{"cells":[{"cell_type":"markdown","metadata":{},"source":["#### [**NICOLAS CACHANOSKY**](http://www.ncachanosky.com) | Department of Economics | Metropolitan State University of Denver | ncachano@msudenver.edu"]},{"cell_type":"markdown","metadata":{},"source":["# LABOR MARKET\n","---"]},{"cell_type":"markdown","metadata":{},"source":["This note illustrates how to code a labor market in Python. The purpose of the note is to walk through Python applications, not to offer a detailed discussion of the labor market or to show best coding practices. The note also assumes familiarity with the neoclassical labor market model and a beginner experience with Python.\n","\n","For a more complete and detailed discussion of Python applications see the material in [Quant Econ](https://quantecon.org/).\n","\n","---"]},{"cell_type":"markdown","metadata":{},"source":["## TABLE OF CONTENTS\n","1. [Labor demand](#1.-LABOR-DEMAND)\n","2. [Labor supply](#2.-LABOR-SUPPLY)\n","3. [Equilibrium](#3.-EQUILIBRIUM)"]},{"cell_type":"markdown","metadata":{},"source":["## 1. LABOR DEMAND"]},{"cell_type":"markdown","metadata":{},"source":["Labor demand $\\left(N^D\\right)$ comes from a representative firm maximazing its profits $(\\pi)$. Assume output $(Q)$ follows a Cobb-Douglas production function with Hicks-Neutral technology $(A)$, and that $P$ is the market price of the firm's output. Further, assume that $w$ and $r$ are the prices of labor $(N)$ and capital $(K)$ respectively. Then, firm's profit is (where $\\alpha \\in (0, 1)$):\n","\n","\\begin{align}\n"," \\pi &= P \\cdot Q(K, N) - wN - rK \\\\\n"," \\pi &= P \\cdot \\left(A \\cdot K^{\\alpha} N^{1-\\alpha} \\right) - wN - rK\n","\\end{align}\n","\n","With capital and technology as given in the short-run, the firm maximizes its profits by changin the amount of labor. The firm demands labor (that has decreasing marginal returns) up the points of its marginal productivity. It can be seen that labor demand has an hyperbolic shape with respect to real wages $(w/P)$.\n","\n","\\begin{align}\n"," \\frac{\\partial \\pi}{\\partial N} &= P \\cdot (1-\\alpha) \\, A \\left(\\frac{K}{N}\\right)^{\\alpha} - w= 0 \\\\\n"," N^D &= K \\cdot \\left[\\frac{(1-\\alpha)A}{(w/P)}\\right]^{1/\\alpha}\n","\\end{align}\n","\n","The following code plots labor demand and shifts produced by changes in $k$ (in blue), $A$ (in red), and in $\\alpha$ (in green). The first part of the code imports the required packages. The second part defines the parameters and vectors to be used. The third part of the code builds the labor demand function. The fourth section calculates labor demand and the effects of shocks (1) capital $(\\Delta K = 20)$, (2) productivity $(\\Delta A = 20)$, and (3) output elasticity of capital $(\\Delta \\alpha = 20)$. The fifth part of the code plots labor demand and the shock effects."]},{"cell_type":"code","execution_count":11,"metadata":{},"outputs":[{"data":{"image/png":"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\n","text/plain":["
"]},"metadata":{},"output_type":"display_data"}],"source":"\"1|IMPORT PACKAGES\"\nimport numpy as np # Package for scientific computing with Python\nimport matplotlib.pyplot as plt # Matplotlib is a 2D plotting library\n\n\"2|DEFINE PARAMETERS AND ARRAYS\"\n# Parameters\nsize = 50 # Real wage domain\nK = 20 # Capital stock\nA = 20 # Technology\nalpha = 0.6 # Output elasticity of capital\n# Arrays\nrW = np.arange(1, size) # Real wage\n\n\"3|LABOR DEMAND FUNCTION\"\ndef Ndemand(A, K, rW, alpha):\n Nd = K * ((1-alpha)*A/rW)**(1/alpha)\n return Nd\n\n\"4|CALCULATE LABOR DEMAND AND SHOCK EFFECTS\"\nD_K = 20 # Shock to K\nD_A = 20 # Shock to A\nD_a = 0.2 # Shock to alpha\n\nNd = Ndemand(A , K , rW, alpha) \nNd_K = Ndemand(A , K+D_K, rW, alpha) \nNd_A = Ndemand(A+D_A, K , rW, alpha) \nNd_a = Ndemand(A , K , rW, alpha+D_a) \n \n\"5|PLOT LABOR DEMAND AND SHOCK EFFECTS\"\nxmax_v = np.zeros(4)\nxmax_v[0] = np.max(Nd)\nxmax_v[1] = np.max(Nd_K)\nxmax_v[2] = np.max(Nd_A)\nxmax_v[3] = np.max(Nd_a)\nxmax = np.max(xmax_v)\n\nv = [0, 30, 0, size] # Set the axes range\nfig, ax = plt.subplots(figsize=(10, 8))\nax.set(title=\"LABOR DEMAND\", xlabel=r'Nd', ylabel=r'w/P')\nax.grid()\nax.plot(Nd , rW, \"k-\", label=\"Labor demand\", linewidth=3)\nax.plot(Nd_K, rW, \"b-\", label=\"Capital shock\")\nax.plot(Nd_A, rW, \"r-\", label=\"Productivity shock\")\nax.plot(Nd_a, rW, \"g-\", label=\"Output elasticity of K shock\")\nax.yaxis.set_major_locator(plt.NullLocator()) # Hide ticks\nax.xaxis.set_major_locator(plt.NullLocator()) # Hide ticks\nax.legend() \nplt.axis(v) # Use 'v' as the axes range\nplt.show()"},{"cell_type":"markdown","metadata":{},"source":["## 2. LABOR SUPPLY"]},{"cell_type":"markdown","metadata":{},"source":["Labor supply is dervied from the consumer maximizing a constrained utility function. The consumer receives utility from consumption $(C)$ and leisure time $(L)$. While the profit function of the firm has an internal maximum, the utility function is strictly increasing on $C$ and $L$. Therefore, the utility maximization problem includes (1) a binding constrain and (2) the right mix of $C$ and $L$ that will depend on their relative prices.\n","\n","Assume a Cobb-Douglas utility function where $\\beta$ is the consumption elasticity of utilility.\n","\n","\\begin{equation}\n"," U(C, L) = C^{\\beta} L^{1-\\beta}\n","\\end{equation}\n","\n","The individual faces the folllowing budget constraint:\n","\n","\\begin{align}\n"," C &= \\left(\\frac{w}{P} \\right) (24 - L) + I \\\\\n"," C &= \\underbrace{\\left[I + 24 \\left(\\frac{w}{P} \\right) \\right]}_\\text{intercept} - \\underbrace{\\left( \\frac{w}{P} \\right)}_\\text{slope}L\n","\\end{align}\n","\n","where $24$ is the amount of hours the individual can work in given day and $I$ is other (non-labor) income. \n","\n","Before deriving labor supply $N^S$ we can plot the indifference curve between consumption and leisure with the budget constraint. \"Solving\" for $C$ for a given level of utility:\n","\n","\\begin{equation}\n"," C = \\left( \\frac{\\bar{U}}{L^{1-\\beta}} \\right)^{(1/\\beta)}\n","\\end{equation}\n","\n","---\n","We can now maximize the utility with the budget constraint using a Lagrangian $\\left(\\Im\\right)$:\n","\\begin{equation}\n"," \\max_{\\{C, L\\}} \\Im = C^{\\beta} L^{1-\\beta} + \\lambda \\left[C - I - \\frac{w}{P} (24-L) \\right]\n","\\end{equation}\n","\n","The FOC for $\\Im$:\n","\\begin{cases}\n"," \\Im_{L} = (1 - \\beta) \\left( \\frac{C}{L} \\right)^{\\beta} - \\lambda = 0 \\\\\n"," \\Im_{C} = \\beta \\left( \\frac{L}{C} \\right)^{1-\\beta} - \\lambda \\left(\\frac{w}{P} \\right) = 0 \\\\\n"," \\Im_{\\lambda} = C - I - \\left(\\frac{w}{P}\\right) (24-L) = 0\n","\\end{cases}\n","\n","From the firt two FOCs we get the known relationship $\\frac{U_{L}}{U_{C}} = \\frac{w/P}{1}$\n","\n","Solving for $C$ in terms of $L$ yields $C = \\frac{\\beta}{1-\\beta} \\left(\\frac{w}{P}\\right)L$.