{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Lucas (1990) \"Why Doesn't Capital Flow from Rich to Poor Countries?\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Summary and analytical notes on the paper:\n",
    "\n",
    ">Lucas, Robert E. (1990) \"Why Doesn't Capital Flow from Rich to Poor Countries?\" *American Economic Review*: 92-96."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## Neoclassical predictions:\n",
    " - the convergence of factor prices and incomes per-capita over time (Factor Price Equalization Theorem)\n",
    " - via substitute mechanisms: factor movement, trade in products, and/or capital accumulation (e.g. Solow). \n",
    " - rests on assumptions about technology and market competition\n",
    "      - in particular: diminishing returns to the accumulated factor capital (i.e. $F_{KK} < 0$ )."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Simplest model\n",
    "Assume two countries with same aggregate production function, where $X$ is capital stock and $L$ is labor force:\n",
    "\n",
    "$$Y = A X^\\beta L^{1-\\beta}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "**in intensive or per-capita form**:\n",
    "$$y = A x^\\beta$$\n",
    "\n",
    "where \n",
    "$$y = \\frac{Y}{L} \\text{    and    } x = \\frac{X}{L}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "**Marginal Product of Capital (MPK) is:**\n",
    "\n",
    "$$r = A \\beta x^{\\beta -1}$$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "**Write MPK as a function of income per capita:**\n",
    "\n",
    "    \n",
    "$$r = \\beta A^\\frac{1}{\\beta} y^\\frac{\\beta -1}{\\beta}$$   \n",
    "\n",
    "or \n",
    "\n",
    "$$r = A \\beta \\left ( {\\frac{y}{A}} \\right ) ^\\frac{\\beta - 1}{\\beta}$$\n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "\n",
    "Steps:\n",
    "\n",
    "$$y = A x^\\beta  $$\n",
    "so \n",
    "$$x = \\left ({\\frac{y}{A}}  \\right)^\\frac{1}{\\beta}   $$\n",
    "\n",
    "substitute this into $r = A \\beta x^{\\beta -1}$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### The puzzle\n",
    " - Let capital share $\\beta =0.4$ (average of USA and India)\n",
    " - Assume first that $A$ is the *same* in both countries"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    " - In 1988 income per capita in USA was 15 times higher than USA:\n",
    " \n",
    "$$\\frac{y_{US}}{y_{IN}} = 15$$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    " - this implies MPK in India would have to be:\n",
    " \n",
    " $$\\frac{r_{IN}}{r_{US}} = \\left [ { \\frac{y_{US}}{y_{IN}} } \\right] ^ \\frac{1-\\beta}{\\beta} = 58.1$$\n",
    " \n",
    " times higher in India!  Implausibly large."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "What differences in capital per worker account for this large a gap?\n",
    "\n",
    "As $x = \\left ({\\frac{y}{A}}  \\right)^\\frac{1}{\\beta} $ and  $\\frac{y_{US}}{y_{IN}} = 15$, US workers would have to have this \n",
    " \n",
    " $$\\frac{x_{US}}{x_{IN}} = \\left ( {\\frac{y_{US}}{y_{IN}}}  \\right)^\\frac{1}{\\beta} = 871.4$$\n",
    " \n",
    "multiple of the amount of capital per worker compared to India:\n",
    " \n",
    " So if in India the capital-labor ratio is 1 in the USA it must be 871.4 !  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    " - With such huge differences in returns, capital would surely RUSH from USA to India quickly lower the gap in returns and incomes.  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    " -  Evidently it does not.  So what's wrong with the model?  Lucas walks through 4 alternate hyptotheses."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Some plots"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    },
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pylab as plt\n",
    "from scipy.optimize import fsolve, brentq, minimize"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    },
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [],
   "source": [
    "A = 1 \n",
    "rho = 0.05\n",
    "beta = 0.4\n",
    "y_US = 15\n",
    "y_IN = 1\n",
    "\n",
    "def f(x):\n",
    "    return x**beta\n",
    "\n",
    "def mpx(x):\n",
    "    return beta*x**(beta-1)\n",
    "\n",
    "def r(y, A):\n",
    "    return beta * (A**(1-beta)) * y**((beta-1)/beta)\n",
    "    \n",
    "def kap(y, A):\n",
    "    return (y/A)**(1/beta)\n",
    "\n",
    "def xoptimum(rho, beta):\n",
    "    xC = (rho/beta)**(1/(beta-1))\n",
    "    xM = (rho/beta**2)**(1/(beta-1))\n",
    "    return xC, xM"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    },
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [],
   "source": [
    "def lucasplot():\n",
    "    y = np.linspace(0.1,20,100)\n",
    "    plt.figure(figsize=(12, 6))\n",
    "    plt.subplot(2,1,1)\n",
    "    plt.plot(y,kap(y, A))\n",
    "    plt.ylabel(\"$k$ -- capital per worker\")\n",
    "    plt.ylim(0,kap(y_US +1, A))\n",
    "    plt.axvline(y_IN,color='k',ls='dashed')\n",
    "    plt.axvline(y_US,color='k',ls='dashed')\n",
    "    plt.title(\"capital per worker\")\n",
    "\n",
    "    plt.subplot(2,1,2)\n",
    "    plt.plot(y,r(y,A))\n",
    "    plt.xlabel(\"$y$ -- output per worker\")\n",
    "    plt.ylabel(\"$4$ -- marginal product capital\")\n",
    "    plt.title(\"return to capital\")\n",
    "    plt.ylim(0,r(y_IN,A))\n",
    "    plt.axvline(y_IN,color='k',ls='dashed')\n",
    "    plt.axvline(y_US,color='k',ls='dashed')\n",
    "    plt.annotate('India', xy=(y_IN, r(y_IN,A)), xytext=(y_IN +2, r(y_IN,A)*0.75),\n",
    "                arrowprops=dict(facecolor='black', shrink=0.05),)\n",
    "    plt.annotate('USA', xy=(y_US, r(y_US,A)), xytext=(y_US +2, r(y_US,A)+0.1),\n",
    "                arrowprops=dict(facecolor='black', shrink=0.05),);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Return to capital in India relative to USA :  58.1\n"
     ]
    }
   ],
   "source": [
    "print('Return to capital in India relative to USA : {:5.1f}'.format(r(y_IN, A)/r(y_US, A)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The ratio of capital stock per worker in the USA compared to India that is implied by this difference in incomes per capita is even more unbelievable:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Capital per worker in USA relative to India : 871.4\n"
     ]
    }
   ],
   "source": [
