR8/l19Ac34BXReqrz/mOT6if7V5TgoBM2fg4ulpXtABohItIjJE\nenv6OLqvgqP7y+mzOxk3wZ9V98wgJi7U7GgyglReamXzlmyuNHaRFBfKs+vSCPA1b0KBjG099Q39\nq815BbQUFV8fP2d1dycoNYXAOXMISk3Ba/x4k5MOPJVoEZFBZjgNinIvsnd7KR1tPfj6ebDsgQRm\np0Xp5Di5Jbuzq/nlu0X09jl5ZMU0nlidgIteQzKEPl1tbs7LpyW/gK7qi9cf85wwnqA5KQSlzsF/\nxnRTx88NBZVoEZFBVF3VxI5tp7hc04qrm5VFK6cxf2ks7rrxS25Br93Bf2w7yY7jF/DxcuPbG9LJ\nmB5hdiwZI3rq62nOK6A5P5+WopN/sto85/qKs9f4sfWa1Lu4iMggaG22sef3JZwquATArDmRLFub\nqMNS5JZdaezk+a05VNS0MiUygE0b0okI8TE7loxiWm2+OSrRIiIDyN7bv+/5yL7+fc8TogJZfd8M\nonTTl9yG3JKr/Pj1PDpsdlZmTOJvH5iNh5tGH8rA02rzrVOJFhEZAIZhcKawll0fnaGtpRtfPw+W\nP5jI7NSJWLRnVW6Rw2nwxs5S3tpVhrurla8/kszKzGizY8ko4rTbaTtTQnN+Ac15+dgu1lx/zHPC\nBIJSUwiakzLmV5u/iEq0iMiXdLmmlR3vn6K6sgkXFysLlk1l4fI4PDz1Fiu3rrWjh5dfz6OwrJ6I\nEG82rk8ndqKOfZcvr6e+gea8/P5tGsV/stqclnptm0YKnhFabb4ZeocXEblNne097PuklPwT1WBA\n/MwIVt49neBQ7VeV21N6oYkXtuTQ0NpNxvQIvvl4Cr7eOnxHbo/hcNB+toym3Dyac/M+O7f509Xm\n1DkEzJiO1V2vs1ulEi0icoscfU6yj1RxcGcZPd19hEX4sfreGUyZFmZ2NBmhDMPg4yNV/NcHp3A6\nDdavTeTBpXEagSi3zN7Wfm2LRh4t+YX0dXQAYHFzI3BOCsFpcwhKnaPV5gGgEi0icgvOlVxl5/un\naazvxMvbjTUPzCJ17iSsLlazo8kI1d3Tx7+/U8SBghoCfN159sk0kvSBTG6SYRh0nb9wfbW5vewc\nOJ0AuIeGErFwPkFpqQTMnqW9zQNMJVpE5CY0XG1nxwenqSitx2K1kLEwhsWrp+GlS+3yJdTUtbN5\nSw7VV9pJiA7i2+vTCQ3UGET5Yg6bjZbikzTn5tGcl09vY1P/A1Yr/gnx/dM00lLxjp6ExaKrGYNF\nJVpE5At02+wc2HmWnMPncToNYuJCWX3fTMIj/MyOJiPckaJafvZWPrYeB3dnTeErd83AzVVXNOQv\ns12+0l+ac/NoPXUao68PAFc/P8IWLyIobQ6BKcm4+em9aaioRIuI/AWG06A4r4bdH52hs6OXoBBv\nVt0zg2kzxmllR76UPoeTLb8/w7YDFXi6u/DsulQWpUw0O5YMM9cPPLlWnG2Xaq8/5hMTQ9C1vc1+\n0+KwuGh2uBlUokVE/sTlmha2v3eKmgvNuLm7sGxtAnMXT8HVVb+o5MtpbLXx4qu5nKlqYmK4L5s2\npDMpwt/sWDJM9DY394+gy82jpbAYh80GgNXTk+DM9P4xdKlz8AgJMTmpgEq0iMh1tq5e9m0vJffY\nBTBgetJ4Vt49nYAgb7OjyShwsqKBF1/NpaW9h4VJE/iHR5Lx9nQzO5aYyHA66SivoDk3j6bcfDor\nKq4/5hkRQfjypf03Bc6cgdVNr5XhRiVaRMY8p9Og4EQ1ez8uwdZlJ3ScL3fcN1Mj62RAGIbBe/vK\n2bq9BAvw1/fO5O6sKdoWNEb1ddloKSykOSeX5rwC7K2tAFhcXAiYPevaNo1UvCIn6DUyzKlEUG8U\nuAAAIABJREFUi8iYVnOhmU/+9yS1F1tx93Bh5d3TyciKwUUj62QAdNrs/PTNfI6fukKwvycb16eT\nGBNsdiwZYt1X62jKyaU5J/czNwW6BQUSvmIZwWmpBCTNxtVbV71GEpVoERmTOtt72PNxCYXZFwGY\nlRrJirum4+fvaXIyGS2qalvZvCWHyw2dzJ4ayrPr0gj005zescBwOGg/V05zTi5NObmfOSnQZ0oM\nwelpBKWn4Rs7BYtVH9hHKpVoERlTnA4nuUcvsO+TUnq6+xg33p87HphJ9BTdqCMDZ29uNb/4XTG9\ndgcPL4/jydUJuroxyjlsNloKi2jKzqU5Lw97axvQf1JgUOocgtLTCE5PwyNU7zWjhUq0iIwZFyob\n+eS9U1y93IaHpyt33D+TtHnROm1QBkyv3cF/vn+KT46dx8fTlefWZZA5c7zZsWSQ9NTX05Tdv9rc\nevLUH7ZpBAYSvmI5wRlpBCbNxsVTV7hGI5VoERn12lu72f3RGU7mXwIgOSOK5WsT8dGldRlAV5u6\neH5rDuUXW4iZ4M+mDRmMD/UxO5YMIMPppONcOU2fbtM4f+H6Yz4xk6+vNvtOjdU2jTFAJVpERi2H\nw0n2oSoO7DxLb4+D8RMDWPPALCZGB5kdTUaZvNKr/Pj1PNq77CxPj+KrDybh4aa54qOBo7u7f5tG\nTi7NufnYW1qAT7dppPQX57RUPMI0zWesUYkWkVGpuqqJj98tpu5yO17ebtz50AxSMidhtWpklAwc\nh9PgrV1neXPXWVxdrHzt4WRWZU7SaLIRrqe+4VppzqWl+BSG3Q6AW0BA/zSN9GvbNLy8TE4qZlKJ\nFpFRpauzlz0flVCQ3X83fErmJJbfmYi3j7vJyWS0ae3o4Se/zSf/bB3hwd5sWp/O1KhAs2PJbfj0\n0JNPx9B1Vp2//pj35GiCP92mETdV2zTkOpVoERkVDKP/wJTdH53B1mVn3Hh/1j44iyjN5JVBUFbd\nzPNbc6hvtpGWOI5/emIOft76oDaSOHp6aC0q7r8xMDcXe/O1bRqurgSmJF8bQ5eKZ3i4yUlluFKJ\nFpER7+rlNo7tbqS5/jJu7i6svGc6mQtjNHVDBpxhGGw/dp7/3HYKh9PJujsSeHj5NG0TGiHsbW00\n5eTSu2MX2c+/jLO3FwC3AH/Cly0lOCONgKQkXL21TUNuTCVaREas3p4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DBz2YiAy88tI6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TLARJhdMUSfPHmS5557jqeeeop/+7d/Q6/Xc+7cOX71q1/xyiuvMGvWrLGsUwgAmhu7OXGolf4+\nIymzQlixJlHGJE9xJr2e1q+Oo9v5PrkNjQA4hATjv3IF3gtuw8pudEfcGo0mtn1SwO7PS7GxtuLX\nD81kYeqND2MRQoyOjoEuSrQVlGgrOFuXwx8rtzFg+OaMl7WVNdEeYUR6hplDs/RjFj/miiH6L3/5\nC6+99hrx8fHmz02bNo3k5GQ2b97M9u3bx6RAIS6pKGll51uZDA4YWbg8jnmLo+TBbQrTd3bSePAw\nDZ8cRN8+tGXDY/Ys/FcuxzUxYUz+bbR3DfC7t7PIK9MS4OXIi49kEOYvh4eEsDSD0UBlRy3F2nJz\ncG7+zraMQBc/oj3CifIMJcojnBC3QDRqefdIXLsrhuienp7LAvQlCQkJdHZ2jmpRQnzXhawa9u28\ngAoVM+a6cevt0ZYuSVhIb2UV9fs+puXLYyh6PVYODgSsuhttSDDxixeNWR355Vp+ty2Ttq5B5iT6\n88t1KTjItiIhLELb1z4UmFuHAnN5ezX6b3XLcLJxJMU/gRjPcKI9w+mp7mBuxhwLViwmgyuG6L6+\nPgwGAxrN5TcxGAwYDIYrfJUQI0tRFI4dKeHLQ0XY2Vuz9tF0WjsqLV2WGGOKyUT72XPU791P54Uc\nAOz8/PC/ayU+ixaicbCnLTt7bGpRFD46Vs6b+/MBeOyu6ayaHynviggxRnQGHeXt1RQPrzCXaCto\n6+8wX1er1IS6BhLtFU6MZwTRnuH4OXlf9juaXTc2jxdicrtiiJ43bx6vvPIKL7zwgvlzRqORzZs3\ns2DBgrGoTUxxRoOJ/btyuJBZg5uHPQ89MQsvX2dasystXZoYI8aBAZo/+4L6fR8zUF8PgGtiAgF3\n34l76kxUVmP71mvfgJ4/vXee4zn1uDvb8tyGNBIivca0BiGmEkVRaO5tpbj1m8Bc2VGD8VuH/9zs\nXMgInEH08CpzhEeIDDERY+KKIfrZZ5/lZz/7GUuWLCEhIQGj0UheXh5RUVG8+uqrY1mjmIIG+vW8\nvyWLipJWAoLdWPd4Bk7O8qA4VQy2tNJw4BMaDx3B2NuLSqPBZ9FCAu6+E8fwMIvUVNXYxea3Mqlr\n6WF6hCfPbUjDw2V0Dy0KMdX06wcoa6u6bC/zt0dlW6mtiHAPIdorwrw1w8vBQ94JEhZxxRDt4ODA\n1q1bOXPmDLm5uahUKjZu3Cjt7cSo6+ro551/nKa5sZvY6b6sXj8TG9urtjQXk0B3UTH1e/fTeuIk\nmExYu7oS8OBa/JbdgY2bm8Xq+uJsLa++f55BnZHVC6LYuCIejXSFEeKmmBQTDd3NlGgrKG4dCs3V\nXfUoimK+jZeDB3ODU82rzGHuwdKTWYwbV00mGRkZZGRkjEUtQtDS1M32107R1TFAxrxw7rhnuoxK\nnuQUo5HWE6eo37vPPFXQISyUgLvvxPvWeahtbCxWm95g4o29eew/XoG9rYYXN6UzNynAYvUIMZH1\n6voo0VZSoi2nWFtBqbbissl/NlbWxHlFEe0ZToxnOFGeYXjYW+7FsxBXI8t7YtyoqWxjx+tn6O/T\ns3hlPHMXymGtyczQ10/zp0ep37efweaW4amCaQTcfeeYtaj7MS3t/by8NZOi6nZC/Zx58ZEMAr1l\nyIIQ10JRFBp7WihqLaO4tZwibTm1nQ0ofLPK7O/kQ2pAknmVWVrMiYlGQrQYF4ovNrFraxZGo8Ld\na2cwI0OGVUxWg9o2Gj4+QOPBwxh7e1Hb2OC3fBkBd6/EPmB8rPKeK2rmv9/OprtPx4LUIJ5ek4yd\nbCkS4op0Bh1l7VUUtZabQ3P3t/Yy21rZMM0nmhjPCGK9IojyDMdFJv+JCU6eFYTFnT9Tw773L2Bl\npWLto+nETPO1dEliFPRWVVP/4V5ajn2FYjBg7epK4PoH8Vu2FGsXZ0uXB4DJpPD+0WK2HyrESq3m\nqTVJLJ8TZvFVcSHGm7a+Doq0ZebQXNFefVnHDG8HD5JC0oj1iiTGM4JQt0CsZJVZTDISooXFKIrC\nic/LOPpxAfYO1qx7PIPgMA9LlyVGkKIodObmUf/hR7RnnwPAPjCAgFV347NgvkX3O39Xd5+O/3nn\nLFkFTXi72/PCxnRiQtwtXZYQFmc0GanqqKVoeIW5uLWc1r428/VLHTNivCKJ9YogxjMCDwfZyywm\nPwnRwiIUk8Lhvfmc/qoCFzc71v9kNt6+42M1Utw8k8GA9vhJ6j78iN7yCgBcpsUTsOoePNJTUanH\nV2eL0poONm/NpLmtj5QYb36zPhVXJ2mpKKamnsFeirXlQ6vM2nJKtZUMGnXm6y62TqQFJhM7vDUj\nwj0EG834eUEsxFiREC3GnNFg4qMd58k7V4e3nzPrn5yFi5u9pcsSI8DQ10/TkU9p2LefwZZWUKvx\nvGUOgffcjXNsjKXL+x5FUTh8upq/f5CDwWjiwTtiWbskFivpCCOmiEtt5opay82HAOu6G83XVagI\ndg0gxivCHJp9vzP9T4ipSkK0GFODAwZ2vpVJRUkrwWHurHs8A3sHWcGY6Aa1Whr2H6Dx0GGMvX2o\nbW3xX7kc/7vuxN7fz9Ll/aBBvZG/7c7h08xqnB2s+fVDGaTFy358MbnpDDpK2yopHA7MxdoKenS9\n5uv2GjuSfOOHQrNXBNEe4TjYyCKHED9EQrQYM709g7zzj9M01HYSM92XNRtSsbaWgyYTWV91DXUf\nfEjLsa/H7WHBH9LQ2svmLWeoqO8iKsiVFzZl4OvhYOmyhBhxXYM9FLWWUdhSSmFrGeXt1RhNRvN1\nX0cvUvynE+sVQaxXJMEuAajH2XYrIcYrCdFiTHR19vP2307R2txDSkYIK+9LRC0T3yas7qJiand/\nQNvpMwDYBwUScM/d+Cy4bVwdFvwhp/Ma+N93z9I7YGDZnDCevCcBG3kxJyYBRVFo6mmhsLWMwtYy\nilrKLtuaYaVSE+4eQpxXJLHekcR6RuBm72rBioWY2CREi1HXru1l299O0dHWx+z5ESy5a5rsp5uA\nFEWh4/wF6nZ/QGduHgBO0dEE3bcaj4z0cXdY8LuMRhNvHyxk12cl2GjU/HJdCovTQyxdlhA3zGgy\nUtlRa15lLmwto3Ogy3zdXmNHsl88sV5RxHlFEuUZhp1GDswKMVIkRItR1dLYzba/n6Sna5AFy2K5\n9fZoCdATjGI0oj11mtrdH9BbVg6A24xkAtesHheTBa9Fe/cAr7ydTU5pK/6ejrz4SDrhAbICJyaW\nfv0AJdqKoVXm1lKKtZUMGgbN193tXZkbnEqc91BoDnENlK0ZQowiCdFi1NTXdLD9tVP09+m5457p\nzL4twtIlietg0utp/vxL6j74kIH6BlCp8LxlDkH3rsYpKtLS5V2zixVaXt6aRVvXALOm+/HLB2fi\nZG9t6bKEuKq2/o7h/cxlFLaWUtlRi6J8MzY72MWf2OHAHOcdhbeDx4R4USvEZCEhWoyKqnItO14/\nw+CggbseSCZllrxtPlEY+vppOnyE+o/2oWtrQ6XR4LvkdgJX34N94PgYy30tFEVh31flvLEvH0VR\neGTlNO5dGCUhQ4xLJsVEfXeTOTAXtZTR1Ntqvq5Ra4jxjDAH5ljPCJxsHS1YsRBCQrQYcWVFzbz3\nZiYmo8Ka9TOZnhJo6ZLENdB3dlK//wCNBw5i6OlBbWdHwKq7Cbj7Tmw9PS1d3nXpG9Dz553n+fpC\nPW7Otjz3cBqJUV6WLksIM4PRQHl7NQUtpUOhubX8slZzjjYOzAxIHArNXlFEeIRgYyXvoAgxnlgk\nRGu1Wu69917eeOMNIiMnztvC4uoKcxvYve0sKhU88Gg6MdOk7+54N9jSQt2He2k6/CkmnQ6NszMh\nD63Db8UyrJ3Hb5u6K6lu7GLzlkxqm3uYFu7BcxvS8HSVPrfCsgYNOkq0FRS0lFDQUkqxthydUW++\n7u3oSYr/dOK8oojzjiTQxQ+1SvYzCzGejXmI1uv1/Md//Ad2dnZjfddilOVk1fDRexewtlaz7rEM\nwmTlb1zrr6+n9v09tHx5DMVoxMbLi8BVd+O7ZDFWE/T389i5Wv688zwDOiOr5keyaeU0NNJKUVhA\nn66fwtYyClpKKGwppbS96rL+zMGuAcR7RxHvHUWcVxSeDu4WrFYIcSPGPES//PLLrFu3jtdee22s\n71qMoszjlXyyJxc7e2vW/2QWgSHyhDBe9VVXU/P+blq/PgEmE/ZBQQStWYXXbbei1kzMHV56g4lP\nsjo4XVyLva0VL2xM55bkibN/W0x8XQPdFLSWUtA8tNJc2fnNIUC1Sk24ezDx3tFM844i1isSZ1sn\nC1cshLhZY/qMuWfPHjw8PLj11lslRE8iJ78o48i+izg62/LwT2fj6+9i6ZLED+gpL6d25y60J08D\n4BgeRtD99+E5Z9a47/H8Y1o7+nl5ayaFVT0E+zrzb4+kE+Qz8bahiImlta+NguZS8/aMbw81sVZr\niPOKMq80x3hGYG89Md/dEUJcmUr5dr+cUbZ+/XpUKhUqlYqCggLCwsL461//ire39w/ePjs7e6xK\nEzeoNL+bogvd2DmombXICyeXibmSOZmZ6uoxHPsaU0kpAKoAfzS3zkMdM/E7VZQ3DrDreBt9gyYS\nQu25K8MdW+uJ+4JAjE+KotCu76JmoJHa/kZq+hvoNPSYr1urNATa+RJs70ewvT/+tl5o1PJYKMRE\nlJqaes23HdPf8u3bt5s/3rBhA//v//2/KwboS67nf0aMrWNHiim6UI+ruz0bn5qDu+fYtFvKzs6W\nfxfXoDP/IrU7d9Fx/gIAzvFxBD9wH24pMyZ8eDaZFHZ9VsL2z2tRq1X8bHUivnZtpKWlWbo0Mc7c\nyOOFSTFR01lPQUspF4dXmr89CdDJxpG0wGSmeUcR7x1NmFsQVmoZHT+RyPOI+CHXu3grL5XFdVMU\nhS8PF3PscDFuHvZsfGoubh4Oli5LMPR305mTS83OXXTl5QPgmpRI8AP34ZIwfcKHZ4CePh3/8+5Z\nMi824eVqx/Ob0okL9SA7u93SpYkJymQyUdVZR35z8XBoLqFX12e+7m7nytyQNOKHt2gEufpL5wwh\nhOVC9LZt2yx11+ImKIrC558U8vXRUtw9Hdj41Bxc3SVAW5qiKHScPUfNe7voLioCwD01haD778Ml\nPs7C1Y2cstoONm/JpKmtjxnR3jz7cCquTraWLktMMJeF5ubiodCs7zdf93H0JD0geWhPs080vo5e\nk+IFqBBiZMlKtLhmiqLw6f4CTn5RhoeXIxufmoOLm/TftaRL4bn63Z30lJQA4DErg6D71+AcHWXh\n6kbWkdNV/HVPDnqDibVLYnjwjjis1BJsxNVdLTT7OnqREZTCdJ8YpnlH4+XoYcFqhRAThYRocU0U\nReHIvouc+rIcLx8nNvxsDs6uctrcUhRFoePceWp27KS7qBgAzzmzCV53P45hYZYtboQN6o38fU8O\nR85U42RvzYub0kmf5mfpssQ4ZjKZqOyo5WJLMSfqM/lz1Xb6JDQLIUaYhGhxVd8O0N6+QwHayUUC\ntCUoikLnhRyq33nPvG3Dc84sgtc+gGN4mEVrGw2N2l42b8mkvK6TyCBXXtiYjt8YHWAVE8e3Q3N+\nczEFLaWXh2Ynb2YHpTDNJ4ZpPtF4OUhoFkLcPAnR4kcpisLRjwu/WYF+ai5OzrIHdayZw/OOnXQX\nFAJD2zaC1z2AU0S4hasbHWcuNvI/75ylt1/P0tmh/GRVIjbW0gFBXArNNeQ3l5DfUkzhj4RmY+MA\nC2fPt2C1QojJSkK0uCJFUfj8YBEnPi/F09uRDU/NkQA9xhRFoTM3j5p336PrYgEAHrPSh8NzhIWr\nGx1Gk8I7hwrZ+WkxNho1/7p2BrdnhFq6LGFBVwvNfj+y0pytlXkDQojRISFaXNGXh4v5+tMSPLyG\nArSzbOEYU525eVS/+x5d+RcBcE9PI+TBtThFTs7wDNDZM8h/v53FhZJW/DwdeHFTBhGBrpYuS4wx\nRVGo62okr7mI3KZCLjYXX3YQ0M/Jm9nBM5nuPRSaPR3cLVitEGKqkhAtftCxIw2dP+QAACAASURB\nVEN9oC+1sXNxlS4cY6XrYgFV298193l2T0sleN0Dk67bxncVVrbx8tZMWjsHyJjmx68emomTvbWl\nyxJjpKmnhbymIvKai8hrLr5suImPoyezhleap/vESGgWQowLEqLF93x9tIQvDhYND1KRNnZjpae0\njKrt79Jx9hwA7qkzh8JzTLSFKxtdiqKw/+sKXt+bh6IobFwRz5qF0ailfd2k1tbfQX5T8XBoLqKl\nV2u+5mbnwrzQDBJ8YknwicHHycuClQohxA+TEC0uc/KLMj47UDg8ynuuDFIZA33VNVS/swPtyVPA\n0ITBkPUP4hIXa+HKRl//oIFXd57n2Pk6XJ1s+O3DaSRHe1u6LDEKugd7yG8eCs35TcXUdTearzna\nOJARNGMoNPvGEujsJ8NNhBDjnoRoYZZ1opIj+y7i7GrHhp/NkVHeo2ygqYnqd3fS8uUxMJlwiokm\n9OGHcEtOsnRpY6KmqZvNW85Q09RDfJgHz29Mw1O2DU0a/foBClpKh0NzEZUdtSgoANhqbEnxn850\nn1gSfeMIdQ1ErZYx2kKIiUVCtAAgJ6uGA7tzcXSyYcPP5uDhJb14R8ugto3a93fRdOQoisGAQ2gI\noQ8/hHt62pRZffvqfB1/3nmO/kEjd98WwaN3TkdjJSFqItMZ9RS3lg1tz2gqprStEpNiAsBarWGa\nT7R5pTnSIwyNWtoVCiEmNgnRgoKcBj7acR47e2vW/3Q2Xj5Oli5pUtJ3dVG7+wMaDxzEpNNhF+BP\nyIPr8Jo3F9UUWYUzGE28uT+fvcfKsbOx4rkNadw6I9DSZYkbYDQZKWurGg7NRRS1lqE3GQBQq9RE\neoSS4BNLom8sMZ4R2GhsLFyxEEKMLAnRU1xpYTO7387G2saKh56chV+AtBMbaYa+Puo/2kf9R/sw\n9vdj4+VFyLr78Vm0EJXV1FmN03b28/LWLAoq2wj2deLFTRkE+zpbuixxjRRFoaGnmZzGAnKbCslv\nLr6sV3OYW5B5pTnOOwoHa9maI4SY3CRET2GVZa3sfDMTtUrFusczCAqVtlEjyaTT0fDxJ9Tu3oOh\nuwdrV1dC1j+I39IlqG2m1qpcTmkL/70tm46eQW6dEcgzD8zA3lYefsa7zoEucpuGejXnNBWg7Ws3\nX/N18mZuSBpJvnFM84nBxVbewRJCTC3yLDZF1VW3s+P1M5gUhbWPphMWKS2kRopiNNLy5TGqtu9A\n19qKlaMjoRvW479yOVb2U2t1TlEUdn9eyrYDF1GpVPxkVSJ3zgufMnu/J5pBg46CllJymoZWm6s6\nas3XnGwcmR08kyTfeJJ846TtnBBiypMQPQU1N3Sx/bXT6HVG7tuYSnS8r6VLmhQURaE9+yxVW9+m\nr6oalbU1gfeuImjNajROU2+Vrqdfzx/ePcvp/EY8Xe14fkM68eEeV/9CMWZMJhPl7dXm0FzUWo5h\neF+ztVpDom8cib5xJPnGE+YehFo1NfbuCyHEtZAQPcV0tPWx/bXTDPTruefBGcQnBVi6pEmhu7iE\nyi3bhqYMqtX4LF5EyINrsfWemqt1FfWdbH4rkwZtL0lRXvz24TTcnG0tXdaUpygKTT0t5DQVkttU\nSF5zEb26PgBUqAhzDyJxeKU5zitSDgMKIcSPkBA9hfR2D/L230/R3TXA0numk5wWbOmSJrz++nqq\ntr2D9sRJANzTUwnd8DCOoSEWrsxyPj1TzV93X0BnMHH/4mjWL4vHSqYPWkzXYA95TUXm1eZvTwb0\ndvBgVlAKSb7xJPjGyr5mIYS4DhKip4jBAT3v/PM0ba293LI4ilm3RVi6pAlN19FBzY6dNB3+FMVo\nxCkmmrBNG3BNmG7p0ixGpzfy2oe5HDpVhaOdhuc3ppMx3c/SZU05BpOR4tZycpoucqGhgPL2avOQ\nE0drezKCZpj3Nfs6ecv+dCGEuEESoqcAg8HIe29m0VDbSUpGCIuWx1m6pAnL0NdP/Ud7qftwL6aB\nAewC/AndsB7PObOndBhp1Pby0tZMymo7iQhw5YVN6fjLwJ4x09TTwoXGi5xvLCC/qYh+wwAAVmor\n4r2jSPKLJ8k3ngj3EJkMKIQQI0RC9CRnMil8sP0claWtxCb4sfK+xCkd9m6UyWCg6dARat57H31n\nJ9ZuboQ9sgHfJbej1kztX6OsgiZ+vz2bnn49SzJC+Om9SdhaT53+15YwoB8gr7mYC40XudB4kcae\nFvM1PydvbvObRbLfNKb7xGBvbWfBSoUQYvKa2s/+k5yiKHyyJ5eCnAZCIz1Z8/BM1DJa+booikJ7\nVjaVb26hv64etZ0dwQ+uJfCeu6Zcu7rvMpoU3j1cyHtHirHWqHnmgRncMSvU0mVNSibFRGV7LTlN\nBVxovEhhaxlGkxEAe40daYHJzPCLJ9lvGr5O3hauVgghpgYJ0ZPYF4eKyD5ZhW+AC2sfTUcjq4PX\npbeikoo33qIzJxfUavyW3UHwg+uwcZOpjp09g7yyPZvzxS34ejjwwqZ0ooLcLF3WpNIx0EVOYwHn\nGy+S21hA52A3MNRFI8I9hGT/odAc7RmBRi2/20IIMdYkRE9S2Ser+OpICe6eDqx/chZ29taWLmnC\n0LW3U719B02fHgVFwT01hbBHNuIQMnU7bnxbUVUbL23NorWjn7R4X37z0EycHKQV2s0yGA0UtpaZ\nt2hUfmvQibudK/PDZpPsN40k3zhc7GRcuhBCWJqE6EmopKCJA7tzcHC0Yf1PZuPkInsir4VxcJD6\nvfup3bUH08AADiHBhD26CfeZKZYubVxQFIUDJyr550e5mEwKG5bHc9+iaNTSvu6GNfW0cK4hn/ON\nF8lvLmbQMAiARq0h0TeWZL9pJPtNI8Q1UM4yCCHEOCMhepKpr+lg19ZsrKzUrHs8Aw/pkHBVislE\n61fHqdz6NrrWVqxdXQh/dBO+SxajspK3yQEGBg38ZdcFvjhbi4ujDb99OJUZMT6WLmvC0Rv1FLSU\ncrYhj/MN+dR3N5mvBTr7kewXT7L/NKZ5x2Arg06EEGJckxA9iXS09fHu62fQ6408sCmNoFB3S5c0\n7nUVFFLx+lv0lJSg0miGxnTfdy8aR3nxcUltczebt2RS3dhNbKg7z29Ix9t9ah+qvB4tvVrONeRz\nriGPvKYiBo06AGw1tqQFJJHin8AM/2l4O3pauFIhhBDXQ0L0JNHfp+Odf5ymt3uQZasSiEv0t3RJ\n49pAUxOVW95Ge/wEAJ63zCVs08PY+fpauLLx5XhOPX/ccY7+QQN3zgvnsbsSsNZIh5cfM7S3uZSz\nDfmcb8intqvBfC3Q2Y8U/+nM8J9OvHcU1lZyVkEIISYqCdGTwNAwlUxam3uYPT+CjFvDLV3SuGXs\n76fm/d3Uf7QPxWDAKTqa8McfwSVeBtB8m8FoYsvHF/nwyzJsbax4dn0q82cGWbqscau1r43zDfmc\na8gnt6mQgeG9zTZW1sz0TyDFP4EU/+n4OHlZuFIhhBAjRUL0BKeYFD569zzV5W3EJ/mz5M5pli5p\nXFIUhZYvv6JqyzZ0bW3YeHkRtvFhvG69BZVMcLtMW9cAv9uWRX65lkBvJ158JJ1QPxdLlzWuGExG\nilrLzNs0ajrrzdf8nXyGV5sTmOYTjY2sNgshxKQkIXqCO3qgkPzz9QSHubP6oRRU0inhe3rKyin/\nx+t0FxSitrEheN0DBN67CitbW0uXNu7klrXyu21ZdHQPcktyAL94YAYOdhICAdr6OzjfkM/Zhjxy\nmwrp1w+N1ra2sh4KzX7TSfGfjp+zHLgUQoipQEL0BHb+TA0nPi/Fw8uRtY9lyDCV79B3dVH19js0\nHf4UFAXPObMIe/QR7Hwl5HyXoih88EUpWw4UoAKeuCeBu2+NmNJt1UyKibK2KrLrczlbn3tZ32Zf\nRy/mh85mhv90pvtIJw0hhJiKJERPUFXlWvbvuoCdvTUPPpGBg6M8iV+iGI00HjxE1fYdGHt7sQ8O\nIuKJx3CbkWzp0sal3n49f3zvHCdzG/BwseW5DelMj5ianSL69QPkNBWQXZ/Lufo885RAjVpDkm88\nKf7TSQlIwN/JZ0q/wBBCCCEhekJq1/ay881MUOD+TWl4ejtZuqRxoyMnl4p/vkFfVTVWjg6EP/Eo\nfsuXodbIP/UfUlHfyeYtmTS09pIY6cVvN6Ti7jy1hvM092rJrsvhbEMu+c0lGEwGAFztXFgYPpfU\ngESSfOOws55aPxchhBA/TpLFBDM4oGfH62fo79Oz8r5EwqPltD/AoFZLxetvDbWsU6nwXXI7IQ8/\nhI2bq6VLG7c+y6rhL7suoNMbWbMwig3L47GymvyHLE0mE8XaCrLrczhbn0vNt1rQhbsFMzMgkdSA\nRCI8QlCrJv/PQwghxI2RED2BmIwmdm87S0tTD7NuDSd1TpilS7I4k8FAw8cHqH7nPUwDAzjFRBPx\nkydwjo6ydGnjlt5g5B8f5vHJyUoc7DQ8uz6DOZO8r3ifrp/zjRc5W5/LuYY8unW9wNChwJn+CaQG\nJDEzIAFPBxlQJIQQ4tpIiJ5Ajuy/SGlhM1FxPiy5e7qly7G4rosFlP3tNfqqqtE4OxH++FP43r5I\nWtb9iOa2PjZvzaS0poMwfxdefCSdAK/JuR2osbuZrOFDgQUtJRgVEwDu9q7cHjGP1MAkEnxi5VCg\nEEKIGyIheoLIPlnF6WMVePs6sWbDTNRTuJWd0ttLyR//TPNnXwDgu+R2Qjeux9pFehn/mOzCJn6/\nPZvuPj2L0oJ5ak0SdjaT5yHApJgoai0jsy6HrLoL1Hc3ma9FeoSSGpDITP9Ewt2D5VCgEEKImzZ5\nnkEnscrSVj7Zk4uDow3rHp+F7RTt26sYjTQePsLgW9toHhjAMTyciJ89iUtcrKVLG9dMJoX3jhTx\n7pEirNRqnr4vmaWzQydFkNQZdOQ2F5FZe55T1WfpKxvq3WxrZUNaYDJpAYmk+Cfgbi9744UQQows\nCdHjXGd7H7u2ZoMK7n8kDXdPB0uXZBHdJaWU/+01ekrLwNaW8Ccfx3/5UlRW0hv7x3T16vj9O9mc\nLWzGx92eFzalEx08sff9dg/2cLY+j8y6C1xovMigUQeAg5Udi8LnkhaYTJJvHDayTUMIIcQokhA9\njun1Rna+lUVfr44VaxIJnYK9ew29vVRte4fGg4dAUfCefxtdM2cQsGC+pUsb94qr23lpayYt7f2k\nxvnwm/WpODtMzGDZ1NNi3qZR2FqGaXh/s7+zD+mByaQHJtNV2UZ6WrqFKxVCCDFVSIgepxRF4eNd\nOTTUdpKSEULqnFBLlzSmFEWh7dRpyl97HV1bG/ZBgUT89EnckhLJzs62dHnjmqIoHDxVxWsf5GI0\nmVi/LI4HFsdMqH30iqJQ3l5NZt0FsupyqO6sA0CFiijPMHNwDnTxM39NdlWHpcoVQggxBUmIHqcy\nj1eSk1VLQIgby+9NmBT7V6/VYKuW8tf+QdvpTFQaDSEPrSPw3lWorafmXvDrMaAz8NfdOXyWVYOz\ngw3PPpzKzNiJMebcYDSQ31JMZt0Fsuty0fa3A2Ct1jDTP8G8x9lN9jcLIYQYByREj0NVZVoOf5SP\no5MND2xKQ2M9Nfb9KkYjDZ8comrbdkwDA7gkTCfyqZ/iEBRo6dImhPqWHjZvyaSyoYuYEDee35iO\nj/v43kM/oB/gXGM+p2vPc64hj3790MFARxsHbgudRVpgEjP8psm0QCGEEOOOhOhxpqujn11bswC4\nb2MaLm72Fq5obPRWVlL66t/oKSlB4+RExDM/x2fxoim1An8zTubW84cd5+gbMLBibhhP3JOAtWZ8\nvvjq0fWSXZfL6brzXGi8iN6oB8Db0ZOFYXNIC0wm3jsKK/X4rF8IIYQACdHjikFvZOeWLHp7dCxb\nlUBo5OQ/SGgcHKRmx07qPtwLJhNet80j/PFHsXFzs3RpE4LRaGLrgQL2fFGKjbUVv35oJgtTgy1d\n1vd0DHSRVXeB07XnyGsqMg8+CXbxJyMohVlBMwh1C5IXTUIIISYMCdHjhKIofLInj/rqDpLSgkif\nF2bpkkZdx/kLlP317ww0NmHr40PkUz/BfWaKpcuaMNq7Bnh5Wxb55VoCvBx58ZEMwvzHz8CZ1r42\nztSe53TteQpbSlFQAIhwD2HWcHAO+NbBQCGEEGIikRA9Tpw/U8O5M9X4B7my8r6kSb0iZ+jppeLN\nLTR/ehTUagJW3U3Ig2uxspN9r9cqv1zLy1szae8eZE6iP79cl4LDOBjC09DdzOnac5yuPUdZWxUw\n1FEj1ivCvOLs7Tj532ERQggx+UmIHgeaGrr4ZE8udvbW3L8pDetJfJCwLSubsv/7GzptGw5hoUT/\n4l9wioywdFkThqIofHSsjDf3XwTgsbums2p+pMVedCmKQk1nPadqz3Gm9ry5FZ1apSbJN56MoBmk\nBybLxEAhhBCTjoRoCxscMLBrSxYGg4k1G1Jx8xjf3RRulL67m4p/vkHLF8ekbd0N6hvQ88f3znEi\npwF3Z1ue35jOdAsM4FEUhbK2KvOKc2NPCzDUii41IJFZQSmkBSThZOs45rUJIYQQY0VCtAVdGqii\nbell9vwIYhMm5/5Q7clTlP3tH+g7OnCKiiTqmadxDJtaw2NuVlVDF5u3nKGupZfpEZ48vyENd5ex\n2/5yKTifrMnmVM1ZWvraALDV2DInOJVZQTNI8U/AXlrRCSGEmCIkRFvQ2VPV5J2rIyjUncUr4y1d\nzojTd3ZS9vd/oj1+ApW1NaEbHyZw1d2orCbvdpXR8EV2Da/uusCgzsi9C6LYuCIeKyv1qN/vpamB\nJ2uyOVlzlpZeLQD21nbcGprBnOCZJPnGY6OZmKPEhRBCiJshIdpCGus6OfhhHvYO1qzZkDomoWis\nKIpC61fHKf/H6xi6unCOjSXqFz/HISjI0qVNKHqDkdf35vPx8QrsbTW8uCmduUkBo3qfiqJQ0V7N\nyZqznKzJpvlScNZcCs6pJPvFY20l23CEEEJMbRKiLWBwQM+urdkYDSZWPZKGq/vkGaii6+ik7K9/\np+3UadQ2NoQ//ij+K5fL6vN1am7v4+WtmRRXdxDq58yLj2QQ6O00KvelKAqVHbVDK87V2TT1tgJg\np7Fl3vCKc7LfNGwkOAshhBBmEqLHmKIo7NuZQ1trL3MXRhEd72vpkkaM9vQZyv7yN/SdnbhMn0bU\nMz/H3t/f0mVNOGeLmnnl7Wy6+3QsSA3i6TXJ2NmO7K+qoihUddRyYniP86XDgbYaW24JSWNOcCoz\n/KbJVg0hhBDiCiREj7GsE1VcvFBPcLgHi5bHWrqcEWHo66Pin2/SfPQzVNbWhD32CAF3rUSlnjxb\nVMaCyaSw82gx7xwqxEqt5udrklg2J2xE29fVdNZzvDqTk9VnaehpBoaC89yQNOYEzyTFb7oEZyGE\nEOIaSIgeQ80NXRzem4+Dow1rNsxEPQn2QXfm5VPyxz8z2NyCY0Q4Mb/6BQ4hIZYua8Lp7tPx++3Z\nZBc24+1uzwsb04kJcR+R793c08rx6iyOV2eZ+zjbWtkwJzh1KDj7J2ArwVkIIYS4LhKix4hBb+SD\n7ecwGkzctTEZF9eJvQ/apNNR9fY71O/dDyoVQQ/cR/AD90nf5xtQWtPB5i1naG7vZ2asD79+aCau\nTrY39T07Bro4WZ3N8eosirXlAGjUGtICk5kXksbMgETsNDd3H0IIIcRUJiF6jBw9UEhTQxepc0KJ\nnT6x+0H3lJdT/D9/pL+mFrsAf2J++QucY2MsXdaEoygKh09X8bc9uRhNJh66I5YHlsRipb6x7Ru9\nuj7O1J7neHUWuc2FKIqCSqUi0TeWW0LSyQiagZONDEARQgghRoKE6DFQVtTC6WPleHo7csfd0yxd\nzg1TjEZqd39AzY6dKEYjfiuWEbZpA1Z2MmDjeg3oDPxtTw5HM2twdrDmN+szSI27/kOmOoOO7IZc\nvq7K5FxDPgaTAYBojzBuCU1nbnAqbjJyWwghhBhxEqJHWV+vjo92nEOtVrF6/UysbSbmj3ygqYni\n3/+R7qIibDw9iHrmadxTZli6rAmpvrWHl7ZkUlHfRVSwGy9uTMfnOsa9G0xGchoLOF6dSWbdBQYM\ngwAEu/hzS2g6t4Sk4evkPVrlCyGEEAIJ0aNKURT2v3+Bnq5BFq2IIyDYzdIl3ZCWY19R9tfXMPb1\n4XXrLUT+7CdonEanZ/FkdyqvgT+8e5beAQPL54Tx5KoErDVX76GtKAol2gqOVZ7mZE023bpeALwd\nPVkWvYB5IemEuAWOdvlCCCGEGCYhehSdP1NDYW4jIREezF0YZelyrpuxv5/y116n+bPPUdvZEf2v\nz+C9cP6ItlybKoxGE28fLGTXZyXYWFvxqwdTWJR29S4mjT0tfFV5mq+qzph7ObvauZiDc7RnuPx9\nCCGEEBYgIXqUaFt6OPhhHrZ2GlY/lIL6Bg+LWUpPaRlFv/9fBuobcIyMJPbZX2IfMLojpyer9u4B\nXnk7m5zSVvy9HHlxUzrhAVfep9yj6+Vk9VmOVZ6iaLizho2VNfNC0rktbBaJvnFYqWUCpBBCCGFJ\nEqJHgdFo4oN3zqHXGbn34Zm4ul/7fldLU0wm6vfup2rbdhSDgcDV9xCy/kFpXXeDLlZoeXlrJm1d\ng8xO8OOX62biaP/9n6XBaOBsQx7Hqk5ztj4Pg8mAiqHOGreGzmJWUAr21nKAUwghhBgvJESPgq8/\nLaG+uoPE1EASUibOPlVdezslf/gzHecvYO3mRvQvn5HDgzdIURT2flXOm/vyURSFR++cxuoFUZdt\nvfj2PucTNdn0DO9zDnYN4LbQWcwLTcfTYWQGrgghhBBiZEmIHmGN9Z189WkJLq52LF+daOlyrll7\n9llK/vgq+s5O3FNTiPrFM9i4SWu0G9E3oOdPO89z/EI9bs62PPdwGolRXubrTT0tfFV1hmOVpy/b\n57wyZjHzw2YR6hYk+5yFEEKIcU5C9AgyGk3s3XEek0nhzgeSsfuBt+3HG5NeT9W27dR/tA+VRkP4\n44/if+cKVOqJP5LcEqobu/ivtzKpa+lhWrgHz21Iw9PVnj59Pyeqs/my8hRFrWWA7HMWQgghJjIJ\n0SPoxOdlNNZ1kZweTFScj6XLuarBlhYKf/d7eopLsA8MIObZX+EUEWHpsiasL8/W8ur75xnQGVk1\nP5INK+Io1pbyTsFJTteeQ2fUyz5nIYQQYpKQED1CWhq7OXa4GCcX2wkxlbAtK5uSP/wJQ3cP3vNv\nI/Kpn2Blb2/psiYkvcHEG/vy2P91Bfa2Gn6+Lppu+3J+dXAHLb1aAPycvFkQPofbwmbh5eBh4YqF\nEEIIcbMkRI8Ak0lh73vnMRpNrFyThL2DjaVLuiLFaKT6nR3U7tqDytqayJ//FN87lsge3BvU2tHP\nS1szKappxSeiE98oLW+W7wfAVmPLgvA5LAyfQ5xXlPyMhRBCiElEQvQIOPVlOXXVHSSkBBKb4Gfp\ncq5oUNtG8e//l678i9j5+RH7/G9k+8ZNOF/UzMt7jjDoVIljahPdKj3dHRDvHc3C8DnMDkrBTrZr\nCCGEEJOShOibpG3p4YuDhTg62bBsdYKly7mijpxcil/5X/SdnXjOmU3UMz9H4+ho6bImpLa+Tl49\nup8c7TnUEb1oAHd7N+aHz2ZB2Bz8nMf/fnghhBBC3BwJ0TdBMSnsfe8CBoOJVfcm4uA4/rZxKIpC\n3QcfUbVtOyq1mvAnHhvqviFbC66LyWQip6mAQ8XHyG7IBZWC2lZNomcSdyfMJ9EnDrV0NBFCCCGm\nDAnRNyHzeCU1FW3EJ/kzLXn8jcQ29vdT8ue/oD1+EhsPD2KffxaXuFhLlzWhaPva+bziBJ+Vn6C1\nrw0AU78zfsTxb6tWE+Auw1CEEEKIqUhC9A3qaOvj6IEC7B2sWX7v+Buq0l9XT8Hml+mvqcVlWjyx\nz/0GGwl818RoMnK2IY+jZV9zrnFo4qBGZY2pNRhdUyD3z0nnoaXxWKllNV8IIYSYqiRE3wBFUTiw\nJxe9zsjK+5Jwcra1dEmX0Z7OpOQPf8LY14f/XSsJe2Qjao38VV9Nc08rR8uP80XFSdoHOgGIcA9F\n3R5CbqYtTrb2PP/QTNKnjd/Do0IIIYQYG5KsbkBBTgOlBc2ER3uRODPQ0uWYKSYTNTt2UvPe+6ht\nbIj+1S/wWTDf0mWNawajgTN1Fzha/jW5TYUAOFjbszRqPjM8U9m6u47y+k4ig1x5YWM6fp5yGFMI\nIYQQEqKv2+CAnkMf5mOlUbNiTeK4OaBn6Oun+H/+QHtmFra+PsS/+DyO4WGWLmvcau1t49Pyrzha\nfoLOgS4A4rwiWRwxj9nBM7lQ1MZ///Msvf16ls4O5SerErGxlrHcQgghhBgiIfo6fX6wiO6uAebf\nEYOnt5OlywFgoLGRgv98ib7qGlyTk4j97a+xdna2dFnjjkkxkdNYyOHSL8luyEVRFByt7VkRs4jb\nI+cR5OKP0aSw/WAB7x8twUaj5l/XpnB7RoilSxdCCCHEOCMh+jrU13SQ+XUFnt6O3LI4ytLlANCZ\nm0fhy69g6O7G/84VhD/2CCorWTH9tu7BHj6vOMmRsq9o6mkBIMI9hDui5nNLSBq2mqHWhB3dg7yy\nPYsLJa34ezrywqZ0IgJdLVm6EEIIIcYpCdHXSDENHSb8/+3deVzVVf7H8de9l30XEHEXxBV3Ades\nbC+XyrIVbBmbnJqmmRa1scYmJ7Nt+pnTMi2TWaaZZVaaZmrmkiKKKwooLqwKKDsX7r3f3x+OTIsb\nCvcCvp//Ad97zkc7D317Ot/zMQy4fkwv3NxcH1Rzli4j4533wGSi40MTCL/6SleX1GAYhkFaQQbL\n961hw6Ekqh023C3uXBYxiKs7DiMqpMMvnt9zoJAXPkykoKiSAdHhPHpHP/y83V1TvIiIiDR4CtHn\nKDnxMNmHjhPdpxURnUJdWovDZiPj3f+Qu/Rb3AIC6DrpCQKju7u0poaihmGDQQAAIABJREFU0mZl\n3cFElqevIeP4YQBa+oVxVdQlXNZhEH6ev3wx0DAMvlq7n/cXn7jKbtwN3bn5sijMur5OREREzkAh\n+hxUVlTz/ZIU3D0sXDXStWHVVlrKnhkvU7R9Bz7t29Htr5PxaqE207mlR/k2bTWrMzZQXl2ByWQi\nrnUfro4aRo8WXTCbfttNsMJq4/VPk/kxOYsgP0+eiO9Pr6jmLqheREREGhuF6HOwetleykurGH59\nVwKCvF1WR2VeHrv//g8qMrMIHhBL5z//CYu36+pxNcMw2JG3hyVpq9iavRMDgyCvAK7vfDlXRA4l\nxOf0zWUO55UwffYmDueV0q1DMBMTYggJvHh/L0VERKR2FKLPIi+7mMS1GQSH+jLw0kiX1VGSmkbK\ntOlUFxXR6sZRdBgXj8n8293Vi0G1w8aKfT+yNHUVh4tzAOgU3IHrOg9nYJu+uFnOvKx/TM5i5vyt\nVFbZGTUskntHRONmuTh/L0VEROT8KESfgWEYfLtoJ4YB197Uw2UvExZs2Ejqq6/hsNmI/P14Wl5/\nrUvqcLX8skK+Tf+B5Qd+oHK/FYvJzNB2sVzX+XI6hUSc9fPVNgcffL2LxT/ux9vTwpPxMVzSp+E0\nyxEREZHGQyH6DPbuzOXgvgI6d29BVFfnnzs2DIPsxV9x4D8fYvb0pNtfJxEc09/pdbiSYRjsyU9n\nSeoqNmUlYxgGPhYvxnS/nquiLiHYO+icxikoqmDGh5tJOVBI2xZ+TB4XR9sWuktbREREzo9C9GnY\nbHa++2o3ZrOJq0Y5/2VCw25n/zvvk7v0W9ybNaP7M0/hF+m64yTOVmWvZv2hzSxNXVVzy0ZEUFuu\n63w53vlmBvQccM5jbUs7yssfJXG81MqwPq15eGwfvD219EVEROT8KUmcRuK6AxwrKGfAJRFO70xo\nt1rZ+9KrHEvcjE/7dnR/+q94NnfttXrOUmwtZXn6GpalrabIWoLJZGJgm35c1/kyuoZGYTKZSCpM\nOqexHA6DhavS+GhpCiaTiQdu7MmIoRENplW7iIiINF4K0adQXmplzfJUvLzdGXZ1Z6fObSstZfe0\n6ZSk7CGwdy+6TnoCNx8fp9bgCjklR/hm7/esPrCBKns1vu7ejOp6NddGXUqob3CtxyutqOa1T7aw\ncVcuIYFeTEqIpWuH2o8jIiIicioK0aew5rs0rJU2rh4djbePh9PmtRYUsPvZaZQfPEToJUPo9Kc/\nYnZv2l3z9ubv46s9K0jM2oaBQXPfEG7oPJzhEYPxcvc6rzH3ZxXxwuxEcgrK6BUVyhN3xxDk71nH\nlYuIiMjFTCH6V/KPlJK4/gDBob7EDu7gtHnLM7PY/exzWI8cpeUN1xPxu3ub7BV2DoeDxOxtfLVn\nBakF+wHoGNyekV2uYkCbPljM538LyopNh3hz4TaqbA5uvaITd13bDYu6D4qIiEgdU4j+lVVL92A4\nDK4c0Q2Lm3NCbElaOrv//g9sxcW0u+sO2tw6pkme27XaqliVsZ5vUleSV3oUgJhWvRjZ9cqa887n\nq6razr8X7WDZTwfx9XJjYkIscdHhdVW6iIiIyC8oRP9M1qHjpGzPoXW7ILr0cE4AO568jZTpL+Ko\nqqLjQw8SfvVVTpnXmcqqylmW/gNLUldSbC3F3ezGlR0vYUTn4bQKuPDf59yCMl74MJF9mUVEtgpk\n8j2xhIf41kHlIiIiIqemEP0zK5ekAHDFDd2cshOcv24Dqa++BiYTXZ98nJBB535tW2NwvKKIr1NX\n8l36Gipslfi6e3Nz9+u4rtNlBHoF1Mkcm1PyeOXjJEorqrkqrh2/v7kXnu6uaYojIiIiFw+nhujq\n6mqeeuopsrKyqKqqYsKECVxxxRXOLOG09u09SkZaPh27NqdDVP1fJ3dk9Q+k/d8sLP9tohLYs0e9\nz+kseaVHWbznO1ZnbKDaYSPIK4Ax0ddxZcdL8HH3rpM57A6DT5bvYf53qbi7mfnj2D5cPaB9nYwt\nIiIicjZODdGLFy8mKCiIl156iePHj3PjjTc2iBBtOIyaXejh13Wr9/nyvltB+r/ewuLjQ/TUp/Hv\n3Kne53SGQ8ezWJSyjHWHN2MYBi18QxnV9WoujRiIh6Xubhkpq7Qz9Z0NJKcepUWwD5PHxdKxzbl1\nLhQRERGpC04N0ddeey3XXHMNcKKds8XSMP63e8qOHHIyi4ju04qWbQLrda6cb5ay/9/v4ubvT/Tf\nn2kSXQjTCw7w2e4lbMneAUD7wNaM7nYNg9r2u6CbNk5l78FC3v72CMXldmK7t+Avd/TDz4nXEIqI\niIgAmAzDMJw9aWlpKRMmTGDs2LGMHDnytM8lJZ1bZ7oLYTgM1iw5SlmJjUtHhOHrX3//rrBt2Ijt\nu+/B1xeP+Dswh4XV21zOkFV5hHWFW8gozwSgtVcLBjXrTaRP2zo/U24YBolpZXy75TiGAZf3CmBo\nd3/MTfAWExEREXGN/v37n/OzTn+xMCcnh4ceeog777zzjAH6pNr8Ys7Hzq1ZlBbn0CeuLcMu61Nv\n8xz+9DMOffc9HiHBRP99Kj5tWtfbXPVtz9F9fLbrG7bnnTgCEx3WmVuibyA6rH66O1Zabfzrs22s\n3nKcAF8PRg8IYOwNQ+plLmm8kpKS6v3PC2l8tC7kVLQu5FRqu3nr1BCdn5/PfffdxzPPPMOgQYOc\nOfUpORwGa5anYjKbuOTK+jmXbBgGhz7+hMwFC/EMa06P56biFd447y9OOZrGZ7u+YUfeXgB6hHXh\nlugb6B5Wf2e6M4+UMH12IodyS+jSvhmTEmI5uG93vc0nIiIici6cGqLfeustiouLeeONN3jjjTcA\neOedd/DyOr/2zhdqd3I2+UdK6RPXlmb1dK/w4U/mk7lgIV7h4fSYNhXP5s3rZZ76tOtIKp/t+oZd\nR1IB6NWiG7dEX0/X5lH1Ou+6bdn83/wtVFjtjBgawX0je+DuZuZgvc4qIiIicnZODdFTpkxhypQp\nzpzytBwOgzXfpWKux13owwsWcnj+ArzCW9Dj+b/jGRJSL/PUl91H0pi/8ytSjqYB0Du8O7dG30Dn\n0Pp9GdJmdzD7m90s+mEfnh4WHr+rP5f2a1Ovc4qIiIjUxkXbbOXkLnTfuHb1sgud9eVXHPpoLp7N\nQ4l+bmqjCtD7Cg8yb8dituWeODbRt2U0t0TfQKeQiHqfu6CoghfnbGZ3RiGtm/sx+Z5Y2ofXTWMW\nERERkbpyUYZo42e70EOvrPsjCTlLvuXA+x/gERxM9HPP4tVIbuE4XJTN/J1fsSkzGThx5vn2nqPq\nfef5pB378nlxzmaOl1gZ0rsVj4ztg49X3d0vLSIiIlJXLsoQvXdXLvlHSukdW/dnofNWfM/+t9/B\nPTCQ6Of+hnfLhv8SYV7pURbs/IYfD27CwKBTSAR39BxFjxZdnTK/YRh8sTqd2UtSMAG/G92DUZdE\nOqX1uoiIiMj5uOhCtGEYrF2ZDsDgyzvW6dhHVq8hfdabJxqpPDcVnzYN+xxvYflxFu5ewsr967Ab\nDtoHtua2nqPo36qn0wJsWUU1r83bwk87cwkO8GJiQgzdIxrP0RcRERG5OF10IfrgvgKyDx2nS3QL\nmrfwr7Nx89dvIO3/Xj/RyvvZZ/Bt367Oxq5rJdZSvkhZxrL0H6i2V9PSL4yxPUcwqG1/zCaz0+rI\nyC5i+uxEcvLL6BUVyuN396eZv2tuahERERGpjYsuRK9bdWIXesgVdXcjx/HtO0h95TUsnp5E/20K\nfh0bZivvKns136at5ovdSymrriDEpxm3Rt/ApR0G1nl77rNZufkw//psG1XVdm4Z3om7r+2KxeK8\nAC8iIiJyIS6qEJ2bXcS+PUdpFxlMm/bN6mTMsowD7Hl+BgBdn5qIf5f66dp3IRyGg/WHkvhkx5cc\nLSvA18OHhD5juCbqUtwtzn1xr6razjtf7uTbDQfw9XLjibvjGNijpVNrEBEREblQF1WIXr9yHwBD\nhtfNjRyVeUfY9ew07BUVdH78LwT16lkn49al3UdSmZP8OfuOHcTN7MaILldyc/dr8fOon+YyZ5JX\nWM4LHyaSfvg4HVoGMPmeWFqF+jm9DhEREZELddGE6OOF5ezalk1YS3+iul74lXPVxSXsfvY5qo8d\nI+L+e2l+yZA6qLLuZBXn8vG2L9icvR2Awe1iuLPnaML8Ql1ST9KePF75OImS8mqGx7RlwpheeHlc\nNMtPREREmpiLJsVsWpuB4TAYfFnHC755wm61kjJtOhVZ2bS6cRStRo2ooyovXFFlMQt2fcOKfWtx\nGA66NY8ivvcYokI6uKQeu8Ng/nd7mffdXixmMw/f2purB7TX9XUiIiLSqF0UIbrKamPrxkP4+nsS\n3af1BY1l2O2kvvxPSvbupfmlw+gwLr6Oqrww1fZqlqSu4vPdS6mwVdLSP4y7e99MTKteLgusRaVW\nXp27hS17jxDWzJtJ42Lp1LZuzqKLiIiIuNJFEaK3J2VirbQxYFgkFrfzvwHCMAz2vf0OhZsSCezd\ni6g//gGT2bU3ShiGwZacnczeuoDc0qP4e/hyf7/buaLjUNycfOPGz6UeOsYLHyZy9FgF/buG8dhd\n/fH38XBZPSIiIiJ1qcmHaMMwSFybgdliov+g9hc0VuaCheQt+w7fiAi6TnoCs7trW1JnFecye+sC\nknN3YzaZub7T5dzS4waXvDR4kmEYfLvhAP9etBO7w8Hd13bl1is6Yzbr+IaIiIg0HU0+RGek5XM0\nr5Se/VrjH3D+jTzy123g0Mef4Nk8lO5/+ytuPj51WGXtlFdV8Nmub1iatgq74aBni67c0/dW2ga2\ncllNAJVVNt74bBurkjLx9/Hgibv707fLhb/EKSIiItLQNPkQvWltBgCxQyPOe4yStHTSXpuJ2cuL\nblMm49HMNed6DcPgx4ObmLPtc4oqiwnzDSGhzy3Etu7t8hf1so+WMn12IgdyiuncLoiJCbGENXPd\nPzRERERE6lOTDtHHCspI3Z1Hq3ZB591cxVpQwJ7nZ+CorqbbUxPx7dChbos8R5nFObyXNI9dR1Lx\nsLhzW4+RjOx6FR5ObpZyKht2ZPPavK2UV9q4YUgE94+Kxt3NdeexRUREROpbkw7Rm9cfBAMGnOcu\ntN1qJeUfM6gqLKTDveMIjout4wrPzmqrYuHuJXy1dwV2h51+rXpyX9+xLrvv+efsdgezl6Twxep0\nPD0sPHZnPy7r39bVZYmIiIjUuyYbou02B9sSD+Pj60G33rVvK20YBvve/Ddl+/YRNvxyWo0eWQ9V\nntnmrO38Z8t8jpYXEuoTzL39xhLburfT6ziVwuJKXpyzmV37C2jd3JfJ4+Jo3zLA1WWJiIiIOEWT\nDdF7d+VSXlbFgGGRuJ3H0YLcJUs5umo1fp2i6DjhAaeeOS6sOM77SfPZlJWMxWRmdNerGRN9PV5u\nnk6r4Ux27svnxTmbOVZiZXCvlvzptr74eLn+WImIiIiIszTZEL110yEA+g5oV+vPFu3aRcZ7H+Ae\nGEjXiU9g9nDO/cYOw8HK/euYs+1zKqor6dY8it/1v8Plt26cZBgGi37Yxwff7Abg/lHRjB524R0g\nRURERBqbJhmii45VsG/vUVq3b0ZYuH+tPmstKGDvjFcA6DLxMTybO+fscW7JEd7e/DG7jqTi7e7F\n+P53ckXHIZhNrm3mclJ5ZTWvzdvKhh05NPP3ZGJCLNGRIa4uS0RERMQlmmSI3rb5MBjQN652L7md\nbOldXVRExO/uIzA6up4q/B+7w87Xe7/n011fU22vJqZVL37X/w6CfYLqfe5zdTCnmOc/2ER2fhnR\nkSFMjI+h2QXcuS0iIiLS2DW5EG04DJI3HcLdw0J0n9a1+uzBj+ZSvDuFkCGDaDni+nqq8GfzHc/k\njU0fknHsMIGe/twbN45Bbfs1qOMRq5MOM+uzbVir7Iy5PIr467phsTSM3XERERERV2lyITojPZ/j\nhRX0iW2Lp9e5//IKNyeR9fkivMLDiXpoQr0GWbvDzuI93/Hprq+xO+xc1mEQ8X1uxt/Tr97mrK1q\nm513v9zJkvUH8PFy46l7YhnUs2GczRYRERFxtSYXordurP0LhdajR0l7bSYmd3e6THwMN1/f+iqP\nnJIjzNr4AWkFGTTzCuT3sXfTr1WPepvvfBw5Vs6MDxNJPXScDi0DmDwullbNG07AFxEREXG1JhWi\nKyuq2bMzl9AwP9p0OLcOhYbdTuqr/4etpJTIBx/ALzKyXmpzGA6Wp6/ho22fU2WvZki7GO7vdzt+\nnvUX2M/Hlr1HePmjJErKq7i8fxv+cEtvvDya1DIRERERuWBNKh3t3ZWL3eagR7/W53wcI/PzRSfO\nQQ8aSPi1V9dLXfnlhby5aQ478vbg5+HLH+LGMbhd/3qZ63w5HAbzV6TyyfI9WMxm/nBLb64d2L5B\nnc8WERERaSiaVIjelZwNQHSfczu7W5KWzuFP5uMRHEzHPzxYL4Fx/aEk/r35Y8qrK+jXsge/j72b\nZt6BdT7PhSguq+LVuUkk7TlC82beTEqIpXO7c9vJFxEREbkYNZkQXV5Wxf69R2nZJpCQczi/a6+s\nJPXV/8Ow2+n06B9xD6jdfdJnY7VV8Z+tn7Jy/zo8LR78PuYuhkcOaXA7u2mHj/HC7ESOHKugX5cw\nHrurPwG+zmkuIyIiItJYNZkQvWdHDg6HQffe57YLnfH+B1RmZ9PqxlEE9e5Vp7UcOp7FPze8S1Zx\nLh2C2vDooPtpFRBep3NcKMMwWPbTQd7+Ygd2h4M7r+7C2Ku6YDE3rJAvIiIi0hA1mRBdm6Mcx7Zs\nJW/Zd/h0aE/7u++ssxoMw2B5+ho+TP6MaoeN6zpdzt29b8Ld4l5nc9SFyiobby7czsrNh/H3ceex\nu+Lo37WFq8sSERERaTSaRIguLbFyID2f1u2bERTsc8ZnbeXlpP/rLUwWC53+9EfM7nUTcEutZbyV\n+BGbspLx9/Dlz3HjiWldtzvcdSE7v5TpHyRyIKeYqLZBTE6IJewsv2ciIiIi8ktNIkSnbM/BMM5t\nF/rg7DlU5efTZuwt+EVG1Mn8+wsP8cq6tzlaXkj35p14ZOB9Dapt90k/7czhn59sobzSxnWDOzB+\ndA/c3SyuLktERESk0WkSIXpXchaYoHvvlmd87vj2HeR+uxyf9u1oO/aWOpl7dcYG3tk8F5vDzi3R\nN3BL9+sxmxtWW2y73cGcpSksXJWOh7uFP9/Rj+ExbV1dloiIiEij1ehDdHFRBYcyCmkXEUxAoPdp\nn7NXVpI+6w0wm4n640MXfIzDZrfxQfIClqevwdfdm8eG/L7BdR4EOFZSyUtzktixL5+Wob48dU8c\nHVoGuLosERERkUat0YfovTvzwIDos9zKcXj+Aqx5R2h98434d4q6oDkLK47z6rp3SC3YT7vA1jw+\n5AHC/cMuaMz6sGt/AS/OSaSw2Mqgni3502198fVuWC85ioiIiDRGjT5Ep6fkAdCp++lvlyg/dJjs\nL7/CMyyMtrePvaD59hxN59X173C8spjB7WJ4MPZuvNw8L2jMumYYBl+u2c9/vt4FwL0jornpso4N\n7o5qERERkcaqUYfo6mo7Gen5NA/3P+2tHIZhsO/tdzDsdiLH34fF8/wD74p9P/Je0jwMIKHPLdzQ\neXiDC6blldXMnJ/Muu3ZBPl78mR8DD07hrq6LBEREZEmpVGH6IP7CrBVO4jqevqjFPlr1lK8cxfN\nYmMIjos9r3kchoO5279k8Z7l+Hv68ZfB44kO63y+Zdebg7nFTP8gkayjpXSPCGZiQizBAV6uLktE\nRESkyWnUITp9zxEAorqdOkTbysrI+M8HmD08iBx/33nNUWWrYtam2fx0eAst/cOYPOxhwv2an3fN\n9eWHLZm8viAZa5WdGy/tyLgbuuNmaVi3hIiIiIg0FY07RKccwcPTQrsOwaf8+eF5n1J97Djt7roD\nrxa178hXXFnCi2vfIrVgP92aR/HEkAfx8/S90LLrVLXNwfuLd/L1ugy8Pd2YlBDLkHNsfS4iIiIi\n56fRhuiCo6UU5pfRtWc4Frff7rhW5uaSs+RbPFuE0fqm0bUeP7skj+k/zCKvLJ+h7WKZEBff4Np3\nHz1WwYw5iew9eIz24f5MvieO1s39XF2WiIiISJPXaEN0zVGO05yHPjhnLobNRvu776r1ndApR9N4\nae3blFaVcXP367itx8gG9wJhcuoRXvooieKyKi7r14aHbumNl2ej/c8pIiIi0qg02tSVnnL6EF2S\nmkb+2nX4dYoidOjgWo27KTOZ1za8h2E4eDA2nuGRtft8fXM4DBasTOXjb/dgMZuYMKYX1w3q0OBC\nvoiIiEhT1ihDdHWVjQP7CmjRMoCAoF92KTQMgwOz5wDQYVw8plq04F6dsYE3E+fgYfHgiSF/oFd4\ntzqt+0KVllfxytwtbE7JIzTIm0kJMXRpf+rz4CIiIiJSfxpliM5IL8Buc9DxFLvQxxI3//dKu/4E\n9jz3NtxLUlfywdYF+Hr48NSwh+kUElGXJV+w9MzjTJ+dyJHCcvp0bs7jd/Un0K9hNXkRERERuVg0\nyhB98ihHp19dbWfY7RyY/RGYzXRIiD/n8T7fvZR5OxYT5BXAlEsfoV1Q6zqt90It33iQtz7fTrXN\nwe1XdeH2q7tgMev4hoiIiIirNMoQfSijADd3M206NPvF9ws2/ERFZiZhVwzHp13bcxrrZIBu7hPM\n05c/2qDugLZW23lr4XZWJB7Cz9udp+6JI6Zb7a/qExEREZG61ehCtLWymiO5JbSLCMbys2YihmFw\neMFCMJtpc+vN5zTWzwP034b/hTDfkPoqu9Zy8st4YXYi+7OLiGoTyKRxcbQ4TWtzEREREXGuRhei\nsw4dBwPa/OqFumOJmyk/cJDQYZfg3bLlWcdpyAF6065cXp2bRFmljWsGtueBG3vi4W5xdVkiIiIi\n8l+NLkRnHjwGQJv2QTXfMwyDw58uBKDtOexCL0ld2SADtN3u4ONle1jwfRoebmb+dFtfroxr5+qy\nRERERORXGl2IzqoJ0f87D120bTulaWkEDxyAT7szh84fMn7ig60LCPIK4OnLH20wAfp4iZWXPtrM\n9vR8Wob4MvmeWCJaBbq6LBERERE5hUYVog3DIPPgMYKCvfEL8Kr5/uEFJ3ehx5zx84lZ23gzcQ6+\nHj5MufSRBvMSYUpGITPmJFJQVMmA6HAevaMfft4Nq8W4iIiIiPxPowrRhfllVJRX07HL/662K96z\n98S90P374hfV8bSfTTmaxmvr38Xd4s7kSx5qENfYGYbBV2v38/7iXRiGwbgbunPzZVGYdX2diIiI\nSIPWqEL0yfPQrX92Hjp3ybcnvnfTjaf9XE7JEV5a+zYOw8HEIX+gc2hk/RZ6DiqsNl7/NJkfk7MI\n8vPkifj+9IpqGDvjIiIiInJmjSpE/+889ImbOaqLishftx7vNq0J6BF9ys+UWEuZvmYWpVVlPBgb\n3yBaeR/OK2H67E0cziulW4dgJibEEBLoffYPioiIiEiD0KhCdOaBY7i5mQlvFQBA3verMGw2wq+9\nGpPpt0cgqu3VvLT2LXJLj3Jjt2sYHjnY2SX/xo9bs5j56VYqq+yMGhbJvSOicfvZfdciIiIi0vA1\nmhBdZbWRl1NMm/bNsLiZMRwO8pZ9h9nDg7DLL/vN84Zh8M7mT9iTv4+Bbftxe89Rzi/6Z6ptDj74\neheLf9yPt6eFJ+NjuKSP689li4iIiEjtNZoQnZ15HMOA1v+92u74tu1U5uYSdsVw3Pz8fvP89/vX\nsvrABjo2a8/DceMwm1y321tQVMGMDzeTcqCQti38mDwujrYt/F1Wj4iIiIhcmEYTojMPnDgP3bbD\niRCd++1yAMKvvfo3z+4rPMj7Wz7Fz8OXvwwZj4ebh/MK/ZVtaUd56aPNFJVWMaxPax4e2wdvz0bz\n2y4iIiIip9Bo0tzPXyq0FhRQuCkR38gI/DpF/eK5Emspr677N3aHnUcG3ktzFzVTcTgMFq5K46Ol\nKZjNJh64sScjhkac8uy2iIiIiDQujSJEn2yyEhDkhX+gF4fmLQaH4zcvFDoMB6//9B+Olhdya/QN\n9Gl56hs76ltpRTWvfbKFjbtyCQn0YlJCLF07BLukFhERERGpe40iRFdWVFNWWkXn7i0AyP9xLWYP\nD5oPu+QXzy1PX0Ny7m56h3dnTPT1riiV/VlFTJ+9idyCcnp3CuWJu2MI9PN0SS0iIiIiUj8aRYgu\nLbEC4BfgSXlmJhWZWQQPiMPi/b+7lXNKjvDxti/w8/DlD3EJLnmRcMWmg7y5cDtVNgdjr+zMndd0\nxaLugyIiIiJNTqMK0b7+nhRuTAQgZGBczc8dDgdvbJyN1V7FhLh4mnkHOrW+qmo7b3+xg+UbD+Lr\n7c7EcbHEdQ93ag0iIiIi4jyNIkSXndyJ9veicOUmMJtpFhNT8/Ov9q5gb8F+Brftz+B2Macbpl7k\nFpTxwoeJ7MssIrJ1IJPHxRIe4uvUGkRERETEuRpFiD65E+1pqqYkNY2A6O64B5y4ZzmzKIf5O78i\nyCuA+/vf7tS6Enfn8srcLZRVVHNVXDt+f3MvPN0tTq1BRERERJyvUYTokzvRjkP7wDBqjnIYhsF/\ntn6KzWHjgZg78ff8bdOV+mB3GHyybA/zV6Ti7mbmj2P7cPWA9k6ZW0RERERcr1GF6KqU7QAEx50I\n0UnZ29mRt4c+4d2Jad3bKbUUlVp5+aMkktOO0iLYh8njYunYJsgpc4uIiIhIw9AoQvTJ4xyVu7YR\nENEBrxZhVNurmZ28EIvJTELfW5xSx56DhcyYnUh+USVx3cP58x198fNxXTdEEREREXGNRhGiy0qt\nuFnAXF1J8IATu9BL01aRV3qU6ztdTpuAlvU6v2EYLFmXwbuLd+JwGCRc340xl3fCrOvrRERERC5K\njSJElxZb8aQaExA8II7jlcUs3LUUfw9fbulxQ73OXWm1MWvBNn6I/LJSAAAQJUlEQVTYmkmgnwdP\n3BVD787N63VOEREREWnYGnyINhwGZaVW/CuL8Axrjm9EB95N+oQKWyW/6387fh71d53c4bwSps9O\n5HBeCV3bN2NiQiyhQd5n/6CIiIiINGkNPkRXVFTjcBh4VJXh37UrJdZSVmdsoIVfc66IHFpv867d\nlsXM+VupsNoZeUkk946Ixt3N+V0QRURERKThafAh+uRLhR72SrxatGL5vh+pdti4vtPlWMx1fyez\nze7gg6938+WafXh5WHji7v4M69umzucRERERkcarwYfospoQXYF78xCWpa/Ex92byyMG1flcBUUV\nzPhwMykHCmkT5sfkcbG0Cw+o83lEREREpHFr8CG6tKQSAA9bBWkcp6iymJFdrsTL3atO59mRns+L\nczZzvNTK0N6t+OPYPvh4udfpHCIiIiLSNDT4EP3zneiVRTsxm8xc1+nyOhvfMAw+X5XOh0t2YzKZ\nGD+6ByMvicRk0vV1IiIiInJqDT5El5ZUAeDhsLLHXsHA9jGE+gbXydhlFdW8Nm8LP+3MJTjAi4kJ\nMXSPCKmTsUVERESk6WrwIbrsv8c5DC87htnMDZ2H18m4GdlFTJ+dSE5+Gb2iQnn87v4086/bIyIi\nIiIi0jQ1+BBdUlwBQLFHOR2Do+kcGnnBY67cfIh/fbadqmo7t17Ribuu6YrFouvrREREROTcNPgQ\nXXqsHIujmhI/B92bd7qgsaqq7bzz5U6+3XAAXy83nrw7jgE96rdluIiIiIg0PQ0/RJda8bBVUBxk\noVvQ+d/XnFdYzguzN5GeWUREqwAmj4ujZWj9dTsUERERkaarwYfoikoHAfYK8v0sdDjPEL05JY9X\nPk6itKKaK2LbMmFMbzzd675Ri4iIiIhcHBp8iDaME9fblfq70yogvFaftTsM5i3fy/wVe3GzmHn4\n1j5cPaCdrq8TERERkQvS4EM0nGj57duyFW61aPNdVGrllY+T2Jp6lLBgHyYnxBLVNqgeqxQRERGR\ni0WjCNFujgrCW7Y/5+dTDx1j+uxE8o9XENOtBX+5sx/+Ph71WKGIiIiIXEwaRYi2u1np0KztWZ8z\nDIOlGw7wzqId2B0Gd1/blVuv6IzZrOMbIiIiIlJ3GkWIrvaoov1ZXiqstNr418JtrE7KxN/Hgyfu\n7k/fLmFOqlBERERELiaNIkRXeFXRPrD1aX+edbSU6R9s4mBuCV3aNePJhBjCmvk4sUIRERERuZg0\nihDtCDAR4OV/yp+t357Na/O2UmG1MWJIBPeN6oG7m7oPioiIiEj9aRQh2if8t7dq2OwOZn+zm0U/\n7MPTw8Jjd/Xnsn7n34xFRERERORcNfgQbXFUEdLuly8VFhZX8uKczezaX0Dr5r5MvieO9uEBLqpQ\nRERERC42DT5Ee9gqadmhc83XO/flM2POZo6XWBnSqxWP3NYHHy93F1YoIiIiIhebBh+i3R0VdGgZ\nhWEYfLF6H7OX7Abg/lE9GD0sUt0HRURERMTpnBqiHQ4HU6dOZe/evXh4eDBt2jTatz9LExWzlQC3\nZkyfnciGHTkEB3jyZHws0ZEhzilaRERERORXnBqiV6xYQVVVFfPnzyc5OZkXXniBN99884yfMbvZ\neGLmWrLzy+jRMYQn746hWYCXkyoWEREREfktp4bopKQkLrnkEgD69OnDzp07z/qZCsNGdn4ZYy6P\nIv66blgsur5ORERERFzLqSG6tLQUPz+/mq8tFgs2mw03t9OXYbWYeeqeWAb1bOWMEkVEREREzsqp\nIdrPz4+ysrKarx0OxxkDNMANdw6DqhySknLquzxpRJKSklxdgjRAWhdyKloXcipaF3KhnBqi+/Xr\nx6pVq7j++utJTk6mc+fOZ3y+f//+TqpMREREROTcmQzDMJw12cnbOVJTUzEMg+eff56OHTs6a3oR\nERERkTrh1BAtIiIiItIU6KoLEREREZFaUogWEREREaklhWgRERERkVpy6u0c5+q82oNLk7Zt2zZe\nfvll5syZw8GDB5k0aRImk4lOnTrxt7/9DbNZ/x68mFRXV/PUU0+RlZVFVVUVEyZMICoqSuviIme3\n25kyZQoZGRmYTCaeffZZPD09tS4EgIKCAm6++Wbef/993NzctC6Em266qaZ/SZs2bXjwwQdrtS4a\n5Ir5eXvwxx57jBdeeMHVJYkLvfPOO0yZMgWr1QrA9OnTefTRR5k7dy6GYfD999+7uEJxtsWLFxMU\nFMTcuXN59913ee6557QuhFWrVgEwb948Hn30Uf75z39qXQhw4h/ezzzzDF5eXoD+HhGwWq0YhsGc\nOXOYM2cO06dPr/W6aJAh+nzag0vT1a5dO15//fWar3ft2kVcXBwAw4YNY/369a4qTVzk2muv5U9/\n+hMAhmFgsVi0LoQrr7yS5557DoDs7GwCAgK0LgSAGTNmcPvttxMWFgbo7xGBPXv2UFFRwX333UdC\nQgLJycm1XhcNMkSfrj24XJyuueaaX3S2NAwDk8kEgK+vLyUlJa4qTVzE19cXPz8/SktLeeSRR3j0\n0Ue1LgQANzc3Jk6cyHPPPcfIkSO1LoTPP/+c4ODgms050N8jAl5eXtx///289957PPvsszz++OO1\nXhcNMkSfT3twuXj8/HxSWVkZAQEBLqxGXCUnJ4eEhARGjx7NyJEjtS6kxowZM1i2bBlPP/10zTEw\n0Lq4WC1cuJD169cTHx9PSkoKEydOpLCwsObnWhcXp4iICEaNGoXJZCIiIoKgoCAKCgpqfn4u66JB\nhuh+/fqxZs0agHNqDy4Xl+7du7Nx40YA1qxZQ0xMjIsrEmfLz8/nvvvu44knnuCWW24BtC4EFi1a\nxNtvvw2At7c3JpOJHj16aF1c5D7++GM++ugj5syZQ7du3ZgxYwbDhg3TurjIffbZZzXv3OXl5VFa\nWsqQIUNqtS4aZMdCtQeXX8vMzOQvf/kLn376KRkZGTz99NNUV1cTGRnJtGnTsFgsri5RnGjatGks\nXbqUyMjImu/99a9/Zdq0aVoXF7Hy8nImT55Mfn4+NpuN8ePH07FjR/15ITXi4+OZOnUqZrNZ6+Ii\nV1VVxeTJk8nOzsZkMvH444/TrFmzWq2LBhmiRUREREQasgZ5nENEREREpCFTiBYRERERqSWFaBER\nERGRWlKIFhERERGpJYVoEREREZFaUogWETmD0tJSnn32WUaMGMHo0aOJj49n165d5z3e6NGjAdi+\nfTsvvfTSGZ/duHEj8fHx5z3X2SQlJTFq1Kiar0tKSoiOjubNN9+s+d68efOYOHHiOY/5+uuv8/rr\nr9dpnSIiDZFCtIjIaTgcDsaPH09gYCCLFi3iyy+/5KGHHmL8+PEcO3bsvMb88ssvAUhPT/9FdyxX\n6NWrF9nZ2ZSWlgKwfv16Bg4cyNq1a2ue2bx5M0OGDHFViSIiDZZ6aYuInMbGjRs5cuQIjzzySE1b\n8YEDBzJ9+nQcDgc2m42pU6eSlpZGfn4+ERERzJo1i/z8fCZMmEDbtm05ePAgrVq14qWXXiIoKIgu\nXbqQmJjIzJkzKS8v58033yQ+Pp6nnnqKvLw8jhw5QkxMDC+++OJp64qPjycyMpLt27djtVp56qmn\nGDp0KPn5+TzzzDPk5uZiMpl47LHHGDx4MK+//jrJycnk5ORw1113cddddwHg7u5O3759SU5OZujQ\noaxdu5aEhASmTp1KaWkpfn5+bNmyhUmTJuFwOHj++efZsGEDJpOJUaNG8cADD7Bx40ZeeuklHA4H\nnTp1ok2bNgDY7Xb+/Oc/06ZNG5588knWrFnDzJkzsdlstGnThueee45mzZoxfPhwevXqRUpKCnPn\nziUkJKT+/8OKiNQB7USLiJzG7t276dmzZ02APunSSy8lJCSErVu34u7uzvz58/nuu++wWq388MMP\nAKSmpjJu3Di++eYbOnbsyKxZs2o+HxAQwCOPPMLw4cOZMGECq1evplu3bsyfP59ly5aRnJx81iMj\nVVVVfPHFF7zyyitMmjSJqqoq/vGPfzBmzBg+//xz3nzzTZ555pmaXeaqqiqWLFlSE6BPGjRoEFu2\nbAFg06ZNxMXFERcXx08//URWVhb+/v6EhobyySefkJOTw+LFi1mwYAHLly9n9erVABw4cIDZs2cz\nY8YMAAzDYMqUKYSHh/Pkk09SWFjIK6+8wnvvvceiRYsYOnQoL7/8ck0Nw4YNY9myZQrQItKoaCda\nROQ0zGYzZ2rqGhsbS1BQEB9//DH79+/nwIEDlJeXA9ChQwcGDBgAwI033sjjjz9+2nFGjBjB9u3b\n+eCDD9i/fz/Hjx+vGed0xo4dC0C3bt1o3rw5e/fuZf369ezfv5+ZM2cCYLPZOHz4MHDi6MapDBw4\nkBdffJF9+/YRHh6Ot7c3gwcPZuPGjZSVlTF48GDgxK78TTfdhMViwdvbm5EjR7JhwwaGDx9OREQE\n/v7+NWPOmzePkpISvv/+ewC2bdtGTk4OCQkJwIljMoGBgTXP9+7d+4y/VhGRhkghWkTkNHr06MHc\nuXMxDAOTyVTz/VdffZXBgwdTVlbGzJkzSUhI4Oabb+bYsWM1odvN7X9/vBqGgcViOe08c+bMYdmy\nZYwdO5bBgweTmpp6xvAO/GI8h8OBm5sbDoeD2bNnExQUBEBeXh6hoaGsWLECLy+vU47TrVs3Dh06\nxI8//lhz9nnIkCF88sknWK1Wrrnmmpo5fs4wDOx2O8Bvxu7bty/du3dn2rRpzJw5E7vdTr9+/Xjr\nrbcAsFqtlJWV1Tzv6el5xl+riEhDpOMcIiKnERMTQ0hICLNmzaoJjD/++COff/45UVFRbNiwgeuu\nu44xY8YQGhpKYmJizXMZGRmkpKQAsHDhQoYNG/aLsS0WCzabDYB169Zx2223MWrUKEwmE3v27PlN\naP21JUuWALBjxw6Ki4vp3LkzAwcOZO7cucCJFxdHjRpFRUXFGccxmUz06NGDBQsWMHToUABCQ0Ox\n2+1s3bqVmJgY4MSO9aJFi7Db7VRUVPDVV1/V7LT/WteuXRk/fjxpaWmsWrWK3r17k5ycTEZGBgBv\nvPHGGc98i4g0BtqJFhE5DZPJxBtvvMH06dMZMWIEbm5uNGvWjH//+9+EhoZy66238vjjj/Ptt9/i\n4eFBnz59yMzMBCAwMJCZM2dy6NAhunTpwrRp034xdq9evZg1axYvv/wy48aNY+rUqbz//vv4+vrS\nt29fMjMzadeu3WlrO3z4MDfddBMA//znP7FYLEyZMoVnnnmGkSNHAvDiiy/i5+d31l/nwIED2bx5\nM926dav5XkxMDHv37q3ZJb7ttts4cOAAo0ePprq6mlGjRnHVVVexcePGU47p4eHB1KlTmTRpEl9/\n/TXPP/88jz76KA6HgxYtWpz1ej8RkYbOZJzt/xmKiEitZGZmkpCQwMqVK+tl/Pj4eB5++OHT7gSL\niEj903EOEREREZFa0k60iIiIiEgtaSdaRERERKSWFKJFRERERGpJIVpEREREpJYUokVEREREakkh\nWkRERESklhSiRURERERq6f8Bq64jIcKrUTgAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11daf4ba8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "\n",
    "delta = 0.035\n",
    "n = 0.01\n",
    "g = 0.015\n",
    "s = 0.30\n",
    "alpha = 0.5\n",
    "\n",
    "Eh = 1/2\n",
    "E1 = 1\n",
    "E2 = 2\n",
    "\n",
    "output_per_worker = np.zeros((201, 5))\n",
    "\n",
    "for i in range(201):\n",
    "    lowestkoverl = 0\n",
    "    output_per_worker[i, 0] = lowestkoverl + i/4\n",
    "    output_per_worker[i, 1] = (delta+n+g)/s * output_per_worker[i, 0]\n",
    "    output_per_worker[i, 2] = (output_per_worker[i, 0] ** alpha) * Eh**(1-alpha)\n",
    "    output_per_worker[i, 3] = (output_per_worker[i, 0] ** alpha) * E1**(1-alpha)\n",
    "    output_per_worker[i, 4] = (output_per_worker[i, 0] ** alpha) * E2**(1-alpha)\n",
    "    \n",
    "output_per_worker_df = DataFrame(data = output_per_worker, \n",
    "    columns = [\"Capital_per_Worker\", \"Equilibrium Condition\", \n",
    "    \"Output per_Worker (E=0.5)\", \"Output per_Worker (E=1)\",\n",
    "    \"Output per_Worker (E=2)\"])\n",
    "\n",
    "output_per_worker_df.set_index('Capital_per_Worker').plot()\n",
    "plt.xlabel(\"Capital per Worker\")\n",
    "plt.ylabel(\"Output per Worker\")\n",
    "plt.ylim(0, )\n",
    "\n",
    "plt.title(\"Equilibrium Is Where the Curves Cross\", size = 20)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "----\n",
    "\n",
    "&nbsp;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4.3.3.3 Off the Balanced Growth Path\n",
    "\n",
    "To calculate what output per worker would be if the economy were to be on its balanced-growth path is a straightforward three-step procedure:\n",
    "\n",
    "1. Calculate the balanced-growth equilibrium capital-output ratio s/(n + g + δ), the saving rate s divided by the sum of the labor-force growth rate n, the efficiency of labor growth rate g, and the depreciation rate δ.\n",
    "2. Raise the balanced-growth capital-output ratio to the α/(l-α) power, where α is the diminishing-retums-to-investment parameter in the production function. \n",
    "3. Multiply the result by the current value of the efficiency of labor E. The result is the current value of what output per worker would be if the economy were on its balanced growth path, and the path traced out by that result as E grows over time is the balanced-growth path for output per worker.\n",
    "\n",
    "But is this of use if the economy is not on its balanced growth path?\n",
    "\n",
    "How can we use a model which assumes that the economy is on its balanced-growth path to analyze a sit  uation in which the economy is not on that path? We still can use the model—and this is an important part of the magic of economics—because being on the balanced-growth path is an equilibrium condition. In an economic model, the thing to do if an equilibrium condition is not satisfied is to wait and, after a while, look again. When we look again, it will be satisfied.\n",
    "\n",
