diff --git a/README.md b/README.md index 2f8fa00..8fcd192 100644 --- a/README.md +++ b/README.md @@ -44,3 +44,5 @@ See NYU Classes * [Lecture 8](https://github.com/jstac/nyu_macro_fall_2018/raw/master/lectures/lecture8.pdf) * [Lecture 9](https://github.com/jstac/nyu_macro_fall_2018/raw/master/lectures/lecture9.pdf) * [Lecture 10](https://github.com/jstac/nyu_macro_fall_2018/raw/master/lectures/lecture10.pdf) +* Lecture 11 given by TJS +* [Lecture 12](https://github.com/jstac/nyu_macro_fall_2018/raw/master/lectures/lecture12.pdf) diff --git a/lectures/lecture12.pdf b/lectures/lecture12.pdf new file mode 100644 index 0000000..752667b Binary files /dev/null and b/lectures/lecture12.pdf differ diff --git a/optimal_savings/optgrowth.ipynb b/optimal_savings/optgrowth.ipynb new file mode 100644 index 0000000..c908ed0 --- /dev/null +++ b/optimal_savings/optgrowth.ipynb @@ -0,0 +1,723 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Optimal Savings with IID Shocks\n", + "\n", + "#### John Stachurski \n", + "\n", + "Thanks to Natasha Watkins for joint work on the code" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Sun Oct 14 17:29:39 EDT 2018\r\n" + ] + } + ], + "source": [ + "!date" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "\n", + "Taking $ y_0 $ as given, the agent wishes to maximize\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "
\n", + "$$\n", + "\\mathbb E \\left[ \\sum_{t = 0}^{\\infty} \\beta^t u(c_t) \\right]\n", + "$$\n", + "\n", + "(2)\n", + "
\n", + "\n", + "subject to\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "
\n", + "$$\n", + "y_{t+1} = f(y_t - c_t) \\xi_{t+1}\n", + "\\quad \\text{and} \\quad\n", + "0 \\leq c_t \\leq y_t\n", + "\\quad \\text{for all } t\n", + "$$\n", + "\n", + "(3)\n", + "
\n", + "\n", + "where\n", + "\n", + "- $ u $ is a bounded, continuous and strictly increasing utility function and \n", + "- $ \\beta \\in (0, 1) $ is a discount factor \n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Our aim is to iterate with the Bellman operator\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "
\n", + "$$\n", + "Tv(y) := \\max_{0 \\leq c \\leq y}\n", + "\\left\\{\n", + " u(c) + \\beta \\int v(f(y - c) z) \\phi(dz)\n", + "\\right\\}\n", + "\\qquad (y \\in \\mathbb R_+)\n", + "$$\n", + "\n", + "(11)\n", + "
\n" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "from interpolation import interp\n", + "from numba import njit, prange\n", + "from quantecon.optimize.scalar_maximization import brent_max" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "\n", + "We will hold the primitives of the optimal growth model in a class\n", + "\n", + "The distribution $ \\phi $ of the shock is assumed to be lognormal,\n", + "and so a draw from $ \\exp(\\mu + \\sigma \\zeta) $ when $ \\zeta $ is standard normal" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [], + "source": [ + "class OptimalGrowthModel:\n", + "\n", + " def __init__(self,\n", + " f,\n", + " u,\n", + " β=0.96,\n", + " μ=0,\n", + " s=0.1,\n", + " grid_max=4,\n", + " grid_size=200,\n", + " shock_size=250):\n", + "\n", + " self.