    "print('Capital per worker in USA relative to India : {:5.1f}'.format(kap(y_US, A)/kap(y_IN, A)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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O+fDw7v6RmT0DfALUANMJmocUAE+Z2WUEyfm5YflZYc8ns8PyP1CPJoHDDz882SGIiEgbsGpzBT9/4XPenL2a4T3b89B3Dma/3h1itn/dryRVNacf72nuflCc44kb9eMtIiKyc5GI88//LuXuV+dSE4nwk2MHc9noAWSkpyU7NJFWIyb9eANTzOxgd/84RnGJiIhICzF31RZufu4zpi/dxOi9i7jzzH3p1zk/2WGJtCnNSbyPBq4ys8UE7a8N8Bi08ZYYOfvsswF49tlnkxyJiIi0FuVVtfz+7S948L2FtM/N5J5zD+CsA3th1lAnYrGh+5WkquYk3ifFLQqJifXr1yc7BBERaUXembeGnz//OcUbyzlvVG9uPmkfOjZjIJzdpfuVpKrmdCe4xMwOAI4MF73n7p/GJywRERGJlzVbKrj95dm8PHMlA7vk86+xh3HYXp2THZZIm9ecIeOvBa4AngsX/cPMxrv7H+MSmYiIiMRUTW2Ex6Ys4Z435lNVG+G64wZz5df3IjsjPdmhiaSE5jQ1uQw41N1LAczsbmAyoMRbRESkhZu+dCO3Pv85s1Zs4chBRdx++r4MKNLDkyKJ1JzE24Do/rJraXj4dkmSY445JtkhiIhIC7OprIq7X5vHvz5eStd22dz/rQM5eb/ucX14cld0v5JU1Zx+vK8jGEHy3+GiM4CH3f2+uEQWY+rHW0REUkkk4jzzSTF3vTqXzeXVfPeI/vz4uMEUZGvkSZF4ikk/3u5+r5lNBEYT1HR/192nxyZEERERiZXPl2/m5y98zvSlmzioX0f+9/R9GdazfbLDEkl5zfrZ6+6fEAztLi3QSScFPT6++uqrSY5ERESSYVNZFb99Yx7//GgpnfOz+O25B3DWyF6kpbWslqG6X0mqak6vJo8Bkwi6EZwbv5Bkd5WXlyc7BBERSYJIxHl62jLufm0em8qq+M7h/fnJcYPpkJuZ7NAapPuVpKrm1Hj/H0Ezkz+a2V7ADGCSu/8+HoGJiIjIrk1fupFxL83m02WbOLh/R24//VD26aFmJSItUXPaeP/HzN4FDiYcPh4YDijxFhERSbA1JRXc/eo8nv2kmK7tsvnd+Qdwxoj4DvUuInumOU1N3gbyCfrufg842N3XxCswERER2VFVTYSHP1zEH95eQGVNLVePGcgPjt5bvZWItALN+V86EzgI2BfYDGwys8nuroZaLcSpp56a7BBERCSO3pm7hv99eTYL15VyzNCu3HrqsFY5CI7uV5KqmtyP97YNzAqA7wLXA93dPTsegcWa+vEWEZHW6ovVJdzxyhzenb+WAUX53HbqMI4e2jXZYYlIA2LSj7eZXQMcSVDrvQR4iKDJiYiIiMTBxtIqfv/2Fzw2ZQl5Wenceso+fPvw/mRlpCU7NBHZDc1papIL3AtMc/eaOMUje2DMmDEATJw4MalxiIjInqmujfCPKUu4760vKKmo5sJD+nLdcYPpXNAq/si8S7pfSapqTq8mv4lnICIiIqnO3fnP3DX8csIcvlxbytf27szPTx3G0O7qHlCkLdAj0CIiIi3ArBWbufOVOXz45XoGFOUz/pKDOG5YN3UPKNKGNCnxtuB/fW93XxaPIMysEHiQoMcUB74HzAOeBPoDi4Hz3H1jWP5m4DKgFviRu78ej7hERETibdXmCn77RtAfd2FuJuNOG8ZFh/UjM13tuEXamiYl3u7uZvY8wYOV8fB74DV3P8fMsoA84BbgbXe/y8xuAm4CbjSzYcAFBIP39ATeMrPB7l4bp9hERERirrSyhgcmLeRvkxZSG3GuOHIvfnD03i12mHcR2XPNaWoyxcwOdvePYxmAmbUHjgIuBXD3KqDKzE4HxoTFHgEmAjcCpwP/cvdKYJGZLQAOIRjYJ6Wdd955yQ5BRER2obo2wpMfL+O+t75g3dZKTtm/BzeeMJS+nfOSHVrC6H4lqarJ/Xib2WxgCEGzj1LACCrD99+jAMxGAOOB2cABwDTgWmC5uxdGldvo7h3N7E/AFHf/R7j878Cr7v5MA/seC4wF6Nu370FLlizZk1BFRER2m7vz+qzV/Pq1uSxcV8oh/Ttx08lDObBvx2SHJiIxFJN+vIGTYhRPQzEcCPzQ3T8ys98TNCtpTENPmTT468HdxxMk9YwaNap5IwW1QmVlZQDk5aVOrYmISGswbckGfjlhLtOWbGTvrgU8+O1RHLNP15R9cFL3K0lVzUm8lwIXAXu5++1m1hfoTjCYzp4oBord/aNw/hmCxHu1mfVw95Vm1gNYE1W+T9T2vYEVexhDm3DyyScD6hdVRKSl+GJ1Cb9+fR5vzl5N13bZ/Oqs/Tj3oN5kpPiDk7pfSapqTuL9ZyACfAO4HSgBngUO3pMA3H2VmS0zsyHuPg84hqDZyWzgO8Bd4esL4SYvAo+b2b0ED1cOAv67JzGIiIjE0vJN5fzuzfk890kx+VkZ/PS4wVx25ADystSLr0gqa843wKHufqCZTQdw941hDySx8EPgn+H+FgLfBdKAp8zsMoLa9nPD484ys6cIEvMa4Afq0URERFqCDaVV/PmdBTw6Jfhj8GWjB/D9MXvTMT9Wt0sRac2ak3hXm1k6YXtqM+tCUAO+x9x9BtBQI/RjGil/J3BnLI4tIiKyp0oqqnno/cU8+N5CSqtqOOeg3lx77GB6FeYmOzQRaUGak3j/Afg30M3M7gTOAW6NS1QiIiKtQEV1LY9OXsxfJn7JxrJqThjejeuPH8Kgbu2SHZqItEBNTrzd/Z9mNo2vaqHPcPc58QlLdsell16a7BBERFJCVU2EJ6cu449vf8GakkqOGtyF648fzP69C5MdWqug+5Wkqub0450DfB84kqCJyfvAX9y9In7hxc6oUaN86tSpyQ5DRERasZraCP+evpzfv/0FxRvLObh/R64/fgiH7tU52aGJSAsRq368HyXoyeQP4fyFwGOEDz1K8q1btw6AoqKiJEciItK21EacFz9dzu/f+oLF68vYt1d7/veMfRkzuEvK9sW9J3S/klTVnMR7iLsfEDX/jpl9GuuAZPedc845gPpFFRGJlUjEefmzlfz+rfl8ubaUod3bMf6SgzhuWDcl3HtA9ytJVc1JvKeb2WHuPgXAzA4FPohPWCIiIskTiTivzVrFfW/NZ/7qrQzuVsBfLjqQE4Z3Jy1NCbeI7J5m9eMNfNvMlobzfYE5ZvYZ4O6+f8yjExERSaDaiDPhs5X88T9fMH/1VgZ2yeePF47klP16KOEWkT3WnMT7xLhFISIikkS1EeflmSv4438WsGDNVvbuWsDvLxjBqfv3JF0Jt4jESHO6E1wSz0BEREQSraY2wkthwr1wbSmDuxXwp2+N5OR9VcMtIrHXnBpvaeGuvvrqZIcgItIqVNVEeO6TYv488UuWbihjaPd2/PmiAzlRbbgTQvcrSVVN7se7tVM/3iIiUlFdy5MfL+Ov737Jys0V7N+7A9ccvTfH7tNNCbeIxESs+vGWFm7ZsmUA9OnTJ8mRiIi0LCUV1Tz+0VL+9t4i1m2t5OD+Hbnr7P05alCRugVMAt2vJFXtMvE2sxKgoWpxI+jNpH3Mo5LdcskllwDqF1VEpM76rZX83weLeXTyYrZU1DB67yJ++I2RGmkyyXS/klS1y8Tb3dslIhAREZFYKd5Yxt8mLeTJqcuorIlwwrDuXD1mIAf0KUx2aCKSwprV1MTMOgKDgJy6Ze4+KdZBiYiI7I55q0p4YNKXvDhjBQBnjuzFlV8fyN5dC5IcmYhIMxJvM7scuBboDcwADgMmA9+IS2QiIiJN4O5MXrie8ZMWMnHeWnIz0/n24f25/MgB9CzMTXZ4IiLbNKfG+1rgYGCKux9tZkOBX8QnLBERkZ2rqY3w2qxVjJ+0kJnFm+mcn8VPjxvMxYf1o2N+VrLDExHZQXMS7wp3rzAzzCzb3eea2ZC4RSbN9tOf/jTZIYiIxF1pZQ1PT13GQx8sZumGMgYU5XPnmfty9oG9yclMT3Z40gS6X0mqak7iXWxmhcDzwJtmthFYEY+gZPecdtppyQ5BRCRuVm2u4OEPF/P4R0vYUlHDyL6F3HLyUI4b1l3Durcyul9JqmrOkPFnhm/Hmdk7QAfg1bhEJbtl3rx5AAwZoj9EiEjb8fnyzfz9/UW89OkKIu6cuG93Lhu9Fwf165js0GQ36X4lqao5D1fe7e43Arj7u3XLgBtjEYiZpQNTgeXufqqZdQKeBPoDi4Hz3H1jWPZm4DKgFviRu78eixhauyuvvBJQv6gi0vrVRpy35qzm/z5YxJSFG8jPSueSw/vxva8NoE+nvGSHJ3tI9ytJVc1panIcOybZJzWwbHddC8wB6gbkuQl4293vMrObwvkbzWwYcAEwHOgJvGVmg929NkZxiIhIkmypqOapj5fxyOTFLNtQTq/CXG4+aSgXHNKXDrmZyQ5PRGSPNGXkyquB7wN7mdnMqFXtgA9iEYSZ9QZOAe4ErgsXnw6MCd8/AkwkSPJPB/7l7pXAIjNbABxC0LWhiIi0QgvXbuXRyUt4euoySqtqOaR/J245aR+OG9aNjPS0ZIcnIhITTanxfpygLfevCGqd65S4+4YYxXEfcANBMl+nm7uvBHD3lWbWNVzeC5gSVa44XLYDMxsLjAXo27dvjEIVEZFYqI04E+et4ZHJS5g0fy2Z6cZpB/Tke18bwL69OiQ7PBGRmGvKkPGbgc3AhfEIwMxOBda4+zQzG9OUTRpY5g0VdPfxwHiAUaNGNVhGREQSa1NZFU9PLeaxKUtYuqGMbu2zue64wVxwSB+6tsvZ9Q5ERFqppjQ1ed/dR5tZCdsnuAa4u7dvZNOm+hrwTTM7mWAo+vZm9g9gtZn1CGu7ewBrwvLFQJ+o7Xujbg0BuPXWW5MdgohIoz5fvpnHJi/hhU+XU1Ed4ZABnbjxxKEcP7wbmWpOklJ0v5JUZe4tpyI4rPG+PuzV5DfA+qiHKzu5+w1mNpyg+cshBA9Xvg0M2tXDlaNGjfKpU6fG9wOIiMh2KqpreXnmSh6bsoRPl20iNzOd00f05NuH92dYzz2ttxERaXnMbJq7j2poXXN6NUm0u4CnzOwyYClwLoC7zzKzp4DZQA3wA/VoEpgxYwYAI0aMSGocIiKL1pXyzylLeHpaMZvLqxnYJZ9xpw3jzAN7q3cS0f1KUlaTa7zNLIegd5PRBE1O3gf+4u4V8QsvdlKhxnvMmDGA+kUVkeSoqonw+qxVPPHfpXz45Xoy0owT9u3OxYf247C9OmGm0SUloPuVtGWxqvF+FCgB/hjOXwg8RlgTLSIiqWnRulL+9d+lPDOtmPWlVfQqzOX64wdz3qg+dG2vhyVFROo0J/Ee4u4HRM2/Y2afxjogERFp+Sqqa3l91iqe/HgZH365nvQ049h9uvKtQ/tx5N5FpKWpdltEpL7mJN7Tzewwd58CYGaHEqMBdEREpHWYtWIzT328jOdnrGBzeTW9O6p2W0SkqZqTeB8KfNvMlobzfYE5ZvYZQbeC+8c8OhERSbrNZdW8OHMFT368lM+XbyErI40Th3fn/IP7cPhenVW7LSLSRM1JvE+MWxQSE7/85S+THYKItBG1Eef9Bet4euoy3pi9mqqaCEO7t2PcacM4Y2QvCvOykh2itGK6X0mqanLi7e5LzKwjMIhgoJu65ZPiEZg03xFHHJHsEESklVu4divPTCvmuU+Ws2pLBYV5mVx4cB/OOagP+/Zqr55JJCZ0v5JU1eTE28wuB64lGClyBnAYMBn4Rlwik2b78MMPAX2hiUjzbCqr4qWZK3nuk2KmL91EmsHXB3fhttOGccw+XcnOSE92iNLG6H4lqao5TU2uBQ4Gprj70WY2FPhFfMKS3XHLLbcA6hdVRHatqibCO/PW8Nwnxfxn7hqqa50h3dpx00lDOWtkLz0oKXGl+5WkquYk3hXuXmFmmFm2u881syFxi0xERGIqEnGmLd3ICzOW8/LMlWwqq6aoIJtvH96fsw7sxbAeakoiIhJPzUm8i82sEHgeeNPMNgIr4hGUiIjEzrxVJbwwYzkvzFjB8k3l5GSmcdyw7px1YC+O3LuIjPS0ZIcoIpISmvNw5Znh23Fm9g7QAXg1LlGJiMgeWbahjJdnruSFGcuZu6qE9DRj9N5FXH/CYI4f1p387ObUu4iISCw05+HKR4Br3X2Tu78b9nDyAPC9uEUnIiJNtnpLBa/MXMlLM1cwfekmAEb0KWTcacM49YCeFBVkJzdAEZEU15wqj/3dfVPdjLtvNLORsQ9Jdtd9992X7BBEJMHWba3ktc9X8fLMFXy0aAPuMKxHe248cSin7t+DPp3ykh2iyA50v5JU1ZzEO83MOrr7RgAz69TM7SXORowYkewQRCQB6pLtCZ+tZMrC9UQc9uqSz7XHDOLU/Xuyd9eCZIcoslO6X0mqak7ifA/woZk9AzhwHnBnXKKS3fLWW28BcOyxxyY5EhGJtTUlFbw+azUTZq7ko0VfJdvXHL03J+/fgyHd2qlHEmk1dL+SVGXu3vTCZsMIBswx4G13nx2vwGJt1KhRPnXq1GSHEVdjxowB1C+qSFuxbEMZr89axWufr2La0o14mGyful8PJdvSqul+JW2ZmU1z91ENrWtWU5Ew0W41ybaISGvi7nyxZitvzl7Nq5+v5PPlW4CgzfZPjh3Mift2Z1DXAiXbIiKtlNpoi4gkUW3E+WTpRt6YtYo3Z69m8foyAEb2LeSWk4dywvDu9Oucn+QoRUQkFpR4i4gkWFlVDe9/sY635qzm7TlrWF9aRWa6ccTAIi4/ci+OG9aNbhqyXUSkzdmtxNvMurv