{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Consumer Choice and Intertemporal Choice"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We setup and solve a very simple generic one-period consumer choice problem over two goods.  We later specialize to the case of intertemporal trade over two periods and choice over lotteries.  The consumer is assumed to have time-consistent preofereces.  Later, in a separate notebook, we look at a a three period model where consumers have time-inconsistent (quasi-hyperbolic) preferences.\n",
    "\n",
    "[The code](#codesection) to generate the static and interactive figures is at the end of this notebook (and should be run first to make this interactive)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Choice over two goods"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A consumer chooses a consumption bundle to maximize Cobb-Douglas utility \n",
    "\n",
    "$$U(c_1,c_2) = c_1^\\alpha c_2^{\\beta}$$\n",
    "\n",
    "subject to the budget constraint\n",
    "\n",
    "$$p_1 c_1 + p_2 c_2 \\leq I $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To plot the budget constraint we rearrange to get:\n",
    "\n",
    "$$c_2 = \\frac{I}{p_2} - \\frac{p_1}{p_2} c_1$$\n",
    "\n",
    "Likewise, to draw the indifference curve defined by $u(c_1,c_2) = \\bar u$ we solve for $c_2$ to get:\n",
    "\n",
    "$$c_2 = \\left( \\frac{\\bar u}{c_1^\\alpha}\\right)^\\frac{1}{\\beta}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For Cobb-Douglas utility the marginal rate of substitution (MRS) between $c_2$ and $c_1$ is:\n",
    "\n",
    "$$MRS = \\frac{U_1}{U_2} = \\frac{\\alpha}{\\beta} \\frac{c_2}{c_1}$$\n",
    "\n",
    "where $U_1 =\\frac{\\partial U}{\\partial c_1}$ and $U_2 =\\frac{\\partial U}{\\partial c_2}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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krd1V2pvVjDTce2kbAPZn5jI4OZUfdh6uhLIDWPPjrutv1nV9EZFQ4MYtezOB+UC8MWa7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\ngg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x883ec18>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "consume_plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The consumer's optimum\n",
    "\n",
    "$$L(c_1,c_2) = U(c_1,c_2) + \\lambda (I - p_1 c_1  - p_2 c_2) $$\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "Differentiate with respect to $c_1$ and $c_2$ and $\\lambda$ to get:\n",
    "\n",
    "$$ U_1 = \\lambda{p_1}$$\n",
    "\n",
    "$$ U_2 = \\lambda{p_2}$$\n",
    "\n",
    "$$ I = p_1 c_1  + p_2 c_2$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Dividing the first equation by the second we get the familiar necessary tangency condition for an interior optimum:\n",
    "\n",
    "$$MRS = \\frac{U_1}{U_2} =\\frac{p_1}{p_2}$$\n",
    "\n",
    "Using our earlier expression for the MRS of a Cobb-Douglas indifference curve, substituting this into the budget constraint and rearranging then allows us to solve for the **Marshallian demand functions**:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$c_1(p_1,p_2,I)=\\frac{\\alpha}{\\alpha+\\beta} \\frac{I}{p_1}$$\n",
    "\n",
    "$$c_1(p_1,p_2,I)=\\frac{\\beta}{\\alpha+\\beta} \\frac{I}{p_2}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Interactive plot with sliders (visible if if running on a notebook server):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "de701884dcf740d2bfeba29e4db33bf9",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "interactive(children=(FloatSlider(value=1.0, description='p1', max=4.0, min=1.0), FloatSlider(value=1.0, descr…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "interact(consume_plot,p1=(pmin,pmax,0.1),p2=(pmin,pmax,0.1), I=(Imin,Imax,10),alpha=(0.05,0.95,0.05));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The expenditure function"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The indirect utility function:\n",
    "\n",
    "$$v(p_1,p_2,I) = u(c_1(p_1,p_2,I),c_2(p_1,p_2,I))$$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$c_1(p_1,p_2,I)=\\alpha \\frac{I}{p_1}$$\n",
    "\n",
    "$$c_1(p_1,p_2,I)=(1-\\alpha)\\frac{I}{p_2}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$v(p_1,p_2,I) = I \\cdot  \\alpha^\\alpha (1-\\alpha)^{1-\\alpha} \\cdot \n",
    "\\left [ \\frac{p_2}{p_1} \\right ]^\\alpha \\frac{1}{p_2} $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$E(p_z,p_2,\\bar u) = \\frac{\\bar u}{\\alpha^\\alpha (1-\\alpha)^{1-\\alpha} \\cdot \n",
    "\\left [ \\frac{p_2}{p_1} \\right ]^\\alpha \\frac{1}{p_2}}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To minimize expenditure needed to achieve level of utility $\\bar u$ we solve:\n",
    "\n",
    "$$\\min_{c_1,c_2} p_1 c_1 + p_2 c_2 $$\n",
    "\n",
    "s.t.\n",
    "\n",
    "$$u(c_1, c_2) =\\bar u$$\n",
    "\n",
    "The first order conditions are identical to those we got for the utility maximization problem, and hence we have the same tangency\n",
    "\n",
    "$$\\frac{U_1}{U_2} = \\frac{\\alpha}{1-\\alpha} \\frac{c_2}{c_1} = \\frac{p_1}{p_2}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "From this we can solve:   $$c_2 = \\frac{p_1}{p_2} \\frac{1-\\alpha}{\\alpha} c_1  $$\n",
    "\n",
    "Now substitute this into the constraint to get:\n",
    "\n",
    "$$ u \\left ( c_1, \\frac{p_1}{p_2} \\frac{1-\\alpha}{\\alpha} c_1  \\right )=\\bar u$$\n",
    "\n",