β, self.μ, self.s = β, μ, s\n", + " self.f, self.u = f, u\n", + "\n", + " self.y_grid = np.linspace(1e-5, grid_max, grid_size) # Set up grid\n", + " self.shocks = np.exp(μ + s * np.random.randn(shock_size)) # Store shocks" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### The Bellman Operator\n", + "\n", + "Here’s a function that generates a Bellman operator using linear interpolation" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [], + "source": [ + "def operator_factory(og, parallel_flag=True):\n", + " \"\"\"\n", + " A function factory for building the Bellman operator, as well as\n", + " a function that computes greedy policies.\n", + "\n", + " Here og is an instance of OptimalGrowthModel.\n", + " \"\"\"\n", + "\n", + " f, u, β = og.f, og.u, og.β\n", + " y_grid, shocks = og.y_grid, og.shocks\n", + "\n", + " @njit\n", + " def objective(c, v, y):\n", + " \"\"\"\n", + " The right hand side of the Bellman equation\n", + " \"\"\"\n", + " # First turn v into a function via interpolation\n", + " v_func = lambda x: interp(y_grid, v, x)\n", + " return u(c) + β * np.mean(v_func(f(y - c) * shocks))\n", + "\n", + " @njit(parallel=parallel_flag)\n", + " def T(v):\n", + " \"\"\"\n", + " The Bellman operator\n", + " \"\"\"\n", + " v_new = np.empty_like(v)\n", + " for i in prange(len(y_grid)):\n", + " y = y_grid[i]\n", + " # Solve for optimal v at y\n", + " v_max = brent_max(objective, 1e-10, y, args=(v, y))[1]\n", + " v_new[i] = v_max\n", + " return v_new\n", + "\n", + " @njit\n", + " def get_greedy(v):\n", + " \"\"\"\n", + " Computes the v-greedy policy of a given function v\n", + " \"\"\"\n", + " σ = np.empty_like(v)\n", + " for i in range(len(y_grid)):\n", + " y = y_grid[i]\n", + " # Solve for optimal c at y\n", + " c_max = brent_max(objective, 1e-10, y, args=(v, y))[0]\n", + " σ[i] = c_max\n", + " return σ\n", + "\n", + " return T, get_greedy" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The function operator_factory takes a class that represents the growth model,\n", + "and returns the operator T and a function get_greedy that we will use to solve the model\n", + "\n", + "Notice that the expectation in [(11)](#equation-fcbell20_optgrowth) is computed via Monte Carlo, using the approximation\n", + "\n", + "$$\n", + "\\int v(f(y - c) z) \\phi(dz) \\approx \\frac{1}{n} \\sum_{i=1}^n v(f(y - c) \\xi_i)\n", + "$$\n", + "\n", + "where $ \\{\\xi_i\\}_{i=1}^n $ are IID draws from $ \\phi $\n", + "\n", + "Monte Carlo is not always the most efficient way to compute integrals numerically\n", + "but it does have some theoretical advantages in the present setting\n", + "\n", + "(For example, it preserves the contraction mapping property of the Bellman operator — see, e.g., [[PalS13]](zreferences.ipynb#pal2013))\n", + "\n", + "\n", + "" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### An