7qlgEYGZ9gEeB7kAEGO/uvw97TXkS6A8sBs6L6lHlZuAyoBb4kbu/HotYRETiZeXmct6es4a356zmgy/XU1UToV12BkcP7cpxw7oxZkgX2uVkJjtMERGJo92t8Z4AHBijGGqAn7r7J2bWDphmZm8ClxI8wHmXmd0E3ATcGD7geQEwHOgJvGVmg929NkbxtFoPPPBAskMQkVBtxJmxbBMT563hP3PXMGtF0F67X+c8Lj60H8fu05WDB3QiU8O1SwrS/UpS1e4m3jF7ssfdVwIrw/clZjYH6AWcDowJiz0CTARuDJf/y90rgUVmtgA4BJgcq5haqyFDhiQ7BJGUtrG0iklfrOWduWt4d/5aNpZVk2ZwUL+O3HjiUI7dpyt76+FIEd2vJGXtbuL9t5hGETKz/sBI4COgW5iU4+4rzaxrWKwXMCVqs+JwWcp76aWXADjttNOSHIlIaqiNOJ8Wb2LS/LW8O38tny7bRMShU34WRw/pypihXTlqUBGFeVnJDlWkRdH9SlLV7ibez8U0CsDMCoBngR+7+5ad1Ag1tKLBzsjNbCwwFqBv376xCLNFu+eeewB9kYnE06rNFUz6Yi2T5q/l/QXr2FRWjRns37uQa47em6OHdmX/3oWkp6lWW6Qxul9JqmoJbbwxs0yCpPuf7l6X1K82sx5hbXcPYE24vBjoE7V5b2BFQ/t19/HAeAgG0IlVvCKSOkora/ho0Xre+2Id73+xji/WbAWgS7tsjhnaja8P6cLovYvolK9abRER2bmkt/G2oGr778Acd783atWLwHeAu8LXF6KWP25m9xI8XDkI+G+s4hGR1FZdG2Fm8WY+XLCO9xes45OlG6mudbIz0jhkQCfOOag3owcVMaxHe7XVFhGRZmkJbby/BlwCfGZmM8JltxAk3E+Z2WXAUuBcAHefZWZPEYygWQP8QD2aiMjuikScuatK+PDLdXz45Xr+u2gDWytrABjesz3fGz2AI/fuwqj+HcnJTE9ytCIi0prtVuLt7n+OVQDu/j6N16Af08g2dwJ3xioGEUkdkYgzf00JU75cz5SFG/ho0Xo2llUDsFdRPmeM7MkRA4s4bK/Oaj4iIiIxpZEr25DHHnss2SGItDi1EWfuqi18vGjDDol27465fGNoN44Y2Jkj9u5Mjw65SY5WJDXofiWpqsmJt5nd4e631luWrmYeLUefPn12XUikjauqifDZ8k18tGgDHy/awNQlGympCJqO9O6YyzH7dOOwvTpz6IBO9OmUl+RoRVKT7leSqppT493LzC509ycAwn61nwSOjktk0mxPPvkkAOeff36SIxFJnE1lVUxbspGpSzYybfFGPi3eRGVNBICBXfI5df+eHDKgIwf370Tvjkq0RVoC3a8kVTUn8b4SeN3MviToN/v/CEaSlBbiL3/5C6AvMmm7IhFn4bqtfLJ0E5+EyfaCsHu/jDRjeK8OXHRoPw4Z0ImD+3ekc0F2kiMWkYbofiWpapeJt5k9CnwCTAd+ADxO0JvIGe6+IL7hiUgq21xWzYziTUxfupFPlm5ixtKNbAmbjbTPyeCgfh05c2QvDurXkQN6F5KbpV5HRESk5WpKjfcjwAHA98LX/sDHwMVm9rm7PxO/8EQkVVTW1DJ7xRY+XbaJT4s38+myTSxcVwqAGQzp1o5T9u/ByL4dObBvIXsVFZCm0SFFRKQV2WXi7e5vA2/XzZtZBjCMIAk/DFDiLSLNUl0bYd6qEj5fvpmZyzfz+fLNzFm5heraYIDZLu2yGdGnkLMP6s0BvQs5oE8H2uVkJjlqERGRPdPs7gTdvQaYGU7qD0hEdqqyppb5q7by+YrNzFqxmc+Wb2HOyi1UhQ9AtsvJYL9eHfje6AGM7FPIAX0K6d4+R6NCiohIm6N+vNuQZ57RHx8kuTaXVzNnZZBYz1oRTF+sLqEmEtRkt8vOYFjP9lx6RH/27dWB/Xt1oG+nPDUZEUkxul9JqlLi3YYUFRUlOwRJEbURZ/H6UuatKtmWaM9ZWcLyTeXbyhQVZDG8ZweOHtKFfXt1YHjP9vTpqCRbRHS/ktSlxLsNefjhhwG49NJLkxqHtB3uzuotlcxfXcK8VSXMXVXCvNVb+GL11m19ZacZDOxSwEH9OnLxYf3Yp0c7hvVoT5d22WouIiIN0v1KUpW5e7JjSIhRo0b51KlTkx1GXI0ZMwaAiRMnJjUOaX3cnVVbKliwZivzV2/li9UlfLFmK/NXl2wb9RGChx6Hdm/HkG7tGNK9HUO7t2dQtwJyMtWNn4g0ne5X0paZ2TR3H9XQOtV4i6SQiupalm4oY+HarSxYs5Uv15ayYM1WFq7dSmlV7bZynfKzGNS1gNNH9GRwt3YM6hok2p3ys5IYvYiISOumxFukjampjbBiUwWL15eyaF0wLVxXysK1W1m+qZzoP3L17JDDwK4FnDuqDwO7FjCwSz6Du7WjSCM+ioiIxJwSb5FWqKK6luKNZSzdUMbS9WUsXl/GkvWlLFlfxrKNZdv6wwbIz0pnry4FHNi3I2cf2Ju9uuQzoCifgV0KyM/WV4CIiEii6K4r0gJV10ZYtbmCZRvLKN5YHk5lLNsQJNurt1RuVz4/K51+nfPZp0d7Tty3O/0759Ovcx79i/LpqoccRUREWgQl3m3IhAkTkh2CNIG7U1JZw8pNFazYVM7yTeWs2DZVsHxTOSs3lxOJahJiBt3b59CnUx5HDupC30559OucR59OefTpmEdRQZaSaxFpNXS/klSlxLsNycvLS3YIKa824qzfWsnqLZWs3lLBqi0VrN5SwcrNFazaXMHKzeWs2lyx3YOMABlpRvcOOfQszOXg/h3p06kXvTvm0rtjHr075tKjQy5ZGWlJ+lQiIrGl+5WkKiXebcif//xnAL7//e8nOZK2p7SyhvVbq1i7tZJ1WytZU1LJ2pJK1pZUsLYkmF+zpZK1WyupjWzfRWeaQdd2OXTvkMPgbu04anAXenbIpVuHHHoV5tKrMJcu7bJJ18AyIpIidL+SVKXEuw156qmnAH2R7UpdU49NpdVsLKtiQ+lX0/rSKjaUVrKhtIp1W6tYX1rJupIqyqtrd9iPGXTOz6ZLu2y6tstmcLd2dG+fQ7f22XRrn7NtKirIIiNdtdUiInV0v5JU1WoTbzM7Efg9kA486O53JTkkSSB3p6I6QklFNVsqqtlcXsOWimq2lAfTprJqNpVXszl8v7m8io1l1Wwqq2JTWTU1kYYHjspMNzrlZ9EpP5uigiwGFOXTOT+LonbZFBVk07kgiy4FQaLdKV8JtYiIiDRdq0y8zSwduB84DigGPjazF919dnIjk8a4O9W1TnlVLaVVNZRV1VIWvpZX1bK1soayqhq2VtZSWllDaVVN8FpZS0lFNSUVNWytrIl6rd6uy7yG5GWlU5ibSfvcTArzMhnUtYDCvCw65mXSMS+LwvC1Y34WnfOz6FSQRbvsDD2kKCIiInHRKhNv4BBggbsvBDCzfwGnAymfeLsHfTxH3KmNBFNN9GutUxOJUBNxqmqC15raCNXh8uraCFU1TnVt3fvgtbLmq6mqJkJlTS1VNREqqoP3da+V1REqamqpqK6lvLqW8qrItvf12z7vTFZGGgXZGeRnp9MuO5N2ORn06JDDoK4ZFORk0C4nk/Y5mbTPrXufQfvc4LVDbhYdcjP1MKKIiIi0KK018e4FLIuaLwYOTVIsjbr7tblM+GwlwHajBQI4jvv2y90dD8tGot6DEwmXRSLBdrXuwbxDJOLUurNy4XoAhv78tbh+rqz0NLIz0sjKSCMnM53sjDSyM9PJyQyWd8rPIjczndzMdHKy0r96n5lGblYGeVnp4ZRBflY6uVnp5GdnkJ+dQUFWBnnZ6WSqCYeIiIi0Ma018W6oLcAO1almNhYYG85uNbN5cY3qK0XAugQdawdL7j41WYfeE0k9Z62Qzlfz6Hw1n85Z8+h8NV+RmemcNZ2useZL1jnr19iK1pp4FwN9ouZ7AyvqF3L38cD4RAVVx8ymuvuoRB+3NdM5ax6dr+bR+Wo+nbPm0flqPp2z5tH5ar6WeM5a69/zPwYGmdkAM8sCLgBeTHJMIiIiIiKNapU13u5eY2bXAK8TdCf4kLvPSnJYIiIiIiKNapWJN4C7TwAmJDuORiS8eUsboHPWPDpfzaPz1Xw6Z82j89V8OmfNo/PVfC3unJnX725DRERERERirrW28RYRERERaVWUeO8BMzvRzOaZ2QIzu6mB9WZmfwjXzzSzA5MRZ0tgZn3M7B0zm2Nms8zs2gbKjDGzzWY2I5xuS0asLYmZLTazz8LzMbWB9brGQmY2JOramWFmW8zsx/XKpPw1ZmYPmdkaM/s8alknM3vTzL4IXzs2su1Ov/PaokbO12/MbG74f+7fZlbYyLY7/f/bVjVyzsaZ2fKo/3snN7KtrrFg2ZNR52qxmc1oZNuUu8YayydazfeYu2vajYngoc4vgb2ALOBTYFi9MicDrxL0O34Y8FGy407i+eoBHBi+bwfMb+B8jQFeTnasLWkCFgNFO1mva6zh85IOrAL61Vue8tcYcBRwIPB51LJfAzeF728C7m7knO70O68tTo2cr+OBjPD93Q2dr3DdTv//ttWpkXM2Drh+F9vpGmt4/T3AbY2sS7lrrLF8orV8j6nGe/dtG7be3auAumHro50OPOqBKUChmfVIdKAtgbuvdPdPwvclwByCEUhlz+gaa9gxwJfuviTZgbQ07j4J2FBv8enAI+H7R4AzGti0Kd95bU5D58vd33D3mnB2CsFYEhJq5BprCl1j9ZiZAecBTyQ0qBZsJ/lEq/geU+K9+xoatr5+ItmUMinHzPoDI4GPGlh9uJl9amavmtnwxEbWIjnwhplNs2Ak1vp0jTXsAhq/Ueka21E3d18JwU0N6NpAGV1rDfsewV+dGrKr/7+p5pqwec5DjTQD0DW2oyOB1e7+RSPrU/oaq5dPtIrvMSXeu68pw9Y3aWj7VGJmBcCzwI/dfUu91Z8QNA04APgj8HyCw2uJvubuBwInAT8ws6Pqrdc1Vo8Fg2p9E3i6gdW6xnafrrV6zOz/ATXAPxspsqv/v6nkL8BAYASwkqD5RH26xnZ0ITuv7U7Za2wX+USjmzWwLKHXmBLv3deUYeubNLR9qjCzTIL/JP909+fqr3f3Le6+NXw/Acg0s6IEh9miuPuK8HUN8G+CP5NF0zW2o5OAT9x9df0VusYatbquiVL4uqaBMrrWopjZd4BTgYs8bDxaXxP+/6YMd1/t7rXuHgH+RsPnQtdYFDPLAM4CnmysTKpeY43kE63ie0yJ9+5ryrD1LwLfDnueOAzYXPdnkFQTtlP7OzDH3e9tpEz3sBxmdgjB9bk+cVG2LGaWb2bt6t4TPND1eb1iusZ21GgNka6xRr0IfCd8/x3ghQbKNOU7LyWY2YnAjcA33b2skTJN+f+bMuo9e3ImDZ8LXWPbOxaY6+7FDa1M1WtsJ/lE6/geS+STnG1tIuhRYj7BE7L/L1x2FXBV+N6A+8P1nwGjkh1zEs/VaII/58wEZoTTyfXO1zXALIKnjKcARyQ77iSfs73Cc/FpeF50je36nOURJNIdopbpGtv+HD1B8Kf+aoLan8uAzsDbwBfha6ewbE9gQtS2O3znxTHOvwI/34PtHdg7TudrAUE70brvsr/WP1+N/f9NhamRc/ZY+B01kyDR6ZHsa6ylTA2dr3D5w3XfXVFlU/4ao/F8osV9jzU0aeRKEZEWxMwmAv9w9wcTdLz+wCIg07/qqaNFMbMxBOekyb2HmJkDg9x9QbziEhFpLjU1ERFJkLDNZqs/hoiI7B4l3iIicRSOLHejmc0ESs0sw8wOM7MPzWxT2LXhmLDsnQTdh/3JzLaa2Z/MrL+ZeXRCbWYTzezy8P2lZvaBmf3OzDYA48zsYTO738xeMbMSM/vIzAY2EuKk8HVTeMzDzSzNzG41syUWjKj3qJl12MlnPN2+Gi30y7ANNGb2XQtGlysxs4VmdmXUNmPMrNjMbjGzdeF5uihq/cNmdkfYdvVVoGcY31Yz62lmh5jZ5PAcrgzPVVbz/4VERBJHibeISPxdCJwCFALdgFeAO4BOwPXAs2bWxd3/H/AecI27F7j7NU3c/6HAQoJ+a++MOuYvgI4EbZLvbHhT6rofKwyPORm4NJyOJmhHWgD8qaGNw4dUHwV+Fn6+owhG04OgV4FTgfbAd4HfmdmBUZt3B4oI+tH9DjDezIZE79/dSwl6qlkRxlfgQU8OtcBPwu0PJxg06fuNfEYRkRZBibeISPz9wd2XuXs5cDHBgz4T3D3i7m8CUwke+NldK9z9j+5eEx4D4Dl3/2/YbvufBP0nN9VFwL0ejO62FbgZuKCRZiyXAQ+5+5vh51nu7nMB3P0Vd//SA+8CbxDU6Ef7ubtXhutfIRilb5fcfZq7Twk/82LgAeDrzfiMIiIJp8RbRCT+okdK6wecGzaR2GRmmwie0u/R4JbN33+dVVHvywhqrZuqJ7Akan4JkEFQW19fH4LeAXZgZieZ2RQz2xB+zpMJaqjrbAxrtKOP07MpAZrZYDN72cxWmdkW4Jf19i0i0uIo8RYRib/o7qOWAY+5e2HUlO/udzVQFqAuMc2LWtZ9J/vfk9jqrCD4gVCnL8EIjTsMSkTweXZoP25m2QQDXPyWYCjnQmAC248c1zFswx19nIYGs2goxr8Acwl6LmkP3FJv