    "$$ u \\left ( c_1, \\frac{p_1}{p_2} \\frac{1-\\alpha}{\\alpha} c_1  \\right )=\\bar u$$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Intertemporal Consumption choices"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We now look at the special case of intertemporal consumption, or consumption of the same good (say corn) over two periods.  As modeled below the consumer's income is now given by the market value of and endowment bundle $(y_1,y_2)$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The variables $c_1$ and $c_2$ now refer to consumption of (say corn) in period 1 and period 2. \n",
    "\n",
    "As is typical of intertemporal maximization problems we will use a time-additive utility function.  The consumer who has access to a competitive financial market (they can borrow or save at interest rate $r$) maximizes:\n",
    "\n",
    "$$U(c_1,c_2) = u(c_1) + \\delta u(c_2)$$\n",
    "\n",
    "subject to the intertemporal budget constraint:\n",
    "\n",
    "$$ c_1 + \\frac{c_2}{1+r}  = y_1 + \\frac{y_2}{1+r} $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is just like an ordinary utility maximization problem with prices $p_1 = 1$ and $p_2 =\\frac{1}{1+r}$.  Think of it this way, the price of corn is \\$1 per unit in each period, but \\$1 in period 1 can be placed into savings that will grow to $(1+r)$ dollars in period 2.  That means that from the standpoint of period 1 owning one unit of corn (or one dollar worth of corn) in period 2 is the equivalent of owning $\\frac{1}{1+r}$ units of corn today (because placed in savings that amount of period 1 corn would grow to $\\frac{1+r}{1+r} = 1$ units of corn in period 2)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The first order necessary condition for an interior optimum is:\n",
    "\n",
    "$$u'(c_1^*) = \\delta u'(c_2^*)$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's adopt the widely used Constant-Relative Risk Aversion (CRRA) felicity function of the form:\n",
    "\n",
    "$$\n",
    "\\begin{equation}\n",
    "u\\left(c_{t}\\right)=\\begin{cases}\n",
    "\\frac{c^{1-\\rho}}{1-\\rho}, & \\text{if } \\rho>0 \\text{ and } \\rho \\neq 1 \\\\\n",
    "ln\\left(c\\right) & \\text{if } \\rho=1\n",
    "\\end{cases}\n",
    "\\end{equation}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The first order condition then becomes simply\n",
    "\n",
    "$${c_1^*}^{-\\rho} = \\delta (1+r) {c_2^*}^{-\\rho}$$\n",
    "\n",
    "or \n",
    "\n",
    "$$c_2^* = \\left [\\delta (1+r) \\right]^\\frac{1}{\\rho}c_1^* $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "From the binding budget constraint we also have\n",
    "\n",
    "$$c_2^* = E[y](1+r)-c_1^*(1+r)$$\n",
    "\n",
    "where $E[y] = y_1 + \\frac{y_2}{1+r}$\n",
    "\n",
    "Solving for $c_1^*$ (from the FOC and this binding budget):\n",
    "\n",
    "$$c_1^*  = \\frac{E[y]}{1+\\frac{\\left [\\delta (1+r) \\right]^\\frac{1}{\\rho}}{1+r}}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If we simplify to the simple case where $\\delta =\\frac{1}{1+r}$, where the consumer discounts future consumption at the same rate as the market interest rate then at an optimum the consumer will keep their consumption flat at $c_2^* = c_1^*$.  If we specialize further and assume that $r=0$ then the consumer will set  $c_2^* = c_1^* =\\frac{y_1+y_2}{2}$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Saving and borrowing visualized"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us visualize the situation.  The consumer has CRRA preferences as described above (summarized by parameters $\\delta$ and $\\rho$ and starts with an income endowment $(y_1, y_2)$. The market cost of funds is $r$.  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### A savings case\n",
    "In the diagram below the consumer is seen to be saving, i.e.  $s_1^* = y_1 - c_1^* >0$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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mPQDMttY2BGYXvgfoBjQs/CcJeLU4K8i3JZLTPW1uAlP4RzM/2d0sIiISNHxe+tba74E9\nf5p8NXD4/rMTgWuOmv62daQCscaY6qdax+8HCti0J7OkIvtebG3nMD/AsvfgwE5384iISFAw1vp+\nt9gYUxeYaa1tWvg+3Vobe9T8vdbaCsaYmcBz1tr/FU6fDdxvrV1QxHcm4RwNIPKcBq3PH/YS97eN\nplqZwDxtoXz6ClouGQXA+roD2FC3d5HLHThwgJiYGF9Gc1UobW8obStoe4NZKG0ruLO9iYmJpjjL\nhXs7yFkqaiOK/FuKtTYZSAaIqt7Q7sm2vLi0gHdvace5VQLwXzZ7MWybAtuWUW/XbOoNHO383v8n\nKSkpJCYm+j6fS0Jpe0NpW0HbG8xCaVvBv7fXX3aDtx8+bF/4uqNw+mag1lHLxQFbT/Vl5aOcvyts\n35dDn3GprNm+v2TT+oIx0P5WZ3xgG/zyibt5REQk4PlL6X8CDC4cDwY+Pmr6DYVn8ScAGdba30/1\nZRWiDHd1aQTArgM59E1OZeXWfV6I7WVNr4PSlZxxarHOYRQRETkhNy7ZmwLMBeKNMZuNMUOB54Au\nxpi1QJfC9wCfAeuANGA8MKK467mzc0Me6NYYgD0HD9FvfCrLNmeU3Ib4QkT0kZv1bFkAm487lUFE\nRKTY3Dh7v5+1trq1NsJaG2etfcNau9ta29la27DwdU/hstZae5u19lxrbbOiTuA7mVsvPpf/63Ee\nABlZufR/PZVFG/d6Yau8qO1Q8BSeejHvNXeziIhIQPOXw/tec9OF9XjymqYA7M/O44Y35vPTb3++\nYtCPlavhPHYXYMWHsO+Uv26IiIgUKehLH2BQQh3+0asZxsCBnDwGvzmfub/udjtW8bUf7rwW5MFP\nr7ubRUREAlZIlD5An7a1eeG65ngMZB7KZ8hb8/l+TYDc9CauDdRs44wXvAGHDrqbR0REAlLIlD5A\nr9ZxjO7bkjCPISevgJvfXsC3q3ac+oNuMwY63uGMs/bC4snu5hERkYAUUqUPcFXzGozp15Jwj+FQ\nXgFJkxbw5Yptbsc6tSY9oUI9Zzx3DOTnuZtHREQCTsiVPkC3ZtV5dWBrIsM85OZbbntnEf/92c9P\nkPOEQcfbnXH6Rlj5kbt5REQk4IRk6QN0Oa8ayTe0JjLcQ16B5Y4pi/ho8Ra3Y51ciwFHbtYz52Vw\n4bkJIiISuEK29AES46vy1pC2REd4KLDw9+lLmL5gk9uxTiyiFLRLcsa/L4X137ubR0REAkpIlz5A\npwaVmXBjO0pHhmEt3DfjZ96dt9HtWCfW9hYIL+WM57zsbhYREQkoIV/6AAn1KzFpaDvKRjl3vhv1\n4TImzvnN3VAnUqYStBzgjNNmUebAb67GERGRwKHSL9S6TkUm3dyectFO8T/6yQrGf7/O5VQn0OE2\nMM4fXa1NOqFPRESKR6V/lBa1Ynn3lgRiS0cA8PRnv/Cfb9NcTlWEivWdS/iAqju+d87mFxEROQWV\n/p80rVmeqUkJVCoTCcA/v1zN6FlrsP52pnynkQB4bD78qN/2RUTk1FT6RWh8TjmmJiVQpWwUAKNn\nreWfX672r+Kv2QoaXOaMF70N+wPgBkMiIuIqlf4JNKxWlmlJCZxTLhqAsSm/8vR/f/Gv4r/oXuc1\nPwfmvOJuFhER8Xsq/ZOoXyWG6cM6UDPWuUTu9f+t57FPVlBQ4CfFXzuBvbHOY4NZ8CYcDKAnB4qI\niM+p9E+hdqXSTBuWQO2KpQGYOHcDD3203G+Kf0Od3s4gNxNSx7obRkRE/JpKvxjiKjjFX79yGQCm\nzN/Ife//TL4fFH967AUQ19Z5Mz8ZstLdDSQiIn5LpV9M1cuXYmpSAg2rxgAwY+Fm7pq+hLz8AneD\nGXPkt/2cfTB/vLt5RETEb6n0T0PVctFMSUqg8TllAfh4yVb+NnUJuW4Xf8PL