Example\n", + "\n", + "Let’s test out our operator when\n", + "\n", + "- $ f(k) = k^{\\alpha} $ \n", + "- $ u(c) = \\ln c $ \n", + "- $ \\phi $ is the distribution of $ \\exp(\\mu + \\sigma \\zeta) $ when $ \\zeta $ is standard normal \n", + "\n", + "\n", + "As is well-known (see [[LS18]](zreferences.ipynb#ljungqvist2012), section 3.1.2), for this particular problem an exact analytical solution is available, with\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "
\n", + "$$\n", + "v^*(y) =\n", + "\\frac{\\ln (1 - \\alpha \\beta) }{ 1 - \\beta}\n", + "+\n", + "\\frac{(\\mu + \\alpha \\ln (\\alpha \\beta))}{1 - \\alpha}\n", + " \\left[\n", + " \\frac{1}{1- \\beta} - \\frac{1}{1 - \\alpha \\beta}\n", + " \\right]\n", + " +\n", + " \\frac{1}{1 - \\alpha \\beta} \\ln y\n", + "$$\n", + "\n", + "(12)\n", + "
\n", + "\n", + "The optimal consumption policy is\n", + "\n", + "$$\n", + "\\sigma^*(y) = (1 - \\alpha \\beta ) y\n", + "$$\n", + "\n", + "We will define functions to compute the closed form solutions to check our answers" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [], + "source": [ + "def σ_star(y, α, β):\n", + " \"\"\"\n", + " True optimal policy\n", + " \"\"\"\n", + " return (1 - α * β) * y\n", + "\n", + "def v_star(y, α, β, μ):\n", + " \"\"\"\n", + " True value function\n", + " \"\"\"\n", + " c1 = np.log(1 - α * β) / (1 - β)\n", + " c2 = (μ + α * np.log(α * β)) / (1 - α)\n", + " c3 = 1 / (1 - β)\n", + " c4 = 1 / (1 - α * β)\n", + " return c1 + c2 * (c3 - c4) + c4 * np.log(y)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### A First Test\n", + "\n", + "To test our code, we want to see if we can replicate the analytical solution\n", + "numerically, using fitted value function iteration\n", + "\n", + "First, having run the code for the general model shown above, let’s\n", + "generate an instance of the model and generate its Bellman operator\n", + "\n", + "We first need to define a jitted version of the production function" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [], + "source": [ + "α = 0.4 # Production function parameter\n", + "\n", + "@njit\n", + "def f(k):\n", + " \"\"\"\n", + " Cobb-Douglas production function\n", + " \"\"\"\n", + " return k**α" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now we will create an instance of the model and assign it to the variable og\n", + "\n", + "This instance will use the Cobb-Douglas production function and log utility" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [], + "source": [ + "og = OptimalGrowthModel(f=f, u=np.log)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We will use og to generate the Bellman operator and a function that computes\n", + "greedy policies" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [], + "source": [ + "T, get_greedy = operator_factory(og)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now let’s do some tests\n", + "\n", + "As one preliminary test, let’s see what happens when we apply our Bellman operator to the exact solution $ v^* $\n", + "\n", + "In theory, the resulting function should again be $ v^* $\n", + "\n", + "In practice we expect some small numerical error" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "y_grid = og.y_grid\n", + "β, μ = og.