\n","Pluging this result in the third FOC and solving for $L$ yields $L^{*} = (1-\\beta) \\left[\\frac{I + 24 (w/P)}{(w/P)} \\right]$. With $L^*$ we can now get $C^* = \\beta \\left[I + 24 (w/P) \\right]$. Next we plug-in $C^*$ and $L^*$ into the utility function.\n","\n","\\begin{align}\n"," U(C^{*}, L^{*})^* &= \\left(C^*\\right)^{\\beta} \\left(L^*\\right)^{1-\\beta} \\\\\n"," U(C^{*}, L^{*})^* &= \\left[\\beta(I + 24 (w/P)\\right]^{\\beta} \\left[(1-\\beta) \\frac{I+24(w/P)}{(w/P)} \\right]^{1-\\beta}\n","\\end{align}\n","\n","Note that if $I=0$ then $L^*$ and $C^*$ are fixed quantities that depend on the value of $\\beta$.\n","\n","Using the lagrangian method also allows to find the \"optimal\" value of $\\lambda$ or the \"shadow price\":\n","\n","\\begin{align}\n"," \\lambda^* &= (1-\\beta) \\cdot \\left(\\frac{C^*}{L^*} \\right)^{\\beta} \\\\\n"," \\lambda^* &= (1-\\beta) \\cdot \\left[\\frac{\\beta \\left(I+24(w/P)\\right)w}{(1-\\beta)(I+24(w/P)} \\right]^{\\beta} \\\\\n"," \\lambda^* &= (1-\\beta) \\cdot \\left(\\frac{\\beta}{1-\\beta} \\frac{w}{P} \\right)^{\\beta}\n","\\end{align}\n","\n","Now we can use this information to plot the indifference curve with `matplotlib`. Note that the code calculates $U^*$, $L^*$, and $C^*$ and uses these values in the graph. The first part of the code imports the required packages. The second part of the code defines needed parameters and vectors. The third part of the code calculates $U^*$, $L^*$, $C^*$, and builds the functions for the indifference curve and the budget constraint. The fourth part of the code builds the plot."]},{"cell_type":"code","execution_count":17,"metadata":{},"outputs":[{"data":{"image/png":"iVBORw0KGgoAAAANSUhEUgAAAnEAAAHwCAYAAADJiTnYAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDMuMC4yLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvOIA7rQAAIABJREFUeJzs3XmcT3X///HHe2bsy4y1yzZMkSXLGNln+AghW0rhouQKFRJdSqoLaaH4phQVLRSVSFJJ2UbWDJIlRNkmY8/eMMv798d8zG+MbcbM53PmM/O8326f28w5n3Pe53XmXFc9e7/f5xxjrUVEREREfIuf0wWIiIiISPopxImIiIj4IIU4ERERER+kECciIiLigxTiRERERHyQQpyIiIiID1KIExEREfFBCnEikmbGmD3GmBbu3x8yxlhjzFOptok2xrjcv480xsQZY067P78bY942xpRKsb3LGBOdYjnSGBNrjDmT4tPQ/Z01xpxNsf5EijYSU+2Tcr+UbR41xsxJVcPFOs+kbjvFcTcbY/xSrHvJGDM1xXJudzs73TXuMcZ8aIypcI3z+uYaf+tSxpgPjDEx7r/ddmPMC8aYAsaYCu6aAlLtM9UY81KK65PgPs4pY8yvxph27u/yGmNOGGPuuMJxxxtjZqe43v+kqvntq9UsIt6lECciGXEcGGqMKXyNbWZaawsBRYFOwL+A9SlD1BUMsNYWTPFZneK7WinWB6VYfyDVPqn3G2CtLQhUBAoC465QZ8GrtA1QGuh6jZpnAx2AfwOBQC1gPdD8GufV/koNGWOKAquBfEBD99+vJRAE3HKNGlJb7T7nIGAS8LkxJshaGwvMBB5MdVx/oBswLcXq9qlqHpCO44uIBynEiUhGbCMpbAy+3obW2jhr7VagC3AE+K+Ha7taHSeAuUBoOnd9DXghde8XgLt3siXQ0VobZa2Nt9aetNZOtNZ+cANlPgmcBnpYa/e4695vrX3CWrspvY1ZaxOBT4ACQCX36mnAvcaY/Ck2bUXSvxe+v4GaRcTLFOJEJKP+Bwx29x5dl7U2AfgaiPBoVVdhjCkG3APsSueuc4BTwENX+K4FsNZauz9j1V3S3hx3+Mowdw9bLyAO2AtgrV0FxJD0t7joAeBTa218ZhxXRDxLIU5EMsRauxH4ERiajt0OkDS8ejUT3HO2ThhjNqT6bkOK7yakWF86xfqLnwKp2jwJHAWKA4+navf+VPsuTfW9JSmwDjfG5En1XTGSAtH1TEh1jBevsl1a27ueBu65fbEkDR/3sNYeTvH9x7iHVN1D4h25dCgVYG6qmvtkQl0ikgkU4kQkMwwHHjPG/CuN25chaT7d1Qy01ga5P2GpvgtL8d3AFOsPpFh/8XM2VZuBQE2gCFA2VbtfpNq3WeqirLXzgX1A31RfHQOuNcfvSucVZK3931W2u157F3vKcqVan4uk3raL1rjn9hUB5nF57+fHQDNjTBmgM7DLWvtLqm3uTlXzlGvUJSJepBAnIhlmrd1O0nDjs9fb1n2HZ3tguafruhJr7WbgJWCiMcbcQBPPA88BKeeSLQLqGWNSB8MbtQjolPJu2FRiSAprFVKtD8E9XJqStfYM0A94wBhTO8X6fSRdh+4kDaV+nOHKRcRrFOJEJLO8QNK8q9R3dQJgjMlljKkKfEbSHaqve7G21KYBJUm6mzRdrLWRwGagZ4p1i4CFwFfGmDrGmABjTCFjzKPGmP/cQH2vA4WBacaY8gDGmDLGmNeNMTXd8wq/BF42xhRz/227AdW4yk0J1tpjwPsk9ZqmNA0YADQGZtxArSLiEIU4EckU1trd/P87IFPqYow5A5wgaUjvGFDHWnsgk0sobS5/Tty9V6n1AjCBpDlul9SZ6lPyKsd6nsvn9HUG5pP06I6TwBbgdpJ61S56O1X7669S33GgEUm9bT8bY04Di93tXrwhox9JQ9KbgMMkBbG21tpDV6kZ4A3gLmNMzRTrZpM03LrYWnuleXjfpKr5q2u0LyJeZKy1TtcgIiIiIumknjgRERERH6QQJyIiIuKDFOJEREREfJBCnIiIiIgPUogTERER8UGXvcg5OwgKCrIVK1Z0ugy5QWfPnqVAgdRPqRBfoevnu3TtfJuun+9av379UWttifTuly1D3E033cS6deucLkNuUGRkJC6Xy+ky5Abp+vkuXTvfpuvnu4wxl71pJS00nCoiIiLigxTiRERERHyQQpyIiIiID8qWc+JERESysri4OKKjo4mNjc20NgMDA9m2bVumtSeZL2/evJQtW5ZcuXJlSnsKcSIiIl4WHR1NoUKFqFChAsaYTGnz9OnTFCpUKFPaksxnreXYsWNER0cTEhKSKW1qOFVERMTLYmNjKVasWKYFOMn6jDEUK1YsU3tfFeJEREQcoACX82T2NVeIExERyYEKFiyYru0jIyNp164dAPPmzWPMmDEAHDlyhPr161O7dm2WL1/OrFmzqFq1Ks2aNcv0muVSmhMnIiIi6dKhQwc6dOgAwOLFi6lSpQrTpk0DoHXr1kyaNCnNIS4hIQF/f3+P1ZrZslK96okTERHJwS6+6aFz585UqVKF7t27Y60FYMGCBVSpUoXw8HDmzJmTvM/UqVMZMGAAGzdu5Omnn2b+/PmEhobywgsvsGLFCh599FGeeuopEhISeOqpp6hbty41a9bkvffeSz5ms2bN+Pe//02NGjUAmD59OvXq1SM0NJRHHnmEhIQEIKnH8LnnnqNWrVo0aNCAQ4cOAXDo0CE6depErVq1qFWrFqtWrbpmOylFRUXRqFEjatWqRb169Th9+nTyOV3Url07IiMjk2sYPnw49evX55VXXuH++++/5O/Xvn17AH788UcaNmxIWFgY9913H2fOnMmUa3Q16okTERFx0KAFg9h4cGOG20nZQxT6r1DeaP1Gmvf95Zdf2Lp1K6VLl6Zx48asXLmS22+/nT59+rBkyRIqVqxIly5dLtsvNDSUUaNGsW7dOt5++20Ali5dyrhx47j99tuZPHkygYGBREVFcf78eRo3bsydd94JwNq1a9myZQshISFs27aNmTNnsnLlSnLlykW/fv2YMWMGDz74IGfPnqVBgwa8/PLLPP3000yZMoXnn3+egQMH0rRpU7766isSEhI4c+bMNdu56MKFC3Tp0oWZM2dSt25dTp06Rb58+a759zl79izVq1dn1KhRxMfHc/PNNye/q3bmzJl06dKFo0eP8tJLL7Fo0SIKFCjAq6++yuuvv87w4cPTfB3SSyFOREQkh6tXrx5ly5YFkoLZnj17KFiwICEhIVSqVAmAHj16MHny5HS1++OPP7Jp0yZmz54NwMmTJ9m5cye5c+emXr16yY/aWLx4MevXr6du3boA/PPPP5QsWRKA3LlzJ8/Fq1OnDgsXLgRgyZIlfPzxxwD4+/sTGBjIJ598ctV2LtqxYwelSpVK3qZw4cLXPQ9/f3/uvfdeAAICAmjdujXffPMNnTt35rvvvuO1115j2bJl/PbbbzRu3BhICosNGzZM198rvRTiREREHJSeHrNrychz4vLkyZP8u7+/P/Hx8UDG76a01vLWW2/RqlWrS9ZHRkZSoECBS7br2bMno0ePvqyNXLlyJdeRsrarHe9q7aTc5krnFRAQQGJiYvJyykeB5M2b95J5cF26dGHixIkULVqUunXrUqhQIay1tGzZks8+++yqx85smhMnIiIil6lSpQq7d+/mjz/+ALihcNKqVSveeecd4uLiAPj99985e/bsZds1b96c2bNnc/jwYQCOHz/O3r17r9l28+bNeeedd4CkoeRTp06lqZ0qVapw4MABoqKigKTwGx8fT4UKFdi4cSOJiYns37+ftWvXXvXYLpeLDRs2MGXKlORh5gYNGrBy5Up27doFwLlz5/j999+v+zfKCIU4ERERuUzevHmZPHkybdu2JTw8nPLly6e7jd69e1OtWjXCwsKoXr06jzzyyBV70qpVq8ZLL73EnXfeSc2aNWnZsiUxMTHXbPvNN99k6dKl1KhRgzp16rB169Y0tZM7d25mzpzJ448/Tq1atWjZsiWxsbE0btyYkJAQatSowZAhQwgLC7vqsf39/WnXrh3ff/998lBviRIlmDp1Kt26daNmzZo0aNCA7du3p/tvlh7m4h0o2UnlypXtjh07nC5DbtDFO6XEN+n6+S5dO+/Ztm0bVatWzdQ29dot33Cla2+MWW+tvT29baknTkRERMQHKcSJiIiI+CCFOBEREREfpBAnIiIi4oMU4kRERER8kEKciIiIiA9SiBMREcmB/P39CQ0NpVatWoSFhSW/QD6tIiMjk5+RdiNeeeWVG943I9544w3OnTuX7v2GDx/OokWLrrlNZGRkuv+OGaEQJyIikgPly5ePjRs38uuvvzJ69GiGDRvm1eNnxRCXkJBw1f1GjRpFixYtrtm2QpyIiIh41alTpyhSpAhweQ/bgAEDmDp1KgALFiygSpUqhIeHM2fOnORtjhw5QsuWLQkLC+ORRx6hfPnyHD16FIDp06dTr149QkNDeeSRR0hISOCZZ57hn3/+ITQ0lO7du19Wz4IFCwgLC6NWrVo0b94cSHqF1t133538NoRNmzYBMHLkSP7zn//gcrm4+eabmTBhAgBnz56lbdu21KpVi+rVqzNz5kwmTJjAgQMHaNasGc2aNQOgYMGCDB8+nPr167N69WpGjRpF3bp1qV69On379uXiSxEeeughZs+eDUCFChUYMWIEYWFh1KhRg+3bt7Nnzx7effddxo8fT2hoKMuXL8+063M1AR4/goiIiFzVoEGD2LhxY4bbSUhISH5Je2hoKG+88cY1t78YomJjY4mJiWHJkiXX3D42NpY+ffqwZMkSKlasmPzOUIAXXniBO+64g2HDhrFgwQImT54MJL2dYObMmaxcuZJcuXLRr18/ZsyYwZgxY3j77beveN5HjhyhT58+/PTTT4SEhHD8+HEARowYQe3atZk7dy5LlizhwQcfTN5/+/btLF26lNOnT1O5cmUee+wxFixYQOnSpfnuu+8AOHnyJIGBgbz++ussXbqU4sWLA0lhr3r16owaNQpIegXY8OHDAXjggQf49ttvad++/WV1Fi9enA0bNjBp0iTGjRvH+++/z6OPPkrBggUZMmTINf+WmUU9cSIiIjnQxeHU7du3s2DBAh588EGu9SrO7du3ExISQqVKlTDG0KNHj+TvVqxYQdeuXQFo3bp1cq/e4sWLWb9+PXXr1iU0NJTFixfz559/XrOuNWvW0KRJE0JCQgAoWrRo8jEeeOABAO644w6OHTvGyZMnAWjbti158uShePHilCxZkkOHDlGjRg0WLVrE0KFDWb58OYGBgVc8nr+/P/fee2/y8tKlS6lfvz41atRgyZIlbN269Yr73XPPPQDUqVOHPXv2XPOcPEU9cSIiIg66Xo9ZWmXk3akNGzbk6NGjHDlyhICAABITE5O/i42NTf7dGHPF/a8W/qy19OzZk9GjR6e5FmvtFY9zpWNc3C5PnjzJ6/z9/YmPj+fWW29l/fr1zJ8/n2HDhnHnnXcm97CllDdv3uQezNjYWPr168e6desoV64cI0eOvOT8U7p4zIvHc4LHeuKMMR8aYw4bY7akWDfWGLPdGLPJGPOVMSYoxXfDjDG7jDE7jDGtUqxv7V63yxjzjKfqFRERyam2b99OQkICxYoVo3z58vz222+cP3+ekydPsnjxYgCqVKnC7t27+eOPPwD47LPPkvcPDw/niy++AODHH3/k77//BqB58+bMnj2bw4cPA0nz2vbu3QtArly5iIuLu6yWhg0bsmzZMnbv3p28D0CTJk2YMWMGkDRvr3jx4hQuXPiq53TgwAHy589Pjx49GDJkCBs2bACgUKFCnD59+or7XAxsxYsX58yZM8lz4NLqWm17gid74qYCbwMfp1i3EBhmrY03xrwKDAOGGmOqAV2B24DSwCJjzK3ufSYCLYFoIMoYM89a+5sH6xYREcn2Ls6Jg6RermnTpuHv70+5cuW4//77qVmzJpUqVaJ27dpAUo/V5MmTadu2LcWLFyc8PJwtW5L6aUaMGEG3bt2YOXMmTZs2pVSpUhQqVIjixYvz0ksvceedd5KYmEiuXLmYOHEi5cuXp2/fvtSsWZOwsLDkcAZQokQJJk+ezD333ENiYiIlS5Zk4cKFjBw5kl69elGzZk3y58/PtGnTrnl+mzdv5qmnnsLPz49cuXLxzjvvANC3b1/atGlDqVKlWLp06SX7BAUF0adPH2rUqEGFChWoW7duuv6m7du3p3Pnznz99de89dZbREREpGv/9DLXGv/OcOPGVAC+tdZWv8J3nYDO1truxphhANba0e7vfgBGujcdaa1t5V5/yXZXU7lyZbtjx45MOgvxtsjISFwul9NlyA3S9fNdunbes23bNqpWrZqpbWZkODWjzp8/j7+/PwEBAaxevZrHHnssU27WyI6udO2NMeuttbenty0n58T9B5jp/r0MsCbFd9HudQD7U62vf6XGjDF9gb6QlOIjIyMzs1bxojNnzuj6+TBdP9+la+c9gYGBmT7slpCQ4NWhvJR27drFQw89lNzb9sYbbzhWS1YXGxubaf8/cyTEGWOeA+KBi/2nV5opabnynL0rdh1aaycDkyGpJ07/Nem71Bvg23T9fJeunfds27Yt03vNnOyJq127Nr/++qsjx/Y1efPmTR6iziivhzhjTE+gHdDc/v+x3GigXIrNygIH3L9fbb2IiIhIjuXV58QZY1oDQ4EO1tqU77yYB3Q1xuQxxoQAlYC1QBRQyRgTYozJTdLND/O8WbOIiIgneHJOumRNmX3NPdYTZ4z5DHABxY0x0cAIku5GzQMsdD/bZY219lFr7VZjzBfAbyQNs/a31ia42xkA/AD4Ax9aa6/81D0REREfkTdvXo4dO0axYsWu+uw1yV6stRw7doy8efNmWpseC3HW2m5XWP3BNbZ/GXj5CuvnA/MzsTQRERFHlS1blujoaI4cOZJpbcbGxmZqQJDMlzdvXsqWLZtp7emNDSIiIl6WK1eu5NdKZZbIyMhMmzAvvkHvThURERHxQQpxIiIiIj5IIU5ERETEBynEiYiIiPgghTgRERERH6QQJyIiIuKDFOJEREREfJBCnIiIiIgPUogTERER8UEKcSIiIiI+SCFORERExAcpxImIiIj4IIU4ERERER+kECciIiLigxTiRERERHyQQpyIiIiID1KIExEREfFBCnEiIiIiPkghTkRERMQHKcSJiIiI+CCFOBEREREfpBAnIiIi4oMU4kRERER8kEKciIiIiA9SiBMRERHxQQpxIiIiIj5IIS4dzsef59T5U06XISIiIqIQl1ZnL5ylyKtFeHPNm06XIiIiIqIQl1YFchegYtGKLN+33OlSRERERBTi0iMiOILV0auJT4x3uhQRERHJ4RTi0iE8OJwzF87w68FfnS5FREREcjiFuHSIKB8BwIp9KxyuRERERHI6hbh0KFu4LBWCKmhenIiIiDhOIS6dwoPDWb5vOdZap0sRERGRHEwhLp0igiM4fPYwu47vcroUERERycEU4tIpPDgcQEOqIiIi4iiFuHSqWrwqxfIV080NIiIi4iiFuHQyxtA4uLF64kRERMRRCnE3ICI4gl3Hd3HwzEGnSxEREZEcSiHuBkQE63lxIiIi4iyFuBtQu1Rt8gXkY/leDamKiIiIMxTibkBu/9w0KNuAFfvVEyciIiLOUIi7QeHB4Ww8uJFT5085XYqIiIjkQApxNygiOIJEm8ia6DVOlyIiIiI5kELcDWpQtgF+xk/z4kRERMQRCnE3qFCeQtT+V23NixMRERFHKMRlQERwBGui13Ah4YLTpYiIiEgOoxCXAeHB4cTGx7L+wHqnSxEREZEcRiEuA8KDwwE99FdERES8TyEuA24qeBOVilbSe1RFRETE6xTiMigiOIKV+1eSaBOdLkVERERyEIW4DAoPDuf4P8fZdmSb06WIiIhIDqIQl0ER5SMAzYsTERER71KIy6BbitzCvwr+S/PiRERExKsU4jLIGEN4cLhCnIiIiHiVQlwmiAiOYN/Jfew7uc/pUkRERCSHUIjLBHpenIiIiHibx0KcMeZDY8xhY8yWFOuKGmMWGmN2un8Wca83xpgJxphdxphNxpiwFPv0dG+/0xjT01P1ZkTNm2pSKHchhTgRERHxGk/2xE0FWqda9wyw2FpbCVjsXgZoA1Ryf/oC70BS6ANGAPWBesCIi8EvKwnwC6BhuYaaFyciIiJe47EQZ639CTieanVHYJr792nA3SnWf2yTrAGCjDGlgFbAQmvtcWvt38BCLg+GWUJEcARbDm/h73/+droUERERyQECvHy8m6y1MQDW2hhjTEn3+jLA/hTbRbvXXW39ZYwxfUnqxaNEiRJERkZmbuXXUfBEQQDenf8uDYs19Oqxs5szZ854/fpJ5tH18126dr5N1y/n8XaIuxpzhXX2GusvX2ntZGAyQOXKla3L5cq04tKiflx9nt78NCcKn8Dbx85uIiMj9Tf0Ybp+vkvXzrfp+uU83r479ZB7mBT3z8Pu9dFAuRTblQUOXGN9lpMvVz5uL307K/br5gYRERHxPG+HuHnAxTtMewJfp1j/oPsu1QbASfew6w/AncaYIu4bGu50r8uSwoPDiforin/i/nG6FBEREcnmPPmIkc+A1UBlY0y0MeZhYAzQ0hizE2jpXgaYD/wJ7AKmAP0ArLXHgReBKPdnlHtdlhQRHEFcYhxRB6KcLkVERESyOY/NibPWdrvKV82vsK0F+l+lnQ+BDzOxNI9pVK4RAMv3LqdJ+SYOVyMiIiLZmd7YkImK5S/GbSVu07w4ERER8TiFuEwWHhzOqv2rSEhMcLoUERERycYU4jJZRHAEp86fYtOhTU6XIiIiItmYQlwmiygfAaD3qIqIiIhHKcRlsuDAYMoVLqf3qIqIiIhHKcR5QET5CFbsW0HSTbciIiIimU8hzgPCy4UTcyaGP//+0+lSREREJJtSiPMAzYsTERERT1OI84BqJapRJG8RzYsTERERj1GI8wA/40fj4MYKcSIiIuIxCnEeEhEcwe/Hfufw2cNOlyIiIiLZkEKch4QHhwOaFyciIiKeoRDnIXVK1SFvQF6FOBEREfEIhTgPyROQh3pl6mlenIiIiHiEQpwHRQRH8EvML5y5cMbpUkRERCSbUYjzoPDgcBJsAmui1zhdioiIiGQzCnEe1KhcI/yMH8v3akhVREREMpdCnAcVzlOYmjfVZMV+3dwgIiIimUshzsMigiNYE72GuIQ4p0sRERGRbEQhzsMigiM4F3eOXw7+4nQpIiIiko0oxHnYxYf+al6ciIiIZCaFOA8rVagUtxS5RfPiREREJFMpxHlBeHA4K/atwFrrdCkiIiKSTSjEeUFEcARHzx1l+9HtTpciIiIi2YRCnBdcnBen96iKiIhIZlGI84Jbi91KyQIl9R5VERERyTQKcV5gjEmeFyciIiKSGRTivCS8XDi7T+zmr1N/OV2KiIiIZAMKcV4SUT4C0Lw4ERERyRwKcV4S+q9QCuQqoHlxIiIikikU4rwkwC+AhuUaKsSJiIhIplCI86LwcuFsPrSZE7EnnC5FREREfJxCnBdFlI/AYlm1f5XTpYiIiIiPU4jzovpl6hPgF6CbG0RERCTDFOK8qEDuAoSVCtO8OBEREckwhTgviwiOYO1fa4mNj3W6FBEREfFhCnFeFh4czoWEC6w7sM7pUkRERMSHKcR5WeNyjQFYvldDqiIiInLjFOK8rESBElQpXoUV+3Vzg4iIiNw4hTgHRARHsHLfShISE5wuRURERHyUQpwDwoPDOXn+JFuPbHW6FBEREfFRCnEOiAiOADQvTkRERG6cQpwDKgRVoEyhMpoXJyIiIjdMIc4BxhjCg8NZvnc51lqnyxEREREfpBDnkIjgCP46/Rd7TuxxuhQRERHxQQpxDgkPDgfQe1RFRETkhijEOaR6yeoE5gnUe1RFRETkhijEOcTfz59G5RqpJ05ERERuiEKcgyKCI9h2dBtHzx11uhQRERHxMQpxDooon/S8uJX7VjpciYiIiPgahTgH3V76dnL759a8OBEREUk3hTgH5Q3IS70y9RTiREREJN0U4hwWXi6cDTEbOHvhrNOliIiIiA9RiHNYRPkI4hPj+fmvn50uRURERHyIQpzDGpVrhMHoUSMiIiKSLgpxDgvKG0SNm2qwbO8yp0sRERERH6IQlwW0v7U9S3cvZcvhLU6XIiIiIj7CkRBnjBlsjNlqjNlijPnMGJPXGBNijPnZGLPTGDPTGJPbvW0e9/Iu9/cVnKjZkwY3GEzB3AUZETnC6VJERETER3g9xBljygADgduttdUBf6Ar8Cow3lpbCfgbeNi9y8PA39baisB493bZSrH8xRjcYDBzts3hl5hfnC5HREREfIBTw6kBQD5jTACQH4gB7gBmu7+fBtzt/r2jexn3982NMcaLtXrF4IaDCcobxPDI4U6XIiIiIj7A6yHOWvsXMA7YR1J4OwmsB05Ya+Pdm0UDZdy/lwH2u/eNd29fzJs1e0NQ3iCGNBzCt79/y5roNU6XIyIiIllcgLcPaIwpQlLvWghwApgFtLnCpvbiLtf4LmW7fYG+ACVKlCAyMjIzyvWq2vG1CcwVyONzHmdszbFOl+OYM2fO+OT1kyS6fr5L18636frlPF4PcUALYLe19giAMWYO0AgIMsYEuHvbygIH3NtHA+WAaPfwayBwPHWj1trJwGSAypUrW5fL5enz8Ijn8z/PUwufwi/EjyblmzhdjiMiIyPx1esnun6+TNfOt+n65TxOzInbBzQwxuR3z21rDvwGLAU6u7fpCXzt/n2eexn390ustZf1xGUX/er2418F/8X/lv6PbHyaIiIikkFOzIn7maQbFDYAm901TAaGAk8aY3aRNOftA/cuHwDF3OufBJ7xds3elD9Xfp4Nf5af9v7E4t2LnS5HREREsihH7k611o6w1lax1la31j5grT1vrf3TWlvPWlvRWnuftfa8e9tY93JF9/d/OlGzN/Wp04eyhcuqN05ERESuSm9syILyBuTl+YjnWRO9hvk75zsVeEi6AAAgAElEQVRdjoiIiGRBCnFZVK/avQgJCmF45HD1xomIiMhlFOKyqNz+uRnedDgbYjYwd/tcp