{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Introduction to Python for Scientific Computing - Tutorial n°4" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "***Mohammed Ait Lahcen, Economic Theory Group, Faculty of Business and Economics, University of Basel***" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In this tutorial, we will go through some basic economic problems and see how it is possible to leverage the power of Python in order to come up with numerical solutions." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 1. Supply and demand" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Consider a perfectly competitive market where supply is given by\n", "$$ Q_s(p) = \\exp{(\\alpha p)} - \\beta $$\n", "and demand is given by\n", "$$ Q_d(p) = \\gamma p^{-\\delta} $$\n", "where $p$ is the price and $\\alpha, \\beta, \\gamma, \\delta$ are parameters with values:" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "alpha = 0.1\n", "beta = 1.0\n", "gamma = 1.0\n", "delta = 1.0" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's first plot demand and supply as a function of the price:" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "def Q_d(p):\n", " \"\"\"\n", " Returns the quantity demanded as a function of the price p\n", " \"\"\"\n", " \n", " return gamma * p ** (-delta)\n", "\n", "\n", "def Q_s(p):\n", " \"\"\"\n", " Returns the quantity supplied as a function of the price p\n", " \"\"\"\n", " \n", " return np.exp(alpha * p) - beta" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "p_grid = np.linspace(1, 5, 100)\n", "\n", "plt.figure(figsize=(9,6))\n", "plt.plot(p_grid, Q_d(p_grid), 'r-', label='Demand')\n", "plt.plot(p_grid, Q_s(p_grid), 'b-', label='Supply')\n", "plt.xlabel('Price', fontsize=16)\n", "plt.ylabel('Quantity', fontsize=16)\n", "plt.legend(loc='best')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The equilibrium price $p^*$ is the one that clears the market such that $Q_d(p^*) = Q_s(p^*)$. We can use a root finding algorithm to solve for it:" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "The equilibrium price is 2.93\n", "The equilibrium quantity is 0.34\n" ] } ], "source": [ "from scipy.optimize import root\n", "\n", "p_star = root(lambda x: Q_d(x) - Q_s(x),x0 = 3).x\n", "Q_star = Q_d(p_star)\n", "print('The equilibrium price is {:.2f}'.format(p_star[0]))\n", "print('The equilibrium quantity is {:.2f}'.format(Q_star[0]))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 2. Utility maximization" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's try to maximize the following lifetime utility:\n", "$$\n", "U = \\log{c_1} + \\beta \\log{c_2}\n", "$$\n", "subject to the constraint:\n", "$$\n", "c_1 + c_2 \\leq y\n", "$$\n", "\n", "Before trying to find the solution, let's plot the actual utility function:" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "beta = 0.96\n", "y = 10\n", "\n", "def u(c):\n", " return np.log(c[0]) + beta * np.log(c[1])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We create the grids of $c_1$ and $c_2$ and combine the two to create the coordinates for our 3D graph using `meshgrid`:" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "c1_grid = np.linspace(1, 10, 100)\n", "c2_grid = np.linspace(1, 10, 100)\n", "c1, c2 = np.meshgrid(c1_grid, c2_grid)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In order to plot in 3D we need to do some additional imports:" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [], "source": [ "from mpl_toolkits.mplot3d.axes3d import Axes3D\n", "from matplotlib import cm" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig = plt.figure(figsize=(9,6)) \n", "ax = fig.add_subplot(1,1,1, projection='3d') \n", "ax.plot_surface(c1,\n", " c2,\n", " u([c1,c2]),\n", " rstride=2, cstride=2,\n", " cmap=cm.jet,\n", " alpha=0.7,\n", " linewidth=0.25)\n", "ax.set_xlabel(r'$c_1$', fontsize=14)\n", "ax.set_ylabel(r'$c_2$', fontsize=14)\n", "ax.set_zlabel(r'$U(c_1,c_2)$', fontsize=14)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Next, let's plot the budget constraint along with some indifference curves. For the latter we use a contour map:" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(9,6))\n", "plt.contour(c1,c2,u([c1,c2]))\n", "plt.plot(c1_grid,10-c1_grid,'k')\n", "plt.xlim((1, 10))\n", "plt.ylim((1, 10))\n", "plt.xlabel(r'$c_1$',fontsize=16)\n", "plt.ylabel(r'$c_2$',fontsize=16)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In order to solve the maximization problem, we use the contrained optimization solver `SLSQP` available through the Scipy function `minimize`:" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([5.10046633, 4.89953367])" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from scipy.optimize import minimize\n", "\n", "cons = ({'type': 'ineq', 'fun': lambda c: -c[0] -c[1] + y})\n", "\n", "sol = minimize(lambda x: -u(x), ([5, 5]), method='SLSQP', constraints=cons)\n", "\n", "sol.x" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we plot the optimal consumption bundle and the utility level it provides on top of our contour map:" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(9,6))\n", "plt.contour(c1,c2,u([c1,c2]))\n", "plt.plot(c1_grid,10-c1_grid,'k')\n", "plt.contour(c1, c2, u([c1,c2]), levels=[-sol.fun], colors='r')\n", "plt.plot(sol.x[0],sol.x[1],'rx')\n", "plt.xlim((1, 10))\n", "plt.ylim((1, 10))\n", "plt.xlabel(r'$c_1$',fontsize=16)\n", "plt.ylabel(r'$c_2$',fontsize=16)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 3. A simple OLG model" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A young person chooses his young and old age consumption, $c_1$ and $c_2$, in order to maximize his lifetime utility:\n", "\n", "$$\n", "U(c_1,c_2) = c_1^{1/2} + \\beta c_2^{1/2}\n", "$$\n", "\n", "subject to the following budget constraints:\n", "\n", "$$\n", "\\begin{align}\n", "c_1 + v_1 m &\\leq y\n", "\\\\\n", "c_2 &\\leq v_2 m\n", "\\end{align}\n", "$$\n", "\n", "where $m$ is the amount of money acquired by the young and $v_1$ and $v_2$ the price of money in terms of the general good in periods 1 and 2.\n", "\n", "We assume the following laws of motion of the stock of money $M_t$ and the population $N_t$ in the economy:\n", "$$\n", "M_{t} = zM_{t-1}\n", "\\\\\n", "N_{t} = nN_{t-1}\n", "$$\n", "and that all seignorage revenue is used to finance government expenditures.\n", "\n", "
\n", "When faced with a constrained optimization problem like this one we can either solve it directly or try to use some math and rewrite it as an unconstrained problem. We follow the second path. However, depending on the details of the problem this might not always be possible.\n", "\n", "
\n", "Since $U$ is strictly increasing in consumption, we know that the two budget constraints will hold with equality which yields:\n", "\n", "$$\n", "\\begin{align}\n", "c_1 &= y - q\n", "\\\\\n", "c_2 &= \\frac{v_2}{v_1} q\n", "\\end{align}\n", "$$\n", "where $q = v_1 m$ are the real money balances acquired by the young.\n", "\n", "In addition, from the lecture we know that: $\\dfrac{v_2}{v_1} = \\dfrac{n}{z}$.\n", "\n", "Using the definition above and replacing the modified equality constraints into $U$ yields a simple unconstrained optimization problem:\n", "$$\n", "V = \\max_q \\,\\, U\\left(y - q,\\frac{n}{z} q \\right) = \\max_q \\,\\, (y - q)^{1/2} + \\beta \\left(\\frac{n}{z} q\\right)^{1/2}\n", "$$\n", "which we can easily solve using Scipy." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "First we set the parameters of the model in an array for fast access: $y = 100 \\, , \\, z = 1.03 \\, , \\, n = 1.02 \\, , \\, \\beta = 0.95$" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [], "source": [ "params = np.array([100,1.03,1.02,0.95])" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [], "source": [ "from scipy.optimize import minimize\n", "\n", "def U(q,params):\n", " \"\"\"\n", " Returns the lifetime utility of a young person given his choice of real money balances and the parameters of the model\n", " \n", " \"\"\"\n", " y, z, n, beta = params\n", " \n", " u_1 = (y - q) ** (1/2)\n", " \n", " u_2 = (n * q / z) ** (1/2)\n", " \n", " return u_1 + beta * u_2\n", "\n", "\n", "def V(params):\n", " \"\"\"\n", " Returns the solution to the young optimization problem given the parameters of the model\n", " \n", " \"\"\"\n", " \n", " sol = minimize(lambda q, params: -U(q,params), x0 = 10, args=params, method='Nelder-Mead',options={'ftol': 1e-10})\n", "\n", " return sol" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We want now to plot the optimal real balances as a function of the growth rate of money and the growth rate of the population:" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [], "source": [ "z_grid = np.linspace(1.0,11.0,100)\n", "q_star = np.zeros(len(z_grid))\n", "c_1 = np.zeros(len(z_grid))\n", "c_2 = np.zeros(len(z_grid))\n", "u = np.zeros(len(z_grid))\n", "\n", "for i, z in enumerate(z_grid):\n", " params[1] = z\n", " q_star[i] = V(params).x\n", " c_1[i] = params[0] - q_star[i]\n", " c_2[i] = q_star[i] * params[2] / params[1]\n", " u[i] = U(q_star[i],params)\n", "\n", "c = c_1 + c_2" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(9,6))\n", "plt.plot(z_grid,q_star)\n", "plt.ylabel(r'Real money balances, $q$',fontsize='12')\n", "plt.xlabel(r'Money growth rate, $z$',fontsize='12')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Next, we plot $c_1$ and $c_2$ for different levels of $z$ using the previous calculations:" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "data": { "image/png": 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+N8+s2sUzq3extd67zf3U4UVcumAsCycOZvbIEjL13B0RkYQQl8LinNtqZj8FNgNtwN+AJUC9cy7s71YNVMYjjwxMdS0hnl69i7+v3ME/3q2lrbOL3Mx0PjahnK8fO55jJg1mSJEGN4uIJKJ4nRIqBU4FxgD1wF+AT/Wxa5/X75rZJcAlACNHjoxRSklF2xvaeOLtHTzx9g5e37iHbgdDirI5bU4lx08ZwkfHlpGTqat5REQSXbxOCR0PbHDO1QCY2QPAfKDEzDL8oyxVwLa+3uycuwW4BWDu3Lm6KYm8r827W3ns7e08/vYO3txSD8BhQwr4l4Xj+cSUIUyvLCYtLXUufRcRGQjiVVg2A/PMLA/vlNBxwGLgWeB0vCuFzgcejFMeSTHVda08+tZ2Hl2+nbeqGwCYUVXMVZ+cyInThjKuoiDghCIi8mHEawzLq2Z2H96ly2HgDbwjJo8C95jZDf62W+ORR1LDrqZ2HnlzOw+9uY1l/pGUmVXFXPPpyXxq+lCqSnVVj4hIqrBku+373Llz3eLFi4OOIQFpau/kyRU7eXDZVl5cW0u3gynDijh55nBOmjFMlx6LiCQZM1vinJt7sP10a05JeF3djn+ureX+JdU8uWIHHeFuRg7K4/JjxnPqrOGMH1wYdEQREYkxFRZJWGt3NfOXJVv4vze2srOxg+LcTM6YW8XnZlcxZ2RJSj0zSkRE3p8KiySU1lCYR9/azp9f38LiTXWkpxkLD6vgRydXcdzkwWRn6BJkEZGBSIVFEsLbWxu467XNPLRsG80dYcZW5PP9T03itDlVVBRmBx1PREQCpsIigWnv7OKRt7bzx1c2sWxLPTmZaXxm+nDOPHIEc0eV6pSPiIjspcIicbdlTyt3vryRexdX09DWybiKfH508hROm1NFca6egCwiIu+lwiJx4Zzj5fW7uf3FjTy1aidpZpw4dSjnzBvJR8eW6WiKiIi8LxUWiamOcBcPLtvGbf/cwOodTQzKz+LyheM5Z95IhhXnBh1PRESShAqLxERDayd/fHUTf3hpIzVNHUwaWsh/nj6DU2YO18MGRUTkA1NhkX61rb6N372wnj+/voXWUBcfn1DOf39hFkeN12kfERE5dCos0i821rbw2+fXcf/SapyDU2YO5ysLxjJ5WFHQ0UREJAWosMiHsmZnE796di0Pv7mNjPQ0zjpyJJcsGKsHD4qISL9SYZFDsnZXM794eg2PvLWNvMx0vvLxsVz88TEMLswJOpqIiKQgFRb5QDbUtnDz02t4cNlWcjLTuezocXzl42Mpzc8KOpqIiKQwFRaJyo6Gdn7+1Lv8ZUk1menGVz4+lksWjKWsQLfNFxGR2FNhkffV0NrJb55fx+0vbqDbOc6dN4rLjxmv5/uIiEhcqbBInzrCXdz50iZ+9exaGts7+eysSr71icMYMUiDaUVEJP5UWGQ/zjn+tnInP3lsFZt2t7LgsAq+e+JEpg4vDjqaiIgMYCossteKbQ38+JGVvLJ+DxMGF3DHRUdy9GEVQccSERFRYRGobw3xn0++w92vbaYkN5Mff3YaZx0xgoz0tKCjiYiIACosA1p3t+O+JdXc+MRqGto6uXD+GK44fgLFuZlBRxMREdmPCssAtWJbA//v/95m6eZ6jhhdyvWnTtNt9EVEJGGpsAwwbaEufv7Uu/zuhfWU5mXx0zNm8vk5lXowoYiIJDQVlgHkpbW1fP+vy9m0u5WzjhzB906cTHGeTv+IiEjiU2EZABraOvnJo6v48+ItjC7L466vfIT548qDjiUiIhI1FZYU9/y7NVx935vUNoe49OixfPP4w8jJTA86loiIyAeiwpKiWkNhfvLYKv74ymYmDC7gd+fNZUZVSdCxREREDokKSwpasqmOb9+7jE17Wvnyx8bwnU9O1FEVERFJaiosKaSr23Hz02v45TNrGFacy91fmce8sWVBxxIREfnQVFhSxPaGNq64ZxmvbdjDaXMque6UqRTm6AogERFJDSosKeCplTv5zn1vEgp387MvzOS0OVVBRxIREelXKixJrLOrmxsfX82t/9zAlGFF/Ors2YytKAg6loiISL9TYUlSuxrbufyupby+sY4L5o/m+5+eRHaGBtaKiEhqUmFJQos37uGyPy2luT3MzWfN5pSZw4OOJCIiElMqLEnEOcedL2/ix4+spKo0l0UXH8mkoXpgoYiIpD4VliQRCndzzV+X85cl1Rw3aTA/++IsinN1FZCIiAwMKixJoK4lxKV/XMJrG/bwjeMmcOVxE0hL09OVRURk4FBhSXDrapq56A+vs72hnV+cOYtTZ1UGHUlERCTuVFgS2Itra7nsj0vITE/j7q/M4/BRpUFHEhERCYQKS4J6YGk1V9/3FmMr8rn1/CMYMSgv6EgiIiKBUWFJQL/7x3r+7bFVzB9Xxm/PPZwi3WJfREQGOBWWBOKc48bHV/O//1jPZ6YP42dfnKmbwYmIiKDCkjDCXd1874Hl3LekmnPnjeLaU6aSriuBREREABWWhNAR7uLyP73BU6t2cuXxE7jiuAmYqayIiIj0SItmJzM7z8xm9No208zOjU2sgaO9s4tLFy3hqVU7uf7UqVx5/GEqKyIiIr1EVViAHwNbem3bAtzQv3EGlvbOLr5y52Kef7eGG0+bznkfHR10JBERkYQU7SmhIqCx17YGoKR/4wwcbaEuvnzn67y0bjf/8fkZfGHuiKAjiYiIJKxoj7CsBD7fa9vngFX9G2dgaA2FufAPr/Hyut3cdMZMlRUREZGDiPYIy3eBx8zsi8A6YDxwHPDpWAVLVT2ngV7bsIf//qJutS8iIhKNqI6wOOf+CUwFXgfygdeAac65F2OYLeWEu7r5+t1v8OLa3fzX6TNVVkRERKIU9WXNzrktwI0xzJLSursdV9/3Fn9fuZPrTpnK5w+vCjqSiIhI0oh2DIt8CM45rn14BQ+8sZXvnHAY588fHXQkERGRpKLCEgc3/e1d7nx5E5csGMvlx4wPOo6IiEjSUWGJsUWvbOJXz67lzCNG8P1PTdJN4URERA6BCksMPbt6Fz968G2OnTSYGz47TWVFRETkEB1yYTGzZ8zsx2ZW2p+BUsWKbQ187a6lTB5WxC/Pmk1GurqhiIjIofowf4s+DwwDno5mZzMrMbP7zGy1ma0ys4+a2SAz+7uZrfHnKVF+tje0cdEfXqcoN5PbLjiC/Gw9Y1JEROTDOOTC4py7zjn3ZefcnCjf8gvgCefcJGAm3l1yvwc87ZybgFd8vneoeRJFc0eYi/6wmJaOLm674AiGFOUEHUlERCTpfaD/9TezwUBB5Dbn3Poo3lcELAAu8N8TAkJmdiqw0N/tDuA5vLvqJqXubscVd7/BuzubuO2CI5g8rCjoSCIiIikhqsJiZicCtwJDgciRow5Ij+IjxgI1wO1mNhNYAlwBDHHObQdwzm33C1HSuvmZNTy9ehfXnTKVow+rCDqOiIhIyoj2lNCvgR8DBc65tIgpmrICXjGaA/zGOTcbaOEDnP4xs0vMbLGZLa6pqYn2bXH19Kqd/PypNZw2p5LzPjoq6DgiIiIpJdrCUgr8r3Ou7RB/TjVQ7Zx71V+/D6/A7DSzYQD+fFdfb3bO3eKcm+ucm1tRkXhHLjbUtnDln5cxrbKIn3xuui5fFhER6WfRFpZbgQsP9Yc453YAW8xsor/pOGAl8BBwvr/tfODBQ/0ZQWnpCHPposVkpBm//dLh5GRGe9BJREREohXtoNt5wDfM7HvAjsgXnHMLovyMrwN/MrMsYD1eAUoD7jWzi4HNwBlRflZCcM5x9f1vsXZXM3de9BGqSvOCjiQiIpKSoi0sv/enQ+acWwbM7eOl4z7M5wbpzpc38ehb2/nuiZP42ITyoOOIiIikrKgKi3PujlgHSTartjfyb4+t4thJg/nq0WODjiMiIpLSor5xnJld6N+O/x1/fshjWpJdW6iLr9/9BsW5mfzX6TM0yFZERCTGor0PyzXAecBNwCZgFHC1mQ13zv1bDPMlpB8/upK1u5pZdPGRlBVkBx1HREQk5UU7huXLwELn3KaeDWb2JPAPYEAVlife3s5dr27m0gVj+fiExLvEWkREJBVFe0ooH+9OtZF2A7n9Gyexbatv47v3L2dGVTHfPmHiwd8gIiIi/SLawvIE3iXJE80s18wm4T3758nYRUss3d2Ob927jHBXNzefOZusjA/zoGsRERH5IKL9W/drQBPwJtAMLMO7vf7XY5Qr4fzx1U28sn4PPzp5KqPL84OOIyIiMqBEe1lzI3CemV0AlAO1zrnuWAZLJFv2tHLj46tZcFgFZ8ytCjqOiIjIgHPAwmJmo51zG/3l3jcaKei5lNc5tz5m6RKAc47vP7AcA/79ND0nSEREJAjvd4RlOVDoL68FHND7b2sHpPTDc+5dvIV/rq3lhs9Oo7JkQI0xFhERSRgHLCzOucKI5QE5wnRHQzs3PLKKeWMHcfaRI4OOIyIiMmBFVUTM7OYDbP95/8ZJHM45rvnrcjq7u/mPz88gLU2ngkRERIIS7ZGTCw6w/dx+ypFwHnpzG0+v3sVVn5zEqDJdFSQiIhKk971KyMwu6tkvYrnHWKA2JqkC1tTeyQ2PrmLmiBIumD866DgiIiID3sEua+45gpLF/kdTHLATOD8WoYL2i6fWUNvcwe/Pm0u6TgWJiIgE7n0Li3PuGAAzu8E598P4RArWuzubuP2ljZx5xAhmjigJOo6IiIgQ/Y3jfmhmJcBngOHANuAx51xdLMPFm3OOax9aQUF2Bld9clLQcURERMQX7VVCxwIbgW8AR+Ddkn+DmR0Xu2jx99jyHby0bjffOeEwBuVnBR1HREREfFEdYQF+BVzinLu3Z4OZnQH8GkiJQxEtHWFueHQlU4YVcfZHRgUdR0RERCJEe1nzcOD+Xtv+Cgzt3zjB+fWza9ne0M71p07VQFsREZEEE21huRO4vNe2y/ztSW9jbQu/e2E9p82pZO7oQUHHERERkV6iPSU0B7jMzK4GtgKVwGDgVTP7R89OzrkF/R8x9oaX5HLVJyfy2dmVQUcRERGRPkRbWH7nTykpKyONSxaMCzqGiIiIHEC0lzXfEesgIiIiIgcS7REWzOzjwGygIHK7c+4n/R1KREREJFJUhcXMfgl8AXgBaIt4ycUilIiIiEikaI+wnANMc85ti2UYERERkb5Ee1nzFqAjlkFEREREDiTaIywXA78zs7vxntK8l3PuH32/RURERKR/RFtYDgc+BSzgvWNYRvZ3KBEREZFI0Z4S+glwsnOu3Dk3ImJKjbLSUA23ngDvPB50EhEREelDtIWlBUjdUz955bB1KWx+JegkIiIi0odoC8u/Aj83s6FmlhY5xTJc3GTmwNBpsHVJ0ElERESkD9EWjtuAr+I9R6jTn8L+PDVUHg7b3oDurqCTiIiISC/RDrodE9MUiaByLrz+e6h9FwZPDjqNiIiIRIj2WUKbYh0kcJWHe/OtS1RYREREEky0t+ZfxAFuw++cO69fEwWlbDxkF0P1Ypj9paDTiIiISIRoTwmt7bU+FDgd+FP/xglQWhpUztbAWxERkQQU7Smh63pvM7NbgR/1e6IgVR4O//w5dLZBZm7QaURERMT3YS5LXgYc3V9BEkLlXHBdsP3NoJOIiIhIhGjHsBzba1MecCawst8TBSly4O3IecFmERERkb2iHcNya6/1FrwjLGf1b5yAFQ6B4hHewFsRERFJGNGOYUn9+7D0qJyjgbciIiIJJqoxLGZWYWYF/nK6mV1oZuelzK35I1UeDvWboKU26CQiIiLii7ZwPAJM8Jd/AnwH+BZwUyxCBapyrjfXURYREZGEEW1hOQxvzArAOcCngGPxBt6mlmEzwdJUWERERBJItINuu4AsMzsMaHDObfZPBxXELlpAsgtg8BQVFhERkQQSbWF5HLgXKAPu8bdNwXt6c+qpnAOrHgbnwCzoNCIiIgNetKeEvgw8ind587/728qBa2OQKXiVh0NbHexZH3QSERERIfrLmjuAW3ptey4WgRLC3oG3S6FsXLBZREREJOo73Q7CuzJoFr3GrTjnFsQgV7AqJkFmHmxdDDPOCDqNiIjIgBftGJa7gGy8cSytsYuTINIzYLjAxq3rAAAeEklEQVSe3CwiIpIooi0s84EK/9TQwFA5B169BTrbITMn6DQiIiIDWrSDbt8CqmIZJOGM+hh0dUD1a0EnERERGfCiPcLyDPCEmd0O7Ih8wTl3W7+nSgSjjwJLh/XPwZjUG6YjIiKSTKItLB8HqoFP9NrugNQsLNmFUDXXKyzH/WvQaURERAa0aC9rPqY/fpiZpQOLga3OuZPMbAzejegGAUuBc51zof74Wf1i7EL4x39BWz3klgSdRkREZMCK+mnLZlbqP6H5+/689BB+3hXAqoj1/wD+2zk3AagDLj6Ez4ydsQvBdcPGfwadREREZECLqrCY2UeBdcBXgRnApcA6f3tUzKwK+Azwe3/d8B6geJ+/yx3AZ6NOHg+VcyEz3zstJCIiIoGJdgzLz4F/cc71PEcIM/sicDNwxAf4jKuBQn+9DKh3zoX99WqgMsrPio+MLBg1HzY8H3QSERGRAS3aU0KH4d00LtJ9wPho3mxmJwG7nHORd2Lr66mC7gDvv8TMFpvZ4pqammh+ZP8ZuxBq34WG1HzOo4iISDKItrCsAc7ste0MvNNE0TgKOMXMNuINsj0W74hLiZn1HOWpArb19Wbn3C3OubnOubkVFRVR/sh+MnahN9dRFhERkcBEW1iuBH5lZq+Y2Z/N7FXgf4BvRPNm59z3nXNVzrnReMXnGefcOcCzwOn+bucDD36g9PEweArklcN6FRYREZGgRFVYnHMvAeOAXwFLgF8C4/3tH8Z3gW+Z2Vq8MS23fsjP639paTD2aG/grevzjJWIiIjEWLRPa64EWp1zf4zYVmpmw51zfZ7GORDn3HPAc/7yeuDID/L+QIxdCG/fDzXvwOBJQacREREZcKI9JfR/vPdZQlXAX/s3ToIac7Q31+XNIiIigYj6KiHn3PLIDf76wDjcUDoKSsdo4K2IiEhAoi0sNWa23yXM/vru/o+UoMYuhA0vQFf4YHuKiIhIP4u2sNwG3G9mJ5nZFDM7Ge8+LL+PXbQEM3YhhJpg29Kgk4iIiAw40d7p9kagE/gpMALYjHdFz89ilCvxjFkAmDeOZUTijxMWERFJJdFe1tztnPsv59wk51y+c26yc+6nzrnuWAdMGHmDYPhseOfxoJOIiIgMOFE/rVmAySd7p4TqtwSdREREZEBRYfkgppzqzVc9HGwOERGRAUaF5YMoGweDp8Kqh4JOIiIiMqCosHxQU06Bza9A086gk4iIiAwYB7xKyMwuiuYDnHO39V+cJDD5FHju32H1w3DEl4NOIyIiMiC832XN50bxfod3j5aBY/BkKBsPKx9SYREREYmTAxYW59wx8QySNMy8oywv/gJa93iXO4uIiEhMfeAxLOZJ65liESrhTTkFXBesfjToJCIiIgNCVIXDzCrN7K9mthsI4931tmcaeIbNgpKRulpIREQkTqI9QvJbIAQcBzQDc4CHgK/GKFdi6zkttO5ZaG8IOo2IiEjKi7awzAcucs4tA5xz7k3gYuDbMUuW6CafAt2d8O6TQScRERFJedEWli68U0EA9WZWAbQAlTFJlQyqjoDCYbDywaCTiIiIpLxoC8urwKf95SeBPwMPAItjESoppKXBpJNg7dMQagk6jYiISEqLtrCcCzzvL18JPAO8DZwdi1BJY8qpEG7T1UIiIiIx9n43jtvLOVcfsdwG3BCzRMlk1FFQMgqW3gkzvhB0GhERkZQV7WXN2Wb2b2a23swa/G0nmNnXYhsvwaWlwZzzYOMLsHtd0GlERERSVrSnhP4bmAacg3c7foAVwGWxCJVUZp0DlgZvLAo6iYiISMqKtrB8DjjbOfcy0A3gnNvKQL5KqEfRMJjwSVh2F3QNzPvoiYiIxFq0hSVEr/Eu/qXNu/s9UTKacx4074Q1fws6iYiISEqKtrD8BbjDzMYAmNkw4FfAPbEKllQmnAAFQ73BtyIiItLvoi0sPwA2AsuBEmANsA24Pjaxkkx6Bsw+xzvC0rgt6DQiIiIpJ6rC4pwLOeeudM4VAEOAQufcN51zHbGNl0RmfwlcNyz7U9BJREREUk60R1j2cs7VOOecmc0ws7/EIlRSGjQWxiyApYuguzvoNCIiIinlfQuLmeWZ2Y/N7GEz+5mZFZnZWDP7K/ASsCs+MZPEnPOhfhNseP7g+4qIiEjUDnaE5dfAycBK4Hjgfrxb9K8ARjvnLo9tvCQz6STILYWldwSdREREJKUc7Nb8nwRmOed2mdkvgc3A0c65F2IfLQll5ng3knv1t1C/GUpGBp1IREQkJRzsCEuBc24XgHOuGmhWWTmIef7Nf1/+dbA5REREUsjBjrBkmNkxgPVs6L3unHsmRtmSU3EVTP+Cd0+WBVdDflnQiURERJLewQrLLuC2iPXdvdYdMLa/QyW9o66AN++C126BY74fdBoREZGk976FxTk3Ok45UsvgSTDx0/Da/8JR34Cs/KATiYiIJLUPfB8WidLHvgltdbpdv4iISD9QYYmVEUfCqKPgpV/pKc4iIiIfkgpLLB11JTRWw/L7gk4iIiKS1FRYYmnCJ2DwVHjx57pdv4iIyIegwhJLZvCxK6FmNbz7eNBpREREkpYKS6xNPc17MOLT10NXOOg0IiIiSUmFJdbSM+D4a72jLMv+GHQaERGRpKTCEg+TT4ERH4FnfwIdzUGnERERSToqLPFgBifcAM074eVfBZ1GREQk6aiwxMuII2HKqfDizdC0M+g0IiIiSUWFJZ6O+xF0heC5nwSdREREJKmosMRT2Tg44mLvdv27VgedRkREJGmosMTbgqshqwD+/q9BJxEREUkaKizxll8GH/82rHkSVj8WdBoREZGkoMIShHn/4t2y/9FvQXtD0GlEREQSngpLEDKy4NRfepc5//1HQacRERFJeCosQak83DvSsuR22PjPoNOIiIgkNBWWIB3zAygdDQ99HTrbgk4jIiKSsFRYgpSVDyf/Avash+duDDqNiIhIwlJhCdrYhTD7S/DSL2HbsqDTiIiIJKS4FBYzG2Fmz5rZKjNbYWZX+NsHmdnfzWyNPy+NR56Ec8INkF8Of70UQi1BpxEREUk48TrCEga+7ZybDMwDLjezKcD3gKedcxOAp/31gSe3FD77G6h5Bx67Oug0IiIiCScuhcU5t905t9RfbgJWAZXAqcAd/m53AJ+NR56ENP44WPAdWPZHWHZ30GlEREQSStzHsJjZaGA28CowxDm3HbxSAwyOd56EcvT3YNTHvBvK1bwTdBoREZGEEdfCYmYFwP3Alc65xg/wvkvMbLGZLa6pqYldwKClZ8Dnfw+ZeXDv+RBqDTqRiIhIQohbYTGzTLyy8ifn3AP+5p1mNsx/fRiwq6/3Ouducc7Ndc7NraioiE/goBQNg9NugZrV8LjGs4iIiED8rhIy4FZglXPuZxEvPQSc7y+fDzwYjzwJb/xx3gMS31gEi28POo2IiEjgMuL0c44CzgWWm1nPzUZ+ANwI3GtmFwObgTPilCfxLfw+bH8THv02lIyA8ccHnUhERCQw5pwLOsMHMnfuXLd48eKgY8RHRxPc9imo2wgXPQFDpwWdSEREpF+Z2RLn3NyD7ac73Say7EI4+8+QXQB3fQEatwedSEREJBAqLImuuBLOvhfaG7zS0tEcdCIREZG4U2FJBsNmwOm3w8634b4LIRwKOpGIiEhcqbAki8NOgM/8DNb8zSstXZ1BJxIREYkbFZZkMvdCOPE/YPUjcN9FKi0iIjJgqLAkm3lfhU/+BFY9BA98BbrCQScSERGJuXjdh0X600cvh+4u+Pv/A0uHz/2vd1t/ERGRFKW/5ZLVUd8A1wVPXQtdITjtd5CZE3QqERGRmNApoWT2sW/CCf/mnR5a9Dloqws6kYiISEyosCS7+V+Dz98K1a/DbSdC/ZagE4mIiPQ7FZZUMP10OPcBaNwGt34CdrwddCIREZF+pcKSKsYsgAsf95Zv/xS883iweURERPqRCksqGToNLv47DBoDd58Jz/4EuruDTiUiIvKhqbCkmpIRcNGTMPNseP4/4O4vajCuiIgkPRWWVJSZC5/9H/jMTbDuWbhlIexYHnQqERGRQ6bCkqrM4IgvwwWPQmc7/O5YeOlXOkUkIiJJSYUl1Y38CHz1nzD+ePjbNbDoVGioDjqViIjIB6LCMhAUVMCZd8HJN0P1EvjNfFh+X9CpREREoqbCMlCYweHnw1dfgPLD4P6L4Z5zdLRFRESSggrLQFM2Di58Ao6/FtY+Db/+CLzyG+9hiiIiIglKhWUgSs/wnkP0Ly/DyHnwxPe8Qbnb3gg6mYiISJ9UWAayQWPgnPvg9NuhaTvccgz83794t/gXERFJICosA50ZTDsNLn/Ne5Di8r/ALw+HZ/8dQi1BpxMREQFUWKRHbgmccINXXCacAM/fCDfPgcW3QzgUdDoRERngVFhkf4PGwBfu8G7vXzICHrnSO+Ky5A7o6gw6nYiIDFAqLNK3kfO8Byme/RfIL4OHv+EVl6WLdMRFRETiToVFDswMDjsBvvIsnH0v5JbCQ1+DX8yEF38B7Q1BJxQRkQFChUUOzgwO+yRc8hyccz+Uj4e//yv8bCo8eY1uPiciIjGXEXQASSJmMOF4b9q2DF76pXfTuVd+AxM/BUdcDGMWQpp6sIiI9C9zzgWd4QOZO3euW7x4cdAxpEf9Zlh8Gyy9E1p3w6BxMPcimHmWN/ZFRETkfZjZEufc3IPup8Ii/SLcASsfgtd/D1tegbRMmHgizDrHe1J0embQCUVEJAFFW1h0Skj6R0Y2zDjDm3augGV3wVt/hlUPQ34FTP8CTP88DJ/jnVoSERH5AHSERWKnqxPWPgXL/gTvPAHdnVA6Gqae5t1dd8g0lRcRkQFOp4QksbTVwepH4e0HYP1z4Lq88S6TPgOTT4bKuRqsKyIyAKmwSOJqqYWVD8LqR2DDP6A7DAVDvCuNJnwSxiyA7IKgU4qISByosEhyaKuHNX/3ysvapyDUDOlZMOoomPAJb8Bu+WE6dSQikqJUWCT5hEOw+WVY8zevvNSs9rYXDoOxC71pzNFQNCy4jCIi0q9UWCT51W2C9c/C+udhw/PefV4AysbDqPneUZhR86FkZLA5RUTkkKmwSGrp7oadb3vFZeOLsPmlfc8yKh4BI46EER+BqiNg6HTd90VEJEnoPiySWtLSYNgMb5r/da/A7FoJm16ETS/B5lfg7fu9fTNyYfgsqDwchs+GyjlQOkbjYEREkpgKiySntDQYOs2bPnKpt62hGra85k1bl3h33Q23e6/llsKwmTB0hjcfNtO7rFqXUouIJAUVFkkdxVXeNO00b72r0zsKs3UpbFsK29+CV38LXSHv9cw8GDwZhkz1bmI3ZCoMngJ5g4L7HUREpE8qLJK60jP3HU3hQm9bOAS178D2N2HHcu8xAqse9h7e2CN/MFRM9MpMxSTvsuryw6BgsE4riYgERIVFBpaMLG9Q7tDp+7Y5B007vPJSswp2rfbmy+7y7gvTI7sIyidA2QQoGweDxvrzcZBTFP/fRURkAFFhETHz7u1SNAwmHL9vu3PQuBVq34Xatf78Hdj4Arx1z/6fkVfuPSdp0BhvgG/paCgd5V1yXVQJaenx/I1ERFKOCovIgZjtGxcz7tj9Xwu1Qt0G2L0Odq+Fuo3e+uZXvauVXPe+fdMyvNJSMtK7BLtkhDfv+eyiSsjKi+uvJiKSbFRYRA5FVp4/WHfqe18Lh6BhC9Rv8m5+V7/ZW67f4j34sWk70Ov+RzklfnkZ7t3Zd7/5UG85d5CuahKRAUuFRaS/ZWR5Y1vKxvX9ejjknWpqqIbGbdBYDQ1bvW2N22DbG9BS8973pWVAwVAoHOI9LLJgsDfPr/CW8wf783JvvI0GCItIClFhEYm3jCxvrMugMQfeJxyC5h3QuN07ItO805s37fS212+G6te9J1/3PloDkJ7tFZf8cm98TX6FvzwI8sr8yV/PHeTdpyZdfxyISOLSn1AiiSgjyxvzcrDnJHWFvaMxLTXQsssrMM27/OXd0Frrbatd4y13th74s7KLIa90X4HZbyrxTlvtNy/2lrPydTRHRGJOhUUkmaVn7LvCKRqhVmjb4z1IsqUW2uqgdY+/zZ+31XlT3QZvW3sDfR7F6ZGW4ZWX7CLv8u69yxHbsgu95exCf91fzirwXyvUlVQi8r5UWEQGkqw8byquiv493d3Q0eiVmPZ6aKv3Skx7g7fe3uBt62j0tzVC8zp/vRFCTdH9nMw8v8AU7CsyWfneclZ+xLq/LTMv4vW8feuZ/u+YVaCHYIqkEBUWEXl/aWneKaDckkN7f3eXdwO+9kboaIqYGqCj2Xuto9krOD3LoRZvuXkXhNb76/62yEvGD5o9AzLzITN3X6nJzPPW3zPP8ZYz/HlmjvcgzUx/ysj213P2n2dke6/rCJFITKmwiEhspaX7412KP/xnOeeNwwm1QmdPiWn1ikzP9sjlTn8KtfjL7fu2te3x9gm3Q2ebN4XbPsTvmbGvwGTkHGDuT+nZ+29Pz/KXs/zX/PWe5fRs72jR3vdmee/pmTL819P9z0pL17giSTkqLCKSPMz2nRaiov8/v7vbKzC9S0xnex/ziGnveof3erjDe29XaN/2ULM3dijcAV0d/r7t3hVhXR3QHe7HX8R6FZmsiLm/nBa5vWc