    "Whenever the capital-output ratio K/Y is above its balanced-growth equilibrium value s/(n + g + δ), K/Y is falling: Investment is insufficient to keep the capital stock growing as fast as output. Whenever K/Y is below its balanced-growth equilibrium value, K/Y is rising: Capital stock growth outruns output. And as the capital-output ratio converges to its balanced-growth value, so does the economy’s level of output per worker converge to its balanced-growth path.\n",
    "\n",
    "The fact that an economy converges to its balanced-growth path makes analyzing the _long-run_ growth of an economy relatively easy as well even when the economy is not on its balanced-growth path:\n",
    "\n",
    "1. Calculate the balanced-growth path.\n",
    "2. From the balanced-growth path, forecast the future of the economy: If the economy is on its balanced-growth path today, it will stay on that path in the future (unless some of the parameters—n, g, δ, s, and α—change).\n",
    "3. If those parameters change, calculate the new, shifted balanced-growth path and predict that the economy will head for it.\n",
    "4. If the economy is not on its balanced-growth path today, it is heading for that path—and will get there, eventually.\n",
    "\n",
    "Thus _long run_ economic forecasting becomes simple. All you have to do is predict that the economy will head for its balanced-growth path, and calculate what the balanced-growth path is.\n",
    "\n",
    "----\n",
    "\n",
    "&nbsp;"
   ]
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    "### 4.3.3.4 Converging to the Balanced Growth Path\n",
    "\n",
    "How fast does an economy head for its balanced-growth path? Does the convergence of an economy following the Solow growth model to its balanced-growth path take a year, or five years, or is it a matter of decades?\n",
    "\n",
    "It is a matter of decades. But to see this requires more algebra:\n",
    "\n",
    "Those of you for whom calculus is a tool and an intellectual force multiplier rather than a ritualistic obstacle to thought can start with the output form of the production function:\n",
    "\n",
    "(4.3.9)&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;\n",
    "$ Y = K^α(EL)^{(1-α)}  $\n",
    "\n",
    "Take first logarithms, and then derivatives to obtain:\n",
    "\n",
    "(4.3.10)&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;\n",
    "$\\frac{d(ln(Y_{t}))}{dt} = \\alpha\\frac{d(ln(K_t))}{dt} + (1-\\alpha)\\frac{d(ln(E_t))}{dt} + (1-\\alpha)\\frac{d(ln(L_t))}{dt}$\n",
    "\n",
    "Note that since the derivative of a logarithm is simply a proportional growth rate, that (4.3.10) is an equation that tells us that—on or off of the balanced-growth path—the proportional growth rate of output is a function of the parameter α and of the growth rates of the capital stock, the labor force, and the efficiency of labor.\n",
    "\n",
    "To keep those of you for whom math is not so much a tool and intellectual force multiplier on the same page, we are simply going to write \"g<sub>x</sub>\" for the proportional growth rate of an economic variable X. Thus g<sub>Y</sub> is the proportional growth rate of output Y. g<sub>K</sub> is the proportional growth rate of the capital stock K. And so forth. \n",
    "\n",
    "(4.3.10) can then become a friendlier form: an equation about growth rates, an equation the truth of which isbuilt into the definitions of logarithms, proportional growth rates, and the Cobb-Douglas production function:\n",
    "\n",
    "(4.3.10')&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;\n",
    "$ g_Y = αg_K + (1-α)g_L + (1-α)g_E  $\n",
    "\n",
    "We know what the proportional growth rates of the labor force L and labor efficiency E are in the Solow model: they are n and g:\n",
    "\n",
    "(4.3.11)&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;\n",
    "$ g_Y = αg_K + (1-α)(n + g)  $\n",
    "\n",
    "Now subtract both sides of this from the growth rate of the capital stock:\n",
    "\n",
    "(4.3.12)&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;\n",
    "$ g_K - g_Y = (1-α)g_K - (1-α)(n + g)  $\n",
    "\n",
    "We are almost done. Then to determine what the growth rate of the capital stock is, we simply take its change, sY - δK, and divide it by its level, K—but only on the right hand side:\n",
    "\n",
    "(4.3.13)&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;\n",
    "$ g_K - g_Y = (1-α)\\left(s\\left(\\frac{Y}{K}\\right) - δ\\right) - (1-α)(n + g)  $\n",
    "\n",
    "The proportional growth rate of the quotient of two variables is just the difference between the proportional growth rates of the numerator and the denominator. Thus the left hand side is:\n",
    "\n",
    "(4.3.14)&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;\n",
    "$ g_{K/Y} = (1-α)s\\left(\\frac{Y}{K}\\right) - (1-α)(n + g + δ)  $\n",
    "\n",
    "And since the proportional growth rate of a variable is its rate of change divided by its level, the left hand side is:\n",
    "\n",
    "(4.3.15)&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;\n",
    "$ \\frac{d(K/Y)/dt}{K/Y} = (1-α)s\\left(\\frac{Y}{K}\\right) - (1-α)(n + g + δ)  $\n",
    "\n",
    "Getting rid of the denominator on the left-hand side:\n",
    "\n",
    "(4.3.16)&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;\n",
    "$ \\frac{d(K/Y)}{dt} = (1-α)s - (1-α)(n + g + δ)\\left(\\frac{K}{Y}\\right)  $\n",
    "\n",
    "(4.3.17)&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;\n",
    "$ \\frac{d(K/Y)}{dt} = - (1-α)(n + g + δ)\\left(\\frac{K}{Y} - \\frac{s}{n + g + δ}\\right)  $\n",
    "\n",
    "This equation tells us three things:\n",
    "\n",
    "* When the capital-output ratio K/Y is equal to s/(n+g+δ), it is indeed the case that it is stable.\n",
    "\n",
    "* When K/Y is above that s/(n+g+δ) value, it is falling; when it is below, it is rising.\n",
    "\n",
    "* The speed with which it is falling or rising is always proportional to the gap between K/Y and s/(n+g+δ), with the factor of proportionality equal to (1-α)(n+g+δ)\n",
    "\n",
    "----\n",
    "\n",
    "&nbsp;"
   ]
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    "**Figure 4.3.7: Convergence to a Balanced-Growth Path Capital-Output Ratio of 4**\n",
    "\n",
    "<img style=\"display:block; margin-left:auto; margin-right:auto;\" src=\"http://delong.typepad.com/.a/6a00e551f08003883401bb09f0e868970d-pi\" alt=\"Convergence\" title=\"Convergence.png\" border=\"0\" width=\"600\" height=\"463\" />\n",
    "\n",
    "Suppose the balanced- growth equilibrium capital-output ratio is 4. Whether the capital-output ratio starts above or below its balanced-growth equilibrium value, it converges to the level equal to s/(n + g + δ)\n",
    "\n",
    "----\n",
    "\n",
    "&nbsp;"
   ]
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    "### 4.3.3.5 Solving for the Time Path of the Capital-Output Ratio\n",
    "\n",
    "This march through algebra has just confirmed the arguments made so far. So what extra good—besides serving as a check on correctness—has this algebra done us?\n",
    "\n",
    "It has done us good because equation (4.3.17) is a very special equation: it has a rate of change of something on the left hand side. It has the level of something on the right hand side. It has a negative constant multiplying the level. It is a _convergent exponential_. The function that satisfies this equation is:\n",
    "\n",
    "(4.3.18)&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;\n",
    "$ \\frac{K_t}{Y_t} = \\frac{s}{\\delta + n + g} + \\left(C - \\frac{s}{\\delta + n + g}\\right) e^{-(1 - \\alpha)(\\delta + g + n)t}  $\n",
    "\n",
    "for the appropriate constant C.\n",
    "\n",
    "What is the value of this constant C? Well, we know what the capital-output ratio is right now, when we start our analysis, which we might as well take to be the time t = 0. If we do take now to be time t = 0, and take K<sub>0</sub>/Y<sub>0</sub> for the capital output tday, then we can substitute in for the constant C:\n",
    "\n",
    "(4.3.19)&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;\n",
    "$ \\frac{K_t}{Y_t} = \\frac{s}{\\delta + n + g} + \\left(\\frac{K_0}{Y_0} - \\frac{s}{\\delta + n + g}\\right) e^{-(1 - \\alpha)(\\delta + g + n)t}  $\n",
    "\n",
    "And:\n",
    "\n",
    "(4.3.20)&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;\n",
    "$\\frac{Y_t}{L_t} = \\left(\\frac{s}{\\delta + n + g} + \\left(\\frac{K_0}{Y_0} - \\frac{s}{\\delta + n + g}\\right) e^{-(1 - \\alpha)(\\delta + g + n)t}\\right)^\\left(\\frac{\\alpha}{1-\\alpha}\\right)\\left(E_t\\right)  $\n",
    "\n",
    "This tells us that, when it is off the equilibrium balanced-growth path, the capital-output ratio of a Solow growth model economy is a weighted average of (a) its initial capital-output ratio K<sub>0</sub>/Y<sub>0</sub> and (b) its long-run balanced-growth capital-output ratio s/(n+g+δ), with the weight placed on the first declining exponentially according to the function exp(-(1-α)(n + g + δ)t)\n",
    "\n",
    "This tells us that, in the Solow growth model, an economy will close a fraction (1 — α)(n + g + δ) of the gap between its current position and the balanced-growth path each year. If α = 1/3, n = 1% per year, g = 1.5% per year, and δ = 3.5% per year, then (1 — α)(n + g + δ) turns out to be equal to 4% per year: 0.04. Then the capital-output ratio will close 4% percent of the gap between its current level and its balanced-growth value each year. According to the Rule of 72, an economy closing 4 percent of the gap between its current and its equilibrium value each year will move halfway to equilibrium in 72/4, or 18, years. It would close three-quarters of the gap in 36 years.\n",
    "\n",
    "The Solow growth model is thus definitely a long-run model. It predicts that in the short run things will pretty much stay as they have been. If that is not right—if there are interesting and important fluctuations in the short run—the Solow model knows nothing about them. For them we will have to turn to the models of Chapter 6 and beyond."