8sRERGRLEYhLgvrUbMHtxa7leGRw0m0iU6XIyIiIlmIQlwWFuAXwMimI9lyeAtfbP3C6XJEREQkC1GIy+K6VO/CbSVuY2TkSOIT46+/g4iIiOQICnFZnJ/xY1SzUew4toMZm2Y4XY6IiIhkEQpxPqBTlU7U/ldtRv00iriEOKfLERERkSxAIc4HGGMY1WwUf/79J1M3TnW6HBEREckCFOJ8RNtKbalfpj4v/vQi5+PPO12OiIiIOEwhzkcYY3ix2YvsP7WfKRumOF2OiIiIOEwhzoe0uLkFEcERvLz8Zc7FnXO6HBEREXGQQpwPMcbw0h0vcfDMQd6JesfpckRERMRBCnE+pkn5JrS4uQVjVo7hzIUzTpcjIiIiDlGI80EvNnuRo+eO8tbPbzldioiIiDgkzSHOGFPAk4VI2jUo24C2ldoydtVYTsaedLocERERccB1Q5wxppEx5jdgm3u5ljFmkscrk2sa1WwUf8f+zfg1450uRURERByQlp648UAr4BiAtfZXoIkni5LrCysVRqcqnRi/ZjzHzh1zuhwRERHxsjQNp1pr96daleCBWiSdXnC9wOnzpxm3apzTpYiIiIiXpSXE7TfGNAKsMSa3MWYI7qFVcVaNm2rQpXoXJqydwOGzh50uR0RERLwoLSHuUaA/UAaIBkLdy5IFjGw6ktj4WF5d8arTpYiIiIgXXTfEWWuPWmu7W2tvstaWtNb2sNZqElYWUbl4ZR6o+QCT1k3iwOkDTpcjIiIiXpKWu1NDjDGvG2PmGGPmXfx4ozhJm+FNhxOfGM8ry19xuhQRERHxkoA0bDMX+AD4Bkj0bDlyI24ucjO9Qnsxef1knmr0FOWDyjtdkoiIiHhYWubExVprJ1hrl1prl138eLwySZfnmzyf9G7Vn15yuhQRERHxgrSEuDeNMSOMMQ2NMWEXPx6vTNIlODCYvmF9+WjjR/xx/A+nyxEREREPS0uIqwH0AcYA/+f+6MFkWdCzEc+Syz8Xo34a5XQpIiIi4mFpCXGdgJuttU2ttc3cnzs8XZikX6lCpehftz/TN01n+9HtTpcjIiIiHpSWEPcrEOTpQiRzDG08lHwB+RgZOdLpUkRERMSD0hLibgK2G2N+0CNGsr4SBUowsP5AZm6dyaZDm5wuR0RERDwkLY8YGeHxKiRTDWk0hIlRExkROYKvunzldDkiIiLiAWl5Y8MyYDtQyP3ZpkeMZG1F8xXlyQZPMnf7XNYfWO90OSIiIuIBaXljw/3AWuA+4H7gZ2NMZ08XJhkzqMEgiuQtwvDI4U6XIiIiIh6QljlxzwF1rbU9rbUPAvWA/3m2LMmowLyBPN34aebvnM/nWz53uhwRERHJZGkJcX7W2sMplo+lcT9x2OAGgwkPDqfX171Y+9dap8sRERGRTJSWMLbAfWfqQ8aYh4DvgO89W5ZkhjwBeZhz/xxKFSxFh886sP/kfqdLEhERkUySlhsbngLeA2oCtYDJ1tqnPV2YZI4SBUrwTbdv+Cf+H9p/1p4zF844XZKIiIhkgrTc2BACzLfWPmmtHUxSz1wFTxcmmee2krcxs/NMNh/eTI85PUi0iU6XJCIiIhmUluHUWUDKf+snuNeJD2ldsTXjW43n6x1fM2zRMKfLERERkQxKy8N+A6y1Fy4uWGsvGGNye7Am8ZDH6z3OtiPbeG3Va1QtUZWHQh9yuiQRERG5QWnpiTtijOlwccEY0xE46rmSxFOMMUxoM4HmIc3p+01flu9d7nRJIiIicoPSEuIeBZ41xuwzxuwHhgKPeLYs8ZRc/rmYdd8sQoqE0GlmJ/78+0+nSxIREZEbkJa7U/+w1jYAqgHVrLWNrLW7PF+aeEqRfEX4ttu3JNpE2n3ajpOxJ50uSURERNIpLXen5jHG/BsYCAw2xgw3xuhdTj6uUrFKfHn/l+w8vpMus7sQnxjvdEkiIiKSDmkZTv0a6AjEA2dTfMTHNQtpxqS7JvHDHz/w5A9POl2OiIiIpENa7k4ta61t7fFKxBF96vRh29FtjF8znqrFq/JY3cecLklERETSIC09cauMMTU8Xok4ZmzLsbSt1JbHv3+chX8sdLocERERSYO0hLhwYL0xZocxZpMxZrMxZpOnCxPv8ffz59N7P6VqiarcN+s+th/d7nRJIiIich1pCXFtgErAnUB7oJ37p2QjhfMU5ptu35DbPzftP2vPsXPHnC5JREREruGqIc4YU9j96+mrfCSbqRBUgbld57Lv5D46z+rMhYQL199JREREHHGtnrhP3T/XA+vcP9enWJZsqFG5RnzY4UMi90TS/7v+WGudLklERESu4Kp3p1pr27l/hnivHMkKutfszraj23h5+ctULVGVJxvq8SMiIiJZTVrmxInboUOHnC7Ba0Y1G8W9Ve9lyI9D+Pb3b50uR0RERFJRiEuj8+fPU61aNcLCwpgwYQJHjx51uiSP8jN+TLt7GrVL1abbl93YdEg3JIuIiGQlCnFplJiYyAsvvICfnx9PPPEEpUuX5p577mHevHnExcU5XZ5HFMhdgHld51E4T2Haf9aeQ2dyTk+kiIhIVnetu1OLXuvjzSKzgnz58jFgwADWrVvHpk2bGDhwICtXrqRjx46UKVOGwYMH8+uvvzpdZqYrU7gM87rO48jZI3Sa2YnY+FinSxIRERGu3RN3pbtSdXcqUKNGDcaNG0d0dDTffPMNTZo0YeLEiYSGhlK7dm3efPNNjhw54nSZmaZO6Tp83OljVkevpve83rpjVUREJAu4aoiz1oZYa292/0z9udmbRWZVuXLlol27dsyePZuYmBjeeust/P39GTRoEKVLl6ZTp058/fXX2WK4tXO1zrzU7CVmbJ7BK8tfcbocERGRHC9Nc+KMMUWMMfWMMU0ufjJyUGNMkDFmtjFmuzFmmzGmoXuYdqExZqf7ZxH3tsYYM8EYs8v92q+wjBzbU4oVK5Y83Lp582YGDRrE6tWrufvuu7PNcOuzEc/So2YPnl/6PLN/m+10OSIiIjnadUOcMaY38BPwA/CC++fIDB73TWCBtbYKUAvYBjwDLLbWVgIWu5fh/7/2qxLQF3gng8f2uOrVqzN27Fiio6P59ttvadq0KZMmTSI0NJTQ0FDeeOMNDh8+7HSZ6WaMYUr7KTQq14gHv3qQlftWOl2SiIhIjpWWnrgngLrAXmttM6A2cMMTvtyv82oCfABgrb1grT0BdASmuTebBtzt/r0j8LFNsgYIMsaUutHje1NAQABt27Zl1qxZHDhwgLfffptcuXIxePBgypQpw913383cuXO5cMF3Xm+VNyAvX3X5ijKFy9D84+ZM3zTd6ZJERERypLSEuFhrbSyAMSaPtXY7UDkDx7yZpBD4kTHmF2PM+8aYAsBN1toYAPfPku7tywD7U+wf7V7nU4oVK0b//v2JiopKHm5ds2YNnTp1okyZMgwaNIiNGzc6XWaalCxQktUPr6ZB2QY88NUDDFs0jESb6HRZIiIiOYq53p2GxpivgF7AIOAO4G8gl7X2rhs6oDG3A2uAxtban40xbwKngMettUEptvvbWlvEGPMdMNpau8K9fjHwtLV2fap2+5I03EqJEiXqfPHFFzdSnlclJCQQFRXFggULWLVqFXFxcdxyyy20bt2a5s2bU6RIEadLvKa4xDgm7JrAtzHf0qhYI56r8hz5A/JnuN0zZ85QsGDBTKhQnKDr57t07Xybrp/vatas2Xpr7e3p3e+6Ie6SjY1pCgSSNJ/thsYAjTH/AtZYayu4lyNImv9WEXBZa2Pcw6WR1trKxpj33L9/5t5+x8XtrnaMypUr2x07dtxIeY45fvw4n3/+OVOnTiUqKip5KLZnz560bduW3LlzO13iFVlrmRg1kUELBlGtRDXmdZtHhaAKGWozMjISl8uVKfWJ9+n6+S5dO9+m6+e7jDE3FOLSendquDGml7V2GbCaDAxnWmsPAvuNMReHZJsDvwHzgJ7udT2Br92/zwMedN+l2gA4ea0A56uKFi1Kv379WLt2LVu2bGHw4MH8/PPP3HPPPZQuXZonnniCX375Jcs9o80Yw4B6A/i++/fsP7WfulPqsnzvcqfLEhERyfbScnfqCGAoMMy9KheQ0dnsjwMzjDGbgFDgFWAM0NIYsxNo6V4GmA/8CewCpgD9MnjsLO+2227jtddeY//+/Xz33XfccccdvPvuu4SFhREaGsr48eOz3N2tLW9pyc+9f6ZovqI0/7g5H2z4wOmSREREsrW09MR1AjoAZwGstQeAQhk5qLV2o7X2dmttTWvt3dbav621x6y1za21ldw/j7u3tdba/tbaW6y1Nay1OeZtEQEBAdx111188cUXxMTEMHHiRPLmzcuTTz5JmTJl6NixI1999VWWubv11mK3subhNTQLaUbvb3ozeMFg4hPjnS5LREQkW0pLiLtgk8bwLID7TlLxsovDrT///DNbt27lySefJCoq6pLh1g0bNjg+3FokXxG++/d3PFH/Cd74+Q3afdqOE7EnHK1JREQkO0pLiPvCfXNBkDGmD7AIeN+zZcm1VKtWjVdffZV9+/Yxf/58mjdvzrvvvkudOnWoVasWr7/+OocOHXKsvgC/AN5o/QaT201m8e7FNHi/ATuP7XSsHhERkezouiHOWjsOmA18SdLz4YZbayd4ujC5voCAANq0acPMmTOJiYlh0qRJ5MuXj//+97+UKVOGDh06MGfOHMeGW/vU6cOiBxZx9NxR6r9fn0V/LnKkDhERkewoTXenWmsXWmufstYOAZYYY7p7uC5Jp6JFi/LYY48lD7f+97//Zd26ddx7772ULl2agQMHOjLc2rRCU6L6RFG6UGlaT2/NxLUTvXp8ERGR7OqqIc4YU9gYM8wY87Yx5k73Iz4GkHSn6P3eK1HSK/Vwa4sWLZg8ebJjw60hRUJY9fAq2lRqw4DvB9Dvu37EJcR57fgiIiLZ0bV64j4hafh0M9Ab+BG4D+hore3ohdokgy4Ot37++efExMTwzjvvkD9//kuGW7/88kvOnz/v8VoK5ynM3C5zGdp4KO+se4dW01tx7Nwxjx9XREQku7pWiLvZWvuQtfY9oBtwO9DOWusbL/iUSxQpUoRHH32UNWvW8NtvvzFkyBDWrVtH586dKV26NI8//jjr16/36HCrv58/Y1qM4eO7P2bl/pXUf78+vx35zWPHExERyc6uFeKSx7ustQnAbmvtac+XJJ5WtWpVxowZw759+/j+++9p2bIlU6ZM4fbbb6dmzZr83//9HwcPHvTY8R+o9QCRPSM5c+EMDd5vwPyd8z12LBERkezqWiGuljHmlPtzGqh58XdjzClvFSieExAQQOvWrS8Zbi1YsCBDhgyhbNmytG/f3mPDrQ3LNSSqTxQVi1ak3aft+L9V/+f4M+5ERER8yVVDnLXW31pb2P0pZK0NSPF7YW8WKZ53cbh19erVbNu2jaeeeooNGzZ4dLi1XGA5lvdazj1V72HIwiH8Z95/OB/v+fl5IiIi2UGaHjEiOUuVKlUYPXo0+/btY8GCBdx5553Jw601atRg3LhxmTbcWiB3Ab647wtGNB3B1I1TuePjO/j7wt+Z0raIiEh2phAnV+Xv70+rVq347LPPOHjwIO+++y6FChXiqaeeomzZsrRr147Zs2dneLjVz/gx0jWSmZ1n8kvMLzy87mE+2/yZhldFRESuQSFO0iQoKIhHHnnkkuHWX375hfvuu49SpUoxYMAA1q1bl6Hgdf9t97Om9xpuynsT/57zb1pNb8Wu47sy8SxERESyD4U4SbfUw62tWrXi/fffp27duhkebq15U03erv02b7d5m5//+pnqk6rz4rIXNVdOREQkFYU4uWFXGm4tXLhwhodb/Y0//ev1Z1v/bdxd5W6GRw6n1ru1iNwT6ZkTERER8UEKcZIpLg63rlq1iu3bt/P000+zcePG5OHW/v37ExUVla7h1tKFSvN558/5vvv3xCXG0WxaM3rO7cmRs0c8eCYiIiK+QSFOMl3lypV55ZVX2Lt3Lz/88AOtW7fmww8/pF69elSvXp2xY8cSExOT5vZaV2zNlse28Gz4s3y2+TOqTKzCBxs+INEmevAsREREsjaFOPEYf39/7rzzTj799FNiYmJ47733CAwM5Omnn6Zs2bK0bduWWbNmERsbe9228uXKx8vNX2bjoxu5rcRt9P6mN02nNmXr4a1eOBMREZGsRyFOvCIoKIi+ffsmD7cOHTqUX3/9lfvvv5/SpUunebi1WolqLHtoGR92+JBtR7YR+l4owxYN41zcOS+diYiISNagECded73h1ouvAbsaYwy9avdi+4Dt9KjZgzErx1B9UnW+3/m9F89CRETEWQpx4piUw60HDx5k8uTJBAYG8t5771G2bFnuuusuvvjii6sOtxbPX5yPOn5EZM9I8gTk4a5P7+K+Wfdx4PQBL5+JiIiI9ynESZYQGBhInz59WLVqFdOmTeOZZ55h8+bNdOnShVKlStGvXz/Wrl17xeHWphWasvGRjbzU7CW+/f1bqrxdhbd+fouExAQHzkRERMQ7FOIkywkODubll19mz549/Pjjj9x111189NFH1K9fn9tuu43XXnuNAwcu7W3LE