4Zxmzjj1P5BzwN08\nIiLil1T6p6lyTBRTbkmgac1yAPx32e/c9s4icvLy3Qt19N5+1l746XX3soiIiN9S6Z+BCmUieefm\nBJrXigXgq5XbuXXSQrJzXSz+xj2hSmNn/ONLkLPfvSwiIuKXVPpnqHypCCYPbUfrOhUA+Hb1Tm55\newFZh1wqfo8HEh9wxll7YN44d3KIiIjfUumfhbLREbx9Uzva16sIwA9rd3HjhPkczMlzJ1CTq6Fa\n4XX7c16B7Ax3coiIiF9S6Z+lMlHhTLixHRc2qAxA6ro9DH5zPvuzc30fxuOBxAedcXY6pL7q+wwi\nIuK3VPoloFRkGK8PbkNifBUAFmzYy6A35pOR5ULxN74Sqjd3xnP/A5l7fJ9BRET8kkq/hERHhDFu\nUGsua1INgCWb0hn4+jzSMw/5NogxcMlDzjhnn1P8IiIiqPRLVFR4GGMHtKJb03MAWLYlg77Jqew+\nkOPbIA0vh5ptnPG813RPfhERAVT6JS4y3MMr/VpyVfMaAKzatp++yans2J/tuxDGwKWFe/uHDsCc\nl3y3bhER8VsqfS8ID/Pw7z4t+GurmgCs3XGAvuNS2Zbhw+KvfwnU7uCM5yXDvt99t24REfFLKn0v\nCfMYXriuOX3b1gJg3a6D9Emey5b0LN8EMAYufdgZ52XBd//wzXpFRMRvqfS9yOMxPHNtMwYl1AFg\nw+5Mer82l017Mn0ToO6F0KCLM170NuxK8816RUTEL6n0vczjMTxx9fnc1KkeAFvSs+g9bi7rdx30\nTYDLHgUM2Hz45knfrFNERPySSt8HjDE80qMJt158LgC/Z2TTZ9xc0nb44P745zSDC3o745UfwZaF\n3l+niIj4JZW+jxhjuL9rPHde2gCAHftz6JucyuptPij+S0aBJ8IZz3oMrPX+OkVExO+o9H3IGMNd\nl8dzd5dGAOw6cIi+yXNZsdXL98ivUBfaDnXG67+HX7/x7vpERMQvqfRdcEfnhjzYzXkM7t7MXPqP\nn8fPm9O9u9KL7oXIss541qNQUODd9YmIiN9R6btk2MXn8mjP8wDIyMplwPh5LNq413srLFMZOt7h\njLctg+Xve29dIiLil1T6LrqxUz2evtZ5FO7+nDwGvT6P+eu9+ICcDrdBmarOePbjkOujewaIiIhf\nUOm7bED7Ojzf6wKMgYOH8hn85nzmpO3yzsqiYpyT+gAyNunRuyIiIUal7wd6t63Fi72b4zGQlZvP\njRN+4rs1O72zspaDoKrzswI/vAgHdnhnPSIi4ndU+n7i2pZxvNS3JWEeQ05eAbdMXMDsX7aX/IrC\nwuHyp5zxof3w7TMlvw4REfFLKn0/0rN5Df7TvxURYYZD+QXcOnkhXyzfVvIratD5qNvzToTtK0t+\nHSIi4ndU+n6ma9NzeG1gayLDPOTmW257dxEzf95a8iu6/CkwYWAL4KuHS/77RUTE76j0/VDnJtUY\nP7gNUeEe8gssd05ZzIeLN5fsSqo2htZDnPGvs2HtrJL9fhER8TsqfT91caMqvDWkLaUiwiiwcNf0\npUz/aVPJriTxQYgq54y/HAX5uSX7/SIi4ldU+n6sY4PKTLypHWUiw7AW7nv/Zyanbii5FcRUgb/c\n7Yx3rYafXi+57xYREb+j0vdz7epV5O2h7SkbFQ7Awx8t560f15fcChKGQ0Xn6X98+ywc8NKlgiIi\n4jqVfgBoXacC79zSnnLRTvE//ulKkr//tWS+PDwKuj7njHMyYPZjJfO9IiLid/yq9I0xfzfGrDDG\nLDfGTDHGRBtj6hlj5hlj1hpjphljIt3O6YYL4mKZkpRAhdLOI3JH/XMfFavlcumlF1O3Lrzzzll8\neaPLoeEVznjxZNi88KzzioiI//Gb0jfG1ATuBNpYa5sCYUBf4B/Av621DYG9wFD3Urrr/BrlmZrU\nAfNrbfZ80Yy9OyKw1rBhAyQlnWXxd30Wwgr/PvXZPXoKn4hIEAp3O8CfhAOljDG5QGngd+BSoH/h\n/InAY8BJbxq/adMmEhMTj5nWu3dvRowYQWZmJt27dz/uM0OGDGHIkCHs2rWL66677rj5w4cPp0+f\nPmzatIlBgwYdN//uu++mZ8+erF69mmHDhh03/+GHH+ayyy5jyZIljBw58rj5zzzzDB07dmTOnDmM\nGjXquPmjR4+mRYsWbFo+j60zL8DmHftHl5kJDz0EAwYc99HiqXQudLgd/vcibF0ES96BVsdvp4iI\nBC6/KX1r7RZjzAvARiAL+ApYCKRba/MKF9sM1Czq88aYJCAJICIigvT0Y59Pv2bNGlJSUsjOzj5u\nHsCqVatISUkhIyOjyPkrVqwgJSWFHTt2FDl/2bJllC1blo0bNxY5f+nSpYSHh5OWllbk/EWLFnHo\n0CGWL19e5PwFCxaQnp7O0qVLOZR9aVH/E7BxoyUl5bsi5xVHGO1oF1mJqEO7OfT5Q8zfXYG8iJgz\n/j5vOHDgACkpKW7H8IlQ2lbQ9gazUNpWcGd7/7yjeyLGWuvdJMVkjKkAvA/0AdKB9wrfP2qtbVC4\nTC3gM2tts5N9V3x8vF29erWXE7unbl3YUMSVe+WrHGLPtgg8HnPmX75sBrxf+AtKu2HQ/fkz/y4v\nSElJKfa/3IEulLYVtL3BLJS2FVzb3mL9h99vftMHLgPWW2t3WmtzgQ+AjkCsMebwEYk4wAv3pA0s\nTz8NpUsfO82E5xHefgWjPlxGQcFZ/EWuaS+oc6Ez/mk8bF1y5t8lIiJ+xZ9KfyOQYIwpbYwxQGdg\nJfAtcPhH9sHAxy7l8wvWWgYMgCuueIxq1dKAAuJqFdD4+jXEnL+VqT9t4p4ZS8k/0+I3Bq78F3jC\nnfvyz/w7FOSX6DaIiIg7/Kb0rbXzgBnAImAZTrZk4H7gLmNMGlAJeMO1kH5g+vTpPPDAA9SunU6l\nSlcTG1uJBT/tJGVcfRpWdX5//2DRFv4+bQl5+Wd4Bn7VxtDxTme8dREseLOE0ouIiJv85kQ+AGvt\no8Cjf5q8DmjnQhy/1KdPH+rVq8dll12Gx+Ohdu3aVKtWDYCpSQkMeH0eq7bt55OlW8nNL+Dlfi2J\nCDuDv9tddC8snwHpG2H2k9DkKihbrYS3RkREfMlv9vSleN577z0++OADbrrpJmrUqMHmzZvZvn07\nAJViophySwJNazoP0fl8+TaGT15ETt4ZHJ6PLA3dX3DGORnw1UMltQkiIuISlX6Aue6663juueeI\njY2lXLly1KpV6489fYAKZSJ55+YEWtSKBWDWL9sZNmkh2blnUPyNroAmPZ3xsvdgXUoJbIGIiLhF\npe8HunTpQocOHY6bvmzZMiIiInj33Xf/mOac4wiPPfYY0dHRf7w/WvlSEUwa2o62dSsAkLJ6JzdP\nXEDWoTMo/q7PQUQZZzzzLsjNPv3vEBERv6DS9wMXXnghixcvJicn549p1lpGjBhBx44d6d+/f5Gf\nu/vuu+ndu3eR88pGRzDhxnZ0qF8JgP+l7eLGCfM5mJNX5PInVD4OLim8Q+CeX+H7f57e50VExG+c\nVukbY841xnxrjFlnjHnRGBN91Lz5JR8vNHTq1ImcnBwWL178x7S3336b1NRUxowZc8LP9ezZk44d\nO55wfpmocN4c0pa/NKwMQOq6PQx+cz77s3NPL2D7W6F6c2f842jYtvz0Pi8iIn7hdPf0/4Nz05zr\ngSrALGPM4fu0RpRksFCSkJBAWFgYqampAKSnp3Pfffdx++2306zZiW8+uHr1ajZu3HjS7y4VGcb4\nG9pwSXwVABZs2MvAN+aTkXkaxR8WDleNARMGBXnwye26dl9EJACdbulXs9a+Yq1daK0dBHwNfG2M\nKQv4x/18A1BMTAzNmzf/o/QfeughPB4Pjz/++Ek/N2zYMF588cVTfn90RBivDWpNl/OcE/6Wbkqn\n/+up7D14qPghq18AnQ5fu78Y5r1W/M+KiIhfON3SL3X0G2vt48B/cR6O419PZgkwnTp1IjU1lUWL\nFvHaa6/xz3/+k3LlypXY90eFhzF2QCuubFYdgBVb99FvfCq7DuSc4pNHufh+qHiuM/7mKdj7W4nl\nExER7zvd0l9rjDnmEW/W2qeAz4EGJZYqBHXq1IkNGzZwww030KlTJwYOHFji64gI8/BS3xZc3aIG\nAKu27adfcio79hXzjPyIUnDVy844NxM+HQl+8sAmERE5tVOWvjGmmzGmT+HbQTiPuz2GtfYJoGkJ\nZwspF17oPORm1apVJz1572yFh3l4sXcLrmsdB8DaHQfom5zKtoxiFn/dC6HVYGe87ltY8u7JlxcR\nEb9RnD39x4EEAGtturU24/CTHEpfAAAgAElEQVQMY0wDY0xY4byV3okYGmJiYoiMjOT222/nggsu\n8Oq6wjyG53tdQL92tQFYt+sgvcfNZfPezOJ9QZcnIOYcZ/zFg7Av5B98KCISEIpT+k2AWSeY9zAh\n/gCckvLEE09QsWLFU568d7SHH36YQYMGndH6PB7DM9c2ZXCHOgBs3JNJn3GpbNxdjOIvFQs9Rzvj\nnAz45E4d5hcRCQDFKf0C4Pjbvjk+BxJLLE2IyczMZO7cuTz//PO89NJLjB07lvLlyxf785dddhmt\nW7c+4/UbY3jsqvO5+cJ6AGxJz6L3uLms23ng1B+O7wYX9HXGaV/DknfOOIeIiPhGcUp/MXDFCeZt\nA/TotTM0a9YsOnbsyMsvv8xLL73Etddee1qfX7JkCWlpaWeVwRjDQ1c2YUSic1b+tn3Z9ElOJW3H\n/lN/uNtzxx7mz9hyVllERMS7ilP6/wFuNcYU1UgXANtLNlLouOqqq7DWsnnzZm677bbT/vzIkSNL\n5KQ/Ywz3XhHP3zo3BGDn/hz6jEtl1bZ9J/9gqQpHzubP2Qef3KHD/CIifuyUpW+tfQ94CXjfGPOh\nMWaAMeYSY8ztwGPAl17OKD5gjOHvXRpx7xXxAOw+eIh+yaks35Jx8g82ugKaFz4b4NfZsHiSl5OK\niMiZKtZ1+tbae4D+OCf1TQJmAy8DKwA9aD2I3HZJAx7q3gSAvZm59B+fytJN6Sf/UNdnoaxz0x++\nGAV7N3g5pYiInIli35zHWjvVWtsYOBf4C3CutfYia+0ur6UTV9xyUX0e63keAPuy8xj4+jwWbthz\n4g+UioWrXnHGh/bDR8N1b34RET902o/Wtdaut9b+aK1d741A4h+GdKrHM9c6D/vZn5PHoDfmM2/d\n7hN/oGEXaH2jM97wI8z13g2GRETkzJx26Yv/eOaZZ7j55pu99v3929fm+esuwBjIPJTP4Lfm82Pa\nSQ7sXPE0VKzvjGc/CduWeS2biIicPpV+AOvYsSNNm3r37se929Ti371b4DGQnVvATRN+4rs1O4te\nOLIM/HV84SN4c+GDYZBbzNv7ioiI16n0A9icOXNYvny519dzTcuavNKvFeEeQ05eAbdMXMCslSe4\nUjOuDVx0jzPesQK+fcrr+UREpHhU+gFs1KhRvP766z5Z15UXVOc/A1oREWY4lF/ArZMX8sXy34te\n+KJ7oUZLZzxnDKz/wScZRUTk5FT6UmxXnH8O4wa1JjLcQ16B5bZ3F/PJ0iIethMW4RzmDy8FWPhw\nGGSe5Ox/ERHxCZW+nJZLG1fj9RvaEBXuIb/AMnLqYt5fuPn4BSs3dE7sA9i3RXfrExHxAyp9OW0X\nNarCWze2pVREGAUW7pmxlGk/bTx+wTY3QeMeznjVTFj4lm+DiojIMVT6ckY6nluZiTe1o0xkGNbC\n/e8vY1Lqn+7EZ4xz056yNZz3XzwIO37xfVgREQFU+gFt9OjR3H777a6tv129iky6uT1lo8MBeOSj\n5bz5vz/ds6l0RfhrMmAgLxtmDNVlfCIiLlHpB7AWLVrQoEEDVzO0ql2Bd29OoHypCACemLmS1777\n9diF6v3l2Mv4vn7ExylFRARU+gFt1qxZLFy40O0YNIsrz5RbEqhYJhKA5z5fxcuz1x670MUPQFw7\nZzw/GX751McpRUREpR/AnnrqKSZN8o9H2Z5XoxxTkxKoHBMFwItfr+FfX63GHj5jPywcer0OUeWd\n9x/dBnt/cyesiEiIUulLiWlUrSxTkxKoWtYp/le+SeO5L1YdKf4KdeCa/zjjnAx470bIO+RSWhGR\n0KPSlxLVoGoM04d1oEb5aADGfbeOJ2auPFL8TXpC++HOeOsi+Pr/XEoqIhJ6VPpS4upWLsO0YR2I\nq1AKgLd+/I1HPl5OQUFh8Xd5Amq0csbzXtXv+yIiPqLSF6+oVbE004d1oE6l0gBMTt3Igx8sI7/A\nQngkXP8WRB/1+/6e9Sf5NhERKQkq/QA2btw47rrrLrdjnFCN2FJMH9aB+lXKADBtwSbufW8pefkF\nUKEuXD3WWTAnA6bfALlZ7oUVEQkBKv0AFh8fT+3atd2OcVLVykUzLakDjarFAPDB4i2MnLaE3PwC\naNIDEm5zFtz2M3x2j4tJRUSCn0o/gH366afMmTPH7RinVKVsFFNuSaBJ9XIAzPz5d+54dzGH8gqg\ny+NQu4Oz4OLJsHCii0lFRIKbSj+A/etf/2L69OluxyiWSjFRTLmlPc1qOr/jf7FiGyPeWUiO9cD1\nEyCmmrPgZ/fC1sXuBRURCWIqffGZ2NKRTL65PS1rxwIw65cdJL29kOzoKk7xmzDIz4FpN0DmHnfD\niogEIZW++FT5UhFMGtqetnUrAPDdmp0MnfgTmdXbweVPOgtlbIT3b4aCfBeTiogEH5W++FxMVDgT\nb2pHh/qVAPgxbTdD3vqJAy2T4PxrnYV+nQ3fPOliShGR4KPSF1eUjgznrRvbclGjKgDMX7+HG96c\nz77LX4QqTZyF/vdvWP6BiylFRIKLSj+ATZo0iVGjRrkd44xFR4SRPKg1lzauCsCijekMmrSS/ddM\nPHLjno9vg23LXEwpIhI8VPoBrFatWlStWtXtGGclOiKM1wa25orznbP3l27OoO/7O9jfIxmMB3Iz\nYWp/OLjb5aQiIoFPpR/Apk2bxjfffON2jLMWGe5hTP9WXHlBdQBWbN3H9bNKc/AvDzsLpG+EGUMg\nP8+9kCIiQUClH8BeffVVPvnkE7djlIiIMA8v9WnBtS1rArBq236uXtya7PjCE/vWfw9fBu5PGSIi\n/kClL34jPMzDC9c35/rWcQCk7TzINZv7kVu1mbPA/HHU2PK5iwlFRAKbSl/8SpjH8I9eF9C/vfNM\ngVW78+i7707ySztn+TdcmwzrvnMzoohIwPKr0jfGxBpjZhhjVhljfjHGdDDGVDTGfG2MWVv4WsHt\nnOJdHo/h6WuaMqRjXQAWppdheN7d2LAoDAXOE/l2/+puSBGRAORXpQ+8BHxhrW0MNAd+AR4AZltr\nGwKzC99LkDPG8GjP80i6qD4AX+2rzaMMd2Zmp8O7vSFrr4sJRUQCj9+UvjGmHHAR8AaAtfaQtTYd\nuBo4/Oi1icA17iT0PzNmzODxxx93O4bXGGN4sFtjbr+kAQBvH2xHsi3849+dBu8Ngfxc9wKKiAQY\nY611OwMAxpgWQDKwEmcvfyHwN2CLtTb2qOX2WmuPO8RvjEkCkgCqVKnSOlCePne2Dhw4QExMjNsx\nvO7jtEN8mJaLoYDxUS9xmfkJgK3Vu7Cm0W1gjMsJS16o/Nkepu0NXqG0reDO9iYmJhbrP4L+VPpt\ngFSgk7V2njHmJWAfcEdxSv9o8fHxdvXq1d4N7AcmTJjAqlWreO6559yO4hNjU9J4/ovVlCKbGdFP\ncT7rnBmdH4W/3OVuOC9ISUkhMTHR7Rg+o+0NXqG0reDa9har9P3m8D6wGdhsrZ1X+H4G0ArYboyp\nDlD4usOlfH5nwoQJfPHFF27H8JkRiQ3o1ziSLKIZkn03W6nszJj9OCx/391wIiIBwG9K31q7Ddhk\njIkvnNQZ51D/J8DgwmmDgY9diCd+4oq6ETxx9fnspAJDcu5lvy3lzPhwOGycd/IPi4iEOL8p/UJ3\nAO8YY34GWgDPAM8BXYwxa4Euhe8lhN3QoS7PXNuMtdRieO5Icm0Y5OfA1H66lE9E5CTC3Q5wNGvt\nEqBNEbM6+zqL+Lf+7WsTEWa47314KO8mno8YD5m7YXIvGPo1xFRxO6KIiN/xtz19kWK7vk0tRvdp\nwfv2UsbkXe1M3LveuYY/54C74URE/JBf7enL6fnss8/4/vvv3Y7hqqtb1CQizMOdUyzV8/fQK+wH\n2LrIuYa/3xQIi3A7ooiI39CefgArXbo00dHRbsdwXfdm1Rk7oDUPFyTxXf4FzsS0r2HmSPCTS1JF\nRPyBSj+AjR07lo8++sjtGH7h8vPPYeygBP5m7+LngnrOxMWT4dtn3A0mIuJHVPoBbPr06aSkpLgd\nw29c0rgqrwy+kOH2fjYUVHUmfv88zEt2N5iIiJ9Q6UtQ+UvDKrww5HJuZRS7bDln4uf3ws/vuRtM\nRMQPqPQl6HQ4txJP3nQ1wxn1x817Cj68FdZ+7XIyERF3qfQlKLWpW5FRQ/typ7mPHBuBx+aRN2Wg\n7tonIiFNpS9Bq2XtCtx9y1Du9/ydfGsIL8gm++1esG2529FERFyh0g9gKSkpjB492u0Yfq1pzfIk\n3XIHT3qGAxCdt5/MN3rCrjSXk4mI+J5KX4LeeTXK0f/WUfzb4zy3qXTuHvYld8Pu/c3dYCIiPqbS\nD2AvvPAC06ZNcztGQGhUrSxXD3+G8WF9ACh3aAd7X7sSu+93l5OJiPiOSj+AzZw5k7lz57odI2DU\nrxLD5cNf5N0w5z79FXM2s3NsN+zBXS4nExHxDZW+hJQ6lWO46LZX+Sj8CgCqZq/n9zHdKDi41+Vk\nIiLep9KXkBNXsQztb3+Lr8ITAaiRtYbNY7qSn5nubjARES9T6UtIqh5bhha3v8N34R0BqJ21io2v\ndCcvM8PlZCIi3qPSD2ClSpUiKirK7RgBq2psDOfd/h7/C+8AQL2sFfz2ypXkZu1zOZmIiHeo9APY\n559/zj/+8Q+3YwS0KrExnHfnDFIj2gHQIGsZ617qwaHM/S4nExEpeSp9CXkVy8XQ+I4PWBDRBoD4\n7KX8+vKVZB/UHr+IBBeVfgB78sknefvtt92OERRiy5Wl0d8+YnFkKwCaZC/lt5e7k31Qv/GLSPBQ\n6Qew2bNns2jRIrdjBI1yMWVpeOcnLCks/sY5y3jlxhepXTsfjwfq1oV33nE3o4jI2Qh3O4CIP4mJ\nKUujkZ+y5KVrWLGgDo99ej+ZuWEAbNgASUnOcgMGuBhSROQMBWXpb9q0icTExGOm9e7dmxEjRpCZ\nmUn37t2P+8yQIUMYMmQIu3bt4rrrrjtu/vDhw+nTpw+bNm1i0KBBx82/++676dmzJ6tXr2bYsGHH\nzX/44Ye57LLLWLJkCSNHjjxu/jPPPEPHjh2ZM2cOo0aNOm7+6NGjadGiBbNmzeKpp54CYMmSJeTl\n5ZGYmMi4ceOIj4/n008/5V//+tdxn580aRK1atVi2rRpvPrqq8fNnzFjBpUrV2bChAlMmDDhuPmf\nffYZpUuXZuzYsUyfPv24+SkpKYBza+CZM2ceM69UqVJ8/vnngPOTxOzZs4+ZX6lSJd5//30AHnzw\nwePuMhgXF8fkyZMBGDNmDI899tgx8xs1akRycjIASUlJrFmz5pj5LVq0+OPBRAMHDmTz5s3HzO/Q\noQPPPvssAL169WL37t2EeTwsX/gUmbmlj1k2MxMeekilLyKBSYf3RYqQX1DAjn3Vipy3caOPw4iI\nlBBjrXU7Q4mLj4+3q1evdjuG1/Xq1YudO3fy/fffux3FZ1JSUo47iuMtdes6h/T/LC4uj02bvH+Q\nzJfb6g+0vcErlLYVXNteU5yFtKcfwN5//32eeOIJt2MEraefhtLHHt2ndEQm97V7gN1b1rkTSkTk\nLKj0RU5gwABIToY6dcAYS7UKO0nueQd3NBtP7utXsGvjKrcjioicFpV+AHvwwQcZP3682zGC2oAB\n0K/fg9x//yi27KxE7URn+jl2B+atruxI0yWTIhI4VPoBbO7cuaxYscLtGEFv7ty5zJ07l7AwD51G\njCel2g0AVLJ7KTW5B9tXhM45FSIS2FT6IqfBE+bh4ltf5quatwNQloOUe+86ti/+r8vJREROTaUv\ncpqMMXS5+Sn+W28U+dZQihwqfnwD2+ZOdTuaiMhJqfRFzoAxhu433MdnjZ8lx4YTQR5Vv7yV7d+M\ndTuaiMgJqfQDWFxcHFWqVHE7RtCLi4sjLi7uuOnGGHr2G85nzUZz0EbhwVLt+wfZ+cljEIT3vxCR\nwBeUt+ENFZMnT/7j9rfiPYdvAXwi1143iPejypO4YASVzH6qLPo3uzO3U6n3GPCE+SiliMipaU9f\npAT06nkV33SczKYC58hLpVXvkj6hL+RmuZxMROQIlX4AGzlyJGPGjHE7RtAbOXJkkQ9J+rPrr0hk\n3qVTWFlQB4DYjV+xf3wPyNzj7YgiIsWi0g9gS5YsIS0tze0YQW/JkiUsWbKkWMtel9iWX66YwpyC\n8wAou2MBWa9dCnvWezOiiEixqPRFSlivTuezvcc7fJLfEYBS+9ZzaNylsHmhy8lEJNSp9EW84Np2\n9bF/TebV/KsAiMzZQ/5b3WHVZy4nE5FQptIX8ZKrW9aibu/neSTvJvKtISw/Gzt1AKS+qkv6RMQV\nKv0A1qhRoyKvH5eS1ahRIxo1anRGn+3WrDoX9X+A4fn3kGmjMBTAFw/AZ/dCfl4JJxUROTldpx/A\nkpOTdZ2+DyQnJ5/V57ucV42IQUn0n1SR18Ke5xyzF34aD3t/g+vehOhyJRNUROQUtKcv4gOJ8VW5\nd0hv+hQ89cclfaR9DW9eAekb3Q0nIiFDpR/AkpKSeOGFF9yOEfSSkpJISko66+/p1KAy/7ixGzfw\nBLPyWzoTd6yE8ZfCxnln/f0iIqei0g9ga9asYfPmzW7HCHpr1qxhzZo1JfJdCfUrMW7oRdzluZ83\n87o6Ew/uhIk9YMm7JbIOEZETUemL+FjrOhV5++YOjA6/iQdzh5JrwyD/EHw0HL56BAry3Y4oIkFK\npS/igha1Ynn3lgQ+j+rKwEOj2GNjnBlzXoYp/SA7w92AIhKUVPoiLmlaszxTkxJIK92cqw49xeqC\nwssv134J4ztTKlM/3YhIyVLpB7AWLVrQoEEDt2MEvRYtWtCiRQuvfHfjc8oxNSmBnJha9Dr0GF/n\nt3Zm7F5L64X3wuovvLJeEQlNflf6xpgwY8xiY8zMwvf1jDHzjDFrjTHTjDGRbmf0F6NHj+b22293\nO0bQGz16NKNHj/ba9zesVpZpSQnElKtIUu7feSnvrwCE52fClL7w3T91Bz8RKRF+V/rA34Bfjnr/\nD+Df1tqGwF5gqCupRLyofpUYpg/rQI3YMvw77zqGHfo72SYasPDtUzBtIGTvczumiAQ4vyp9Y0wc\ncCXweuF7A1wKzChcZCJwjTvp/M/AgQN5+umn3Y4R9AYOHMjAgQO9vp7alUozbVgCtSuW5suCtvTM\nfoLdkTWdmatmwvhLYMcqr+cQkeBlrB8dNjTGzACeBcoC9wBDgFRrbYPC+bWAz621TYv4bBKQBFCl\nSpXW06dP91Vs14wcOZL8/HxeeeUVt6P4zIEDB4iJifHpOkeOHAng1UP8R9uTXcDz87PZlmkpxwEm\nln2NlrmLAMj3RLOq8R3srHqhT7L4kht/tm4Kpe0NpW0Fd7Y3MTHRFGc5v7n3vjGmB7DDWrvQGJN4\neHIRixb5txRrbTKQDBAfH28TExOLWiyoxMbGkp6eTihs62EpKSk+397Y2FgAn673wo7ZXPPyN2w9\nEMNf99/F2LjZdN01gbCCbM5f+U8onwWXPQZhET7L5G1u/Nm6KZS2N5S2Ffx7e/3p8H4n4CpjzG/A\nVJzD+qOBWGPM4b+cxAFb3Ykn4jtVy0XzQNtSND6nLBYPwzd34dUaz2CjyzsLzB0DE3rAPv3fQUSK\nz29K31r7oLU2zlpbF+gLfGOtHQB8C1xXuNhg4GOXIor4VLkow5RbEji/hvMUvufX1WFUlTEUnHOB\ns8CmVHjtL/Drty6mFJFA4jelfxL3A3cZY9KASsAbLufxGx06dOD88893O0bQ69ChAx06dHBl3RXK\nRPLuzQk0r+X8xDBlbRjDIp8lr+VgZ4HMXTDpWkh5TrfvFZFT8pvf9I9mrU0BUgrH64B2bubxV88+\n+ywpKSluxwh6zz77rKvrL186gslD2zHkrZ9YuGEvX6/J4MaGA3ijZwKRX9wNuZmQ8ixsnAvXJkPZ\naq7mFRH/FQh7+iIhr2x0BG/f1I529SoC8MPaXdywsB6Zg7+GSg2dhdalwGsX6nC/iJyQSj+A9erV\ni//7v/9zO0bQ69WrF7169XI7BmWiwpl4Yzs6NagEQOq6Pdzw6T72D/4aLujjLHRwh3O4f/aTkJ/n\nYloR8Ucq/QC2e/du9u3TXdq8bffu3ezevdvtGACUigzjjcFtubhRFQAWbNjLoEkryeg6Bq4eCxGl\nAQs/vAATe0D6JncDi4hfUemLBJjoiDCSb2jNZU2c3+6XbEpn4Bvz2dvoerjlW6h6nrPgxrnwWidY\n8ZGLaUXEn6j0RQJQVHgYYwe0olvTcwBYtiWDfuNT2V26Htw8G1oPcRbMzoD3BsMnd8Khg+4FFhG/\noNIXCVCR4R5e6deSq5rXAGDVtv30TU5lR44Her4EvSdBtHOpH4smQnIi/P6ze4FFxHUq/QDWuXNn\nWrVq5XaMoNe5c2c6d+7sdowihYd5+HefFvy1lfNgnrU7DtB3XCrbMrLhvKtg+I9Qp5Oz8K41MP5S\n+PElXdMvEqJU+gHskUce4YYbbnA7RtB75JFHeOSRR9yOcUJhHsML1zWnb9taAKzbdZA+yXPZkp4F\n5eNg8KdwycNgwqAgF77+P3j7ap3kJxKCVPoiQcDjMTxzbTMGJdQBYMPuTHq/NpdNezLBEwYX3wtD\nv4aK9Z0P/PYDvNoJfn7PxdQi4msq/QDWrVs37r//frdjBL1u3brRrVs3t2OcksdjeOLq8xl6YT0A\ntqRn0XvcXH7bVXgCX1xrGPYDtCq8hW9OBnxwM7w3BDL3uBNaRHxKpR/AsrKyyMnJcTtG0MvKyiIr\nK8vtGMVijOHhK5tw68XnAvB7Rja9x80lbccBZ4GoGLjqZeg7BUo7N/lhxYcwNgHWfOlSahHxFZW+\nSJAxxnB/13ju7OzcnnfH/hz6Js9l9bb9RxZq3B1GpEL8lc77A9vh3d7w8e2QrRs+iQQrlb5IEDLG\ncFeXRtxzeSMAdh04RN/kuazYmnFkoZiq0PcduOZViHIe38viSfBqR92/XyRIqfRFgtjtlzZkVPfG\nAOzNzKX/+Hn8vDn9yALGQIv+MHwO1LvYmZaxCSZdA5/+TXv9IkFGpR/AevTo4dpz3kNJjx496NGj\nh9sxzljSRefyaE/n1rwZWbkMGD+PRRv3HrtQbC0Y9BFc+S+IKONMWzihcK//G98GFhGvUekHsHvu\nuYc+ffq4HSPo3XPPPdxzzz1uxzgrN3aqx1PXNAVgf04eg16fx/z1fzpj3+OBtjfDiLlQ7yJnWsYm\n56l9H98GWemISGBT6YuEiIEJdXi+1wUYAwcP5TP4zfnMSdt1/IIV6sCgj4/d6188Gf7THn6Z6dvQ\nIlKiVPoBLDExkZEjR7odI+glJiaSmJjodowS0bttLV7s3RyPgazcfG6c8BPfrdl5/IJH7/Wfe6kz\n7cA2mDYApg+GAzt8G1xESoRKXyTEXNsyjpf6tiTMY8jJK+CWiQuY/cv2oheuUAcGfuCc4X/44T0r\nP4IxbWDR22Ct74KLyFlT6YuEoJ7Na/Cf/i2JCDMcyi/g1skL+WL5tqIXPnyG/23zoclVzrTsDPjk\nDpjQA3at9V1wETkrKn2RENW1aXVeG9iayDAPufmW295dxKdLt574A2WrQZ9J0PddKOs8zpcN/3PO\n8E/5B+Tp7pAi/k6lLxLCOjepxvjBbYgK95BfYPnb1MV8sGjzyT/U+Eq4bR60GwYYyD8EKc845b/u\nO5/kFpEzo9IPYL179w6aE8z8We/evendu7fbMbzm4kZVeGtIW0pFhFFg4e73ljL9p1M8dje6HHR/\nHm6eBVXPd6btToO3r4L3b9GJfiJ+SqUfwEaMGME111zjdoygN2LECEaMGOF2DK/q2KAyE25sS5nI\nMKyF+97/mcmpG079wbg2MOw7uPypI5f3LZsOr7SB+eOhIN+7wUXktKj0A1hmZibZ2dluxwh6mZmZ\nZGZmuh3D69rXr8TbQ9tTNiocgIc/Ws5bP64/9QfDIqDjHc4h/8aFdy7MyYDP7oHxl8Cmn7yYWkRO\nh0o/gHXv3p0HHnjA7RhBr3v37nTv3t3tGD7Ruk4FJt/cnnLRTvE//ulKxn33a/E+HFvLeYBPv6kQ\nW9uZ9vtSeOMy5+l9B4u4EZCI+JRKX0SO0bxWLFOSEqhQOgKAZz9fxZhvTuOyvPhuzuV9F98PYVHO\ntMWT4JVWMC8Z8vO8kFpEikOlLyLHOb9GeaYmdaByTCQAL3y1hhe/XoMt7s14IkrBJaPgtlRoeLkz\nLTsDPr8Xxv1FZ/mLuESlLyJFij+nLFOTOlC1rLO3/vLstfzji9XFL36AivWh/3TnkH+Fus60HSud\ns/ynDYK9xThZUERKjEpfRE6oQdUYpg3rQPXy0QC89t2vPDnzl9MrfmOcQ/4j5kHn/4OI0s70Xz6B\nMW1h9hOQs98L6UXkz1T6AWzIkCF07drV7RhBb8iQIQwZMsTtGK6pV7kM04d1oGZsKQDe/HE9//fx\nCgoKTvO++xHR8Je74Y6F0Ox6Z1p+DvzwL3ilNef8PgsKCko4vYgcTaUfwFT6vhHqpQ9Qq2Jppt/a\ngTqVnL30SakbGPXhstMvfoByNaDX63DTV1CztTPtwHYar34FxifC+h9KLriIHEOlH8B27dpFRkaG\n2zGC3q5du9i1S5eb1YwtxbSkDtSv4tyEZ+pPm7h3xs/kn0nxA9RuD0NnwbXJR+7l//tSmNgD3u37\n/+3dd3xUVf7/8ddnUoDQIfQEqUZphh5ANLK4VpB1UYoLorRlLeCifldkd3/uD/26qyJroYkUkRax\nAIqsogKrEHoJLRBAEjoIoYSSdr5/nBuDCtKS3Jk7n+fjcR6TuTNh3ocL85m599xz4PC2AkqulMqj\nRT+Ade3alb///e9ux/C8rl270rVrV7dj+IWqZYszc0Ac9SuXAuDDNXv4c8I6snOu8rC8zwc3dYMn\nVrGrVo/88/3bPofRcfDpn+HU4QJKr5TSoq+UuiKVS9vCf0PV0gDMWbePJ2euJetqCz9AeEl21+oO\nT6yBpr0AAZMDq96FN6ACkcUAAB5rSURBVGLtKn7nThVMB5QKYlr0lVJXrGKpYszoH0ejGmUAmJ90\ngEHvr+Fc9jXOtV+mGtz3FvzxW6jbwW7LPGVX8XujKaycADlZ15heqeClRV8pdVXKlwxnWr84YqPL\nAbBwy0EGTl3N2awCWGSnaiPo9bFtVZvYbRmH4LOh8HZr2PihjvRX6ipo0VdKXbWyJcKY2rcVLa4r\nD8Ci5MP0m7KKM5kFtLpe3Q4wYDHcPyF/Pv+jO2D2ozD+Vtj+JVzJnAFKBTkt+gFs0KBBdO7c2e0Y\nnjdo0CAGDRrkdgy/Vbp4GFMebUVcnQoAfJtyhEcmryDjXAHNse/zQZMH4PFVcOfLEBFptx/YANO6\nwqS7YfeygnktpTxOi34A69atGx06dHA7hud169aNbt26uR3Dr5UsFsqkPq1oX98W5MSdR3l44gpO\nni3A8++hxSBuEAxeB/HDINwOJCR1KUy6E6beD3tXF9zrKeVBWvQDWFpaGocOHXI7huelpaWRlpbm\ndgy/VyI8hHd6t+C2mEoArNp9jD+8u4Ljpwt44F2x0hD/PzB4PbR5PH8lvx1fwTsdYEYPOJBUsK+p\nlEdo0Q9gvXr14qWXXnI7huf16tWLXr16uR0jIBQPC2Fsr+bc3qAKAOvT0uk5IZFjGZkF/2IlK8Id\nL9pv/i37gc8uBUzyfBh7s13Q58DGgn9dpQKYFn2lVIEqFhrC6IeacXfjqgBs2neCHu8kcuTUucJ5\nwTLV4Z7X4EnnGn8Jsdu3zIWx7SChNxzcVDivrVSA0aKvlCpwYSE+3ujelPti7fS6Ww+cpPv4RA6d\nOFt4L1qupr3G//GVcFNPEOftbfMcGNPWfvPfv6HwXl+pAKBFXylVKEJDfIx8MJbfN4sCIOXQKbqP\nT+TA8UIs/AAV68LvxtjR/jf1yC/+W+bCuPZ2Xn8d8KeClBZ9pVShCfEJr3RtQo9W0QDsPJLBg+OW\nsefY6cJ/8Yp14Xdj4bG8b/7OYf9tn9sBf1Pvh91LCz+HUn4k1O0A6uoNHTqUpCQdpVzYhg4d6naE\ngObzCS92aUxYiI/3lu0m9ehpuo1LZEb/OGo6S/UWqsh69pv/rc/Ct6/DuumQm2VH++/4Cmq2gfZD\noV5HECn8PEq5SL/pB7BOnTrRtm1bt2N4XqdOnejUqZPbMQKazye80Lkh/W6uDcDe9DM8OG4ZOw8X\n4SI6FWpD5zfgybXQsn/+pX6py+wkP+Nucab3LaDZBJXyQ1r0A1hycjKpqalux/C85ORkkpOT3Y4R\n8ESE5++5kUHxdQE4cOIs3cYnknLoZNEGKRcN97wKQ5Kg3ZD8SX4ObLDT+77ZzC7sk3WmaHMpVQT8\npuiLSLSIfCMiW0Rkk4gMdrZXEJEvRWS7c1ve7az+YuDAgYwcOdLtGJ43cOBABg4c6HYMTxARnr0j\nhsG/qQ/A4ZPn6DYuka0HThR9mNJV4PYX4KkkuG04RFS02499bxf2GdUYlrwCp48WfTalConfFH0g\nGxhqjLkRiAMeE5EGwF+Ar4wx9YGvnPtKqQAlIjx1+/U8c0cMAD9kZNJjfCK7T7h0WL1Eebj1GRiy\nEe56JX9hn4zD8PUIeL0hzH8Wju5yJ59SBchvir4xZr8xZo3z80lgC1ADuA+Y4jxtCtDFnYRKqYL0\n2G31eP7uGwE4djqLf644y/q0dPcChUdA6wHwxFq7ql+VxnZ71mlYMc4e9k94GNJWupdRqWskxg+X\npRSRWsASoBGQaowpd95jx4wxvzjELyIDgAEAlSpVap6QkFA0YV00ZMgQcnJyePPNN92OUmROnTpF\nqVKlivQ1hwwZAsCoUaOK9HXd6KsbvtydxbQtdpreEqHw5+bFqV8+xOVUgDGUP7ae6LRPqHBs7U8e\nOl4mhj1RnTkS2Qbju7qswbJ/Ibj6Cu70Nz4+/rIuPfG7oi8ipYDFwIvGmI9EJP1yiv75YmJiTDAM\nvIqPjyc9PZ1169a5HaXILFq0iPj4+CJ9zbzXW7RoUZG+rht9dcv05akM+9hefhoRHsKkPi1pXaei\ny6nOc2AjLHsbkj6wl/vlKRNljw40621PE1yBYNq/wdRXcK2/l1X0/ebwPoCIhAEfAtOMMR85mw+K\nSDXn8WqALivnGD58uC4EUwSGDx/O8OHD3Y7haT1b16Rvo3BE4HRmDg9PWsF3KUfcjpWvaiN7rf+Q\nJGj/NJSoYLef2ANf/g1GNoB5Q+DQFndzKnUJflP0RUSAd4Etxpjzh6TPBR52fn4YmFPU2fxVx44d\nad68udsxPK9jx4507NjR7Rie1z4qjNcfjMUncDYrl0cnr2TxtsNux/qpMtXgN3+FpzbBvaMg0g5G\nJOs0rJ4Eo+NgSmfY+ple76/8kt8UfaAd0AvoICLrnHY38DJwu4hsB2537itg3bp1pKSkuB3D89at\nWxdUp1Dc1KVpDd7s0YwQn3AuO5f+U1axcPNBt2P9UngEtHgEHlsOvT6G6+/kx6OruxbDzJ7w71j4\n70jI8KMjFiro+c00vMaYb7n4OYnfFGWWQDFkyBDS09Pp16+f21E8LW8gX1Gf0w9W9zSpRmiI8Pj0\nNWTm5PLH91fzVs+m3NmomtvRfkkE6naw7YcddlKfte/DuRNwPBW+egEWvQwNfwct+0FUC53qV7nK\nn77pK6UUAHc0rMq4Xs0JD/WRnWt4bPpa5q7f53asX1exLtz5v/DnLXDv61C5gd2ecw42zIR3O8LY\n9rBqIpwr4lkIlXJo0VdK+aUON1RhQu8WFAv1kZNrGDJzLR+u3uN2rEsrVgpaPAqDlkKf+dCgC/ic\ng6oHk+DTp+C1G6m/bQzs09NGqmhp0VdK+a1brq/EpD4tKREWQq6Bp2evZ9bKAFlvQgRqtYMHp9iB\nfx2GQ1m7xDCZJ6mxbwGMvxXG3QqrJum3f1UktOgrpfxa23qRTHm0FSXDQzAG/ufDJKYu+97tWFem\ndFW45RkYvB56zIT6v8XkDWHavw4+HQKvxsCcxyBtBfjZ/CnKO/xmIJ+6ci+99BJr1qxxO4bnvfTS\nS25HCHqtaldgar/WPDxxBSfPZvPXOZvIzDH0dZbqDRi+EIi5C2LuInHBB7QplgJrp8KJvZCVYQcB\nrn3fXgrYrDfc1B1KRrqdWnmIftMPYG3btqVRo0Zux/C8tm3b0rZtW7djBL1mNcszvV8cZUuEAfD/\nP93M2MU7XE519c4VrwS3PQeDN0CPWXDDvSDOlL5HkuGL5+G1GJj5EGydDzlZv/4HKnUZtOgHsKVL\nl7Jx40a3Y3je0qVLWbp0qdsxFNA4qiwz+sdRoWQ4AC9/vpU3vtrucqprFBIKMXdC92l25H/HF6Bi\nPftYbjZs/RRm9oCRN8J/nrdTAit1lbToB7Bhw4YxYcIEt2N43rBhwxg2bJjbMZSjQfUyzBwQR2Sp\nYgCM/HIbr32RjL+tI3JVSleBm4fA46vgkQXQtBeEOwu3ZByGZW/B2HYw5mZY+hac9MOJi5Rf06Kv\nlAo411cpzcwBcVQubQv/m1+n8PKCrd4o/GBH/l/XBu57C57eBl3GQq32+Y8fTLKH/0feCO93hQ0J\nkJnhXl4VMLToK6UCUr3KpUgY2IbqZYsDMG7xTv7x6WbvFP484SUhtgf0+dQu+HPbcKhQ1z5mciDl\nS/ioP7xSHz7sD9sXQk62u5mV39Kir5QKWLUiSzJrYBuiypcAYNJ33/PXORvJzfVY4c9Tribc+gw8\nsRr6LoQWffOX9M3KgKQEmPZ7OwDws6GQmgi5ue5mVn5Fi75SKqBFV4ggYWAbalWMAOD9xFSe+yiJ\nHK8WfrCH/6Nbwr0jYeg2e+1/w99BiD3dwekjdh2AiXfAv5vAF3+FfWv1+n+l1+kHslGjRrFq1Sq3\nY3jeqFGj3I6gLqF6uRLMGtiGnu8ksuNwBrNWpZGVk8srD9xEiM/jC9yEhv947T9nj9tlfZM+gJ2L\n7eH/42mw9A3bKtSBhvdDo/vt2gC6+E/Q0aIfwGJjY0lPT3c7hufFxsa6HUFdhiplijNzQBsempDI\ntoOn+GjtXrJyDSMfvImwkCA5qFm8LMT2tO3UYdj8CSTNhrRE+/jRnfDfV22rWB8adoEG90GVRvoB\nIEgEyf8Eb1q4cCGrV692O4bnLVy4kIULF7odQ12GSqWLMaN/HDdWKwPAvPX7eGL6WjKzg/C8dqlK\n0Ko/9P2Pnfv/ty9C9Wb5j/+wHZa8AmNvhjebw8IXYO8aPQXgcVr0A9iIESOYOnWq2zE8b8SIEYwY\nMcLtGOoyVSxVjBn9W9MkqiwACzYd4E/TVnMuO8flZC4qGwVtH4cB38CT6+wEQNWb5j9+dAd8OxLe\nuQ1GNYYFz8HupZAbxH9nHqVFXynlOeUiwnm/X2ua1iwHwMIthxjw3mrOZmkRo0JtOwHQgEV2AaDb\n/wE1muc/fjwNEkfDpLvsVQBzn4Bt/4Gss24lVgVIi75SypPKFA9jat/WtKpVAYDF2w7Td8pKTmfq\nNew/Kl8L2g2G/l/bUwB3/hOuuxnEKQ0Zh2HNezD9QXilLiT0hvUz4fRRV2Orq6dFXynlWaWKhTL5\n0Za0qVMRgO9SfqDPpJWcOqeF/xfKRkHcH+GRz+xlgJ3fhPp35F8GmHkKNs+BjwfaDwCT7oalb8KR\nFHdzqyuiRV8p5WkR4aFM7NOS9vXtErUrdh2l97vLOXFWV627qFKV7NK+DyXAszvggSnQ+AF7dQCA\nyYXd38EXw+Gt5vBGM1gwzF4mmJ3pbnb1q/SSvQA2btw4li9f7nYMzxs3bpzbEdQ1KhEewju9W/Cn\naWv4eush1qSm02vCct57tDVlI8LcjuffipW2l/Y17GKX901dBsmf2/kA0nfb5xzdAYlv2xZeGurG\nQ/3fQr3boUw1V+Orn9KiH8BiYmLYv3+/2zE8LyYmxu0IqgAUDwth7B+a8/j0NXyx+SDr9xyn54RE\npvZt/eNSveoSQsKg9i223fESHNkG2xbYgX6py+wRgMyTsGWebQBVG1M7/HqoFQpRrexkQso1eng/\ngM2bN0/XeS8C8+bNY968eW7HUAUgPNTH2w81454m9tvnpn0n6PlOIkdOnXM5WQASgUoxdiDgI/Ph\nmR3w+3ehSTeIqJj/vANJXJf6IUy+B/5VG2b0tFMEH93pXvYgpt/0A9hrr71Genq6rvVeyF577TUA\nOnXq5HISVRDCQnz8u1ss4SE+Pl67l60HTtJ9fCLT+7WmcpnibscLXBEVoHFX23Jz7Fz/27+AlIWY\nvWsQjB0MmPyZbWCvHqjbwbZa7aFEOVe7EAy06Culgk5oiI9XH7iJUJ/wweo9pBw6RbfxiUzv35pq\nZUu4HS/w+UIgqoVttw1j6RdzaVctE1IW2pZx2D7v2PewaqJt4rMzBtaJty26FYQWc60LXqVFXykV\nlEJ8wj9/34SwUB/Tl6ey60gGD45bxvR+cURXiHA7nqdkhZeBxvHOUYBcOLQJdnxt2+5lkHPOjgfY\nu8q2/74KocWhZpwzhuBWqBYLIVqyrpX+DSqlgpbPJ7zYpRHhIT4mL/2etKNn7KH+/q25rmJJt+N5\nk88HVRvb1m4wZJ62gwB3LrLtwAb7vOyz+dvAXhVwXRuodbNtVW/SDwFXQf/GlFJBTUT4e6cGhIf6\nGL9kJ3vTz9BtXCLT+rembqVSbsfzvvAIqPcb2wAyjsCuJfnt6A67PfOkHSOw/Qvn90rbIwHXtbUf\nAqrF6pUBl0GLfgCbOnUqy5YtczuG5+miRt4nIjx31w2EhQhvf7ODAyfO0m1cIjP6t6Z+ldJuxwsu\nJSOh0f22ARzfA7v+C987LT3Vbs88CSlf2gYQFgFRLaFmG/thIKolFNMPbT+nRT+ARUdHs2PHDrdj\neF50dLTbEVQREBGe/m0M4SEhvL5wG0dOnaP7eHsdf4PqZdyOF7zKRkFsD9sAju22swHu+q+9zZsg\nKOs07FpsG4CEQLUmEB0HNVvbW50oSIt+IJs1axabNm0iPj7e7SieNmvWLAC6devmchJV2ESEwR3r\nExYq/GtBMj9kZNJzQiLv921Noxpl3Y6nAMpfZ1tsT3v/+B47GHD3t/b2SLLdbpzLBvetheVj7Lay\nNe0HgKhWEN0SqjSyEw4FES36AWzMmDGkp6fzj3/8w+0onjZmjH3D0KIfPP4UX4/wEB8jPttC+uks\ner6TyHt9WxMbrdeR+52yUdDkAdsAMn6AtEQ7OHD3Mti/HnKddRaOp0JSKiR9YO+HloAazeylhTVa\n2FMCHj8aoEVfKaUuoF/7OoSH+vjbnE2cOJvNHyYsZ/IjLWnhLNWr/FTJinDDPbYBZJ2x3/ZTEyFt\nOaStgDPO0sDZZ+wpgt3f5f9+mRpQo7nTmtkBgsW9c3pHi75SSl1E7za1CAvxMezjJE6dy6b3xBVM\n7NOSuDoVL/3Lyj+ElbAj/K9ra+8bY6cATlsBe1ZA2ko7b4DJtY+f2GvblrnOHyAQeX3+B4DqTe3l\nhuGBOZeDFn2llPoVPVrVJCzEx7Oz13M6M4c+k1YwoXdLbnaW6lUBRgQq1rUtb3BgZgbsW2cnBtqz\nEvausYUfAGPHCRxJhvUznD/DB5VusB8Cqt1kW9XGAXG1gBZ9pZS6hK7NowgLEf6csJ6zWbk8OmUl\n43o157aYym5HUwUhvCTUamdbnpMHYd8a2LvafgjYtzb/tIDJhUObbVs/3fkFgYr1oGpjos+UgpRs\nO4FQqUpF3p1fo0U/gM2ePZvvvvvu0k9U12T27NluR1B+4L7YGoSF+Hhyxloys3MZ+N5q3n6oGbc3\nqOJ2NFUYSleBmLtsA3taID3VFv/965zb9XDmmPMLBn7YDj9spy7Azvfs5pKVoWoje6VA1cZQpSFU\nrO/aREJa9ANYZGQkZcvqZUSFLTJSD+Mq6+7G1Qj1CY9NX0NmTi6D3l/NGz2acndjb4/4VtjTAnmX\nCzbsYrcZYy8Z3L/efhA4kAT7N8DJffm/l3Eof52BPL4wO06gSgP7IaByA6h8I5SNtq9TiLToB7DJ\nkyezdetWvU6/kE2ePBmAPn36uJpD+YffNqzK+F4tGPj+ajKzc3lixlqycnK5L7aG29FUUROBctG2\n3Xjvj5u/+2IO7eqWth8CDmyEgxvhyDbIzbZPyM2ygwcPbcq/fBAgvJQdK1D5Bnub18pGFdiHAS36\nAWzy5Mmkp6fz8ssvux3F07Toq5+77YbKvPtwC/q/t4qzWbk8NWsdWTmGrs2j3I6m/EBWeFmoGw91\nO+RvzD4Hh7fCwc222B/cZH8+dSD/OZmn8lcaPF9YSYisD5Vi7BGCvNvyta/4NIEWfaWUugrt61di\nUp9W9J2yktOZOTwzez3ZObl0b1XT7WjKH4UWyx/pf77TR+HQFmdg4BbbDm85b6wAkJVhTx/sX/fT\n35UQKF/LfgDoOfPyYlxbL5RSKni1qVuR9x5tRZ9JKzl1Lpu/fJREZk4uvdvUcjuaChQRFX555YAx\ndrXBw1vgcLI9QnBkGxze9tMjAybHrkJ49PLXYNGir5RS16BFrQpM7duK3hNXcPJsNn+bs4nM7Fz6\nta/jdjQVqETspX6lKkHtW3762Jl0OGKvEuDINufnlMv+o7XoK6XUNWpaszzT+8XRa+Jy0k9nMeKz\nLWTm5PKn+HpuR1NeU6KcXSwouuVV/boW/QA2f/58lixZ4nYMz5s/f77bEVQAaBxVlun94vjDu8s5\nmpHJvxYkk5VtGNyxvtvRlPqRz+0A6upFRERQvHhxt2N4XkREBBERgTnPtipaDaqXYeaAOCJLFQPg\n9YXbePU/yRhjXE6mlKVFP4CNHj2aTz75xO0Ynjd69GhGjx7tdgwVIK6vUppZA+OoUsYW/re+SeF/\nP9+qhV/5BS36ASwhIYFFixa5HcPzEhISSEhIcDuGCiB1K5UiYWAbapQrAcD4JTt5Yd5mLfzKdVr0\nlVKqEFxXsSQzB8QRXcEW/slLv2f4JxvJzdXCr9wTEEVfRO4UkWQRSRGRv7idRymlLkd0hQhmDWhD\n7ciSAExbnspfPtpAjhZ+5RK/L/oiEgK8DdwFNAB6iEgDd1MppdTlqV6uBLMGxFG3ki38Cav28PQH\n67XwK1f4fdEHWgEpxpidxphMYCZwn8uZlFLqslUuU5yZA9oQU6U0AB+v3cu4DefIysl1OZkKNoFw\nnX4NIO28+3uA1j9/kogMAAY4d8+JyMYiyOYPIkXkiNshilAk4Ep/pZCXvLwA1/rqkqDq726I/OCp\noOlvUO1b3OnvAmPMnZd6UiAU/Qu90/7iuJgxZjwwHkBEVhljWhR2MH8QTH2F4OpvMPUVtL9eFkx9\nBf/ubyAc3t8DRJ93PwrY51IWpZRSKmAFQtFfCdQXkdoiEg50B+a6nEkppZQKOH5/eN8Yky0ijwP/\nAUKAicaYTZf4tfGFn8xvBFNfIbj6G0x9Be2vlwVTX8GP+ys6Q5RSSikVHALh8L5SSimlCoAWfaWU\nUipIeKroe326XhGJFpFvRGSLiGwSkcHO9goi8qWIbHduy7udtaCISIiIrBWRT537tUVkudPXWc7g\nTk8QkXIiMltEtjr7uI1X962IPOX8G94oIjNEpLiX9q2ITBSRQ+fPF3KxfSnWG8771gYRaeZe8qtz\nkf6+4vxb3iAiH4tIufMee87pb7KI3OFO6qtzob6e99jTImJEJNK573f71jNFP0im680GhhpjbgTi\ngMecPv4F+MoYUx/4yrnvFYOBLefd/yfwutPXY0BfV1IVjn9jJ9i4AbgJ22/P7VsRqQE8CbQwxjTC\nDtDtjrf27WTg5xOlXGxf3gXUd9oAYEwRZSxIk/llf78EGhljmgDbgOcAnPes7kBD53dGO+/fgWIy\nv+wrIhIN3A6knrfZ7/atZ4o+QTBdrzFmvzFmjfPzSWxRqIHt5xTnaVOALu4kLFgiEgXcA0xw7gvQ\nAZjtPMVLfS0D3AK8C2CMyTTGpOPRfYu9cqiEiIQCEcB+PLRvjTFLgKM/23yxfXkf8J6xEoFyIlKt\naJIWjAv11xjzhTEm27mbiJ1jBWx/ZxpjzhljdgEp2PfvgHCRfQvwOvAsP508zu/2rZeK/oWm663h\nUpZCJyK1gKbAcqCKMWY/2A8GQGX3khWoUdj/RHkTlFcE0s97I/HSPq4DHAYmOaczJohISTy4b40x\ne4FXsd+I9gPHgdV4d9/mudi+DIb3rkeBz52fPddfEekM7DXGrP/ZQ37XVy8V/cuartcLRKQU8CEw\nxBhzwu08hUFE7gUOGWNWn7/5Ak/1yj4OBZoBY4wxTYEMPHAo/0Kcc9n3AbWB6kBJ7GHQn/PKvr0U\nL/+7RkSex56anJa36QJPC9j+ikgE8Dzwtws9fIFtrvbVS0U/KKbrFZEwbMGfZoz5yNl8MO+QkXN7\nyK18Bagd0FlEvseequmA/eZfzjkkDN7ax3uAPcaY5c792dgPAV7ctx2BXcaYw8aYLOAjoC3e3bd5\nLrYvPfveJSIPA/cCD5n8SWG81t+62A+w6533qyhgjYhUxQ/76qWi7/npep1z2u8CW4wxI897aC7w\nsPPzw8Ccos5W0IwxzxljoowxtbD78mtjzEPAN0BX52me6CuAMeYAkCYiMc6m3wCb8eC+xR7WjxOR\nCOffdF5fPblvz3OxfTkX6O2M9I4DjuedBghkInIn8D9AZ2PM6fMemgt0F5FiIlIbO8hthRsZC4Ix\nJskYU9kYU8t5v9oDNHP+T/vfvjXGeKYBd2NHie4Annc7TyH072bsoaENwDqn3Y091/0VsN25reB2\n1gLudzzwqfNzHewbRArwAVDM7XwF2M9YYJWzfz8Bynt13wIvAFuBjcBUoJiX9i0wAzteIQtbBPpe\nbF9iDwG/7bxvJWGvanC9DwXQ3xTs+ey896qx5z3/eae/ycBdbue/1r7+7PHvgUh/3bc6Da9SSikV\nJLx0eF8ppZRSv0KLvlJKKRUktOgrpZRSQUKLvlJKKRUktOgrpZRSQUKLvlJKKRUktOgrpa6aiDwg\nIotF5ISInBKRlSJyj9u5lFIXpkVfKXVVRORV7BTJm4A/AD2ApUAZN3MppS5OJ+dRSl0xEemOnZns\nAWPM7Es9XynlH/SbvlLqarwAzLtYwReRv4pIsojkikiXCz1HKVX0tOgrpa6IiNQBrsfOj38xX2KX\ny11SJKGUUpcl9NJPUUqpn6ju3F50iVBjTCKAXURPKeUv9Ju+UupK5RX7hq6mUEpdMf2mr5S6UruA\nb4EXnG/yG4Aq2GWeXzTGbHMxm1LqV2jRV0pdEWOMEZHfAy8CT2ML/kFgMfYDgVLKT2nRV0pdMWPM\nIaC/2zmUUldGr9NXShU4Efl/QD+gEnASOAvEGWP2uJlLqWCnRV8ppZQKEjp6XymllAoSWvSVUkqp\nIKFFXymllAoSWvSVUkqpIKFFXymllAoSWvSVUkqpIKFFXymllAoSWvSVUkqpIKFFXymllAoS/wfY\nlplQG3Kg6wAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xa4f5470>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "consume_plot2(r, delta, rho, y1, y2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Interactive plot with sliders (visible if if running on a notebook server):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "4e681dfc590344c3adfccd61e903ad82",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "interactive(children=(FloatSlider(value=0.0, description='r', max=1.0), FloatSlider(value=0.7, description='de…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "interact(consume_plot2, r=(rmin,rmax,0.1), rho=fixed(rho), delta=(0.5,1,0.1), y1=(10,100,1), y2=(10,100,1));"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "c1e, c2e, uebar = find_opt2(r, rho, delta, y1, y2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this particular case the consumer consumes:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(50.0, 50.0)"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c1e, c2e"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Her endowment is "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(80, 20)"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y1,y2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And she therefore saves "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "30.0"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y1-c1e"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "in period 1.  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### A borrowing case\n",
    "In the diagram below the consumer is seen to be borrowing, i.e.  $s_1^* = y_1 - c_1^* <0$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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cfRpWdX5//2DRFv4+bQl5+Wd4Bn7VxtDxTme8dREseLOE0ouIiJv85kQ+AGvt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\nlplQG3Kg6wAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x8fb3a58>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "y1,y2 = 20,80\n",
    "consume_plot2(r, delta, rho, y1, y2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id='codesection'></a>\n",