   ]
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    "# convergence to the balanced growth path\n",
    "#\n",
    "# we need to alter our dataframe in order to add a BGP line\n",
    "#\n",
    "# # we are going to want to see what happens for lots of\n",
    "# different model parameter values and initial conditions,\n",
    "# so stuff our small simulation program inside a function, so \n",
    "# we can then invoke it with a single line...\n",
    "\n",
    "def sgm_bgp_100yr_run(L0, E0, K0, n=0.01, g=0.02, s=0.15, alpha=0.5, delta=0.03, T = 100):\n",
    "\n",
    "    sg_df = pd.DataFrame(index=range(T),columns=['Labor', \n",
    "        'Efficiency',\n",
    "        'Capital',\n",
    "        'Output',\n",
    "        'Output_per_Worker',\n",
    "        'Capital_Output_Ratio',\n",
    "        'BGP_Output',\n",
    "        'BGP_Output_per_Worker',\n",
    "        'BGP_Capital_Output_Ratio',\n",
    "        'BGP_Capital'],\n",
    "        dtype='float')\n",
    "\n",
    "    sg_df.Labor[0] = L0\n",
    "    sg_df.Efficiency[0] = E0\n",
    "    sg_df.Capital[0] = K0\n",
    "    sg_df.Output[0] = (sg_df.Capital[0]**alpha * (sg_df.Labor[0] * sg_df.Efficiency[0])**(1-alpha))\n",
    "    sg_df.Output_per_Worker[0] = sg_df.Output[0]/sg_df.Labor[0]\n",
    "    sg_df.Capital_Output_Ratio[0] = sg_df.Capital[0]/sg_df.Output[0]\n",
    "    sg_df.BGP_Capital_Output_Ratio[0] = (s / (n + g + delta))\n",
    "    sg_df.BGP_Output_per_Worker[0] = sg_df.Efficiency[0] * sg_df.BGP_Capital_Output_Ratio[0]*(alpha/(1 - alpha))\n",
    "    sg_df.BGP_Output[0] = sg_df.BGP_Output_per_Worker[0] * sg_df.Labor[0]\n",
    "    sg_df.BGP_Capital[0] = sg_df.Labor[0] * sg_df.Efficiency[0] * sg_df.BGP_Capital_Output_Ratio[0]*(1/(1 - alpha))\n",
    "\n",
    "    for i in range(T):\n",
    "        sg_df.Labor[i+1] = sg_df.Labor[i] + sg_df.Labor[i] * n\n",
    "        sg_df.Efficiency[i+1] = sg_df.Efficiency[i] + sg_df.Efficiency[i] * g\n",
    "        sg_df.Capital[i+1] = sg_df.Capital[i] - sg_df.Capital[i] * delta + sg_df.Output[i] * s \n",
    "        sg_df.Output[i+1] = (sg_df.Capital[i+1]**alpha * (sg_df.Labor[i+1] * sg_df.Efficiency[i+1])**(1-alpha))\n",
    "        sg_df.Output_per_Worker[i+1] = sg_df.Output[i+1]/sg_df.Labor[i+1]\n",
    "        sg_df.Capital_Output_Ratio[i+1] = sg_df.Capital[i+1]/sg_df.Output[i+1]\n",
    "        sg_df.BGP_Capital_Output_Ratio[i+1] = (s / (n + g + delta))\n",
    "        sg_df.BGP_Output_per_Worker[i+1] = sg_df.Efficiency[i+1] * sg_df.BGP_Capital_Output_Ratio[i+1]**(alpha/(1 - alpha))\n",
    "        sg_df.BGP_Output[i+1] = sg_df.BGP_Output_per_Worker[i+1] * sg_df.Labor[i+1]\n",
    "        sg_df.BGP_Capital[i+1] = (s / (n + g + delta))**(1/(1-alpha)) * sg_df.Efficiency[i+1] * sg_df.Labor[i+1]\n",
    "        \n",
    "    fig = plt.figure(figsize=(12, 12))\n",
    "\n",
    "    ax1 = plt.subplot(3,2,1)\n",
    "    sg_df.Labor.plot(ax = ax1, title = \"Labor Force\")\n",
    "    plt.ylabel(\"Parameters\")\n",
    "    plt.ylim(0, )\n",
    "\n",
    "    ax2 = plt.subplot(3,2,2)\n",
    "    sg_df.Efficiency.plot(ax = ax2, title = \"Efficiency of Labor\")\n",
    "    plt.ylim(0, )\n",
    "    \n",
    "    ax3 = plt.subplot(3,2,3)\n",
    "    sg_df.BGP_Capital.plot(ax = ax3, title = \"BGP Capital Stock\")\n",
    "    sg_df.Capital.plot(ax = ax3, title = \"Capital Stock\")\n",
    "    plt.ylabel(\"Values\")\n",
    "    plt.ylim(0, )\n",
    "\n",
    "    ax4 = plt.subplot(3,2,4)\n",
    "    sg_df.BGP_Output.plot(ax = ax4, title = \"BGP Output\")\n",
    "    sg_df.Output.plot(ax = ax4, title = \"Output\")\n",
    "    plt.ylim(0, )\n",
    "\n",
    "    ax5 = plt.subplot(3,2,5)\n",
    "    sg_df.BGP_Output_per_Worker.plot(ax = ax5, title = \"BGP Output per Worker\")\n",
    "    sg_df.Output_per_Worker.plot(ax = ax5, title = \"Output per Worker\")\n",
    "    plt.xlabel(\"Years\")\n",
    "    plt.ylabel(\"Ratios\")\n",
    "    plt.ylim(0, )\n",
    "\n",
    "    ax6 = plt.subplot(3,2,6)\n",
    "    sg_df.BGP_Capital_Output_Ratio.plot(ax = ax6, title = \"BGP Capital-Output Ratio\")\n",
    "    sg_df.Capital_Output_Ratio.plot(ax = ax6, title = \"Capital-Output Ratio\")\n",
    "    plt.xlabel(\"Years\")\n",
    "    plt.ylim(0, )\n",
    "\n",
    "    plt.suptitle('Solow Growth Model: Simulation Run', size = 20)\n",
    "\n",
    "    plt.show()\n",
    "    \n",
    "    print(n, \"is the labor force growth rate\")\n",
    "    print(g, \"is the efficiency of labor growth rate\")\n",
    "    print(delta, \"is the depreciation rate\")\n",
    "    print(s, \"is the savings rate\")\n",
    "    print(alpha, \"is the decreasing-returns-to-scale parameter\")"
   ]
  },
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    {
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I66+/bn6+mJgY5s2bh729PXPnzmXkyJFFtsdKRB5c/fr1w9b27xG7VapU4dtv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/GfNYfIcxRi7HyUaGsk0/pdGuiQzqlTNvDJycncfffdWK1W3nrrLWw2Gx9//DHPPvsszz777Gl3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U6d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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11d962c88>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.05 is the labor force growth rate\n",
      "0.01 is the efficiency of labor growth rate\n",
      "0.03 is the depreciation rate\n",
      "0.225 is the savings rate\n",
      "0.5 is the decreasing-returns-to-scale parameter\n"
     ]
    }
   ],
   "source": [
    "sgm_bgp_100yr_run(1000, 1, 100, n=0.05, g=0.01, s=0.225, alpha=0.5, delta=0.03)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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lbGyMadOmYdq0aUhISMCVK1dw+fJlnD17Fv/++y+mTZuGnTt3wsXF5YXtlH4+jIyMAJR9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\nqeMQkRWzrrX4zFBZZTn+nf4d2rRywEuhz/GjSyKyGA3tLLxz5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REREZElYdNNRERERGRi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\nREQmxqabiIiIiMjE/j8o496rIUwvbwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11d86b358>"
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     "text": [
      "0.05 is the labor force growth rate\n",
      "0.01 is the efficiency of labor growth rate\n",
      "0.03 is the depreciation rate\n",
      "0.24 is the savings rate\n",
      "0.5 is the decreasing-returns-to-scale parameter\n"
     ]
    }
   ],
   "source": [
    "# convergence to the balanced growth path—log graphs\n",
    "#\n",
    "# we need to alter our dataframe in order to add a BGP line\n",
    "#\n",
    "# # we are going to want to see what happens for lots of\n",
    "# different model parameter values and initial conditions,\n",
    "# so stuff our small simulation program inside a function, so \n",
    "# we can then invoke it with a single line...\n",
    "\n",
    "def log_sgm_bgp_100yr_run(L0, E0, K0, n=0.01, g=0.02, s=0.15, alpha=0.5, delta=0.03, T=100):\n",
    "\n",
    "    sg_df = pd.DataFrame(index=range(T),columns=['Labor', \n",
    "        'Efficiency',\n",
    "        'Capital',\n",
    "        'Output',\n",
    "        'Output_per_Worker',\n",
    "        'Capital_Output_Ratio',\n",
    "        'BGP_Output',\n",
    "        'BGP_Output_per_Worker',\n",
    "        'BGP_Capital_Output_Ratio',\n",
    "        'BGP_Capital'],\n",
    "        dtype='float')\n",
    "\n",
    "    sg_df.Labor[0] = L0\n",
    "    sg_df.Efficiency[0] = E0\n",
    "    sg_df.Capital[0] = K0\n",
    "    sg_df.Output[0] = (sg_df.Capital[0]**alpha * (sg_df.Labor[0] * sg_df.Efficiency[0])**(1-alpha))\n",
    "    sg_df.Output_per_Worker[0] = sg_df.Output[0]/sg_df.Labor[0]\n",
    "    sg_df.Capital_Output_Ratio[0] = sg_df.Capital[0]/sg_df.Output[0]\n",
    "    sg_df.BGP_Capital_Output_Ratio[0] = (s / (n + g + delta))\n",
    "    sg_df.BGP_Output_per_Worker[0] = sg_df.Efficiency[0] * sg_df.BGP_Capital_Output_Ratio[0]*(alpha/(1 - alpha))\n",
    "    sg_df.BGP_Output[0] = sg_df.BGP_Output_per_Worker[0] * sg_df.Labor[0]\n",
    "    sg_df.BGP_Capital[0] = (s / (n + g + delta))**(1/(1-alpha)) * sg_df.Efficiency[0] * sg_df.Labor[0]\n",
    "\n",
    "    for i in range(T):\n",
    "        sg_df.Labor[i+1] = sg_df.Labor[i] + sg_df.Labor[i] * n\n",
    "        sg_df.Efficiency[i+1] = sg_df.Efficiency[i] + sg_df.Efficiency[i] * g\n",
    "        sg_df.Capital[i+1] = sg_df.Capital[i] - sg_df.Capital[i] * delta + sg_df.Output[i] * s \n",
    "        sg_df.Output[i+1] = (sg_df.Capital[i+1]**alpha * (sg_df.Labor[i+1] * sg_df.Efficiency[i+1])**(1-alpha))\n",
    "        sg_df.Output_per_Worker[i+1] = sg_df.Output[i+1]/sg_df.Labor[i+1]\n",
    "        sg_df.Capital_Output_Ratio[i+1] = sg_df.Capital[i+1]/sg_df.Output[i+1]\n",
    "        sg_df.BGP_Capital_Output_Ratio[i+1] = (s / (n + g + delta))\n",
    "        sg_df.BGP_Output_per_Worker[i+1] = sg_df.Efficiency[i+1] * sg_df.BGP_Capital_Output_Ratio[i+1]**(alpha/(1 - alpha))\n",
    "        sg_df.BGP_Output[i+1] = sg_df.BGP_Output_per_Worker[i+1] * sg_df.Labor[i+1]\n",
    "        sg_df.BGP_Capital[i+1] = (s / (n + g + delta))**(1/(1-alpha)) * sg_df.Efficiency[i+1] * sg_df.Labor[i+1]\n",
    "\n",
    "        \n",
    "    fig = plt.figure(figsize=(12, 12))\n",
    "\n",
    "    ax1 = plt.subplot(3,2,1)\n",
    "    np.log(sg_df.Labor).plot(ax = ax1, title = \"Labor Force\")\n",
    "    plt.ylabel(\"Parameters\")\n",
    "    plt.ylim(0, )\n",
    "\n",
    "    ax2 = plt.subplot(3,2,2)\n",
    "    np.log(sg_df.Efficiency).plot(ax = ax2, title = \"Efficiency of Labor\")\n",
    "    plt.ylim(0, )\n",
    "    \n",
    "    ax3 = plt.subplot(3,2,3)\n",
    "    np.log(sg_df.BGP_Capital).plot(ax = ax3, title = \"BGP Capital Stock\")\n",
    "    np.log(sg_df.Capital).plot(ax = ax3, title = \"Capital Stock\")\n",
    "    plt.ylabel(\"Values\")\n",
    "    plt.ylim(0, )\n",
    "\n",
    "    ax4 = plt.subplot(3,2,4)\n",
    "    np.log(sg_df.BGP_Output).plot(ax = ax4, title = \"BGP Output\")\n",
    "    np.log(sg_df.Output).plot(ax = ax4, title = \"Output\")\n",
    "    plt.ylim(0, )\n",
    "\n",
    "    ax5 = plt.subplot(3,2,5)\n",
    "    np.log(sg_df.BGP_Output_per_Worker).plot(ax = ax5, title = \"BGP Output per Worker\")\n",
    "    np.log(sg_df.Output_per_Worker).plot(ax = ax5, title = \"Output per Worker\")\n",
    "    plt.xlabel(\"Years\")\n",
    "    plt.ylabel(\"Ratios\")\n",
    "    plt.ylim(0, )\n",
    "\n",
    "    ax6 = plt.subplot(3,2,6)\n",
    "    np.log(sg_df.BGP_Capital_Output_Ratio).plot(ax = ax6, title = \"BGP Capital-Output Ratio\")\n",
    "    np.log(sg_df.Capital_Output_Ratio).plot(ax = ax6, title = \"Capital-Output Ratio\")\n",
    "    plt.xlabel(\"Years\")\n",
    "    plt.ylim(0, )\n",
    "\n",
    "    plt.suptitle('Solow Growth Model: Simulation Run', size = 20)\n",
    "\n",
    "    plt.show()\n",
    "    \n",
    "    print(n, \"is the labor force growth rate\")\n",
    "    print(g, \"is the efficiency of labor growth rate\")\n",
    "    print(delta, \"is the depreciation rate\")\n",
    "    print(s, \"is the savings rate\")\n",
    "    print(alpha, \"is the decreasing-returns-to-scale parameter\")\n",
    "    \n",
    "log_sgm_bgp_100yr_run(1000, 1, 100, n=0.05, g=0.01, s=0.24, alpha=0.5, delta=0.03)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "----\n",
    "\n",
    "&nbsp;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Box 4.3.4: How Fast Do Economies Converge?: An Example**\n",
    "\n",
    "Consider an economy in which the rate of labor-force growth n = 1 percent per year, in which the efficiency of labor grows at a rate g = 2 percent per year, in which the depreciation rate δ = 5 percent per year, and in which the diminishing-returns-to-investment parameter α = 1/2.\n",
    "\n",
    "This economy will, according to the Solow growth model, each year close a fraction of the gap between its current capital-output ratio and its balanced-growth capital-output ratio equal to:\n",
    "\n",
    "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;\n",
    "$ (1-\\alpha)(n+g+\\delta) = \\left(1-\\frac{1}{2}\\right) (0.01+0.02+0.05) = 0.04  $\n",
    "\n",
    "That is 4 percent per year. According to the rule of 72, the economy's capital-output ratio will close half of the gap to its balanced growth path value in 18 years.\n",
    "\n",
    "----\n",
    "\n",
    "&nbsp;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Box 4.3.5: The Return of the West German Economy to Its Balanced-Growth Path**\n",
    "\n",
    "Economies do converge to and then remain on their balanced-growth paths. The West German economy after World War II is a case in point.\n",
    "\n",
    "We can see such convergence in action in many places and times. For example, consider the post-World War II history of West Germany. The defeat of the Nazis left the German economy at the end of World War II in ruins. Output per worker was less than one-third of its prewar level. The economy’s capital stock had been wrecked and devastated by three years of American and British bombing and then by the ground campaigns of the last six months of the war. But in the years immediately after the war, the West German economy’s capital-output ratio rapidly grew and con  verged back to its prewar value. As Figure 4.11 shows, within 12 years the West German economy had closed half the gap back to its pre-World War II growth path. And within 30 years the West German economy had effectively closed the entire gap between where it had started at the end of World War II and its balanced-growth path.\n",
    "\n",
    "----\n",
    "\n",
    "&nbsp;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Figure 4.3.8: \n",
    "\n",
    "<img style=\"display:block; margin-left:auto; margin-right:auto;\" src=\"http://delong.typepad.com/.a/6a00e551f08003883401b8d2d7ee5e970c-pi\" alt=\"German convergence\" title=\"German_convergence.png\" border=\"0\" width=\"600\" height=\"430\" />\n",
    "\n",
    "###### Source: J. Bradford DeLong and Barry Eichengreen, \"The Marshall Plan: History's Most Successful Structural Adjustment Programme,\" in Rudiger Dornbusch, Willhelm Nolling, and Richard Layard, eds., Postwar Economic Reconstruction and Lessons for the East Today (Cambridge, MA: MIT Press, 1993), pp. 189-230.\n",
    "\n",
    "----\n",
    "\n",
    "&nbsp;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4.3.4 RECAP: Understanding the Solow Growth Model\n",
    "\n",
    "**When the economy’s capital stock and its level of real GDP are growing at the same proportional rate, its capital-output ratio—the ratio of the econ  omy’s capital stock K to annual real GDP Y—is constant, and the economy is in balanced-growth equilibrium. In equilibrium, the capital-output ratio K/Y will equal the constant ratio s/(n + g + 8). The standard growth model analyzes how this balanced-growth equilibrium is determined by four factors: the economy’s saving-investment rate s, the economy’s labor-force growth rate n, the growth rate of the efficiency of labor g, and the capital stock depreciation rate 8.**\n",
    "\n",