9c99+aRkR+2b0vW9apjeOau96Rq/XM/bflpa+//a9r/Vez1TpkvcIvLCY2YnAL4B04PfOuRsDjiQiA1Va2r5xPvHW3RVRZkK95h1++ek175nCHd7TybtC/tx/T3c4Yr9Of1unv0/nvtdCzf5y2HtvV/i9+3V39nOpioKl9yozEctpvV57z3oGWFqvbRHrez873S9HH2S957N7tkfO0/btt99raX3se6DtaX1/vqXt23/v65HvT+2CF2hhMbN04NfAJ4Bq4HUze8g5tzLIXCIicZeW7helBH5Mg3MRJcgvMF2d+8pNdzhiW8Rr3eF9JWjv9q73vm+/18IHnroill3Xvm0u8n1+AXRd/ud17b9/d9g7otbt/7wD7Zds9iszkSUn7b2FyPyS855tab3el+Yd1Tz/4UB/taCPsBwJrHXOrQcws3uAUwEVFhGRRGO277TQQNHdHVFgespM975S1LPddXn7ut6lp7vXPn3s29d2193rte6Ibb336eO1yO29Pwvn/5yIz+n9Wb2njJyg/0kEXlgqgS0R69XARwLKIiIisr+0NEjLCjqFAEE/Sa2vE27vuUOVmV1iZovNbHFNTR/PWBEREZGUFnRhqQZGRKxXAdt67+Scu8U5N9c5N7eiIgZXBoiIiEhCC7qwvA5MMLMxZpYFnAk8FHAmERERSTCBjmFxzoXN7GvAk3iXNd/mnFsRZCYRERFJPEEPusU59xjwWNA5REREJHEFfUpIRERE5KBUWERERCThqbCIiIhIwlNhERERkYSnwiIiIiIJT4VFREREEp4Ki4iIiCQ8FRYRERFJeObce541mNDMrAbYFHSOBFIO1AYdYgDR9x0/+q7jR991fOn73t8o59xBHxSYdIVF9mdmi51zc4POMVDo+44ffdfxo+86vvR9HxqdEhIREZGEp8IiIiIiCU+FJfndEnSAAUbfd/zou44ffdfxpe/7EGgMi4iIiCQ8HWERERGRhKfCkqTMbISZPWtmq8xshZldEXSmVGdm6Wb2hpk9EnSWVGZmJWZ2n5mt9v/9/mjQmVKZmX3T/zPkbTO728xygs6UKszsNjPbZWZvR2wbZGZ/N7M1/rw0yIzJRIUleYWBbzvnJgPzgMvNbErAmVLdFcCqoEMMAL8AnnDOTQJmou88ZsysEvgGMNc5Nw1IB84MNlVK+QNwYq9t3wOeds5NAJ721yUKKixJyjm33Tm31F9uwvtDvTLYVKnLzKqAzwC/DzpLKjOzImABcCuAcy7knKsPNlXKywByzSwDyAO2BZwnZTjn/gHs6bX5VOAOf/kO4LNxDZXEVFhSgJmNBmYDrwabJKX9HLga6A46SIobC9QAt/un335vZvlBh0pVzrmtwE+BzcB2oME597dgU6W8Ic657eD9jycwOOA8SUOFJcmZWQFwP3Clc64x6DypyMxOAnY555YEnWUAyADmAL9xzs0GWtAh85jxx0+cCowBhgP5ZvalYFOJ9E2FJYmZWSZeWfmTc+6BoPOksKOAU8xsI3APcKyZ/THYSCmrGqh2zvUcLbwPr8BIbBwPbHDO1TjnOoEHgPkBZ0p1O81sGIA/3xVwnqShwpKkzMzwzvOvcs79LOg8qcw5933nXJVzbjTegMRnnHP6v9AYcM7tALaY2UR/03HAygAjpbrNwDwzy/P/TDkODXKOtYeA8/3l84EHA8ySVDKCDiCH7CjgXGC5mS3zt/3AOfdYgJlE+sPXgT+ZWRawHrgw4Dwpyzn3qpndByzFu/LwDXQX1n5jZncDC4FyM6sGfgTcCNxrZhfjFcYzgkuYXHSnWxEREUl4OiUkIiIiCU+FRURERBKeCouIiIgkPBUWERERSXgqLCIiIpLwVFhEREQk4amwiIiISMJTYRGRlGNmG83s+KBziEj/UWERSWD+X7whMyvvtX2ZmTn/Sd0DWrzLicqQSDBUWEQS3wbgrJ4VM5sO5AYX58Mzs4R8LEii5hIRFRaRZLAIOC9i/XzgzsgdzGyymT1nZvVmtsLMTol4baOZfcfM3jKzBjP7s5nlRLw+3MzuN7MaM9tgZt/wt19lZvf3+jm/NLOf9xXSzOaY2Rtm1mRmf/F/zg29cnzXzN4CWsws40C5zexCM3s44r1rzezeiPUtZjbLzBYBI4GHzazZzK6OiDTrQL9zr9x95fqema3zf5eVZvY5f98+f96BvsNomNm9/mf1TM7Mvhbt+0UGDOecJk2aEnQCNgLHA+8Ak4F0YAswCnDAaCATWAv8AMgCjgWagIkRn/EaMBwYhPc03q/6r6UBS4B/9d87Fu+Bg58EhgEtQIm/bwawCzi8j5xZwCbgCj/PaUAIuKHX77IMGIF3hOiAuf0c9X6+Yf5nb/U/ZyxQB6RFfkd9fG99/s4H+I735vK3neG/Nw34ov89DOvr573fd3gI/7y/hfcAwkFB/7unSVOiTTrCIpIceo6yfAJYDWyNeG0eUADc6JwLOeeeAR4h4jQScLNzbptzbg/wMDDL334EUOGcu95/73rgd8CZzrntwD/Y9zTZE4Fa59ySPvLNwys0NzvnOp1zD+AVht5uds5tcc61vV9uP0eTn/No4Elgq5lN8tdfcM51H+Q7O9DvfKB9e3LhnPuL/95u59yfgTXAkQd47wG/w4Pk24+ZXYH3z/h4P7OIRND5WpHksAivPIyh1+kgvCMBW3r9Bb4JqIxY3xGx3Oq/B7wjNcPNrD7i9XTgBX/5DuAyvL+Av+Tn6MtwvCMgkY9/39LHfpHbDpb7eWAhMN5frscrKx/11w/mQL9zX/bLambn4R3tGO1vKgDK6dvBvsOD8k8BXQwc65zbHe37RAYSHWERSQLOuU14g28/DTzQ6+VtwAgzi/zveST7H4U5kC3ABudcScRU6Jz7tP/6/wEzzGwacBLwpwN8znag0swsYtuIvn6VD5C7p7B83F9+Hq+wHM3+hSXyMw/V3s8ws1F4Be1rQJlzrgR4G7De+/oO9h2+LzO7DLgUOM45V/thfxGRVKXCIpI8ev4PvKXX9lfxxlhcbWaZZrYQOBm4J4rPfA1o9Aed5ppZuplNM7MjAJxz7cB9wF3Aa865zQf4nJeBLuBr/qDVUznwKZRocz8PHIM3rqQa74jFiUAZ3jiPHjvxxo30l3y8UlID3gBgYNr7/Lz3/Q7N7A9m9oe+fpCZXYJXjI53ztX04+8gknJUWESShHNunXNucR/bQ8ApwKeAWuB/gPOcc6uj+MwuvJIwC+8ITi3we6A4Yrc7gOkc+HRQT4bT8EpVPd7po0eAjoO854C5nXPvAs34p1acc414g1lf9HP3+Hfgh/6VRt852O98MM65lcBNeCVsJ97v/uKBfl4U3+GIXu+P9J/AOGBdxFVC537Y30EkFdn+p5xFRPZnZiPxBvoO9UtDtO97Ffitc+72mIVLcGaWBbwJzHDOdQadRySZ6QiLiByQP77kW8A9BysrZna0mQ31TwmdD8wAnohHzkTlXzU0WWVF5MPTVUIi0iczy8c7JbIJb+zIwUwE7sW7omYdcLp/abSIyIemU0IiIiKS8HRKSERERBKeCouIiIgkPBUWERERSXgqLCIiIpLwVFhEREQk4amwiIiISMJTYREREZGEp8IiIiIiCe//A7ikigaxzUvUAAAAAElFTkSuQmCC\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(9,6))\n", "plt.plot(z_grid,c_1,label=r'$c_1$')\n", "plt.plot(z_grid,c_2,label=r'$c_2$')\n", "plt.ylabel(r'Real