β, og.μ\n", + "\n", + "v_init = v_star(y_grid, α, β, μ) # Start at the solution\n", + "v = T(v_init) # Apply the Bellman operator once\n", + "\n", + "fig, ax = plt.subplots(figsize=(9, 5))\n", + "ax.set_ylim(-35, -24)\n", + "ax.plot(y_grid, v, lw=2, alpha=0.6, label='$Tv^*$')\n", + "ax.plot(y_grid, v_init, lw=2, alpha=0.6, label='$v^*$')\n", + "ax.legend()\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The two functions are essentially indistinguishable, so we are off to a good start\n", + "\n", + "Now let’s have a look at iterating with the Bellman operator, starting off\n", + "from an arbitrary initial condition\n", + "\n", + "The initial condition we’ll start with is $ v(y) = 5 \\ln (y) $" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "v = 5 * np.log(y_grid) # An initial condition\n", + "n = 35\n", + "\n", + "fig, ax = plt.subplots(figsize=(9, 6))\n", + "\n", + "ax.plot(y_grid, v, color=plt.cm.jet(0),\n", + " lw=2, alpha=0.6, label='Initial condition')\n", + "\n", + "for i in range(n):\n", + " v = T(v) # Apply the Bellman operator\n", + " ax.plot(y_grid, v, color=plt.cm.jet(i / n), lw=2, alpha=0.6)\n", + "\n", + "ax.plot(y_grid, v_star(y_grid, α, β, μ), 'k-', lw=2,\n", + " alpha=0.8, label='True value function')\n", + "\n", + "ax.legend()\n", + "ax.set(ylim=(-40, 10), xlim=(np.min(y_grid), np.max(y_grid)))\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The figure shows\n", + "\n", + "1. the first 36 functions generated by the fitted value function iteration algorithm, with hotter colors given to higher iterates \n", + "1. the true value function $ v^* $ drawn in black \n", + "\n", + "\n", + "The sequence of iterates converges towards $ v^* $\n", + "\n", + "We are clearly getting closer\n", + "\n", + "We can write a function that iterates until the difference is below a particular\n", + "tolerance level" + ] + }, + { + "cell_type": "code", + "execution_count": 30, + "metadata": {}, + "outputs": [], + "source": [ + "def solve_model(og,\n", + " use_parallel=True,\n", + " tol=1e-4,\n", + " max_iter=1000,\n", + " verbose=True,\n", + " print_skip=25):\n", + "\n", + " T, _ = operator_factory(og, parallel_flag=use_parallel)\n", + "\n", + " # Set up loop\n", + " v = np.log(og.y_grid) # Initial condition\n", + " i = 0\n", + " error = tol + 1\n", + "\n", + " while i < max_iter and error > tol:\n", + " v_new = T(v)\n", + " error = np.max(np.abs(v - v_new))\n", + " i += 1\n", + " if verbose and i % print_skip == 0:\n", + " print(f\"Error at iteration {i} is {error}.