3yIiLY4SbxGRxPoHcJqZnWBm6WaWEz5oWNdV3mqCdtUAuPtaYDlwcVj+ezSQ6O6BtUAk+pgE/Qr/JBxkooCgNvnJRrob/DvwXTM7Jnwos5eZDQWygOxw/zVmdhLBAB/1/cLMsszsSIL24E83UGY10LneA57tgC3A1vB4VzfnQ4uIJIMSbxGRBHL3ZcDpBDW0awlqjH/GV9/HvwfOMbONZvaHcNkVYZn1wHDgwxjGU0bw4OUHYdOXw4CHCAY8mUTQx3cF8MNGtv8v4YOTwGbgXaCfu5cAPwKeAjYC32LHEeJWhetWELRDv6qufXi9Y8wl+DGwMIyxJ8FDqd8CSgiGIG90WG0RkZZCA+iIiEjC7c6gOCIirZ1qvEVEREREEqDFJd5mdqKZzTOzBWZ2007KHWxmtWZ2TiLjExERERHZHS2qqYmZpQPzgeOAYuBj4EJ3n91AuTcJ2h0+5O7PJDpWEREREZHmaGk13ocAC8JBG6qAfxE8hFTfDwm6qVqTyOBERERERHZXS0u8e7H9QBDF4bJtzKwXcCbw1wTGJSIiIiKyRxoa/jeZGhr8oH5bmPuAG9291mznYyWY2VhgLEB+fv5BQ4cOjUWMLdZns+ZQE3FG7jeMjRs3Ulpairvj7kQiESKRyLb56OXR8126dKFr167J/igiItKGzZs3D4AhQ4YkORKR2Js2bdo6d+/S0LqWlngXEww/XKc3O45iNgr4V5h0FwEnm1mNuz9ff2fuPh4YDzBq1CifOnVqPGJuMYaMPIwl60t5490PufdXt/PLX/6S5rThz8rK4t577+Wcc/S8qoiIxM+YMWMAmDhxYlLjEIkHM1vS2LqW1tTkY2BQOFpaFnAB9QZccPcB7t7f3fsDzwDfbyjpTkU5mcE/55L1pfziF7/g8MMPJzMzs8nbd+nShbPOOite4YmIiIiktBaVeIfDEV8DvA7MAZ5y91lmdpWZXZXc6Fq+nIx0AJZuKCM9PZ0XXniBwsLCJm1bUFDA//7v/5KW1qIuCREREZE2I2ZNTcyshB3bY0PQbtvdvX1T9uPuE4AJ9ZY1+CClu1/azDDbtB7duvD5+ghL1pcBUFRUxIQJEzjqqKMoLy/f6bZVVVX83//9H0OGDOGII45IRLgiIpKiOnfunOwQRJKiRfXjHU+p0MYb4NBfvsXovbtwz3kHbFv2wAMPcN1111FWVrbL7fPy8hgyZAi/+tWvOP7449nVA6wiIiIi8hUzm+buoxpap3YFbUy/Tvks3VC63bIrr7ySM844g9zc3F1uX1ZWxvTp0zn77LMZMmQITz/9NLW1tfEKV0RERCRlxCXxNrOOZnaImR1VN8XjOLK9m2++mSWvP7itqUm0v//97/Tr16/JbbhLS0v54osv+N73vke/fv146KGHqKqqinXIIiKSgm6++WZuvvnmZIchknAxT7zN7HJgEsEDkr8IX8fF+jiyo8mTJ7Nh0eesKamkrKpmu3U5OTm89tprFBQUbLc8NzeXLl267LC8ztatW1m+fDnXXnstPXv25L777mtSkxUREZHGTJ48mcmTJyc7DJGEi0eN97XAwcASdz8aGAmsjcNxpAHRPZvU169fP5566qltTU6ys7O5+uqrWbFiBX/+85/p27fvThPw9evXc+utt9K9e3duv/12Nm3aFLfPISIiItLWxCPxrnD3CgAzy3b3uYCGpkqQ7G19eTdcK33CCSdwww03kJubi5lxww03kJGRwSWXXMKiRYv4xz/+wT777EN+fn6D25eWllJSUsJdd91Fr169+OlPf8rq1avj9nlERERE2op4JN7FZlYIPA+8aWYvAMvjcBxpQE5mWOPdSOINcNttt3HkkUdy6aWX0q1bt23L09LSOP3005k1axYvvPAChxxyCHl5eQ32bFJeXk5ZWRn3338//fv35/LLL2fJkkYHahIRERFJefFIvOe7+yZ3Hwf8HPg7MDcOx5F6evfuTf++fWifk8GSej2bREtLS+O1117j/vvvb3C9mXHMMcfw0Ucf8c4773DMMceQm5vb4IOZlZWVVFRU8OijjzJ06FDOPfdc5syZE7PPJCIibU/v3r3p3bt3ssMQSbiY9+NtZp+4+4H1ls109/1jeqBmSpV+vAFO++P7FOZl8thlh8Zsn7NmzeK2225jwoQJ1NTUUFNT02C59PR0MjMzOeqoo7jjjjs4+OCDYxaDiIiISEuXkH68zexqM/sMGGpmM6OmRcDMWB1Hdq1v57wGH67cE8OHD+fZZ59l9uzZXHLJJeTk5JCVlbVDudraWioqKnjzzTcZM2YMRxxxBBMnTiRVBmoSERERaUwsm5o8DpwGvBC+1k0HufvFMTyONOLHP/4xP/7xj+nXKY/lG8upqY3E/BgDBgzgoYceYuHChVx99dXk5eWRk5OzQzl3p6ysjMmTJ3Pqqaey33778dJLLxGJxD4mERFpXeruVyKpJmaJt7tvdvfF7n6huy+JmjbE6hiyczNmzGDGjBn065xHTcRZsakibsfq0aMH9913H8XFxdxwww0UFBSQl5fXYNnS0lJmzZrFt771LQYOHMg///nPRpuqiIhI21d3vxJJNbFsavJ++FpiZluiphIz2xKr48iu9escdAW4eH3jD1jGSseOHfnFL37BqlWruP322+nUqVOjXRFu3bqVxYsXc9VVV9G7d2/+8pe/UFERvx8HIiIiIi1JLGu8R4ev7dy9fdTUzt3bx+o4smv9Ogc1z0ti3M57Z/Lz8/npT3/KihUruPfee+nRo8dOB+NZvXo1P/vZz+jRowe//vWv2bp1a8JiFREREUmGeHQnKEnWrV0OWRlpLE1AjXd92dnZjB07lmXLlvHggw8ycODARhPw0tJSNm3axC9+8Qt69OjB//t//4/169cnOGIRERGRxIh54m1mOWZ2nZk9Z2bPmtlPzGzHp+8k5gYPHszgwYNJSzP2Kspn7qqSpMWSnp7O+eefzxdffMFTTz3FAQcc0GgTlLKyMrZu3cq9995Lnz59uOaaa1i+XGMuiYi0VXX3K5FUE49+vJ8CSoB/hIsuBDq6+7kxPVAzpVI/3gA3PzeTV2auZMZtx5OWtuPIk8nw3nvvccsttzBt2jQqKioa7WIwKyuLtLQ0zj33XP7nf/6HgQMHJjhSERERkd2TkH68owxx98vc/Z1wGgvoZ22CjehTyJaKGhYloblJY4488kjee+89PvjgA0466SRycnJIT0/foVxVVRUVFRU8/vjj7Lvvvpx++unMnKmu4EVERKR1i0fiPd3MDqubMbNDgQ/icBypZ+zYsYwdOxaAkX07AjB96aYkRtSwkSNH8sorrzBjxgzOO+88cnJyyMzM3KFc3WA8L7/8MocddhhHH300kydPTkLEIiISS9H3K5FUEo/E+1DgQzNbbGaLgcnA183sMzNTtWUczZ8/n/nz5wOwd5cC2mVnMH3pxiRH1bghQ4bw+OOPM3/+fL73ve+Rm5vb4GA8kUiE8vJyJk6cyNe+9jU2b96chGhFRCRWou9XIqkkHon3icAA4OvhNAA4GTiVYCRLSYC0NGP/Ph2YsWxTskPZpT59+vDXv/6VJUuW8KMf/Yj8/Hxyc3N3KGdmHH/88XTo0CEJUYqIiIjsmZgn3u6+BNgCdAP61U11I1nG+njSuJF9OjJ3VQnlVbXJDqVJunTpwt13382KFSu49dZb6dChw3Y9oeTm5nLHHXckMUIRERGR3ReP7gQvByYBrwO/CF/Hxfo4smsj+xZSG3E+W966mma0b9+eW265hZUrV3LXXXfRpUsXsrOzOeCAAxg1qsGHhEVERERavIw47PNa4GBgirsfbWZDCRJwibMRI0ZsP9+nEIDpSzdyyIBOiQ9oD+Xm5nLNNddw5ZVX8vTTT+/w+UREpHXS97mkqngk3hXuXmFmmFm2u881syFxOI7Uc999920337kgm76d8lpFO++dyczM5Fvf+tZOyxQUFDRr2PmJEyfy29/+lpdffpkXX3yR2bNnc9NNN+1pqCIi0gT171ciqSIeiXexmRUCzwNvmtlGYEUcjiNNMLJvIR8t3JDsMFq0b37zm3zzm99MdhgiIiLSxsXj4coz3X2Tu48Dfg78HTg91seRHV188cVcfPHF2y0b0aeQVVsqWLm5PElRJdbEiRMZM2YM55xzDkOHDuWiiy7aNkLma6+9xtChQxk9ejTPPffctm0efvhhrrnmGgBeeuklDj30UEaOHMmxxx7L6tWrk/I5RETasobuVyKpIB4PVz4S1njj7u8C7wEPxPo4sqPi4mKKi4u3W1Y3kM6MFjiQTrxMnz6d++67j9mzZ7Nw4UI++OADKioquOKKK3jppZd47733WLVqVYPbjh49milTpjB9+nQuuOACfv3rXyc4ehGRtq+h+5VIKohHP977u/umuhl33wiMbOrGZnaimc0zswVmtkOjWzM73cxmmtkMM5tqZqNjE3bbtE+PdmSlpzG9lbfzbo5DDjmE3r17k5aWxogRI1i8eDFz585lwIABDBo0CDNrtKaluLiYE044gf3224/f/OY3zJo1K8HRi4iISFsVj8Q7zcw61s2YWSea2JbczNKB+4GTgGHAhWY2rF6xt4ED3H0E8D3gwVgE3VZlZ6QzvFf7lKrxzs7O3vY+PT2dmpoaIBiAZ1d++MMfcs011/DZZ5/xwAMPUFFREbc4RUREJLXEI/G+h2DI+P81s9uBD4Gm/r3+EGCBuy909yrgX9RrH+7uW72u0S7kA47s1Mg+HZm5fBPVtZFkh5I0Q4cOZdGiRXz55ZcAPPHEEw2W27x5M7169QLgkUceSVh8IiIi0vbF4+HKR4GzgdXAWuAsd3+siZv3ApZFzReHy7ZjZmea2VzgFYJabwEOP/xwDj/88B2Wj+hbSEV1hHmrSpIQVcuQk5PD+PHjOeWUUxg9ejT9+vVrsNy4ceM499xzOfLIIykqKkpwlCIiqaGx+5VIW2dfVR4nn5mdC5zg7peH85cAh7j7DxspfxRwm7sf28j6scBYgL59+x60ZElqjli/bEMZR/76Hf73jH255LCGE04RERER2XNmNs3dGxxqOx5NTfZEMdAnar43O+kD3N0nAQPNrMGqSXcf7+6j3H1Uly5dYhtpK9K7Yy5FBdlMX7ox2aGIiIiIpKyWlnh/DAwyswFmlgVcALwYXcDM9rbwKTkzOxDIAtYnPNIW6Oyzz+bss8/eYbmZMaJPYasfwVJERNqGxu5XIm1dPPrxvrspyxri7jXANcDrwBzgKXefZWZXmdlVYbGzgc/NbAZBDyjne0tqL5NE69evZ/36hn+DjOxbyMK1pWwqq0pwVCIiItvb2f1KpC2LR433cQ0sO6mpG7v7BHcf7O4D3f3OcNlf3f2v4fu73X24u49w98Pd/f0Yxd2mjexTCKBabxEREZEkiVnibWZXm9lnwJBwgJu6aREwM1bHkd2zf59CzJR4i4iIiCRLkwa2aaLHgVeBXwHRI06WuPuGGB5HdkNBdgZDurVjegoNpCMiIiLSksQs8Xb3zcBm4MJY7VOa55hjjtnp+hF9Cnn181W4e5NGcRQREYmHXd2vRNqqWNZ4A2BmjwDXuvumcL4jcI+7a6CbOPv5z3++0/Uj+xbyr4+XsWhdKXt1KUhQVCIiItvb1f1KpK2Kx8OV+9cl3QDuvhEYGYfjSDON7NsRQM1NRERERJIgHol3WljLDYCZdSIONeuyo5NOOomTTmq8A5mBXQooyM7QA5YiIpJUu7pfibRV8UiI7wEmm9nT4fy5wC/jcBypp7y8fKfr09OCgXQ+WqS+U0VEJHl2db8SaatiXuPt7o8CZwGrw+mscJm0AMfs05X5q7eyaF1pskMRERERSSnxGLnyNuAcoFM4nRMukxbghOHdAXh91qokRyIiIiKSWuLRxrs0aqolGLWyfxyOI7uhZ2EuB/TuwKufK/EWERERSaSYt/F293ui583st8CLsT6O7OjUU09tUrkT9u3Or1+bx4pN5fQszI1zVCIiIttr6v1KpK0xd4/vAYIeTv7r7oPieqBdGDVqlE+dOjWZIbQYC9du5Rv3vMu404Zx6dcGJDscERERkTbDzKa5+6iG1sWjjfdnZjYznGYB84A/xPo4svv26lLA4G4FvKZ23iIiIiIJE4/uBKP/flQDrHb3mjgcR+oZM2YMABMnTtxl2ROHd+dP7yxg/dZKOhdkxzcwERGRKM25X4m0JTFLvM3sup2sw93vjdWxZM+dsG93/vCfBbw1ZzXnH9w32eGIiIiItHmxbGrSLpxGAVcDvcLpKmBYDI8jMTCsR3v6dMrlNfVuIiIiIpIQMavxdvdfAJjZG8CB7l4Szo8Dnt7JppIEZsaJw7vzyIdL2FJRTfuczGSHJCIiItKmxaMf775AVdR8FerHu0U6cd/uVNVGeGfummSHIiIiItLmxePhyseA/5rZvwEHzgQeicNxpJ7zzjuvWeVH9ulIl3bZvD5rFaeP6BWnqERERLbX3PuVSFsRl368zexA4MhwdpK7T4/5QZpJ/Xg37NbnP+PZacuZfttx5GSmJzscERERkVYtof14A7j7J+7++3BKetKdKsrKyigrK2vWNicO70F5dS2T5q+NU1QiIiLb2537lUhbEI+mJpjZAXxV4/2eu38aj+PI9k4++WSgef2iHrpXJzrkZvLarFUcP7x7nCITERH5yu7cr0TagniMXHkt8E+gazj9w8x+GOvjSGxkpqdx7D7deGv2aqprI8kOR0RERKTNikdTk8uAQ939Nne/DTgMuCIOx5EYOXHf7mypqGHKwvXJDkVERESkzYpH4m1AbdR8bbhMWqgjBxWRl5WuwXRERERE4igeiff/AR+Z2bhw8JwpwN/jcByJkZzMdI4e0pXXZ62isqZ21xuIiIiISLPF9OFKMzOCUSonAqMJarq/q55NEuPSSy/d7W3PP7gPr3y2kpc+Xck5B/WOXVAiIiL17Mn9SqQ1i3k/3mHfhQfFdKcxoH68d87dOfG+9zCDV689kuA3lIiIiIg0R6L78Z5iZgfv7sZmdqKZzTOzBWZ2UwPrLzKzmeH0Ydh1oQDr1q1j3bp1u7WtmXHZkQOYu6qE9xfs3j5ERESaYk/uVyKtWTwS76MJku8vw+T4MzOb2ZQNzSwduB84CRgGXGhmw+oVWwR83d33B/4XGB/D2Fu1c845h3POOWe3tz99RE+KCrJ58L1FMYxKRERke3t6vxJpreIxgM5Je7DtIcACd18IYGb/Ak4HZtcVcPcPo8pPAdQgOUayM9L5zuH9uOfN+cxfXcLgbu2SHZKIiIhImxGPGu/VwNnA74B7gbPCZU3RC1gWNV8cLmvMZcCruxGjNOLiw/qRk5nGg+8tTHYoIiIiIm1KPBLvR4HhwB+BPwH7AI81cduGnuhr8OlPMzuaIPG+sdGdmY01s6lmNnXt2rVNDCG1dczP4pyDevP89BWsKalIdjgiIiIibUY8Eu8h7n6Zu78TTmOBwU3cthjoEzXfG1hRv5CZ7Q88CJzu7o0Ot+ju4919lLuP6tKlSzM+Qmr73tcGUB2J8I/JS5IdioiIiEibEY823tPN7DB3nwJgZocCHzRx24+BQWY2AFgOXAB8K7qAmfUFngMucff5sQu79bv66qtjsp+9uhRwzNBuPDZlCVeP2ZvcrPSY7FdERARid78SaW3i0Y/3HGAIsDRc1BeYA0QAD3sj2dn2JwP3AenAQ+5+p5ldRbDxX83sQYI25HXVsTWN9ZUYTf14N89HC9dz/vgp3HHGvlx8WL9khyMiIiLSKuysH+94JN47zdLcPSntF1Ih8V62LHgutU+fPrsouWvuzun3f8DWihreuu7rpKVpQB0REYmNWN6vRFqanSXeMW9qkqzEWuCSSy4BYOLEiXu8LzPjstEDuPZfM/jP3DUcO6zbHu9TREQEYnu/EmlN4vFwpbQRJ+/Xg54dcvibuhYUERER2WNKvKVRmelpfG/0AD5atIFJ89Udo4iIiMieUOItO3XxYf3o3zmPcS/OorKmNtnhiIiIiLRaMUu8zazEzLY0MJWY2ZZYHUcSKycznXHfHM7CdaU8+N6iZIcjIiIi0mrF7OFKd28Xq33J7vnpT38al/2OGdKVE4d354//+YIzRvaiV2FuXI4jIiKpIV73K5GWLubdCQKYWUdgEJBTt8zdJ8X8QM2QCt0JxtPyTeUcc89Evj64Cw9csstu00VERERS0s66E4x5G28zuxyYBLwO/CJ8HRfr48iO5s2bx7x58+Ky716FufzwG4N4fdZq3pm3Ji7HEBGR1BDP+5VISxaPhyuvBQ4Glrj70cBIQF1iJMCVV17JlVdeGbf9X37kAPYqymfci7OoqNaDliIisnvifb8SaanikXhXuHsFgJllu/tcgiHkpZXLzggetFyyvoy/TVLf3iIiIiLNEY/Eu9jMCoHngTfN7AVgRRyOI0lw1OAunLxfd/70zgKWbShLdjgiIiIirUbME293P9PdN7n7OODnwN+B02N9HEmen586jPQ04xcvzU52KCIiIiKtRjwersw2s2+Z2S3A14ERwM2xPo4kT48OufzomEG8NWc1/55enOxwRERERFqFmPXjHeUFYDMwDaiMw/6lEbfeemvCjnXZ6AG8M3cNNz/3GUO6tWdYz/YJO7aIiLRuibxfibQkMe/H28w+d/d9Y7rTGFA/3rG3tqSSU//4HtkZ6bx0zWg65GUmOyQRERGRpEpoP97Ah2a2Xxz2K7swY8YMZsyYkbDjdWmXzZ8vOpCVm8u57qkZRCKxH4xJRETankTfr0RainjUeM8G9gYWETQ1McDdff+YHqiZUqHGe8yYMQBMnDgxocd9dPJibnthFj85djDXHjsooccWEZHWJ1n3K5FE2FmNdzzaeJ8Uh31KC3bJYf2YsXQT9709n/37dODoIV2THZKIiIhIixOP7gSXNDTF+jjScpgZd565H0O7t+faJ6azdL369xYRERGpL2aJt5m9H76WmNmWqKnEzLbE6jjSMuVmpfPAxQdhZlz5j2mUV2lIeREREZFoMUu83X10+NrO3dtHTe3cXX3NpYC+nfO474IRzF21hSv/MY2KaiXfIiIiInXi0cZbkuSXv/xlskPg6CFdufus/bnxuZmMfWwa4y85iJzM9GSHJSIiLUhLuF+JJEM8ejW5roHFm4Fp7j4jpgdrhlTo1aQleerjZdz43EyOGtSFB5R8i4iIALB48WJOPfVUPv/8823Lxo0bR0FBAaNHj+baa6+lsrKSyspKzj//fMaNG7et3LXXXsszzzzDsmXLSEuLR4/QEguJ7sd7FHAV0CucxgJjgL+Z2Q1xOJ6EPvzwQz788MNkhwHAeQf34e6z9ufd+Wu5Ss1OREQkSku6X7Uk3/nOdxg/fjwzZszg888/57zzztu2LhKJ8O9//5s+ffowadKkJEYpeyIeTU06Awe6+1YAM/sf4BngKIJh5H8dh2MKcMsttwAtp1/U8w7ug+Pc+OxnXP2Pafz1koPIzlDNt4hIqmtp96uWYs2aNfTo0QOA9PR0hg0btm3dO++8w7777sv555/PE088sa0vdGld4lHj3ReoipqvBvq5eznBgDqSQs4/uC93nbUf78xby1WPTaOyRjXfIiIiDfnJT37CkCFDOPPMM3nggQeoqKjYtu6JJ57gwgsv5Mwzz+Tll1+muro6iZHK7opH4v04MMXM/ies7f4AeMLM8oHZcTietHAXHNKXX4XJ9yV//y/rtur3l4iIpCYza3T5bbfdxtSpUzn++ON5/PHHOfHEEwGoqqpiwoQJnHHGGbRv355DDz2UN954I5FhS4zEtKmJBVfTw8AEYDTBcPFXuXvdU40XxfJ40npceEhf8rLSueGZmXzzj+8z/tuj2LdXh2SHJSIiklCdO3dm48aN2y3bsGEDAwYMAGDgwIFcffXVXHHFFXTp0oX169fzwQcfsHnzZvbbbz8AysrKyMvL45RTTkl4/LJnYlrj7UEXKc+7+zR3/7273xeVdDeJmZ1oZvPMbIGZ3dTA+qFmNtnMKs3s+pgFL3F3+ohePHv1EQCc/ZcPeWHG8iRHJCIiklgFBQX06NGDt99+GwiS7tdee43Ro0fzyiuvUNfb3BdffEF6ejqFhYU88cQTPPjggyxevJjFixezaNEi3njjDcrKNFJ0axOP7gTvBx529493Y9t0YD5wHFAMfAxc6O6zo8p0BfoBZwAb3f23Tdl3KnQnOGPGDABGjBiR1Dh2Zd3WSr7/z0/476INjD1qL244YQgZ6eoWSUQkVbSW+1W8zJ49mx/84Afbar5/9rOfcdFFF3HBBRfwySefkJeXR0ZGBnfeeSdHHnkkvXv3ZvHixbRv/9V4hGeddRbnn38+559/frI+hjRiZ90JxiPxng0MBpYApQTNTdzd92/CtocD49z9hHD+ZoKNf9VA2XHAViXerVN1bYT/fXk2j05ewpGDivjjhSMpzMtKdlgiIiIie2RniXc8uhM8aQ+27QUsi5ovBg7ds3BSx1tvvQXAsccem+RIdi0zPY3bT9+X4T3b8/PnZ3Hife/xy7P25RtDuyU7NBERibPWdL9qrsrKSiKRCLm5uckORVqgmP99392XAFuAbgRNQuqmpmjoUd/drpI3s7FmNtXMpq5du3Z3d9Nq3HHHHdxxxx3JDqNZzj+4L89efQQdcjP53sNTue6pGWwqq9r1hiIi0mq1xvvVrrg7jz/+OL169eKkk/akDlLaspgn3mZ2OTAJeB34Rfg6rombFwN9ouZ7Ayt2NxZ3H+/uo9x9VJcuXXZ3NxJn+/XuwIs//Bo/+sbevDhjBcf9bhJvzFqV7LBERESa5OOPP2bEiBGMHTuW9evXM3XqVF577bVkhyUtUDyeaLsWOBhY4u5HAyOBplY3fwwMMrMBZpYFXAC8GIcYpYXJzkjnuuOH8MI1X6OoIJuxj03jh09MZ0Opar9FRKRlWrFiBeeeey5f//rXmTlzJqWlpQCUlpYyduxYDXIjO4hH4l3h7hUAZpbt7nOBIU3Z0N1rgGsIasnnAE+5+ywzu8rMrgr32d3MioHrgFvNrNjM2je+V2lNhvfswIvXfI3rjhvMa5+v5OjfTuTB9xZqxEsREWkxysvLGTduHIMGDeKFF16gvLx8hzKrV6/mkUceSUJ00pLF4+HKYjMrBJ4H3jSzjTSjuYi7TyAYgCd62V+j3q8iaIIibVRmeho/OmYQJ+7bnTtfmcMdr8zh4Q8X87MThnDa/j1JS2t41C8REZF4cneeeuopfvjDH1JaWtpoP9p5eXkcdthhHH/88QmOUFq6mHcnuN3Ozb4OdABec/ekthlIhe4E582bB8CQIU36A0Or8f4X6/jlhDnMXrmF/Xp14OaTh3LEwKJkhyUiIrupNd6vPvnkEy6//HLmz5+/rUlJffn5+RQVFTF+/Hgl3Sksof14t1SpkHi3ZZGI88Kny/nt6/NZvqmcrw/uwg+O3puD+3fETDXgIiISH6tWreInP/lJo01KALKzs8nKyuLOO+/k6quvJiMjHg0KpLVI9AA6o4D/R9CF4LYrrykD6MRTKiTeL730EgCnnXZakiOJn4rqWh7+cDHjJy1kQ2kVI/sWcuVRAzl+WDc1QRERaSVaw/2qoqKC3/zmN9x1111UV1c3+KBkWloa2dnZfPvb3+ZXv/oVHTt2TEKk0tIkOvGeB/wM+AyI1C0P+/dOmlRIvMeMGQPAxIkTkxpHIpRX1fLMtGWMf28hyzaUs1dRPlcctRdnjuxFTmZ6ssMTEZGdaMn3K3fn2Wef5Qc/+AFbt25ttB13fn4+Bx10EA888ABDhw5NcJTSkiV65Mq17q4uACWucrPSueTw/lx4SF9e/XwVD0z6kpuf+4x73pjHOQf14YKD+9C/KD/ZYYqISCsyY8YMLr/8cubOnbvTdtydOnVi/PjxnHjiiQmOUFq7eCTe/2NmDwJvA5V1C939uTgcS1JcRnoapx3Qk1P378GHX67n/z5YxPhJX/LXd7/k8L06c8EhfThheHfVgouISKNWr17NT3/6U5577rmdtuPOzMzk9ttv55prriEzMzPBUUpbEI/E+7vAUCCTr5qaOKDEW+LGzPja3kV8be8iVm2u4NlPivnXx0u59l8zKMzL5IwRvThjZC8O6N1BD2OKiAgAlZWV3Hvvvdxxxx3U1NRQVbVjB2xmRk5ODhdddBF33XUXnTt3TkKk0lbEI/E+wN33i8N+RZqke4ccfnD03lz99YFMXrieJ/67lMc/WsrDHy6md8dcTtm/B6fu15N9e7VXEi4ikoLcneeff57vf//7bNmyZaftuA844ADGjx/P8OHDExyltEXxeLjyb8Dv3H12THe8h1Lh4cply5YB0KdPnyRH0vJsLq/mzdmreWXmCt77Yh01Eadf5zxO2a8Hxw3rxgG9C9UriohIgiTzfjVz5kyuuOIKZs2atdN23IWFhfz1r3/llFNOUSWNNEuiezWZAwwEFhG08TbA1Z2gtBSbyqp4Y9ZqXpq5gg+/XE9txOmcn8XXB3fh6KFdOWpwFzrkqu2eiEhbsnbtWq6//nqeeuopKisraSj/ycrKIjMzk3HjxvGjH/2IrKysJEQqrV2iE+9+DS1Xd4Lx9+STTwJw/vnnJzmS1mNTWRXvzl/LO3PXMHH+WjaVVZOeZhzUryNHDSri8IGd2b93IZnpackOVUSkzUjk/aqqqor77ruP22+/nerq6p22477gggu4++676dKlS9zjkrZLI1eSGol3S+4XtTWojTgzlm3knblr+c/cNcxeuQWAvKx0Du7ficMHduaIgZ0Z3rMD6WqWIiKy2xJxv3J3XnrpJa6++mo2b96802Yl++67L3/729/Ybz89oiZ7LtH9eIu0SkFNdycO6teJ608YwobSKj5auJ4Pv1zP5IXruevVuQDkZ6Uzom8hB/btyIH9OnJgn450yFPTFBGRlmLWrFlcccUVzJw5s9GEOy8vj/bt2/OXv/yF008/Xe24JSHimnibWXd3XxXPY4jES6f8LE7arwcn7dcDgDVbKpi8cD1TF2/kk6Ubuf+dBUTCPxjt3bWAkX0K2a93B/bt1YFhPdqr73ARkQRbt24dN954I0888QQVFRWNtuPOyMjg5z//OT/5yU/Izs5OQqSSquJd4z0BODDOxxBJiK7tczh9RC9OH9ELgNLKGj4t3sQnSzYybclG3p67hqenFQNB7fmgrgUM79mBfXu1Z2j39gzt3o6O+XpQR0Qk1qqrq/njH//I//zP/1BdXU1lZeUOZeracZ999tncc889dO3aNQmRSqqLd+Ktv9tIm5WfncERA4s4YmARELQnXLm5gs+Wb+bz5Zv5bPlm3p2/hmc/Kd62Tbf22QwJk/Ah3doxqFsBe3UpoCBbrb5ERBqyefNmOnTo0Oj6CRMmcOWVV7Jx48adtuPeZ599+Nvf/saIESPiFKnIrsX14Uoz+767/zluB2iGVHi4ct26dQAUFRUlORKp4+6sLalk7qoS5q7aEryuLGHBmq1U1Ua2levRIYeBXQrYu2sBA7vkM6CogH6d8+hZmKsHOUWkzWnq/eq5557jW9/6FvPmzaNfv+07TZszZw5XXnkln3zyyU7bcbdr147777+fs846S+24JSGS1qtJS2rjnQqJt7Qe1bURlqwvZcGaUr5cu5Uv12wNXteWsrWyZlu5rPQ0+nTKpX/nfPp1zqdvp1z6dMqjT6c8enfMJS9LNeUi0jatX7+egQMHUlJSwsknn8xLL70EwIYNG7jpppt47LHHqKqqIhKJ7LBtZmYmmZmZ3HzzzVx//fXk5OQkOnxJYcns1URtvBPo4YcfBuDSSy9Nahyya5npaezdtR17d2233XJ3Z/WWShavL2XxulIWry8LX0v58Mv1lFfXble+qCCLXh2DJLxXYS49O+TQozB8X5hLx7xM1fCISIvTlPvVZZddRnl5OZFIhP/85z+8++67zJgxg1tvvbXRdtwAubm5nHHGGdx777107949DtGL7L5413hPd/eRcTtAM6RCjbf68W7b3J11W6tYtrGMZRvKKN5YTvHGMpZtKGf5pnJWbCqnsmb7mp/sjDS6d8ihW/scurfP2e591/bZdCnIpmv7bNWci0hC7ep+9dxzz3HJJZdQVla2bZmZkZeXt9N23IMGDeLvf/87Bx6oOj9JnmTWeP8tzvsXSRlmRpd22XRpl82BfTvusN7d2VBaxYpNFSzfFCTjqzaXs2pLJas3VzBj2SZWzaqgqmbHP8sWZGfQtV02Re2CZLyoIIvOBdkUhe+L2mXTOT+LjvlZtMvOUC26iMTN+vXrueyyy7ZLuiH4jmso6c7LyyM/P58//elPnHvuufp+khYtrol3S3mwUiQVmBmdC7LpXJDNfr0b7gHA3dlUVs2qLRWsLalkTUkla0oqWLOlkrUlwTRn5RbWba1kS0VNg/vISk+jY34mnfKDZLwwL5NO+VkU5mXRMS+TjnnBsrrXDrmZtMvJ1EOiItIkV1xxxQ5Jd0MyMzPJyMjghhtu4IYbbiA3NzcB0YnsGf19WSSFmBkdw5rrfXrsvGxlTS0bSqtYV1LFutJKNmytYkNpFetLq9hQWrnt/fJN5WworWJLRTWNtVwzg/Y5QRJeN7XPzQheczJpn5tJ+5wM2udm0i4ng3Y5wfLgfQb5WRmkKXEXafOef/55Xn/9daqqqnZaLjc3l9NOO43f/e539OzZM0HRiew5Jd4i0qDsjHR6dMilR4em1SLVRpzN5dVsLKtiU1kVm8qq2VRWzebyajaVV7O5rIpN5dVsKQ+WrdpSweZwvn7b9IYUZAdJeEF2BgV1r9kZ5G97TacgO5OC7HTysoLl+eH7guwM8rLSyQ9fszPS9OdokRZmw4YNfPe7391lbXdGRgaPPvoo55xzToIiE4mdeA8Z/6i7fzuex5CvTJgwIdkhSApLTzM65WfRaTdG56yormVLRTUlFTXhVM2W8uC1pKKGksoatlbUsLWymq2VNdvKrdpcQWllDVvDKdLEZ8XTDPKygiQ8Lyud3Oj3menkbnufQW5WWrgsI3wN5nPCKXe71zSyw9esdCX3Io1p6H7V1CYm7s5DDz2kxFtapZgl3mb2Yv1FwNFmVgjg7t+M1bGkYXl5eckOQWS31CWx9XpXbBZ3p6I6QkllNWWVtZRW1VBWVcvWyppgvrKGsqoaSqtqKa8K1gevtZRHlV1bUklZVS1lVbVUVNdSVtX0hD6aGeRkBEl4TmZQy173ml1/PiOd7My0r95npJGVkfZV2fS0beuzMtLISk8PXjOCBD87TPTr5rMy0shMTyMz3ZT8S4tU/371wgsv8Nprr+2yiQlAbW0t7777LpMmTeKoo46KV4gicRHLGu/ewGzgQcAJEu9RwD0xPIbsxJ//HDzL+v3vfz/JkYgknpmRmxXUVrMHCXx97k51rVNeHSTsda8VNbVUhK/lVREqqoN1FdW1VNYE88EU2W5Z3WtJRZDkV9VGqKyOUFkTobImWN9QzzO7a/tk3LYl5fUT9Mz0ILHPTE8jI1yWlZ5GRrgu+n3dNhlpaWRmpJGZZuF2X63PSDcy0+qWBWXr1mdElU9Piy6XRnqakZGmHwxtXfT9asOGDVx66aVNamKSlZVFeno6VVVV3HzzzXzwwQeJCFckZmKZeI8CrgX+H/Azd59hZuXu/m4MjyE78dRTTwFKvEViyczIyggS1g65mQk5ZiTiQUIeJuFBcl673XxV+L4uYa+qiVBd61TV1G6/vjZCdY1THS6rrg2WVdVEqKkNt6mNsLWyho1ldcuDZdXh+rptayJO7e5U/++GugQ8I83ICJP1jKgE/qv1O59PD5dtNx+uTzcjPap8MB+US4sq/9W2aaSnse01zer2HbxPjyqfXn8+zbYrs+29GWlpRL2Peo1eH5ZvKz9Iou9XL7zwAqWlpbRv337bEO/t2rWjsLCQjh070rlzZ4qKiujYsSMdOnSgffv2dOjQgb333jvJn0Kk+WKWeLt7BPidmT0dvq7enf2b2YnA74F04EF3v6veegvXnwyUAZe6+yd7Gr+ISEuRlmbkpAXNb1qaSMSpjgQJeU1t8COgpta3Jes1kTDRj9Qtj1Ad8W1Jfm3EgzL11tXUBtvU1jo1YZmauve1XyX9wT6+2q42ArWRSFguKFNRU0sk4tu2+WrbyA7L6z5PJAI1kchuNStKJLMgCU+LSsjTohL54DX4IRCd6NdtV5e8R5dJM75aHu63Kevq9psWtc7CberKbIs3KoY0M4o3lgHG79/6gvR+o/nd67O3Ha9uu23z4fHr1mGwxYwZm42ZnxRvVz56O4v6DA2VsXpx1m1jbL+8sXJpUWWjy0W/GtGxBPOWxnbbpYU/prbbNvy3bis/tOQrMX+40t2LgXPN7BRgS3O2NbN04H7gOKAY+NjMXnT32VHFTgIGhdOhwF/CVxERibO0NCM7LZ3sNtonlvv2yXpdcl7r28/XrY94kPBHoteH7+u227aPuvL1tnVn2/7rtv3qPTssq7884tExBj+OIh7MB8vZVqZuW69b71Hlw2NU1dYdZ/t125Zt21cD7z3Yd902HrW81j1cB8s3lgPwu7fmJ/lfvOWr/4OAuuQ/KqkPFwc/Uviq/Hbr6if6aeEPgahkn/qJf7getv+BUXdstsUVfcxgPfWOG33s6LLRx4Ov4o0+fv19fvVD5qt9EV0+3P7g/p04d1Sf+P8jNUPcvjrd/RXglWZudgiwwN0XApjZv4DTCdqO1zkdeNSDse6nmFmhmfVw95WxiFtERFKXWdikpeX9saFNGfPhrwF4+5cnb/sx4R50S+oEybpH+OqHhjs4UQl+A+W3Jf51y7dP/Ot+JDhELd++jIfzjhOJfLUcvtpH/W3r5oP9fhVDXUwO236c1JXZdoyofRKWq/s8kTDQrz4f27/fFgvbfVaPmt/ueFFxRradz+3PR/hRG9kP2z7Pts9V75zVHSd6u5pIZLtY6s4D9Y8dVQZ23I9Hxbf9vr46LkTHSMKaBzZHS6uz6AUsi5ovZsfa7IbK9AKUeIuIiLQi6WlGOmpOIamjpSXeDf3vq9/irillgoJmY4Gx4exWM5u3B7E1RxGwLkHH2kErbROW1HPWCul8NY/OV/PpnDWPzlfzFZmZzlnT6RprvmSds36NrWhpiXcxEN0YpzewYjfKAODu44HxsQywKcxsqruPSvRxWzOds+bR+Woena/m0zlrHp2v5tM5ax6dr+ZriecsLdkB1PMxMMjMBphZFnABUH9gnheBb1vgMGCz2neLiIiISEvXomq83b3GzK4BXifoTvAhd59lZleF6/8KTCDoSnABQXeC301WvCIiIiIiTdWiEm8Ad59AkFxHL/tr1HsHfpDouJop4c1b2gCds+bR+Woena/m0zlrHp2v5tM5ax6dr+ZrcefM6rptERERERGR+GlpbbxFRERERNokJd57wMxONLN5ZrbAzG5qYL2Z2R/C9TPN7MBkxNkSmFkfM3vHzOaY2Swzu7aBMmPMbLOZzQin25IRa0tiZovN7LPwfExtYL2usZCZDYm6dmaY2RYz+3G9Mil/jZnZQ2a2xsw+j1rWyczeNLMvwteOjWy70++8tqiR8/UbM5sb/p/7t5kVNrLtTv//tlWNnLNxZrY86v/eyY1sq2ssWPZk1LlabGYzGtk25a6xxvKJVvM95nUjK2lq1kTw8OeXwF5AFvApMKxemZOBVwn6Hj8M+CjZcSfxfPUADgzftwPmN3C+xgAvJzvWljQBi4GinazXNdbweUkHVgH96i1P+WsMOAo4EPg8atmvgZvC9zcBdzdyTnf6ndcWp0bO1/FARvj+7obOV7hup/9/2+rUyDkbB1y/i+10jTW8/h7gtkbWpdw11lg+0Vq+x1Tjvfu2DW/v7lVA3fD20bYNb+/uU4BCM+uR6EBbAndf6e6fhO9LgDkEI47KntE11rBjgC/dfUmyA2lp3H0SsKHe4tOBR8L3jwBnNLBpU77z2pyGzpe7v+HuNeHsFILxJCTUyDXWFLrG6jEzA84DnkhoUC3YTvKJVvE9psR79zU2dH1zy6QcM+sPjAQ+amD14Wb2qZm9ambDExtZi+TAG2Y2zYKRWOvTNdawC2j8RqVrbEfdPBwPIXzt2kAZXWsN+x7BX50asqv/v6nmmrB5zkONNAPQNbajI4HV7v5FI+tT+hqrl0+0iu8xJd67L6bD26cKMysAngV+7O5b6q3+hKBpwAHAH4HnExxeS/Q1dz8QOAn4gZkdVW+9rrF6LBh865vA0w2s1jW2+3St1WNm/w+oAf7ZSJFd/f9NJX8BBgIjgJUEzSfq0zW2owvZeW13yl5ju8gnGt2sgWUJvcaUeO++mA5vnwrMLJPgP8k/3f25+uvdfYu7bw3fTwAyzawowWG2KO6+InxdA/yb4M9k0XSN7egk4BN3X11/ha6xRq2ua6IUvq5poIyutShm9h3gVOAiDxuP1teE/78pw91Xu3utu0eAv9HwudA1FsXMMoCzgCcbK5Oq11gj+USr+B5T4r37NLx9M4Tt1P4OzHH3exsp0z0sh5kdQnB9rk9clC2LmeWbWbu69wQPdH1er5iusR01WkOka6xRLwLfCd9/B3ihgTJN+c5LCWZ2InAj8E13L2ukTFP+/6aMes+enEnD50LX2PaOBea6e3FDK1P1GttJPtE6vscS+SRnW5sIepSYT/CE7P8Ll10FXBW+N+D+cP1nwKhkx5zEczWa4M85M4EZ4XRyvfN1DTCL4CnjKcARyY47yedsr/BcfBqeF11juz5neQSJdIeoZbrGtj9HTxD8qb+aoPbnMqAz8DbwRfjaKSzbE5gQte0O33ltfWrkfC0gaCda91321/rnq7H/v6kwNXLOHgu/o2YSJDo9dI01fr7C5Q/XfXdFlU35a2wn+USr+B7TyJUiIiIiIgmgpiYiIiIiIgmgxFtEREREJAGUeIuIiIiIJIASbxERERGRBFDiLSIiIiKSAEq8RUREREQSQIm3iIiIiEgCKPEWEWnFzKzQzL6frO2Txcz6m1mbH6VPRNoWJd4iIq1bIbAnifOebt8oC8T0PhOLfcYjLhGRptAXj4jIHjCz/czsg6j5A83sP3uwv+vM7PNw+nG4bLvaXTO73szGhbN3AQPNbIaZ/SYsO9fMHjGzmWb2jJnl7WQf221fL5YG9xW1/mIz+2+47QNmlh5uM8fM/gx8AvSJKn+Dmf0ofP+7uvNkZseY2T928fkb3Ge4fi8zm25mBzcUU1P2ISKSCEq8RUT2zCyCxDU9nL8HuH53dmRmBwHfBQ4FDgOuMLORu9jsJuBLdx/h7j8Llw0Bxrv7/sAWdl6j3dD20Rrcl5ntA5wPfM3dRwC1wEVR2zzq7iPdfUnUviYBR4bvRwEFZpYJjAbe28Xnb3CfZjYEeDbcbutOYtpZXCIiCaHEW0RkD7h7hCD5Hm5mZwNL3f2T3dzdaODf7l7q7luB5/gqUW2OZe5eVwv/j3C/u6uxfR0DHAR8bGYzwvm9wnVL3H1KA/uaBhxkZu2ASmAyQQJ+JPAeO//8De2zC/ACcLG718XQWEw7i0tEJCEykh2AiEgbMAX4GkFt8In1V5rZD4ArwtmngXPD9ye7+4rooo3sv4btK0pydhGPNzDf3H3sbF8QxPqIu98cvdLM+gOlDe7IvdrMFhPUTn8IzASOBgYCc4DjdxJHQ/vcDCwjOPezGotpF/sQEUkY1XiLiOy5KcAdBLW1y+uvdPf7w6YcI9z9zqj3K+oVnQScEbbJzgfOJKgJXg10NbPOZpYNnBq1TQnQrt5++prZ4eH7C4H3d7KPhrbf1b4A3gbOMbOuAGbWycz67WQ/0Z/x+vD1PeAqYIa7+04+f2OqgDOAb5vZt/YgJhGRhFDiLSKy5+YSNJ24e092EjZReRj4L/AR8KC7T3f3auD2cNnL4fHqtlkPfBA+jFj3cOQc4DtmNhPoBPylsX00sn20HfYVbjcbuBV4I1z3JtCjCR/zvbDcZHdfDVSEyxr9/Ls4Z6UEPyJ+AgzazZhERBLCgkoGERHZXWb2J+Bjd3+kBcTSH3jZ3fdtSfsSERHVeIuI7DYzG2hmc4HclpB0i4hIy6YabxERERGRBFCNt4iIiIhIAijxFhERERFJACXeIiIiIiIJoMRbRERERCQBlHiLiIiIiCSAEm8RERERkQRQ4i0iIiIikgBKvEVEREREEuD/A4juxloANhUhAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 864x432 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "lucasplot()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## The four hypotheses:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    " 1.  Differences in Human Capital (effective labor) \n",