consumption, c',fontsize='12')\n", "plt.xlabel(r'Money growth rate, $z$',fontsize='12')\n", "plt.legend(loc='best',fontsize='12')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can also plot the lifetime consumption and utility as a function of $z$:" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(9,6))\n", "plt.subplot(2, 1, 1)\n", "plt.plot(z_grid,c,label=r'$c$')\n", "plt.ylabel(r'Lifetime consumption',fontsize='12')\n", "\n", "plt.subplot(2, 1, 2)\n", "plt.plot(z_grid,u,label=r'$U$')\n", "plt.xlabel(r'Money growth rate, $z$',fontsize='12')\n", "plt.ylabel(r'Lifetime utility',fontsize='12')\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Assume now that the newly printed money is used as seignorage revenue by the government:\n", "$$\n", "S_t = \\left(1- \\frac{1}{z}\\right)v_t M_t\n", "$$\n", "\n", "Using the money market clearing condition: $v_t M_t = N_t (y - c_{1,t})$ we can write the seignorage income as:\n", "$$\n", "S_t = \\left(1- \\frac{1}{z}\\right)N_t (y - c_{1,t})\n", "$$\n", "\n", "The seignorage income per capita $s_t$ will be:\n", "$$\n", "s_t = \\left(1- \\frac{1}{z}\\right)q^*\n", "$$\n", "which we can plot below:" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "s = ( 1 - (1/z_grid)) * q_star\n", "\n", "plt.figure(figsize=(9,6))\n", "plt.plot(z_grid,s)\n", "plt.ylabel(r'Seignorage income per capita, $s$',fontsize='12')\n", "plt.xlabel(r'Money growth rate, $z$',fontsize='12')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can clearly see that the seignorage income is increasing and then decreasing in the growth rate of money. This means there is a money growth rate maximizing the seignorage income for the government. We can easily compute it by writing a new function that takes the model's parameters as given and returns the seignorage income per capita given the money demand of individuals using the function $V$:" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [], "source": [ "def opt_s(params):\n", " \n", " params_new = np.copy(params) # Make a copy in order to preserve the initial parameters\n", " \n", " def s(z,params): # This is the objective function which takes z as an argument and returns the seignorage income\n", " \n", " params[1] = z\n", " \n", " return - ((1 - (1/z)) * V(params_new).x)\n", " \n", " sol = minimize(s, x0 = 1, args=params_new, method='Nelder-Mead',options={'ftol': 1e-10})\n", " \n", " return sol.x[0]" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "The money growth rate maximizing seignorage income is: 2.3863282034755713\n" ] } ], "source": [ "print('The money growth rate maximizing seignorage income is:', opt_s(params))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now assume that the government uses the seignorage income $S_t$ and lump-sum tax income $N_t \\tau$ to finance a stream of government expenditures $G_t$ such that:\n", "$$\n", "G_t = \\left(1- \\frac{1}{z}\\right)v_t M_t + N_t \\tau\n", "$$\n", "\n", "Replacing with the money demand and rewriting this in per capita terms we get:\n", "$$\n", "g_t = \\left(1- \\frac{1}{z}\\right)q^* + \\tau\n", "$$\n", "\n", "Assume $g_t = 20$. We can easily compute the share of $G_t$ financed through lump-sum taxes as a function of money growth rate:" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(9,6))\n", "\n", "g = 20\n", "\n", "tau = (g - s)/g\n", "\n", "plt.plot(z_grid,tau)\n", "plt.ylabel(r'% of taxes in government budget',fontsize='12')\n", "plt.xlabel(r'Money growth rate, $z$',fontsize='12')\n", "plt.show()" ] } ], "metadata": { "anaconda-cloud": {}, "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.7.4" } }, "nbformat": 4, "nbformat_minor": 4 }