    "## Code section \n",
    "Run the code below first to re-generate the figures and interactions above."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from ipywidgets import interact, fixed"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Code for simple consumer choice"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def U(c1, c2, alpha):\n",
    "    return (c1**alpha)*(c2**(1-alpha))\n",
    "\n",
    "def budgetc(c1, p1, p2, I):\n",
    "    return (I/p2)-(p1/p2)*c1\n",
    "\n",
    "def indif(c1, ubar, alpha):\n",
    "    return (ubar/(c1**alpha))**(1/(1-alpha))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def find_opt(p1,p2,I,alpha):\n",
    "    c1 = alpha * I/p1\n",
    "    c2 = (1-alpha)*I/p2\n",
    "    u = U(c1,c2,alpha)\n",
    "    return c1, c2, u"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Parameters for default plot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "alpha = 0.5\n",
    "p1, p2 = 1, 1\n",
    "I = 100\n",
    "\n",
    "pmin, pmax = 1, 4\n",
    "Imin, Imax = 10, 200\n",
    "cmax = (3/4)*Imax/pmin"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def consume_plot(p1=p1, p2=p2, I=I, alpha=alpha):\n",
    "    \n",
    "    c1 = np.linspace(0.1,cmax,num=100)\n",
    "    c1e, c2e, uebar = find_opt(p1, p2 ,I, alpha)\n",
    "    idfc = indif(c1, uebar, alpha)\n",
    "    budg = budgetc(c1, p1, p2, I)\n",
    "    \n",
    "    fig, ax = plt.subplots(figsize=(8,8))\n",
    "    ax.plot(c1, budg, lw=2.5)\n",
    "    ax.plot(c1, idfc, lw=2.5)\n",
    "    ax.vlines(c1e,0,c2e, linestyles=\"dashed\")\n",
    "    ax.hlines(c2e,0,c1e, linestyles=\"dashed\")\n",
    "    ax.plot(c1e,c2e,'ob')\n",
    "    ax.set_xlim(0, cmax)\n",
    "    ax.set_ylim(0, cmax)\n",
    "    ax.set_xlabel(r'$c_1$', fontsize=16)\n",
    "    ax.set_ylabel('$c_2$', fontsize=16)\n",
    "    ax.spines['right'].set_visible(False)\n",
    "    ax.spines['top'].set_visible(False)\n",
    "    ax.grid()\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Code for intertemporal Choice model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def u(c, rho):\n",
    "    return (1/rho)* c**(1-rho)\n",
    "\n",
    "def U2(c1, c2, rho, delta):\n",
    "    return u(c1, rho) + delta*u(c2, rho)\n",
    "\n",
    "def budget2(c1, r, y1, y2):\n",
    "    Ey = y1 + y2/(1+r)\n",
    "    return Ey*(1+r) - c1*(1+r)\n",
    "\n",
    "def indif2(c1, ubar, rho, delta):\n",
    "    return  ( ((1-rho)/delta)*(ubar - u(c1, rho)) )**(1/(1-rho))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def find_opt2(r, rho, delta, y1, y2):\n",
    "    Ey = y1 + y2/(1+r)\n",
    "    A = (delta*(1+r))**(1/rho)\n",
    "    c1 = Ey/(1+A/(1+r))\n",
    "    c2 = c1*A\n",
    "    u = U2(c1, c2, rho, delta)\n",
    "    return c1, c2, u"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Parameters for default plot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "rho = 0.5\n",
    "delta = 1\n",
    "r = 0\n",
    "y1, y2 = 80, 20\n",
    "\n",
    "rmin, rmax = 0, 1\n",
    "cmax = 150"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def consume_plot2(r, delta, rho, y1, y2):\n",
    "    \n",
    "    c1 = np.linspace(0.1,cmax,num=100)\n",
    "    c1e, c2e, uebar = find_opt2(r, rho, delta, y1, y2)\n",
    "    idfc = indif2(c1, uebar, rho, delta)\n",
    "    budg = budget2(c1,  r, y1, y2)\n",
    "    \n",
    "    fig, ax = plt.subplots(figsize=(8,8))\n",
    "    ax.plot(c1, budg, lw=2.5)\n",
    "    ax.plot(c1, idfc, lw=2.5)\n",
    "    ax.vlines(c1e,0,c2e, linestyles=\"dashed\")\n",
    "    ax.hlines(c2e,0,c1e, linestyles=\"dashed\")\n",
    "    ax.plot(c1e,c2e,'ob')\n",
    "    ax.vlines(y1,0,y2, linestyles=\"dashed\")\n",
    "    ax.hlines(y2,0,y1, linestyles=\"dashed\")\n",
    "    ax.plot(y1,y2,'ob')\n",
    "    ax.text(y1-6,y2-6,r'$y^*$',fontsize=16)\n",
    "    ax.set_xlim(0, cmax)\n",
    "    ax.set_ylim(0, cmax)\n",
    "    ax.set_xlabel(r'$c_1$', fontsize=16)\n",
    "    ax.set_ylabel('$c_2$', fontsize=16)\n",
    "    ax.spines['right'].set_visible(False)\n",
    "    ax.spines['top'].set_visible(False)\n",
    "    ax.grid()\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Interactive plot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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KOOMpT+jdvojICfhN6RcJB2KMMeFALLAJuBiYULT9PeAal7KFtG4ta/LaTa2I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\nJ/akneLuEd8zLT6W+lVKn/1Fda+FIUth6duw6DX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      "text/plain": [
       "<matplotlib.figure.Figure at 0xa1b9240>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "interact(consume_plot2, r=(rmin,rmax,0.1), rho=fixed(rho), delta=(0.5,1,0.1), y1=(10,100,1), y2=(10,100,1));"
   ]
  },
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   "execution_count": null,
   "metadata": {
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   },
   "outputs": [],
   "source": []
  }
 ],
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krd1V2pvVjDTce2kbAPZn5jI4OZUfdh6uhLIDWPPjrutv1nV9EZFQ4MYtezOB+UC8MWa7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\nR2HDp7D6384p/8I85yzA8unOElUd2vR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          "text/plain": "<matplotlib.figure.Figure at 0x90fd4a8>"
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KOOMpT+jdvojICfhN6RcJB2KMMeFALLAJuBiYULT9PeAal7KFtG4ta/LaTa2I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\njhY13Q6t6IssCbVa2y2PMXB0ty3++zbaiYMOJJO9dyPhOfl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          "text/plain": "<matplotlib.figure.Figure at 0xa4f5710>"
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