    "**According to the Solow growth model, capital intensity and growth in the efficiency of labor together determine the destiny of an economy. The value of the balanced-growth equilibrium capital-output ratio and the economy's diminishing-returns-to-investment parameter determine the multiple that balanced- growth output per worker is of the current efficiency of labor. The growth rate of output per worker along the economy’s balanced-growth path is equal to the growth rate of the efficiency of labor. And if the economy is not on its balanced-growth path, the Solow growth model tells us that it is converging to it—although this convergence takes decades, not years.**\n",
    " \n",
    "----\n",
    "\n",
    "&nbsp;\n",
    "\n",
    "#### GLOSSARY\n",
    "\n",
    "**Balanced growth**: When output per worker Y/L and capital per worker K/L are growing at the same rate.\n",
    "\n",
    "**Balanced-growth path equilibrium steady-state capital- output ratio**: The value of the capital- output ratio to which an economy with constant saving rate, depreciation rate, labor-force growth rate, and efficiency growth rate converges overtime. Equal to s/(n + g + δ).\n",
    "\n",
    "**Convergence**: The tendency for a country to approach its balanced-growth path with a constant capital-output ratio.\n",
    "\n",
    "\n",
    "----\n",
    "\n",
    "&nbsp;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4.3.4 Exercises: Understanding the Solow Growth Model\n",
    "\n",
    "**Task 1: Equilibrium Output per Worker Graphically**\n",
    "\n",
    "The code cell immediately below contains a small program to plot the balanced-growth path output per worker and capital per worker levels graphically for values of the parameters n, g, δ, α, and s, and for the current level of the efficiency of labor E. It is set to calculate for n = 0, g= 0, δ = .03, α = 0.5, s = 0.15, and E = 1.\n",
    "\n",
    "Alter the inputs to the cell above the line of \"# ----\" and rerun the cell multiple times, or use some other means of your choosing, to set the variables in the further cells below:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true,
    "jupyter": {
     "outputs_hidden": true
    }
   },
   "outputs": [],
   "source": [
    "delta = 0.03\n",
    "n = 0\n",
    "g = 0\n",
    "s = 0.15\n",
    "alpha = 0.5\n",
    "E = 1\n",
    "lowestKoverLconsidered = 0\n",
    "\n",
    "#----\n",
    "\n",
    "array = np.zeros((201, 3))\n",
    "\n",
    "for i in range(201):\n",
    "    array[i, 0] = lowestKoverLconsidered + i/4\n",
    "    array[i, 1] = (array[i, 0] \n",
    "        ** alpha) * E**(1 - alpha)\n",
    "    array[i, 2] = ((delta + n + g)/s * array[i, 0] )\n",
    "\n",
    "capital_and_output_per_worker_df = DataFrame(data = \n",
    "    array, columns = [\"Capital_per_Worker\", \"Output_per_Worker\", \n",
    "    \"Equilibrium Condition\"])\n",
    "\n",
    "capital_and_output_per_worker_df.set_index('Capital_per_Worker').plot()\n",
    "\n",
    "plt.xlabel(\"Capital per Worker\")\n",
    "plt.ylabel(\"Output per Worker\")\n",
    "plt.ylim(0, )\n",
    "plt.title(\"Balanced Growth Equilibrium Is Where the Curves Cross\", size = 20)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true,
    "jupyter": {
     "outputs_hidden": true
    }
   },
   "outputs": [],
   "source": [
    "# 1.1 For n = 0, g= 0, δ = .03, α = 0.5, \n",
    "# s = 0.15, and E = 1.\n",
    "\n",
    "YoverL11 = ___\n",
    "KoverL11 = ___\n",
    "\n",
    "# 1.2 For n = 0.01, g = 0.01, δ = .03, α = 0.3333, \n",
    "# s = 0.25, and E = 2.\n",
    "\n",
    "YoverL12 = ___\n",
    "KoverL12 = ___\n",
    "\n",
    "# 1.3 For n = 0.01, g= 0.02, δ = .03, α = 0.3333, \n",
    "# s = 0.36, and E = 1.\n",
    "\n",
    "YoverL13 = ___\n",
    "KoverL13 = ___\n",
    "\n",
    "# 1.4 For n = .01, g= 0.02, δ = .03, α = 0.4, \n",
    "# s = 0.50, and E = 1.\n",
    "\n",
    "YoverL14 = ___\n",
    "KoverL14 = ___\n",
    "\n",
    "# 1.5 For n = .01, g= 0.02, δ = .03, α = 0.2, \n",
    "# s = 0.50, and E = 1.\n",
    "\n",
    "YoverL15 = ___\n",
    "KoverL15 = ___\n",
    "\n",
    "# 1.6 For n = .01, g= 0.015, δ = .025, α = 0.33333, \n",
    "# s = 0.50, and E = 1\n",
    "\n",
    "YoverL16 = ___\n",
    "KoverL16 = ___\n",
    "\n",
    "# 1.7 For n = .01, g= 0.015, δ = .025, α = 0.9, \n",
    "# s = 0.125, and E = 0.5\n",
    "\n",
    "YoverL17 = ___\n",
    "KoverL17 = ___\n",
    "\n",
    "# 1.8 For n = .01, g= 0.015, δ = .035, α = 0.75, \n",
    "# s = 0.25, and E = 0.5\n",
    "\n",
    "YoverL18 = ___\n",
    "KoverL18 = ___\n",
    "\n",
    "# 1.9 For n = .01, g= 0.015, δ = .025, α = 0.5, \n",
    "# s = 0.5, and E = 0.5\n",
    "\n",
    "YoverL19 = ___\n",
    "KoverL19 = ___"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Catch Our Breath\n",
    "\n",
    "<img src=\"https://tinyurl.com/20181029a-delong\" width=\"300\" style=\"float:right\" />\n",
    "\n",
    "* Ask me two questions…\n",
    "* Make two comments…\n",
    "* Further reading…\n",
    "\n",
    "<br clear=\"all\" />\n",
    "\n",
    "----\n",
    "\n",
    "Understanding the Solow Growth Model: <https://www.icloud.com/keynote/0PejUtBxFLIXN3wTCkbqhadQg>   \n",
    "Lecture Support: <http://nbviewer.jupyter.org/github/braddelong/LSF18E101B/blob/master/Growth%20Theory%20%28Part%20III%2C%20Ch.%204%29/D%26O3_4..3%20Understanding%20the%20Solow%20Growth%20Model.ipynb>\n",
    "\n",
    "&nbsp;\n",
    "\n",
    "----"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## <font color=\"880000\">4.3 Understanding the Solow Growth Model</font>\n",
    "\n",
    "### <font color=\"000088\">Solow Growth Model: Equilibrium</font>\n",
    "\n",
    "#### K/Y = s/(n+g+δ)\n",
    "\n",
    "* <strike>Supply = Demand</strike>\n",
    "\n",
    "* Let's see if we can figure out why this is the equilibrium condition here...\n",
    "\n",
    "&nbsp;\n",
    "\n",
    "### <font color=\"000088\">Solow Growth Model: Equilibrium</font>\n",
    "\n",
    "* Our equilibrium condition is that the capital-output ratio be constant.\n",
    "* When the labor force and/or the efficiency-of-labor are increasing, when the capital-output ratio is constant the economy's equilibrium is not one of stable and stagnant balance but rather one of _balanced growth_. \n",
    "    * Output per worker is then growing at the same rate as the capital stock per worker.\n",
    "    * They are both growing at the same rate as the efficiency of labor.\n",
    "    * Output is growing and the same rate as the capital stock.\n",
    "    * They are growing at the same rate as the sum of labor efficiency growth and labor force growth.\n",
    "    \n",
    "&nbsp;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### <font color=\"000088\">The Balanced Growth Capital-Output Ratio</font>\n",
    "\n",
    "* At what value will the economy’s capital-output ratio be constant?\n",
    "* When K/Y = s/(n + g + δ)\n",
    "* Suppose the economy is in balanced growth. How much is it investing? \n",
    "    * There must be investment equal to δK to replace depreciated capital. \n",
    "    * There must be investment equal to nK to provide for the extra workers in the labor force.\n",
    "    * Since the efficiency of labor is growing at rate g, there must be investment equal to gK in order for the capital stock to keep up with increasing efficiency of labors.\n",
    "* These are the economy's investment requirements\n",
    "    * Set them equal to savings, and the capital-output ratio will be constant.\n",
    "    \n",
    "&nbsp;\n",
    "\n",
    "### <font color=\"000088\">Marching Through Algebra</font>\n",
    "\n",
    "> $ (n + g + δ)K = sY $\n",
    "\n",
    "> $ \\left(\\frac{K}{Y}\\right) = \\frac{s}{n+g+δ}  $\n",
    "\n",
    "This is thus the balanced-growth equilibrium condition. \n",
    "\n",
    "> $ \\frac{Y}{L} = \\left(\\frac{K}{L}\\right)^α \\left(E\\right)^{1-α} $\n",
    "\n",
    "Break the capital-labor ratio down into the capital-output ratio times output per worker:\n",
    "\n",
    "> $ \\frac{Y}{L} = \\left(\\frac{K}{Y}\\frac{Y}{L}\\right)^α \\left(E\\right)^{1-α} $\n",
    "\n",
    "Regroup:\n",
    "\n",
    "> $ \\frac{Y}{L} = \\left(\\frac{Y}{L}\\right)^α\\left(\\frac{K}{Y}\\right)^α \\left(E\\right)^{1-α} $\n",
    "\n",
    "Collect terms:\n",
    "\n",
    "> $ \\left(\\frac{Y}{L}\\right)^{1-α} = \\left(\\frac{K}{Y}\\right)^α \\left(E\\right)^{1-α} $\n",
    "\n",
    "And clean up:\n",
    "\n",
    "> $ \\left(\\frac{Y}{L}\\right) = \\left(\\frac{K}{Y}\\right)^{\\frac{α}{1-α}} \\left(E\\right) $\n",
    "\n",
    "* _If the capital-output ratio K/L is constant, then the proportional growth rate of output per worker is the same as the proportional growth rate of E_. \n",
    "* And the proportional growth rate of labor efficiency E is the constant g. \n",
    "* Recall that the labor force is growing at a constant proportional rate n. \n",
    "* With output per worker growing at rate g and the number of workers growing at rate n, total output is growing at the constant rate n + g. \n",
    "* Thus for the capital-output ratio K/Y to be constant, the capital stock also has to be growing at rate n + g. \n",
    "\n",
    "&nbsp;\n",
    "\n",
    "### <font color=\"000088\">From Algebra Back to Economics</font>\n",
    "\n",
    "The balanced-growth equilibrium capital-output ratio is equal to the share of production that is saved and invested for the future—the economy’s saving-investment rate s—divided by the sum of three things:\n",
    "\n",
    "* The growth rate of the labor force n.\n",
    "* The growth rate of the efficiency of labor g.\n",
    "* The depreciation rate δ at which capital breaks down and wears out.\n",
    "\n",
    "Suppose the current capital-output ratio is lower than s/(n + g + δ):\n",
    "\n",
    "* Then (n + g + δ)K would be less than the economy’s total investment\n",
    "* Thus saving and investment will more than provide new workers with the capital they need to be fully productive, more than cover the increase in output due to the increase in labor efficiency, and more than com  pensate for the wearing out of capital through depreciation. \n",
    "* The capital stock would grow faster than n + g. \n",
    "* Since n + g is the rate at which output grows, the capital-output ratio would rise.\n",
    "\n",
    "Suppose instead the current capital-output ratio were above s/(n + g + δ):\n",
    "\n",
    "* Then sY will be less then the economy’s total investment sY will be insufficient to keep the capital stock growing at rate n + g. \n",
    "* And since n + g is the rate at which output grows, the capital-output ratio will fall.\n",
    "\n",
    "&nbsp;\n",
    "\n",
    "### <font color=\"000088\">Solow Growth Model Extremely Simple</font>\n",
    "\n",
    "It delivers one equilibrium condition: telling us that the stable capital-output ratio will be s/(n + g + δ), and that the economy will evolve over time to reduce the gap between the current capital-output ratio K/Y and its equilibrium balanced-growth value.\n",
    "\n",
    "It consists of five behavioral relationships:\n",
    "\n",
    "* A production function.\n",
    "* A rate of labor-force growth: n.\n",
    "* A rate of growth in the efficiency of labor: g.\n",
    "* A rate of depreciation of capital: δ.\n",
    "* The saving-investment rate: s.\n",
    "\n",
    "“Bob Solow got the Nobel Prize for that?!” you may ask. Ah, but what he got the Nobel Prize for was taking a complicated subject and making a useful model of it that was very simple indeed. The model is simple to write down. But it is powerful. And now we get to use it to generate  insights.\n",
    "\n",
    "&nbsp;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Output per Worker Along the Balanced Growth Path\n",
    "\n",
    "Output per worker as a constant multiple of labor efficiency\n",
    "\n",
    "* What is the multiple?\n",
    "    * It is the balanced-growth capital-output ratio: s/(n+g+δ)\n",
    "    * Raised to the: α/(1-α) power\n",
    "\n",
    "> $ \\left(\\frac{Y}{L}\\right) = \\left(\\frac{K}{Y}\\right)^{\\frac{α}{1-α}} \\left(E\\right) $\n",
    "\n",
    "> $ \\left(\\frac{Y}{L}\\right) = \\left(\\frac{s}{n+g+δ}\\right)^{\\frac{α}{1-α}} \\left(E\\right) $\n",
    "\n",
    "> $ \\left(\\frac{s}{n+g+δ}\\right)^{\\frac{α}{1-α}}  $\n",
    "\n",
    "Now it is time to introduce time subscripts, for we want to pay attention to where the economy is now, where it was whence, and where it will be when:\n",
    "\n",
    "> $ \\left(\\frac{Y_t}{L_t}\\right) = \\left(\\frac{s}{n+g+δ}\\right)^{\\frac{α}{1-α}} \\left(E_t\\right) $\n",
    "\n",
    "* $ E_t = E_0(1 + g)^t  $ \n",
    "* $ L_t = L_0(1 + n)^t  $\n",
    "* We can plug in and solve for what Y/L and Y will be at any time t—as long as the economy is on its balanced-growth path:\n",
    "\n",
    "> $ \\frac{Y_t}{L_t} = \\left(\\frac{s}{n+g+\\delta}\\right)^\\left(\\frac{\\alpha}{1-\\alpha}\\right)E_t  $\n",
    "\n",
    "> $ E_t = E_0{(1 + g)^t}  $\n",
    "\n",
    "&nbsp;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Output per Worker and the Efficiency of Labor on the Balanced Growth Path\n",
    "\n",
    "<img style=\"display:block; margin-left:auto; margin-right:auto;\" src=\"http://delong.typepad.com/.a/6a00e551f08003883401b7c94d7d3a970b-pi\" alt=\"Output per Worker a Constant Multiple\" title=\"Output_per_Worker_a_Constant_Multiple.png\" border=\"0\" width=\"600\" />\n",
    "\n",
    "&nbsp;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Get Out Your iClickers…\n",
    "\n",
    "If labor efficiency E=10000, s=20%, n=1%, g=1%, δ=3%, and α = 0.5… What is the balanced-growth capital-output ratio?\n",
    "\n",
    "1. 15\n",
    "2. 4\n",
    "3. 0.05\n",
    "4. None of the above\n",
    "5. It cannot be determined from the information given\n",
    "\n",
    "&nbsp;\n",
    "\n",
    "If labor efficiency E=10000…  If s=20%, n=1%, g=1%, δ=3%, and α = 0.5… What is BGP output per worker?\n",
    "\n",
    "1. 15 x Et = 150000\n",
    "2. 4 x Et = 40000\n",
    "3. 0.05 x Et = 500\n",
    "4. None of the above\n",
    "5. It cannot be determined from the information given\n",
    "\n",
    "&nbsp;\n",
    "\n",
    "If labor efficiency E=10000… If s=25%, n=1%, g=1%, δ=3%, and α = 0.5… What is the BGP capital-output ratio?\n",
    "\n",
    "1. 15\n",
    "2. 4\n",
    "3. 0.05\n",
    "4. 5\n",
    "5. NotA/WCC\n",
    "\n",
    "&nbsp;\n",
    "\n",
    "If labor efficiency E=10000… s=25%, n=1%, \n",
    "If g=1%, δ=3%, and α = 0.5… What is BGP output per worker?\n",
    "\n",
    "1. 15 x E\n",
    "2. 4 x E\n",
    "3. 0.05 x E\n",
    "4. 5 x E = 50000\n",
    "5. NotA/WCC\n",
    "\n",
    "&nbsp;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### <font color=\"000088\">Interpreting the Balanced Growth Path for Output per Worker</font>\n",
    "\n",
    "* We now see how capital intensity and technological and organizational progress drive economic growth. \n",
    "    * Capital intensity—the economy’s capital-output ratio—determines what is the multiple of the current efficiency of labor E that balanced-growth path output per worker Y/L is.   \n",
    "        * Things that increase capital intensity—raise the capital-output ratio—make balanced-growth output per worker a higher multiple of the efficiency of labor, and make the economy richer.\n",
    "        \n",
    "&nbsp;\n",
    "\n",
    "#### Examples\n",