    " 2. External Benefits of Human Capital (increasing returns) \n",
    " 3. Capital Market Imperfections I (political risk) \n",
    " 4.  Capital Market Imperfections II (monopoly distortions) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Hypothesis 1: Human Capital differences\n",
    "\n",
    "Human capital per worker differs substantially between USA and India. Let's adapt the framework to take this into account.\n",
    "\n",
    "Redefine $y$ and $x$ to be output and capital per *effective* worker (replace every $L$ by $E \\cdot L$). \n",
    "\n",
    "$$y = \\frac{AX^\\beta (E \\cdot L)^{(1-\\beta)}}{E \\cdot L}$$\n",
    "or\n",
    "$$y=Ax^\\beta \\cdot E ^{-\\beta}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Lucas' cites evidence from Anne Krueger that leads him to suggest a value of $E =5$, which is to say that for the same technology and capital a US worker produces five times as much as his/her Indian counterpart. \n",
    "\n",
    "To see this first note that if we take the ratio of US to Indian income per effective worker we get:\n",
    "\n",
    "$$\\frac{y_{US}}{y_{IN}} = \\frac{Y_{US}}{E \\cdot L_{US}} \\cdot \\frac{L_{IN}}{Y_{IN}}=\\frac{15}{5} = 3$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "With this we can easily calculate the implied difference in marginal products of capital:\n",
    "\n",
    "$$\\frac{r(y_{IN})}{r(y_{US})}= \\left ( \\frac{y_{US}}{y_{IN}} \\right )^\\frac{1-\\beta}{\\beta}$$\n",
    "\n",
    "$$=3^{1.5} = 5.2$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "So this lowers the factor of proportionality from 58 to 5. As Lucas puts it: \"This is a substantial revision but it leaves the original paradox very much alive: a factor of five differnce in rates of return is tstill large enough to lead one to expect capital flows much larger than anything we observe (p. 93).\"  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Hypothesis 2: Human Capital Spillovers"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "We've assumed thus far that the total factor productivity parameter $A$ is the same across countries.  This is unlikely.  An easy way to resolve the paradox is to simply solve for the level of A_{US}/A_{IN} that makes he gap dissappear. \n",
    "\n",
    "In this section Luca isn't quite doing that but he is in effect letting the values of A differ between the two countries.  He motivates this with a stripped down version of his own Lucas (1988) paper on external economies, a model where human capital plays a role and where there is a positive external effect in human-capital accumulation in that he assumes that the marginal product of one's human capital is augmented by the average level of human capital in the economy.  In this paper he doesn't work out this model in full but uses the story to rewrite the production function as:\n",
    "\n",
    "$$y=A h^\\gamma x^\\beta $$\n",
    "\n",
    "and he then gives us some 'guestimates' as to the differences in human capital per worker in each country.  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "As it turns out this is in effect equivalent to sticking to the original model and just assuming that \n",
    "$$\\frac{A_{US}}{A_{IN}} = 5$$\n",
    "\n",
    "A country with a higher level of $A$ will have everywhere higher return on capital. After a little math the adjusted ratio now becomes\n",
    "\n",
    "$$\\frac{r(y_{IN})}{r(y_{US})}= \\left ( \\frac{y_{US}}{y_{IN}} \\right )^\\frac{1-\\beta}{\\beta}$$\n",
    "\n",
    "$$=\\frac{3^{1.5}}{5} = 1.04$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "This would seem to almost resolve the paradox but Lucas in fact dismisses it as not entirely realistic.  It assumes for example that knowledge spillovers across borders are zero.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    " ### Hypothesis 3: Capital Market Imperfections\n",
    " \n",
    " I haven't written this up yet..."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    " ### Hypothesis 4: Market power distortions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "This is the least often mentioned but possibly the most interesting of Lucas' hypotheses.  The hypothesis is that local elites (or 'an imperial power') are able to collude to control the entry of capital into India to drive up captial rents and drive down real wages in such a way that increase firm profits.  Implictly the story is that local elites control the organization of production and hence firm profits.   \n",
    "\n",
    "While at first it might seem far-fetched to believe a story like this in modern times (less far-fetched in the time of the East India Company) there is plenty of evidence that capital inflows into India and other developing countries were historicallycontrolled in part to protect the rents of local elites.  Rajan and Zingales' (2013) book [Saving Capitalism from the Capitalists](http://press.princeton.edu/titles/7822.html) is full of examples of local elites lobbying government bureaucrats to establish market power."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "The elite is assumed to have access to international capital markets where they can borrow capital at the rate $\\rho $"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "If the elite ran the country as a monopoly they would choose the capital-labor ratio (by varying how much capital enters the country) to maximize profits per capita:\n",
    "\n",
    "$$f(x) - \\left [{f(x)-xf'(x)} \\right ] -rx$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Here (by Euler's Theorem) $f(x)-xf'(x)$ is the wage."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Implicit in Lucas' formulation is the idea that there is a large monopolist and a 'fringe' of smaller competitive firms, all producing the common output.  The competitive fringe hires factors until the marginal value product equals the market factor price.  By restricting capital into the economy the monopolists drives up the domestic rental price of capital.  With less capital to work with the competitive fringe hires less labor and this drives down the mearket equilibrium real wage.  Monopolist profits rise due to this monopsony power effect."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "$$f(x) - \\left [{f(x)-xf'(x)} \\right ] -rx$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    },