5CH55o8x5bHttCwXEMGLhhI/ffrs/7AeofOQkRExLMU4iTL8vf3p2XLlsyYMSN5uLVIkSIMHTqUcuXKXXG49Zait7Cg+wI+v/dz/jr9F/Xer8cT3z/BqfOnHDwTERGRzKcQJz7h4nDrypUr2bFjxzWHW40xdKnehW39t/FonUd5a+1bVJ1YlVlbZ2Xo3a4iIiJZiUKc+Jxbb701ebh14cKFtG3bNnm4tVq1arz66qscOHCAoLxBTGw7kdUPr6ZkgZLcP/t+6kyuw5xtc/SgYBER8XkKceKz/P39adGiBdOnT+fgwYNMmTKFYsWK8cwzz1CuXDnatGnDzJkzqVW8FlF9ovio40ecuXCGe7+4l1rv1uLzLZ/r5gcREfFZCnGSLQQGBtK7d29WrFjB77//zrBhw9iyZQtdu3alVKlSPN7/caqer8rWfluZcc8MEm0i3b7sRrVJ1Zi2cRrxifFOn4KIiEi6KMRJtlOpUiVeeumlS4Zbp02bRoMGDahZvSb75+9nQYcFzLpvFvkC8vHQ1w9x61u3MmX9FC4kXHC6fBERkTRRiJNs60rDrcWLF+eZZ56hQvkKfPDfD3gm6BlmdZpFsfzF6PttXypOqMjEtROJjb/++1xFREScpBAnOULhwoXp3bs3y5cv5/fff+fZZ59l69atdOvWjd5NehO2LozXq71O2cJlGfD9AG5+82bGrx6vd7KKiEiWpRAnOU6lSpV48cUX2bNnD4sWLaJ9+/Z88sknPHn/kxwfe5zeZ3sT4h/Ckz8+SYU3KvDqilc5ff6002WLiIhcQiFOciw/Pz+aN2/OJ598wsGDB3n//fcpUaIE7499nzX/XUO9pfUotacUzyx4hvJvlGfUslGciD3hdNkiIiKAQpwIkDTc+vDDD7N8+XJ27tzJs88+S8yfMWyatImCbxWk8MLCjPhkBMHjg3l+yfMcO3fM6ZJFRCSHyzEhLiEhgdq1a9OuXTsAHnroIUJCQggNDSU0NJSNGzcCEBkZSWBgYPL6UaNGXbG93bt3U79+fSpVqkSXLl24cEF3NWYXFStWvGS49e4Od3N41WH4AOzblpdfeZlyL5Tj6YVPc+jMIafLFRGRHCrHhLg333yTqlWrXrJu7NixbNy4kY0bNxIaGpq8PiIiInn98OHDr9je0KFDGTx4MDt37qRIkSJ88MEHHq1fvC/1cOsHH3xA7Vtqw2L4Z+w/jH1sLOX+U44BXw9g99+7nS5XRERymBwR4qKjo/nuu+/o3bt3prRnrWXJkiV07twZgJ49ezJ37txMaVuypsKFC/Of//yHn376iZ07d/K/5/9H6fOliZsVx8SuE7m55c3UH1Gf2VtnE5cQ53S5IiKSA+SIEDdo0CBee+01/PwuPd3nnnuOmjVrMnjwYM6fP5+8fvXq1dSqVYs2bdqwdevWy9o7duwYQUFBBAQEAFC2bFn++usvz56EZBkVK1Zk1KhR7N+7n8WLF9OpQycCtgSwdtRa7mt6H0XaF6HfZ/3YdXyX06WKiEg2lu1D3LfffkvJkiWpU6fOJetHjx7N9u3biYqK4vjx47z66qsAhIWFsXfvXn799Vcef/xx7r777svatNZets4Y45kTkCzLz8+PO+64gzkz53Ds8DGmTJnCbSG3cfb7s7zT/R0q1atE9ceqM339dM7Hn79+gyIiIumQ7UPcypUrmTdvHhUqVKBr164sWbKEHj16UKpUKYwx5MmTh169erF27VogadisYMGCANx1113ExcVx9OjRS9osXrw4J06cID4+6X2b0dHRlC5d2rsnJlnKxYcJb4nawq5duxj09CCCzgax9d2tPND4AYLCg+j+Rnd2HN3hdKkiIpJNZPsQN3r0aKKjo9mzZw+ff/45d9xxB9OnTycmJgZI6lWbO3cu1atXB+DgwYPJPW1r164lMTGRYsWKXdKmMYZmzZoxe/ZsAKZNm0bHjh29eFaSld1yyy2MHzOeY38dY+GihbS4qwVxG+P4dPCnVKlchZDOIby18C292ktERDIk24e4q+nevTs1atSgRo0aHD16lOeffx6A2bNnU716dWrVqsXAgQP5/PPPk4dK77rrLg4cOADAq6++yuuvv07FihU5duwYDz/8sGPnIlmTn58fLZq3YOGchfx95G/GTxpPSLkQ9ny5h4F3DqRQtUK0GdqG9XvXM2MGVKgAfn5JP2fMcLp6ERHJ6syV5nf5usqVK9sdOzRs5asiIyNxuVxOl+ExO3ftZNSEUcz5fA7njpwD/25g34fE/Mnb5M8PkydD9+4OFnqDsvv1y8507Xybrp/vMsast9bent79smVP3P79+5k6dSoAcXFxuFwupk+fDsC5c+dwuVzMnDkTgJMnT+JyuZgzZw4AR48exeVy8c033wBJw6sul4sFCxYkt+1yuVi0aBEAf/75Jy6Xi2XLlgGwY8cOXC4Xq1atAmDLli24XC6ioqIA2LhxIy6XK/nhwlFRUbhcLrZs2QLAqlWrcLlcXAyhy5Ytw+Vy8eeffwKwaNEiXC4X+/fvB2DBggW4XC4OHjwIwDfffIPL5UqexzdnzhxcLhcnT54EYObMmbhcLs6dS3qx+/Tp03G5XMTFJT0WY+rUqZf8Q2DKlCm0aNEieXnSpEm0adMmefnNN9+kQ4cOycvjxo3j3nvvTV4eM2YMXbt2TV5+8cUX6dGjR/Ly8OHD6dWrV/LysGHDGDduXPLykCFD6N+/f/LyoEGDGDRoUPJy//79GTJkSPJy3759GTZsWPJyr169LnnWX48ePXjxxReTl7t27cqYMWOSl++9995Ljt+hQwfefPPN5OU2bdowadKk5OUWLVowZcqU5GWXy3Xd/+1tWL+BTyZ8QvSOaG6rcRsBfmMvCXBJ28JzzyEiInJV2TLEifgCPz8/ihctTkL8lW+K2bs3kd4v9Wbf0X1erkxERHyBhlMly8lpQwIVKsDevVf4wm8vJFaAPFC6QWm6P9CdIV2GULJgSS9XmD457fplJ7p2vk3Xz3dpOFXER738ctIcuJTy54ePp5ZjypdTqNG0BjGrYxjbeyw3lb+JWzrfwuhvR3Pk7BFnChYRkSxBIU7EYd27J93EUKTIKcBSvnzS8gMP+NH7nt5s+mETJ46c4IU3XiC4XDB/fvknz7Z/lpI1S3Lbo7cxYcUEDp897PRpiIiIlynEiWQB3btDeHgP2rfvyJ49l9+VWrhwYYY/MZy9G/fyxx9/8NiQxwg8F8hv7/3GE82f4KYmNxH2fBiT1k7i0JlDjpyDiIh4l0KcSBYxb9485s2bd93tbr75ZiaNncTxv46zdOlSOnbqSK7fcvHLy7/Qv01/SnUsRcPXGzIpahIHzxz0QuUiIuIEhTgRH+Xn54fL5WLu53M5fuQ4H330EfWq1sMusawZsob+XfpT6sFSRLwXwcS1ExXoRESyGYU4kSxi3LhxlzyjLj0KFizIQw89xM8rfmb37t28MPIFyiaUha9g1aBVDHh0AKUGlqLJR014e+3bHDh9IJOrFxERb1OIE8kiVq9ezerVqzPcToUKFRg+fDh7d+9l2bJl9OzWk3w78sFHsObpNTz+zOOUGV6GsPfCeG7xcyzfu5z4xPhMOAMREfGmAKcLEJEkX375Zaa25+fnR5MmTWjSpAkTJkxgzpw5TJ06laVLl2IiDbur7GZ01dG8UuUVAgsF0uLmFrSp2IZWFVtRtnDZTK1FREQyn0KcSA5QsGBBHnzwQR588EH27Nnz/9q77/Coyrz/4+87CYEkQCgBElKACAapiXRRQEEFFFGKwRUl66MgRUEpoo+7FhRQQSKCiroSFBUsIOAqIjwr/CwgLSAIUZSWRhOQKgL3748MswkhNEnOmeTzuq65ZuacMzPfs7cn++F8T+Htt99m2rRp7Ju1j6CQIKq1qsbi9MV8/OPHYKBh1YZ0rN2RTrU70TqmNYH+gU6vgoiInEbtVBGXGDt2bJ77uBaWU+3WTZs2sWTJEu5IvIPMpZnsnryb6GnR3JB+A2WPlCV5aTLXvX0dlZ+vzK0zbuW1Fa+xdd+Zbi0hIiJO0J44EZdITU0t0t8zxnDNNddwzTXX5Gm3LnhzAQBt27UloVMCB2IPsDB9IXPS5gBQN6wunWp3omPtjrSp0YYyAWWKtG4REcmhECfiEjNmzHDst0NCQrjrrru466672Lp1K2+//TYpKSksfmQxZcuWpWfPnlx323XsCtvF/F/m88ryV5iwdAJBAUFcW+tab6irXam2Y+sgIlLSOBbijDH+wAogw1p7sxjeSmAAACAASURBVDGmFjADqASsAu6y1h4zxpQG3gaaAHuARGvtFofKFin2atSowT/+8Q8ef/xxvv76a1JSUvjggw+YOnUqsbGx9OnTh+Q7ktnMZuZvms/nmz7ns58/A6B2pdrULV2XjEoZtK3ZVidIiIgUIiePiRsMbMj1/jlggrW2DrAX+B/P9P8B9lprawMTPMuJFDujRo1i1KhRTpfhdard+q9//Yvs7GzeeecdatWqxZNPPkm9y+sxrt84mu5qSuo9qfz8wM9M6jSJumF1+c/O/9B7dm+iJ0Rz2cTLuGfOPUxLncbmvZux1jq9WiIixYYjIc4YEwXcBLzpeW+A64CPPItMA271vO7qeY9nfnvP8iLFSlpaGmlpaU6XcUYhISH07t2bhQsXsnnzZkaNGsW2bdvo06cP4eHhjB42moZHGzK311zmtJ7Dqr6rmHDjBBpVa8SctDkkzUkidmIsNZJrcNfsu3hz1Zv8vOdnhToRkb/AOPFH1BjzETAGKAcMA5KApZ69bRhjooHPrbUNjDHrgI7W2nTPvF+AFtba3QV9f1xcnHXr/xnKuX311Ve0a9fO6TLkHKy1fPPNN95264EDB4iNjaVNmzY88cQT1KxZE4CT9iTrd65n8dbFLN66mCVbl7Dz0E4AIspG0KZGG9rWaEvbmm25IuwK9G8052jb820aP99ljFlprW16wZ8r6hBnjLkZ6GytHWCMaUdOiPs78N1pIe4za21DY8x64MbTQlxza+2e0763L9AXoEqVKk0++OCDIlsnubQOHjxI2bJlnS5DLsCRI0f4+uuvmT9/PqtXr8ZaS0JCAjfeeCNt2rQhKCjIu6y1lu1HtpO6L5U1+9ewdt9adh/L+TdZaKlQGoU2onFoYxpXaExsSCx+RldCKira9nybxs93XXvttT4T4sYAdwHHgTJAeWA2cCMQbq09boxpBTxprb3RGPOF5/V3xpgAIBuoYs9SuPbE+baS+q/Jf/7znwA8/fTTDlfy18ycOZNNmzaRkpLCpk2bKFu2LD169CApKYlrrrkGP7+8ocxayy97f2HJ1iU5e+u2LGbr/pzr0VUsU5FralxDm5g2XB1zNfHh8ZQOKO3EapUIJXXbKy40fr7rYvfEFfnZqdbaR4FHAU7tibPW3mmM+RDoQc4Zqn2AOZ6PzPW8/84z///OFuBEfNX27dudLuGSqFatGomJiTz22GN8++23pKSkMHPmTFJSUqhVqxZ9+vTh7rvvplatWkDOCRS1K9WmdqXa3JNwDwBb9231Brol25YwN20uAIH+gSSEJ9AisgUtolrQIrIFsRVj1YIVkRLJkWPivD/+3xB3szEmlv9eYmQ10Nta+4cxpgzwDpAA/Ab0stb+erbv1Z4436Z/Tfq2M43f4cOHmT17NikpKSxatAhrLe3atSMpKYnu3bufswWU8XsGS9OXsjR9KcsylrEicwVHjh8BICw4jOaRzWkZ2ZIWUS1oHtmcCmUqFNbqFWva9nybxs93+cwxcUVBIc636Q+RbzvX+G3bto133nnH224NCQmhZ8+eBbZbz+T4yeOs27mOZenLWJqxlGXpy9iw+79XLIqrHOfdU9cisgWNqjWilH+pS7F6xZq2Pd+m8fNdPtNOFZEze/TRRwEYM2aMw5UUrpiYGP73f//3vNutZxLgF0B8eDzx4fH0a9oPgP1H97M8cznL0pexLGMZ8zfN5+01bwNQJqAMTSKa5GnDxoTGqA0rIj5NIU7EJfbs2XPuhYoRYwytW7emdevWvPTSS8yePZtp06bx1FNP8eSTT9K2bVuSkpLo0aPHeZ1xF1omlA6xHegQ2wHIOWFi6/6tOS1YT7CbvHwyLy59EYBqIdW8gS4hPIGEiATCy4YX6jqLiFxKCnEiLvH66687XYJjgoODufPOO7nzzjvZvn27t93697//nUGDBnnPbm3Tps15tVshJyTWrFCTmhVq0qtBLwCOnTjG2h1r87RhT500ARBeNjwn0HlCXUJ4gk6cEBHXUogTEVeJjo7mscce49FHH+W7777ztlunTZtGzZo1ve3W2NjYC/7uQP9AmlZvStPqTRnIQAD2Hd1HanYqq7NWszp7NanZqSz4ZQEn7AkAypcuT3x4fJ5wd0XYFTrGTkQcpxAn4hLDhg0DYNy4cQ5X4g7GGK666iquuuoqkpOT+eSTT0hJSeHpp5/mqaeeuuB2a0EqlKlAu5rtaFeznXfa0eNHWbdznTfYrc5ezesrX/eeEVvavzQNqjYgITwhJ+BFJNC4WmNCAkP+6mqLiJw3hTgRlzhy5IjTJbhWcHAwf/vb3/jb3/7mbbdOmzYtT7u1T58+tG3b9rzbrWdTJqCMd4/dKSdOnuCnPT/lhDpPuJu1cRZvrn4TAIPh8sqXe9uwCeEJNKrWiKohVdWOFZFCoUuMiOvoNHnfVlTjZ61l6dKlpKSkMGPGDH7//Xdq1KhBnz596NOnz0W1Wy+mhu2/b2d1Vk4b9tReu237t3mXCQsOo36V+jSo2sD7qF+lPhWDKhZ6fRdK255v0/j5Ll1iRERKFGMMrVq1olWrVnnaraNGjeLpp5+mTZs23nZruXLlCq2GmNAYYkJj6Fq3q3f6nsN7SM1OZf2u9azbuY51O9fx9pq3OXDsgHeZyHKR3kB3KtzVq1JPLVkROW8KcSIuMWTIEACSk5MdrsT3BAUFcccdd3DHHXeQnp7uPbv1nnvuyXN266Vqt55L5eDKtI9tT/vY9t5pp/banQp1pwLeKyte4ejxo97lYivG5gt3cZXjdM9YEclHIU5EipWoqCgeffRRRo4cmafd+vbbb3vbrXfffTeXXXZZkdaVe69d5zqdvdNPnDzBr3t/zRfuPvv5M46fPA6Av/Hn8sqXU79qfRpUydljVzesLnUq16FMQJkiXQ8RcQ8dEyeuo+M6fJsbx+/IkSN88sknTJs2jQULFmCt5ZprriEpKYmePXsWWrv1rzh24hg/7fkpX7j75bdfsOT83TbkXAsvLiyOupXrUjesbs7rsLpUC6l2wSdUuHHs5Pxp/HyXjokTESnA6e3W6dOnk5KSwv/8z//wwAMP0L17d5KSkmjXrl2RtFvPR6B/oLedmtvhPw/z056f2Lh7I2m709i4ZyMbd29kydYlHP7zsHe58qXLUzfME+wqx3mfa1eqrdasSDGhECfiEgMH5lx8dvLkyQ5XUrxFRUUxcuRIHnnkEZYtW8bUqVOZOXMm77zzDjExMd6zW4u63Xq+gksFe+8bm9tJe5L039Nzgt3ujaTtyXle9Osi7z1kAfyMH7Uq1Mof8MLiKI6dGZHiTCFOxCWCgoKcLqFEMcbQsmVLWrZsSXJyMnPmzCElJYVnnnmGUaNGub7dejo/4+c95u76y67PM+/AHwf4ac9P3mB3KuQt2rwoz0kVZQPKcsWmK6hdqXa+R5XgKrrenYjL6Jg4cR0d1+HbfH38crdb09LSCA4OdmW79VI4aU+ybf82b2v2/374P44GHWXTb5vYsm8LJ+1J77LlAsvlC3aXVbyM2pVqE1EuAj9TfP538VW+vu2VZDomTkTkEsjdbv3+++9JSUnh/fff97Zb7777bvr06UPt2rWdLvUv8zN+1KxQk5oVatKxdkcaH23sDQHHThxj676tbPpt038fezexZscaZm+c7T1zFiAoIIjLKuUEutoV8wa9qPJR+Pv5O7SGIsWbQpyIS/Tt2xeA119/3eFKBHLarS1atKBFixa8+OKLzJ07l5SUFEaPHs0zzzzD1Vdf7W23li9f3ulyL7lA/0DqVK5Dncp18s07fvI42/dvzxfwftrzE5///Dl/nPgjz/fEVoylVoVaOY+KeZ/deOcKEV+hECfiEpUrV3a6BClAUFAQiYmJJCYmkpGR4W233nvvvXnObr322muLVbu1IAF+ATkhrGKtfMffnbQnyfg9I1/A27x3M9+lf8e+o/vyLB9aOtQb6GpWqJkn4NWsUFN3sBA5C4U4EZcYM2aM0yXIeYiMjOSRRx5hxIgRedqt06dPL3bt1ovhZ/yIDo0mOjSaa2tdm2/+vqP72Lx3M5v3bWbz3s1s2beFzfs2k7Ynjfmb5nPk+JE8y1cNqZp3D96psFexFjGhMQT6BxbVqom4jkKciMhFyN1unTBhQolrt16sCmUqkBCRQEJEQr551lp2HtrpDXi5n7/P+J6Pfvwoz7F4fsaP6uWqExMaQ43QGt6zc3O/Dy0TWpSrJ1KkFOJEXOLvf/87AFOnTnW4ErlQZcqU4fbbb+f2228nMzOT6dOnM3XqVG+7tVu3biQlJXHdddeViHbrxTLGUK1sNaqVrUbLqJb55p84eYKMAxl5At7W/VvZtn8byzKW8dGPH/HnyT/zfKZ86fJnDXkR5SII8NP/FYpv0n+5Ii4RHR3tdAlyCVSvXp0RI0YwfPhwli9f7m23vvvuu0RHR3vbrXXq5D9hQM7O38/fG8La0jbf/JP2JDsO7mDb/m3ecJf79Xfp3/Hbkd/yfqfxJ7J8ZL6QFxMaQ1T5KKLKR1GxTEVdI09cSdeJE9fRtY58m8Yvv6NHj3rbrV988QUnT56kdevWJCUlcfvtt7um3VoSxu7gsYPecHd6yNu2fxvpv6fnadlCziVUTgW6gh5hwWGOXyuvJIxfcaXrxImIuNSZ2q0pKSncd999PPjgg95267XXXou/v66pVpjKBpalXpV61KtS74zzT5w8QdbBLLbt30bG7xmk/56e8ziQ87x462IyD2TmC3qB/oFElos8a9CrFlJN18yTS0ohTsQlevfuDcD06dMdrkQKU+5264oVK0hJSeG9995Tu9Ul/P38vaGrICdOnmDnoZ3egJdxIFfY+z2d7zO+Z9aGWXmulwc5rduIchFEloskolwE1ctWp3q5/I9KQZXUvpXzohAn4hJxcXFOlyBFyBhDs2bNaNasGePHj2fevHmkpKQwZswYnn32WW+7tWfPnoSG6gxLN/H3ywljEeUiaBbZ7IzLWGvZc2RPnnB36pF5IJOf9/zMkq1L8h2jBzl79XKHuoiyEWcMe6GlQxX2SjgdEyeuo+M6fJvG76/JzMzk3XffZerUqWzYsIGgoCBuu+0279mthdlu1dgVvSN/HiH7YDaZBzLzPg7mPGcdyCLzQCb7/9if77NBAUH/DXrlIjix7wRN6zYlomwE4WXDvY+w4DC1cV1Ox8SJiBQD1atXZ/jw4QwbNszbbn3//fd57733iIqK8rZbL7/8cqdLlUsgqFSQ9+4XZ3Po2CGyDmblD3sHMsk6mMXqrNVk7M/g44yP833Wz/hRNaRqnmB3etA79SgXWE5793yIQpyIS/Tq1QuAGTNmOFyJuEFB7daxY8cyevRorrrqKu/ZrWq3Fn8hgSHUrlSb2pUKvhPIV199RbOrmrHj0A6yDmSRfTA77+NQzvO6nevIPpid7+QMyNm75w165SIIDwnPuXZfSDWqhlSlWlnPc0g1ygaWVeBzmEKciEvEx8c7XYK4VJkyZejZsyc9e/YkKyvL227t27dvnrNbC7vdKu4XEhhCbGAssRVjz7rcSXuS3478lj/oHcwm62BOANy4eyNfbfnqjMftQU7gOz3Y5XnONb1SUCW1dAuBQpyIS4wcOdLpEsQHREREMGzYMIYOHcrKlSu9Z7eq3SoXws/4ERYcRlhwGA2qNjjrssdOHGPXoV3sOLSDnYd2suOg5/nQf5+379/OysyV7Dy0kxP2xBl/r0pwlXzhrkpwFaqEVPHOO/W6fOny2st3HhTiRER8kDGGpk2b0rRp0wLbrX369CExMVHtVvlLAv0DiSwfSWT5yHMue9KeZO+RvWcNfDsP7eSX335hx6EdHP7zcIG/GRYc5g15VUOq5rzOFfpyh78KZSqUyNCnECfiEt27dwfg44/zH5gscjalS5emR48e9OjRw9tuTUlJoV+/fgwePNh7dmv79u3VbpVC5Wf8qBxcmcrBlQu8oHJuh/88zK5Du9h1eFee552Hdua89rz/de+v7Dq0iwPHDpzxewL8AvKEvirBVbx7GsOCw6gcVDnP+7DgMIJKBV3q1S9yCnEiLtGqVSunS5BioKB26/vvv09kZKS33arrEoobBJcKpkaFGtSoUOO8lj96/OgZQ583/B3eya5Du1idvZrdh3cXeDzfqd8uKOCdaXrl4MqUCShzqVb9klCIE3GJYcOGOV2CFCOnt1s//fRTUlJSeP755xkzZgytWrXynt1aoUIFp8sVOS9lAsoQHRpNdGj0eS1//ORx9h7Zy+7Du72PPUf25Hl/6vHr3l/Zc2QP+47uK/D7Lqt4GZse3HSpVucvU4gTESnmSpcuTffu3enevTvZ2dnes1tPb7eq1SrFTYBfQE57NaTKeX/mzxN/8tuR3/KFvD1H9uBv3LWNKMSJuMQtt9wCwNy5cx2uRIqz8PBwhg4dysMPP8yqVavytFvDwsK499576dOnD3Xr1nW6VBFHlPIvlXNtvLLVnC7lnPycLkBEcrRv35727ds7XYaUEMYYmjRpwssvv0xmZiYffvghderU4YUXXuCKK66gVatWTJkyhX37Cm4tiYizFOJEXGLw4MEMHjzY6TKkBDp1duvo0aNJT09n3LhxHDx4kPvvv5/w8HDuuOMOvvjiC06cyH/9LxFxjkKciIh4nWq3rl27lpUrV9K3b18WLFhAx44diYmJ4dFHH2Xjxo1OlykiKMSJuEanTp3o1KmT02WIADnt1iuvvJKJEyeSmZnJxx9/TJMmTfK0W1977TX27t3rdKkiJZZCnIhLdOnShS5dujhdhkg+pUuXplu3bsydO5eMjAzGjx/PwYMH6d+/PxEREfTq1Yv58+er3SpSxBTiRFxiwIABDBgwwOkyRM6qWrVqPPzww3narV9++SWdOnUiJiaGkSNHsmHDBqfLFCkRFOJEROSCFdRuHTduHPXq1aNly5Zqt4oUMoU4EZfo0KEDHTp0cLoMkQt2erv1xRdf5PDhw2q3ihQyhTgRl0hMTCQxMdHpMkT+kmrVqvHQQw+xZs0aVq1aRb9+/Vi4cCGdOnUiOjqaRx55RO1WkUtEIU7EJe677z7uu+8+p8sQuSSMMSQkJPDSSy+RmZnJrFmzaNasGePHj6devXq0aNGCV199Ve1Wkb9AIU5ERApVYGAgt912G3PmzPG2W48cOcKAAQMIDw8nMTGRzz//nOPHjztdqohPUYgTcYl27drRrl07p8sQKVSnt1vvv/9+Fi1aROfOnYmJiWHEiBH8+OOPTpcp4hMU4kRcIikpiaSkJKfLECkSp7dbZ8+eTfPmzZkwYQL169enefPmvPLKK/z2229OlyriWgpxIi6hECclVWBgILfeeiuffPIJGRkZTJgwgT/++IOBAwcSERHB7bffzmeffaZ2q8hpFOJEXOLPP//kzz//dLoMEUdVrVqVIUOGsGbNGlavXk3//v35z3/+w0033UR0dDQjRoxg/fr1Tpcp4goKcSIucf3113P99dc7XYaIa8THx5OcnExGRgazZ8+mRYsWTJgwgQYNGtCsWTMmT56sdquUaApxIi5x7733cu+99zpdhojrnKndeuzYMQYNGkRERAQ9e/bk3//+t9qtUuIoxIm4RO/evendu7fTZYi42unt1gEDBvDVV19x8803ExUVxfDhw1m3bp3TZYoUCYU4EZc4fPgwhw8fdroMEZ8RHx/PhAkTyMjI4JNPPqFVq1YkJyfTsGFDmjVrxqRJk9izZ4/TZYoUGoU4EZfo3LkznTt3droMEZ8TGBhI165dmT17NpmZmSQnJ3P8+HEeeOABIiIi6NGjB59++qnarVLsKMSJuET//v3p37+/02WI+LQqVaowePBgVq9ezerVqxk4cCCLFy+mS5cuREVFMWzYMLVbpdgo8hBnjIk2xvzHGLPBGLPeGDPYM72SMeZLY8zPnueKnunGGDPRGLPJGLPWGHNlUdcsUhQSExNJTEx0ugyRYuNM7daXXnqJhg0b0rRpU7Vbxec5sSfuODDUWnsF0BIYaIypB4wEFllr6wCLPO8BOgF1PI++wKtFX7JI4du/fz/79+93ugyRYudM7dYTJ07kabfOmzdP12kUn1PkIc5am2WtXeV5fQDYAEQCXYFpnsWmAbd6XncF3rY5lgIVjDERRVy2SKHr2rUrXbt2dboMkWItd7s1NTWVQYMGsWTJEm655RaioqIYOnQoP/zwg9NlipwXR4+JM8bUBBKAZUA1a20W5AQ9oKpnsUhge66PpXumiRQrDz74IA8++KDTZYiUGI0bN+bFF18kIyODOXPm0Lp1ayZOnEijRo1o0qQJL7/8Mrt373a6TJECGWutMz9sTFlgMfCstXaWMWaftbZCrvl7rbUVjTH/BsZYa7/2TF8EjLDWrjzt+/qS026lSpUqTT744IMiWxe5tA4ePEjZsmWdLkMuksbPd2nsYN++fSxcuJAFCxbw888/ExAQQKtWrejYsSPNmzcnICDA6RILpPHzXddee+1Ka23TC/2cIyHOGFMK+BT4wlr7omdaGtDOWpvlaZd+Za2NM8ZM8bx+//TlCvr+uLg4m5aWVvgrIoXiq6++ol27dk6XUeRO/Ys/LCzM4Ur+mpI6fsWBxi6vNWvWMG3aNKZPn86uXbuoWrUqvXv3JikpiYYNGzpdXj4aP99ljLmoEOfE2akG+Bew4VSA85gL9PG87gPMyTX9bs9Zqi2B/WcLcCK+qkePHvTo0cPpMkTEI3e7de7cuVx99dW8/PLL3nbrxIkT1W4VRzlxTFxr4C7gOmNMqufRGRgLXG+M+Rm43vMe4DPgV2AT8AYwwIGaRQrd0KFDGTp0qNNliMhpSpUqRZcuXfj444/JzMxk4sSJAAwePJjq1avTrVs35s6dq7NbpcgVeXPfc2ybKWB2+zMsb4GBhVqUiAt06dLF6RJE5BzCwsJ44IEHeOCBB1i7dq233Tp79myqVKnibbc