    "\n",
    "* Suppose that α is 1/2, so that α/(l—α) is 1, and that s is equal to three times n + g + δ, so that the balanced-growth capital-output ratio is 3. \n",
    "* Then balanced-growth output per worker is simply equal to three times the efficiency of labor. \n",
    "* If we consider another economy with twice the saving rate s, its balanced-growth capital-output ratio is 6, and its balanced-growth level of output per worker is twice as great a multiple of the level of the efficiency of labor.\n",
    "\n",
    "&nbsp;\n",
    "\n",
    "### <font color=\"000088\">Growth Oriented Toward Investment and Capital Accumulation</font>\n",
    "\n",
    "* The higher is the parameter α:\n",
    "    * the slower diminishing returns to investment set in\n",
    "    * the stronger is the effect of changes in the economy’s balanced-growth capital intensity on the level of output per worker\n",
    "    * the more important are thrift and investment incentives and other factors that influence s relative to those that influence the efficiency of labor.\n",
    "\n",
    "&nbsp;\n",
    "\n",
    "* Suppose that the balanced-growth capital-output ratio is 4.     * If α is 1/3, α/(1—α) is 1/2\n",
    "    * The balanced-growth path level of output per worker is twice the level of the efficiency of labor\n",
    "    * You multiply the efficiency of labor by the square root of the capital-output ratio. \n",
    "    * Most economists think that 1/3 is a reasonable parameter value for the United States today.\n",
    "\n",
    "* Suppose α is 1/2\n",
    "    * α/(l—α) is equal to 1\n",
    "    * With a balanced-growth capital-output ratio of 4, the level of output per worker is fully four times the level of the efficiency of labor\n",
    "    * You then multiply the efficiency of labor by the capital-output ratio.\n",
    "    * Most economists think that 1/2 is a reasonable parameter value for the United States a century ago or for relatively poor countries today.\n",
    "\n",
    "* But some economists—for example, Paul Romer—believe that the evidence points at still higher values of α. \n",
    "    * If α = 2/3\n",
    "    * With a balanced-growth capital-output ratio of 4\n",
    "    * The level of output per worker is fully sixteen times the level of the efficiency of labor\n",
    "    * You then multiply the efficiency of labor by the square of the capital-output ratio.\n",
    "    \n",
    "&nbsp;\n",
    "\n",
    "### <font color=\"000088\">Shifting the BGP Up or Down vs. Changing Its Slope</font>\n",
    "\n",
    "* Changes in the economy’s capital intensity shift the balanced-growth path up or down to a different multiple of the efficiency of labor\n",
    "    * But the growth rate of Y/L along the balanced-growth path is simply the rate of growth g of the efficiency of labor E. \n",
    "    * The material standard of living grows at the same rate as labor efficiency. \n",
    "* To change the very long run growth rate of the economy you need to change how fast the efficiency of labor grows. \n",
    "* This is what tells us that technology, organization, worker skills, education—all those things that increase the efficiency of labor and keep on increasing it—are likely to be ultimately more important to growth in output per worker than saving and investment.\n",
    "\n",
    "&nbsp;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Calculating Balanced Growth Path Output per Worker: An Example**\n",
    "\n",
    "n is 1 percent per year, g is 2 percent per year, δ is 3 percent per year, α is 1/2, s is 18 percent.\n",
    "\n",
    "* Then the balanced-growth equilibrium capital-output ratio s/(n + g + δ) equals 3\n",
    "* α/(l—α) equals 1.\n",
    "\n",
    "> $ \\frac{Y_t}{L_t} = \\left(\\frac{0.18}{0.06}\\right)^\\left(\\frac{0.5}{1-0.5}\\right)E_t  $\n",
    "\n",
    "> $ \\frac{Y_t}{L_t} = \\left(3\\right)^\\left(1\\right)E_t  $\n",
    "\n",
    "> $ \\frac{Y_t}{L_t} = 3(E_t)  $\n",
    "\n",
    "* When the efficiency of labor is 10,000 per year, balanced-growth output per worker is 30,000 per year. \n",
    "* When the efficiency of labor rises to 20,000 per year, balanced-growth output per worker rises to 60,000 per year.\n",
    "* Because balanced-growth output per worker is a constant multiple of the efficiency of labor, its growth rate is the same as g: 2 percent per year.\n",
    "\n",
    "&nbsp;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Diagrams\n",
    "\n",
    "<img style=\"display:block; margin-left:auto; margin-right:auto;\" src=\"http://delong.typepad.com/.a/6a00e551f08003883401b8d2d47336970c-pi\" alt=\"Equilibrium Is Where the Curves Cross\" title=\"Equilibrium_Is_Where_the_Curves_Cross.png\" border=\"0\" width=\"600\" />\n",
    "\n",
    "&nbsp;\n",
    "\n",
    "<img style=\"display:block; margin-left:auto; margin-right:auto;\" src=\"http://delong.typepad.com/.a/6a00e551f08003883401b7c94d7f7a970b-pi\" alt=\"Where the curves cross\" title=\"where_the_curves_cross.png\" border=\"0\" width=\"600\" height=\"505\" />\n",
    "\n",
    "&nbsp;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### <font color=\"000088\">On the Balanced Growth Path</font>\n",
    "\n",
    "To calculate what output per worker would be if the economy were to be on its balanced-growth path is a straightforward three-step procedure:\n",
    "\n",
    "1. Calculate the balanced-growth equilibrium capital-output ratio s/(n + g + δ), the saving rate s divided by the sum of the labor-force growth rate n, the efficiency of labor growth rate g, and the depreciation rate δ.\n",
    "2. Raise the balanced-growth capital-output ratio to the α/(l-α) power, where α is the diminishing-retums-to-investment parameter in the production function. \n",
    "3. Multiply the result by the current value of the efficiency of labor E. The result is the current value of what output per worker would be if the economy were on its balanced growth path, and the path traced out by that result as E grows over time is the balanced-growth path for output per worker.\n",
    "\n",
    "&nbsp;\n",
    "\n",
    "### <font color=\"000088\">Off the Balanced Growth Path</font>\n",
    "\n",
    "What if you are not on the balanced growth path?\n",
    "\n",
    "* You are converging to it\n",
    "* How fast?\n",
    "* That is a matter of algebra…\n",
    "* Let’s crank through the algebra…\n",
    "\n",
    "&nbsp;\n",
    "\n",
    "> $ Y = K^α(EL)^{(1-α)}  $\n",
    "\n",
    "Take first logarithms, and then derivatives to obtain:\n",
    "\n",
    "> $\\frac{d(ln(Y_{t}))}{dt} = \\alpha\\frac{d(ln(K_t))}{dt} + (1-\\alpha)\\frac{d(ln(E_t))}{dt} + (1-\\alpha)\\frac{d(ln(L_t))}{dt}$\n",
    "\n",
    "Since the derivative of a logarithm is simply a proportional growth rate, this tells us that—on or off of the balanced-growth path—the proportional growth rate of output is a function of the parameter α and of the growth rates of the capital stock, the labor force, and the efficiency of labor.\n",
    "\n",
    "&nbsp;\n",
    "\n",
    "### <font color=\"000088\">Working with the Growth Rates</font>\n",
    "\n",
    "Write \"g<sub>x</sub>\" for the proportional growth rate of an economic variable X. Thus g<sub>Y</sub> is the proportional growth rate of output Y. g<sub>K</sub> is the proportional growth rate of the capital stock K. And so forth. \n",
    "\n",
    "> $ g_Y = αg_K + (1-α)g_L + (1-α)g_E  $\n",
    "\n",
    "> $ g_Y = αg_K + (1-α)(n + g)  $\n",
    "\n",
    "> $ g_K - g_Y = (1-α)g_K - (1-α)(n + g)  $\n",
    "\n",
    "> $ g_K - g_Y = (1-α)\\left(s\\left(\\frac{Y}{K}\\right) - δ\\right) - (1-α)(n + g)  $\n",
    "\n",
    "> $ g_{K/Y} = (1-α)s\\left(\\frac{Y}{K}\\right) - (1-α)(n + g + δ)  $\n",
    "\n",
    "> $ \\frac{d(K/Y)/dt}{K/Y} = (1-α)s\\left(\\frac{Y}{K}\\right) - (1-α)(n + g + δ)  $\n",
    "\n",
    "> $ \\frac{d(K/Y)}{dt} = (1-α)s - (1-α)(n + g + δ)\\left(\\frac{K}{Y}\\right)  $\n",
    "\n",
    "> $ \\frac{d(K/Y)}{dt} = - (1-α)(n + g + δ)\\left(\\frac{K}{Y} - \\frac{s}{n + g + δ}\\right)  $\n",
    "\n",
    "&nbsp;\n",
    "\n",
    "### <font color=\"000088\">What We Now Know</font>\n",
    "\n",
    "* When the capital-output ratio K/Y is equal to s/(n+g+δ), it is indeed the case that it is stable.\n",
    "\n",
    "* When K/Y is above that s/(n+g+δ) value, it is falling; when it is below, it is rising.\n",
    "\n",
    "* The speed with which it is falling or rising is always proportional to the gap between K/Y and s/(n+g+δ), with the factor of proportionality equal to (1-α)(n+g+δ)\n",
    "\n",
    "----\n",
    "\n",
    "&nbsp;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### <font color=\"000088\">The Transition</font>\n",
    "\n",
    "The fact that an economy converges to its balanced-growth path makes analyzing the _long-run_ growth of an economy relatively easy as well even when the economy is not on its balanced-growth path:\n",
    "\n",
    "1. Calculate the balanced-growth path.\n",
    "2. From the balanced-growth path, forecast the future of the economy: If the economy is on its balanced-growth path today, it will stay on that path in the future (unless some of the parameters—n, g, δ, s, and α—change).\n",
    "3. If those parameters change, calculate the new, shifted balanced-growth path and predict that the economy will head for it.\n",
    "4. If the economy is not on its balanced-growth path today, it is heading for that path—and will get there, eventually.\n",
    "\n",
    "Thus _long run_ economic forecasting becomes simple. All you have to do is predict that the economy will head for its balanced-growth path, and calculate what the balanced-growth path is.\n",
    "\n",
    "&nbsp;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Example: Convergence to a Balanced-Growth Path Capital-Output Ratio of 4\n",
    "\n",
    "<img style=\"display:block; margin-left:auto; margin-right:auto;\" src=\"http://delong.typepad.com/.a/6a00e551f08003883401bb09f0e868970d-pi\" alt=\"Convergence\" title=\"Convergence.png\" border=\"0\" width=\"600\" height=\"463\" />\n",
    "\n",
    "Suppose the balanced- growth equilibrium capital-output ratio is 4. Whether the capital-output ratio starts above or below its balanced-growth equilibrium value, it converges to the level equal to s/(n + g + δ)\n",
    "\n",
    "&nbsp;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### <font color=\"000088\">Solving for the Time Path of the Capital-Output Ratio\n",
    "\n",
    "* We have a rate of change of something on the left hand side. \n",
    "* We have the level of something on the right hand side.\n",
    "* We have a negative constant multiplying the level.\n",
    "* This is a _convergent exponential_:\n",
    "\n",
    ">$ \\frac{K_t}{Y_t} = \\frac{s}{\\delta + n + g} + \\left(C - \\frac{s}{\\delta + n + g}\\right) e^{-(1 - \\alpha)(\\delta + g + n)t}  $\n",
    "\n",
    "for the appropriate constant C.\n",
    "\n",
    "&nbsp;\n",
    "\n",
    "What is the value of this constant C? \n",
    "\n",
    "* We know the capital-output ratio when we start our analysis at time t = 0.\n",
    "* Write K<sub>0</sub>/Y<sub>0</sub> for the capital output tday:\n",
    "\n",
    "> $ \\frac{K_t}{Y_t} = \\frac{s}{\\delta + n + g} + \\left(\\frac{K_0}{Y_0} - \\frac{s}{\\delta + n + g}\\right) e^{-(1 - \\alpha)(\\delta + g + n)t}  $\n",
    "\n",
    "> $\\frac{Y_t}{L_t} = \\left(\\frac{s}{\\delta + n + g} + \\left(\\frac{K_0}{Y_0} - \\frac{s}{\\delta + n + g}\\right) e^{-(1 - \\alpha)(\\delta + g + n)t}\\right)^\\left(\\frac{\\alpha}{1-\\alpha}\\right)\\left(E_t\\right)  $\n",
    "\n",
    "In the Solow growth model, an economy will close a fraction (1 — α)(n + g + δ) of the gap between its current position and the balanced-growth path each year.\n",
    "\n",
    "<img style=\"display:block; margin-left:auto; margin-right:auto;\" src=\"https://delong.typepad.com/.a/6a00e551f080038834022ad3794beb200c-pi\" alt=\"Lecture Understanding the Solow Model MRE Macro key\" title=\"Lecture-_Understanding_the_Solow_Model__MRE__Macro_key.png\" border=\"0\" width=\"600\" height=\"358\" />"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### How Fast Do Economies Converge?: An Example**\n",
    "\n",
    "n = 1 percent per year, g = 2 percent per year, δ = 5 percent per year, α = 1/2.\n",
    "\n",
    "This economy will each year close a fraction of the gap between its current capital-output ratio and its balanced-growth capital-output ratio equal to:\n",
    "\n",
    "> $ (1-\\alpha)(n+g+\\delta) = \\left(1-\\frac{1}{2}\\right) (0.01+0.02+0.05) = 0.04  $\n",
    "\n",
    "* That is 4 percent per year. \n",
    "* According to the rule of 72, the economy's capital-output ratio will close half of the gap to its balanced growth path value in 18 years.\n",
    "\n",
    "&nbsp;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### <font color=\"000088\">Appendix: Some Easy Mathematical Tools</font>\n",
    "\n",
    "1. The growth-of-a-product rule: The growth rate of a product is equal to the sum of the growth rates of its components. Since total output Y is equal to output per worker Y/L times the number of workers L, the growth rate of total output Y will be equal to the growth rate of Y/L plus the growth rate of L.\n",
    "\n",
    "2. The growth-of-a-quotient rule: The proportional change of a quotient is equal to the difference between the proportional changes of its components. Since output per worker Y/L is equal to the quotient of output Y and the number of workers L, its growth rate will be the difference between their growth rates.\n",
    "\n",
    "3. The growth-of-a-power rule: The proportional change of a quantity raised to a power is equal to the proportional change in the quantity times the power to which it is raised. For example, suppose that we have a situation in which output Y is equal to the capital stock K raised to the power a: Y = Ka. Then the growth rate of Y will be equal to a times the growth rate of K.\n",
    "\n",
    "4. The rule of 12: A quantity growing at k percent per year doubles in 72/k years. A quantity shrinking at k percent per year halves itself in 72/k years.\n",
    "\n",
    "These four mathematical rules of thumb contain 95 percent of what calculus is used for in intermediate macro  economics. \n",
    "\n",
    "* You do need calculus if you want to do more than just take them on faith, and instead have a deep understanding of just why these rules of thumb work.\n",
    "\n",
    "&nbsp;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Catch Our Breath\n",
    "\n",
    "<img src=\"https://tinyurl.com/20181029a-delong\" width=\"300\" style=\"float:right\" />\n",
    "\n",
    "* Ask me two questions…\n",
    "* Make two comments…\n",
    "* Further reading…\n",
    "\n",
    "<br clear=\"all\" />\n",
    "\n",
    "----\n",
    "\n",
    "Understanding the Solow Growth Model: <https://www.icloud.com/keynote/0PejUtBxFLIXN3wTCkbqhadQg>   \n",
    "Lecture Support: <http://nbviewer.jupyter.org/github/braddelong/LSF18E101B/blob/master/Growth%20Theory%20%28Part%20III%2C%20Ch.%204%29/D%26O3_4..3%20Understanding%20the%20Solow%20Growth%20Model.ipynb>\n",
    "\n",
    "&nbsp;\n",
    "\n",
    "----"
   ]
  }
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