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [],
   "source": [
    "x = np.linspace(0.1,40,100)\n",
    "\n",
    "\n",
    "def profit(x, rho):\n",
    "    return  f(x) -(f(x) -mpx(x)*x) - rho*x\n",
    "\n",
    "def monopolyplot(rho):\n",
    "    prf = profit(x, rho)\n",
    "    xC, xM = xoptimum(rho, beta)\n",
    "    fig, ax = plt.subplots(1, 1, figsize=(12, 6))\n",
    "    plt.plot(x,prf)\n",
    "    plt.ylim(0,max(prf)*1.1)\n",
    "    plt.title('Monopoly Profits')\n",
    "    plt.axvline(xC,ls='dashed')\n",
    "    plt.axvline(xM,ls='dashed')\n",
    "    plt.axhline(0,ls='dashed')\n",
    "    plt.xlabel(\"$x$ -- capital per worker\")\n",
    "    plt.annotate('Competitive', xy=(xC, 0), xytext=(xC+3, 0.1),\n",
    "                arrowprops=dict(facecolor='black', shrink=0.05),)\n",
    "    plt.annotate('Market Power', xy=(xM, profit(xM,rho)), xytext=(xM+3, profit(xM,rho)-0.1),\n",
    "                arrowprops=dict(facecolor='black', shrink=0.05),)\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 864x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "monopolyplot(rho=0.05)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "In an open competitive economy all firm profits would be zero and the capital-labor ratio $x$ would be simply set from \n",
    "\n",
    "$$f'(x) = \\rho$$\n",
    "\n",
    "where $\\rho$ is the world market price of capital.  This implies we can find the capital labor ratio as a function of $\\rho$:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "$$\\beta x^{\\beta -1}=ρ$$\n",
    "$$x = \\left ( \\frac{\\rho}{\\beta} \\right ) ^\\frac{1}{\\beta - 1}$$\n",
    "\n",
    "Suppose we normalize the world rate or return to capital to $\\rho=0.05$. Then equlibrium capital per worker in the competitive economy would be:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    },
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "32.0\n"
     ]
    }
   ],
   "source": [
    "rho, beta = 0.05, 0.4\n",
    "xC, _ = xoptimum(rho, beta)\n",
    "print('%.1f' % xC)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "The monopolist on the other hand sets x to:\n",
    "\n",
    "$$f'(x) = \\rho - xf''(x)$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Note that $f''(x)$ can be written:\n",
    "\n",
    "$$f''(x) =(\\beta -1) \\frac{f'(x)}{x}$$\n",
    "\n",
    "which allows us to simplify the monopoly FOC to:\n",
    "\n",
    "$$f'(x) = \\frac{\\rho}{\\beta}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Given our assumed value of beta, this means a monopolist might maintain the rate of return on capital $1/ \\beta$ times higher than the international market rate $\\rho$, and resists capital inflows that might push this rate down. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Solving for $x$ in this monopolized market gives:\n",
    "\n",
    "$$x = \\left ( \\frac{\\rho}{\\beta^2} \\right ) ^\\frac{1}{\\beta - 1}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    },
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Capital per worker in the market-power distorted equilibrium: 6.9\n",
      " 22% of the competitive level\n"
     ]
    }
   ],
   "source": [
    "_ , xM = xoptimum(rho, beta)\n",
    "print('Capital per worker in the market-power distorted equilibrium: {:2.1f}'.format(xM))\n",
    "print(' {:.0%} of the competitive level'.format(xM/xC))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Indian income per capita will be only"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    },
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   54 percent\n"
     ]
    }
   ],
   "source": [
    "print(\"{:5.0f} percent\".format(100*f(xM)/f(xC)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "as high as in a competitive market without barriers to capital inflows."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "This is an inefficient outcome but the elites who capture the profits/rents do pretty well. They earn "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    },
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "profits =  0.52 or 24% of total output\n"
     ]
    }
   ],
   "source": [
    "print('profits = {:5.2f} or {:.0%} of total output'.format(profit(xM, rho), profit(xM,rho)/f(xM)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Extensions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Lucas does not cite their work but models of this sort were explored by trade economists in the 1980s (e.g. Feenstra (1980). \n",
    "\n",
    "In a model described later, Conning (2006) explores similar factor market power distortions in a model with heterogenous agents to make predictions about the size distribution of firms within each sector."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "### Solving for maxima and roots numerically\n",
    "This was an easy model to solve analytically, but let's solve it numerically to illustrate the use of the root solving (fsolve function from scipy optimize library) and minimization techniques (brentq from the same library). See the code section below first."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "Let's setup first order condition functions to find the x that sets them to zero. \n",
    "\n",
    "For the competitive case: $f'(x) - \\rho $ \n",
    "For the monopoly case:  $f'(x) - \\rho -x f''(x)$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "def cfoc(x):\n",
    "    return mpx(x) - rho\n",
    "\n",
    "def mfoc(x):\n",
    "    return mpx(x) - rho + (beta-1)*mpx(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "and solve for the root:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "32.0"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "xC = fsolve(cfoc, 20)[0]\n",
    "xC"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "Same as the analytical solution of course. \n",
    "\n",
    "Now let's find the $x$ that maximizes monopoly profits (we need to provide a guess value):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "6.948909098482633"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "xM = fsolve(mfoc, 5)[0]\n",
    "xM"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "We could have instead directly maximized profits (minimized negative profits) with an optimization routine:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "6.94891357421875"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def negprofit(x):\n",
    "    return - profit(x, rho)\n",
    "\n",
    "res = minimize(negprofit, 5, method='Nelder-Mead')\n",
    "res.x[0]"
   ]
  }
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