2atTI6VKlBNAdG0RcIjs7m+zsbKfLEJHz1KhRI8aPH096ejpz587lmmuuYdKkSTRu3Jgrr7xS7VYpdApxIi7Rq1cvevXq5XQZInKBztRuNcao3SqFTiFOxCVGjhzJyJEjz72giLjWqXbrypUrWbt2LQ8++CDffPMNXbt2JTIykoceeog1a9Y4XaYUEwpxIi7RsWNHOnbs6HQZInKJNGzYkHHjxpGens68efNo06YNkydPJj4+noSEBF566SV27drldJniwxTiRFxi+/btbN++/dwLiohPKVWqFDfffDMfffQRWVlZvPzyy/j7+zNkyBCqV6/Obbfdxpw5c9RulQumECfiEnfddRd33XWX02WISCGqXLkygwYNYsWKFaxdu5bBgwfz3Xffceutt6rdKhdMIU7EJR5//HEef/xxp8sQkSJyqt26fft2tVvloijEibhEhw4d6NChg9NliEgRO73dOmnSJAICArzt1ltvvZVPPvmEY8eOOV2quIxCnIhL/Prrr/z6669OlyEiDqpcuTIDBw5k+fLl/PDDDwwZMoSlS5dy2223ERkZyZAhQ0hNTXW6THEJhTgRl7jnnnu45557nC5DRFyiQYMGvPDCC6Snp/Ppp5/Srl07Xn31VRISEoiPjyc5OZmdO3c6XaY4SCFOxCWeeuopnnrqKafLEBGXCQgI4KabbuLDDz8kMzOTSZMmUapUKR566CEiIyO97Vad3VryKMSJuETbtm1p27at02WIiIudrd3as2dPtVtLGIU4EZdIS0sjLS3N6TJExEec3m6Nj4/3tlsbN27MhAkT1G4t5hTiRFyiX79+9OvXz+kyRMTHnGq3Pvnkk2RlZTF58mRKly7Nww8/TGRkJF27dmX27Nk6u7UYUogTcYnRo0czevRop8sQER9WqVIlBgwYwPfff8+6det46KGH+P777+nWrRvVq1dn8ODBrF69Gmut06XKJaAQJ+ISV111FVdddZXTZYhIMVG/fn2ef/55tm/fzr///W+uu+46XnvtNa688kri4+PVbi0GFOJEXGLdunWsW7fO6TJEpJgJCAigc+fOfPDBB2q3FjMKcSIuMWjQIAYNGuR0GSJSjOVut65fv56HH344T7v1wQcfZNWqVWq3+giFOBGXeOGFF3jhhRecLkNESoh69erx3HPPsX37dj777DPat2/PlClTaNKkCY0bN+bFF19kx44dTpcpZ6EQJ+ISzZo1o1mzZk6XISIlTEBAAJ06dWLmzJlkZWXxyiuvEBQUxNChQ4mMjOSWW25h1qxZare6kEKciEukpqbqIp0i4qhKlSrRv39/li1bxvr16xk6dCgrVqyge/fuare6kEKciEsMGTKEIUOGOF2GiAjw33brtm3b1G51KYU4EZdITk4mOTnZ6TJERPLI3W7Nzs7m1VdfJTg42Ntu7dKlCx9//DF//PGH06WWOApxIi4RHx9PfHy802WIiBSoYsWK3H///SxdupQff/yRYcOGsXLlSnr06EH16tV54IEHWLlypdqtRUQhTsQlli9fzvLly50uQ0TkvFxxxRWMHTuWbdu28fnnn3P99dfzxhtv0LRpUxo1asT48ePJzs52usxiTSFOxCWGDx/O8OHDnS5DROSCBAQE0LFjR2bMmEFWVhavvvoqISEhDBs2jKioKLVbC5FCnIhLTJo0iUmTJjldhojIRTtTu3XVqlVqtxYShTgRl2jQoAENGjRwugwRkUsid7t1/vz53HDDDd52a8OGDRk3bpzarX+RQpyIS3z77bd8++23TpchInJJ+fv7c+ONN/L++++TnZ3Na6+9Rrly5Rg+fDhRUVHcfPPNfPTRR2q3XgSFOBGXeOyxx3jsscecLkNEpNBUqFCBfv368d1337FhwwaGDx/O6tWr6dmzJxEREQwaNIgVK1ao3XqeFOJEXGLKlClMmTLF6TJERIpE3bp1GTNmjLfdeuONN/Lmm2/SrFkzb7s1KyvL6TJdTSFOxCXi4uKIi4tzF5v9yQAACs9JREFUugwRkSJ1tnZrdHS02q1noRAn4hKLFy9m8eLFTpchIuKY3O3WjRs3MmLECFJTU73t1oEDB7J8+XK1Wz0U4kRc4oknnuCJJ55wugwREVeIi4tj9OjRbN26lS+++IKOHTvy1ltv0bx5cxo0aMALL7xQ4tutCnEiLvHWW2/x1ltvOV2GiIir+Pv7c8MNN/Dee++RlZXFlClTCA0NZcSIEURFRXHTTTfx4YcfcvToUadLLXIKcSIuERsbS2xsrNNliIi4VoUKFejbty/ffvstGzdu5JFHHmHNmjXcfvvtVK9evcS1WxXiRFxi4cKFLFy40OkyRER8wunt1k6dOnnbrfXr1+f5558nMzPT6TILlUKciEs888wzPPPMM06XISLiU061W999912ys7OZMmUKFStW5JFHHiE6OprOnTvzwQcfFMt2q0KciEu88847vPPOO06XISLis0JDQ+nbty/ffPMNaWlpjBw5kh9++IHExEQiIiIYMGAA33//fbFptyrEibhEdHQ00dHRTpchIlIsXH755Tz77LNs2bKFBQsW0LlzZ6ZOnUqLFi2KTbtVIU7EJebPn8/8+fOdLkNEpFjx9/fn+uuv97Zb33jjDSpVqlQs2q0KcSIuMXbsWMaOHet0GSIixVZoaCj33nsvX3/9NWlpaTz66KN52q39+/dn2bJlPtNuVYgTcYkZM2YwY8YMp8sQESkRLr/8cp555hm2bNnCl19+yU033cS0adNo2bIl9erV47nnniMjI8PpMs9KIU7EJcLDwwkPD3e6DBGREsXf358OHTowffp0srKyeOONN6hcuTIjR44kJiaGTp06MXPmTFe2WxXiRFxi3rx5zJs3z+kyRERKrNzt1p9++onHHnuM9evX06tXL0JDQ2nUqBHHjx93ukwvhTgRlxg/fjzjx493ugwREQHq1KnDqFGj2LJlCwsXLqRChQps376dgIAAp0vzck8lIiXcRx995HQJIiJyGj8/P9q3b88VV1zhdCn5KMSJuERYWJjTJYiIiA9RO1XEJWbNmsWsWbOcLkNERHyE9sSJuMTEiRMB6Natm8OViIiIL1CIE3GJOXPmOF2CiIj4ELVTRVwiNDSU0NDQfNPT0tKIj4/3PsqXL09ycnKeZfbv30+XLl1o3Lgx9evXZ+rUqUVVtoiIOER74kRcYubMmQAkJibmmR4XF0dqaioAJ06cIDIykttuuy3PMpMnT6ZevXrMmzePXbt2ERcXx5133klgYGDRFC8iIkVOIU7EJV599VUgf4jLbdGiRVx22WXUqFEjz3RjDAcOHMBay8GDB6lUqZKrrmUkIiKXnv7Ki7jEZ599ds5lZsyYwR133JFv+qBBg7jllluoXr06Bw4cYObMmfj56WgJEZHiTH/lRVwiODiY4ODgAucfO3aMuXPn0rNnz3zzvvjiC+Lj48nMzCQ1NZVBgwbx+++/F2a5IiLiMIU4EZeYPn0606dPL3D+559/zpVXXkm1atXyzZs6dSrdunXDGEPt2rWpVasWGzduLMxyRUTEYQpxIi7x5ptv8uabbxY4//333z9jKxUgJiaGRYsWAbBjxw7S0tKIjY0tlDpFRMQdfOaYOGNMR+AlwB9401o71uGSRC6pL7/8ssB5hw8f5ssvv2TKlCneaa+99hoA999/P//4xz9ISkqiYcOGWGt57rnndBsvEZFizidCnDHGH5gMXA+kA8uNMXOttT86W5nIpVOqVKkC5wUHB7Nnz5480+6//37v6+rVq7NgwYJCq01ERNzHV9qpzYFN1tpfrbXHgBlAV4drErmkUlJSSElJcboMERHxEb4S4iKB7bnep3umiRQbCnEiInIhfKKdCpgzTLN5FjCmL9DX8/YPY8y6Qq9KCksYsNvpIpxizJn+c/cpJXr8fJzGzrdp/IpAIf2NjruYD/lKiEsHonO9jwIycy9grX0deB3AGLPCWtu06MqTS0nj59s0fr5LY+fbNH6+yxiz4mI+5yvt1OVAHWNMLWNMINALmOtwTSIiIiKO8Yk9cdba48aYQcAX5Fxi5C1r7XqHyxIRERFxjE+EOABr7WfAuW8umeP1wqxFCp3Gz7dp/HyXxs63afx810WNnbHWnnspEREREXEVXzkmTkRERERyKXYhzhjT0RiTZozZZIwZ6XQ9cmGMMVuMMT8YY1Iv9mwdKRrGmLeMMTtzX87HGFPJGPOlMeZnz3NFJ2uUghUwfk8aYzI821+qMaazkzXKmRljoo0x/zHGbDDGrDfGDPZM1/bnA84yfhe8/RWrdqrn9lw/kev2XMAduj2X7zDGbAGaWmt1rSOXM8a0AQ4Cb1trG3imPQ/8Zq0d6/lHVEVr7SNO1ilnVsD4PQkctNaOc7I2OTtjTAQQYa1dZYwpB6wEbgWS0PbnemcZv9u5wO2vuO2J0+25RIqItXYJ8Ntpk7sC0zyvp5Hzh0lcqIDxEx9grc2y1q7yvD4AbCDnLkba/nzAWcbvghW3EKfbc/k+Cywwxqz03IVDfEs1a20W5PyhAqo6XI9cuEHGmLWedqvacS5njKkJJADL0Pbnc04bP7jA7a+4hbhz3p5LXK+1tfZKoBMw0NPyEZGi8SpwGRAPZAHjnS1HzsYYUxb4GBhirf3d6Xrkwpxh/C54+ytuIe6ct+cSd7PWZnqedwKzyWmRi+/Y4Tne49RxHzsdrkcugLV2h7X2hLX2JPAG2v5cyxhTipwA8K61dpZnsrY/H3Gm8buY7a+4hTjdnsuHGWNCPAd5YowJAW4A1p39U+Iyc4E+ntd9gDkO1iIX6FQA8LgNbX+uZHLuwP4vYIO19sVcs7T9+YCCxu9itr9idXYqgOeU3GT+e3uuZx0uSc6TMSaWnL1vkHM3kfc0fu5ljHkfaAeEATuAJ4BPgA+AGGAb0NNaq4PnXaiA8WtHTivHAluAfqeOsRL3MMZcDfw/4AfgpGfyY+QcV6Xtz+XOMn53cIHbX7ELcSIiIiIlQXFrp4qIiIiUCApxIiIiIj5IIU5ERETEBynEiYiIiPgghTgRERERH6QQJyIlgjHm4AUse4vnBuIiIq6lS4yISIlgjDlorS1bxL/pb609UZS/KSIlh/bEiUiJZYypYoz52Biz3PNo7ZmeZIyZ5Hnd0xizzhizxhiz5PT5nvefGmPaeV4fNMY8bYxZBrQyxjQxxiw2xqw0xnxx2lXZRUQuWoDTBYiIOOglYIK19mtjTAzwBXDFacv8E7jRWpthjKlwHt8ZAqyz1v7Tc3/ExUBXa+0uY0wi8CxwzyVcBxEpoRTiRKQk6wDUy7mVIQDlT92/N5dvgBRjzAfALM7tBDk3tgaIAxoAX3p+wx/QbaxE5JJQiBORkswPaGWtPZJ7Yq5Qh7X2fmNMC+AmINUYEw8cJ+/hKGVyvT6a6zg4A6y31rYqjOJFpGTTMXEiUpItAAadeuMJaHkYYy6z1i6z1v4T2A1Ek3Nz6nhjjJ8xJhpoXsD3pwFVjDGtPN9VyhhT/xKvg4iUUNoTJyIlRbAxJj3X+xeBB4HJxpi15Pw9XALcf9rnXjDG1CFnr9oiYI1n+mbgB2AdsOpMP2itPWaM6QFMNMaEen4jGVh/aVZJREoyXWJERERExAepnSoiIiLigxTiRERERHyQQpyIiIiID1KIExEREfFBCnEiIiIiPkghTkRERMQHKcSJiIiI+CCFOBEREREf9P8B+GuOMlgueCQAAAAASUVORK5CYII=\n","text/plain":["
"]},"metadata":{"needs_background":"light"},"output_type":"display_data"}],"source":"\"1|IMPORT PACKAGES\"\nimport numpy as np # Package for scientific computing with Python\nimport matplotlib.pyplot as plt # Matplotlib is a 2D plotting library\n\n\"2|DEFINE PARAMETERS AND ARRAYS\"\nT = 25 # Available hours to work\nbeta = 0.7 # Utility elasticity of consumption\nI = 50 # Non-labor income\nL = np.arange(1, T) # Array of labor hours from 0 to T\nrW = 25 # Real wage\n\n\"3|CALCULATE OPTIMAL VALUES AND DEFINE FUNCTIONS\"\nUstar = (beta*(I+24*rW))**beta * ((1-beta)*(I+24*rW)/rW)**(1-beta)\nLstar = (1-beta)*((I+24*rW)/rW)\nCstar = beta*(I+24*rW)\n\ndef C_indiff(U, L, beta): # Create consumption function\n C_indiff = (U/L**(1-beta))**(1/beta)\n return C_indiff\n\ndef Budget(I, rW, L): # Create budget constraint\n Budget = (I + 24*rW) - rW*L\n return Budget\n\nB = Budget(I, rW, L) # Budget constraint\nC = C_indiff(Ustar, L, beta) # Indifference curve\n\n\"4|PLOT THE INDIFFERENCE CURVE AND THE BUDDGET CONSTRAINT\"\ny_max = 2*Budget(I, rW, 0)\n\nv = [0, T, 0, y_max] # Set the axes range\nfig, ax = plt.subplots(figsize=(10, 8))\nax.set(title=\"INDIFFERENCE CURVE\", xlabel=\"Leisure\", ylabel=\"Real income\")\nax.grid()\nax.plot(L, C, \"g-\", label=\"Indifference curve\")\nax.plot(L, B, \"k-\", label=\"Budget constraint\")\nplt.axvline(x=T-1 , ymin=0, ymax=I/y_max, color='k') # Add non-labor income\nplt.axvline(x=Lstar, ymin=0, ymax = Cstar/y_max, ls=':', color='k') # Lstar\nplt.axhline(y=Cstar, xmin=0, xmax = Lstar/T , ls=':', color='k') # Cstar\nplt.plot(Lstar, Cstar, 'bo') # Point\nplt.text(0.1 , Cstar+5, np.round(Cstar, 1), color=\"k\")\nplt.text(Lstar+0.2, 10 , np.round(Lstar, 1), color=\"k\")\nax.legend() \nplt.axis(v) # Use 'v' as the axes range\nplt.show()"},{"cell_type":"markdown","metadata":{},"source":["---\n","Labor supply $N^S$ is the number of hours **not spent** in leisure. Note that $N^S$ decreases with $I$ and increases with $(w/P)$.\n","\n","\\begin{align}\n"," N^S &= 24 - L^* \\\\\n"," N^S &= 24 - (1-\\beta) \\left[\\frac{I + 24 (w/P)}{(w/P)} \\right] \n","\\end{align}\n","\n","The following code shows labor supply (in black) and shocks to non-labor income $\\Delta I = 25$ (in blue) and to consumption elasticity of ulility $\\Delta \\beta = 0.10$ (in red). Note that in this construction $N^S$ does not bend-backwards."]},{"cell_type":"code","execution_count":16,"metadata":{},"outputs":[{"data":{"image/png":"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\n","text/plain":["
"]},"metadata":{},"output_type":"display_data"}],"source":"\"1|IMPORT PACKAGES\"\nimport numpy as np # Package for scientific computing with Python\nimport matplotlib.pyplot as plt # Matplotlib is a 2D plotting library\n\n\"2|DEFINE PARAMETERS AND ARRAYS\"\nsize = 50\nT = 25 # Available hours to work\nbeta = 0.6 # Utility elasticity of consumption\nI = 50 # Non-labor income\nrW = np.arange(1, size) # Vector of real wages\n\n\"3|LABOR SUPPLY\"\ndef Lsupply(rW, beta, I):\n Lsupply = 24 - (1-beta)*((24*rW + I)/rW)\n return Lsupply\n\nD_I = 25 # Shock to non-income labor\nD_b = 0.10 # Shock to beta\n\nNs = Lsupply(rW, beta , I)\nNs_b = Lsupply(rW, beta+D_b, I)\nNs_I = Lsupply(rW, beta , I+D_I)\n \n\"4|PLOT LABOR SUPPLY\"\ny_max = np.max(Ns)\n\nv = [0, T, 0, y_max] # Set the axes range\nfig, ax = plt.subplots(figsize=(10, 8))\nax.set(title=\"LABOR SUPPLY\", xlabel=\"Work Hs.\", ylabel=r'(w/P)')\nax.grid()\nax.plot(Ns , rW, \"k\", label=\"Labor supply\", linewidth=3)\nax.plot(Ns_I, rW, \"b\", label=\"Non-labor income shock\")\nax.plot(Ns_b, rW, \"r\", label=\"Consumption elasticy of utility shock\")\nax.yaxis.set_major_locator(plt.NullLocator()) # Hide ticks\nax.xaxis.set_major_locator(plt.NullLocator()) # Hide ticks\nax.legend() \nplt.axis(v) # Use 'v' as the axes range\nplt.show()"},{"cell_type":"markdown","metadata":{},"source":["## 3. EQUILIBRIUM"]},{"cell_type":"markdown","metadata":{},"source":["We can now calculate the equilibrium condition, the value of $(w/P)_0$ which makes $N^D\\left(\\left(\\frac{w}{P}\\right)_0\\right) = N^S\\left(\\left(\\frac{w}{P}\\right)_0\\right)$. Then, we can define a function $\\Theta$ equal to zero at $\\left(\\frac{w}{P}\\right)_0$:\n","\n","\\begin{align}\n"," \\Theta \\left[ \\left(\\frac{w}{P}\\right)_0\\right] &= 0 = N^D \\left[\\left(\\frac{w}{P} \\right)_0\\right] - N^S \\left[\\left(\\frac{w}{P}\\right)_0\\right] \\\\\n"," \\Theta \\left[ \\left(\\frac{w}{P}\\right)_0\\right] &= 0 = \\underbrace{\\left[ K \\cdot \\left[\\frac{(1-\\alpha)A}{(w/P)}\\right]^{1/\\alpha} \\right]}_{N^D} - \\underbrace{\\left[ 24 (1-\\beta) \\left[\\frac{I + 24 (w/P)}{(w/P)} \\right] \\right]}_{N^S}\n","\\end{align}\n","\n","We can ask Python to calculate the value (root) of $\\left( \\frac{w}{P} \\right)$ that makes $\\Theta = 0$. For this we need the \"root\" function from the `SciPy` library. The cade has four sections. Section 1 imports the required packages. Section 2 defines the paramters and arrays. Section 3 find the dequilibrium values. And section 4 plots the results."]},{"cell_type":"code","execution_count":20,"metadata":{},"outputs":[{"data":{"image/png":"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\n","text/plain":["
"]},"metadata":{"needs_background":"light"},"output_type":"display_data"}],"source":"\"1|IMPORT PACKAGES\"\nimport numpy as np # Package for scientific computing with Python\nimport matplotlib.pyplot as plt # Matplotlib is a 2D plotting library\nfrom scipy.optimize import root # Package to find the roots of a function\n\n\"2|DEFINE PARAMETERS AND ARRAYS\"\nsize = 50\nT = 24 # Available hours to work\n# Demand parameters\nK = 20 # Capital stock\nA = 20 # Total factor productivity\nalpha = 0.6 # Output elasticity of capital\n# Supply parameters\nI = 50 # Non-labor income\nbeta = 0.6 # Utility elasticity of consumption\n# Arrays\nrW = np.arange(1, size) # Real wage\n\n\"3|OPTIMIZATION PROBLEM: FIND EQUILIBRIUM VALUES\"\ndef Ndemand(A, K, rW, alpha):\n Nd = K * ((1-alpha)*A/rW)**(1/alpha)\n return Nd\n\ndef Nsupply(rW, beta, I):\n Lsupply = T - (1-beta)*((24*rW + I)/rW)\n return Lsupply\n\ndef Eq_Wage(rW):\n Eq_Wage = Ndemand(A, K, rW, alpha) - Nsupply(rW, beta, I)\n return Eq_Wage\n\nrW_0 = 10 # Initial value (guess)\nrW_star = root(Eq_Wage, rW_0) # Equilibrium: Wage\nN_star = Nsupply(rW_star.x, beta, I) # Equilibrium: Labor\n\n\"4|PLOT LABOR MARKET EQUILIBRIUM\"\nNd = Ndemand(A, K, rW, alpha)\nNs = Nsupply(rW, beta, I)\n\ny_max = rW_star.x*2\nv = [0, T, 0, y_max] # Set the axes range\nfig, ax = plt.subplots(figsize=(10, 8))\nax.set(title=\"LABOR SUPPLY\", xlabel=\"Work Hs.\", ylabel=r'(w/P)')\nax.plot(Ns[1:T], rW[1:T], \"k\", label=\"Labor supply\")\nax.plot(Nd[1:T], rW[1:T], \"k\", label=\"Labor demand\")\nplt.plot(N_star, rW_star.x, 'bo') \nplt.axvline(x=N_star , ymin=0, ymax=rW_star.x/y_max, ls=':', color='k')\nplt.axhline(y=rW_star.x, xmin=0, xmax=N_star/T , ls=':', color='k')\nplt.text(5 , 20, \"Labor demand\")\nplt.text(19, 9, \"Labor supply\")\nplt.text(0.2 , rW_star.x+0.5, np.round(rW_star.x, 1))\nplt.text(N_star+0.3, 0.3 , np.round(N_star, 1))\nplt.axis(v) # Use 'v' as the axes range\nplt.show()"}],"nbformat":4,"nbformat_minor":2,"metadata":{"language_info":{"name":"python","codemirror_mode":{"name":"ipython","version":3}},"orig_nbformat":2,"file_extension":".py","mimetype":"text/x-python","name":"python","npconvert_exporter":"python","pygments_lexer":"ipython3","version":3}}