\")\n", + " v = v_new\n", + "\n", + " if i == max_iter:\n", + " print(\"Failed to converge!\")\n", + "\n", + " if verbose and i < max_iter:\n", + " print(f\"\\nConverged in {i} iterations.\")\n", + "\n", + " return v_new" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can check our result by plotting it against the true value" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Error at iteration 25 is 0.4039123560122704.\n", + "Error at iteration 50 is 0.14556531673825646.\n", + "Error at iteration 75 is 0.0524612622392695.\n", + "Error at iteration 100 is 0.018906866673322753.\n", + "Error at iteration 125 is 0.006813972675239199.\n", + "Error at iteration 150 is 0.002455733381001579.\n", + "Error at iteration 175 is 0.0008850382480112273.\n", + "Error at iteration 200 is 0.00031896487892524306.\n", + "Error at iteration 225 is 0.00011495389518145771.\n", + "\n", + "Converged in 229 iterations.\n" + ] + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "v_solution = solve_model(og)\n", + "\n", + "fig, ax = plt.subplots(figsize=(9, 5))\n", + "\n", + "ax.plot(y_grid, v_solution, lw=2, alpha=0.6,\n", + " label='Approximate value function')\n", + "\n", + "ax.plot(y_grid, v_star(y_grid, α, β, μ), lw=2,\n", + " alpha=0.6, label='True value function')\n", + "\n", + "ax.legend()\n", + "ax.set_ylim(-35, -24)\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The figure shows that we are pretty much on the money" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### The Policy Function\n", + "\n", + "\n", + "\n", + "To compute an approximate optimal policy, we will use the second function\n", + "returned from operator_factory that backs out the optimal policy\n", + "from the solution to the Bellman equation\n", + "\n", + "The next figure compares the result to the exact solution, which, as mentioned\n", + "above, is $ \\sigma(y) = (1 - \\alpha \\beta) y $" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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E/1RWXGXvhjc58NcfU3MsB7DY/uNIWPhLRt2zyC+Dx81qved8vPN/m+d17//dLT3t4MGDvP7667z88stf21Tshz/8If/6r//K2LFjOXHiBNOnT2f//v1fGbd9+3b2799PcHAwo0aNYvr06VRXV/Pmm2+yfft2PB4Po0ePZtKkSQwZMqTe93rppZc4e/Yse/fuJSAggMuXL9OtWzd++MMfUlhYSI8ePXj99de/cvnyxYsXk5OTw9y5c5k1axYbNmz42rn37NmT3bt388ILL/Cb3/yGl19+mWeeeYbIyEj27duHtZbi4mKmT5/Oq6++yp49ewC+9HN66623OHjwIHv37uXixYuMGjWKjIwMAHbt2sXBgweJiopi7NixbN26lbFjx35tTSIi/sZdU03utr9Ttm89puYqAN6oYQxMz6Rn3xhni2thrTd8tDJxcXGMGjWqwXEbNmwgLy+v7n5RUREVFRV06NDhS+OmTp1KeLjvwjCzZs0iJyeHqqoqHnjgATp27Pil7TcKHxs2bODJJ5+su5TuFy3jH3zwQf72t7/xrW99i507d7JkyZKbn/A1rm0lv379+rr3Xr16NeDrdhseHv61oSwnJ4cHH3yQgIAAevXqxcSJE9mxYwfBwcGMHTuW3r1969VTUlI4ceKEwoeItBnW6+Xw7iwu71qFq+Kyb9lstxj6TVhA/7ihTpfniNYbPm7xCEVzCQsLq7vtcrm+1H792vbu1lq2b99OcHDw177e9culjDENtnS/3o1axj/22GM88MADAGRmZjZ4nf9rW9XDjdvVX9tKvinb1X/x+te/h4iIP7PWciJvD+e2LCegtAAXYMOiiBw9j4FDR7fqxm/Nrf3O/Da4XC7Cw8PJz8/H6/WyatWqusfuvPNO/vCHP9Td/+IriOu9//77FBcXU15ezpo1a5gwYQIZGRmsWrWKiooKysrKWLNmzdeuFrn77rt56aWX8Hg8wD9axvfv35+IiAiee+45Hn300QbnM2DAAA4cOEB1dTVFRUWN6qh799138+KLLwK+/8GKiooIDPRl2frCQ0ZGBkuXLsXj8XD+/Hk2bdpEWlqjzksSEfE7507ls/Vv/8GF939DQGkBNqQrXcc+xOhHf0nc8LHtOniAwsct+8UvfsG0adOYMmUK/fr1q9v+hz/8gU2bNpGcnMyQIUP47//+73qfP3HiRB588EFGjhzJwoULSUlJYfTo0SxcuJBRo0YxduxYvv/97zN8+PAb1vC9732PXr16kZyczIgRI1i+fHndYw8++CCxsbHEx8c3OJfY2FhmzZrF8OHDWbRoEampqQ0+5+mnn+b8+fMMGzaMlJSUus603/nOd0hOTv7KiaNz584lMTGRESNGcOedd/Kb3/yGqKioBt9HRMSfXCn8nE9X/o5Tq5/FVZgHgaF0TJ7JHd/+NYmjp+JyqONsa6Oltg549dVX2b9/P7/97W+b7T0WL17MuHHjeOSRR5rtPeSr2svvsIh8WeXVK+Rmv03VkWxf4zdXIMFxGSSmz6FDp65Ol9ci1FiunUtJSSE8PJwXXnjB6VJERNo0d3UleVvWUXbgPXBXAgb6phE/KZPwiF5Ol9dqKXw44ItrgjSXG51nIiIiTcN6PRzduZHC3Wug8goA7h4JxE7MpM8A/2/81txaXfi42VUUIq2FU19hikgLspZTh7bz+da3sGXnAXB36kuvsfMZmDRSf381UqsKH6GhoXUXx9IOFH9iraWwsJDQ0FCnSxGRZnL+xCFO5SzBe/k4AO7QcMJTZ5M4clKb7L/SnFpV+OjXrx8FBQVcvHjR6VJEblpoaOiXVj6JSNtQdP4Ux7KW4j63DwBvYEc6DLuPkWOnNXhNJ6lfqwofQUFBxMbGOl2GiIgIV68U1jV+s9ZiXUEEDJrC8IyZdOzYyeny/FqrCh8iIiJOq6oo4/CmNVTkfYj11IBxYaPHkZAxj/DuEU6X1yYofIiIiABedw15296l5LP/hZpyADw9k4lLz6Rnn2iHq2tbFD5ERKRds14vx/ZmcWnHKqjwtalwd4ul3/hMBgxqn43fmpvCh4iItFsFh3dzZvNyKCkAwBPWk8i0uQwa3r4bvzU3hQ8REWl3LhbkcyJ7Gd6LeQB4grvSecQMhoye0mAncLl9Ch8iItJulFz6nMNZS/EW7MQCNiCUkKSpDJkwnZAQXaenpSh8iIhIm1dRWkxu9ttUH80G68GaAALiJpM4cRadu3Rzurx2R+FDRETarJqqCnI3r6P80Pt1jd9s3zQGZ8ynR2Rvp8trtxQ+RESkzfG63eTv/IDiPe9AVSkAnohEYidm0jt6kMPVicKHiIi0Gdbr5fiBrVzYvgJz1deqw9OlP73HzicmYYT6hrUSCh8iItImnD26n9Obl0HRCQzg6dCD7nfMISFlopbNtjIKHyIi4tcKz53kWPZSvJ/vB8AbFEan4dNJGjOVwKAgh6uT+ih8iIiIXyopvkj+J2/hObXV1/gtIJjg+CkMmTiT0A5hTpcnX0PhQ0RE/EpleSm52auoyv8IvG4wLlyxE4hPn0fXbt2dLk8aQeFDRET8gru6itxt73J133pwVwBge6cQlzGfyJ79Ha5ObobCh4iItGrW6yF/9ydc3rkKU1kMgCc8juiJC+gXm+hwdXIrGgwfxpj+wBtAL8ALvGKt/d11YwzwO+BeoBx41Fq7q+nLFRGRdsNaTuXu4OzWFZjSs74VLGG96DV2HrFJaVrB4scac+TDDfyztXaXMaYzsNMY84G19uA1Y+4BBtf+GQO8VPtfERGRm3buZB6ncpZBYT4G8IZ0pdvI2STcMRmXGr/5vQbDh7X2HHCu9napMeYQ0Be4NnzMBN6w1lpgqzGmmzGmd+1zRUREGqXowhnys5Zhz+4GwAZ2oOPQaSSNu4+g4BCHq5OmclPnfBhjYoCRwLbrHuoLnL7mfkHtti+FD2PME8ATANHR0TdXqYiItFllJUXkZa3AfTwHrBdcgQQNmkxi+mw6hnVxujxpYo0OH8aYTsDbwJPW2pLrH67nKfYrG6x9BXgFIC0t7SuPi4hI+1JVWU7uprVU5n4AnmowBtN/DPEZ8+nWI8rp8qSZNCp8GGOC8AWPN621K+sZUgBcu86pH3D29ssTEZG2yON2k7f9PUo+W4epLgPARg1hYPpCovrGOFucNLvGrHYxwJ+AQ9ba39xg2FrgB8aYpfhONL2i8z1EROR61uvl6GebuLhjJa7yS76TSbtG03d8JtGDk50uT1pIY458TAAeBvYZY/bUbvspEA1grX0ZWI9vme0RfEttv930pYqIiD87nb+Xgs3LcF05jQvwdowkctQc4oaP17LZdqYxq11yqP+cjmvHWOD/NFVRIiLSdlw4c5zj2UvgwiFcgA3uTJcR95Mw6i4CAnWty/ZIe11ERJrFlcLz5GUtxxZ8CtZCQDChSXeROH4GIaEdnS5PHKTwISIiTaq87Aq5OauoOfJJXeO3wLh0EtLn0qlLuNPlSSug8CEiIk2iprqKQ5vXUX7wPUxt4zfTN5VB6fPpHtXX4eqkNVH4EBGR2+L1eMjbuZHi3WtwVV3BALbHYAZMzKT3gASny5NWSOFDRERuifV6OX7wU85vW4Hr6ue+k0k796HPuHlEJ9wB5mvXKkg7pvAhIiI37cyxXE5tWoKr6Jhv2WxoOD3umM3gkZO0bFYapPAhIiKNdvHzUxzLWg6f7/Ud6QjqSKdh95I49h4Cg4KdLk/8hMKHiIg06ErxZQ5nLcd7cktd47fg+CkkTZxFaMdOTpcnfkbhQ0REbqiy4ioHc1ZTnfchxluDMYaAmPEMzphHl24RTpcnfkrhQ0REvsJdU03utvco3fe/uGquYgDTaxhx6Qvp0Tva6fLEzyl8iIhIHev1krcnm8s7VxFQUYgLIDyG/uMX0CduqNPlSRuh8CEiIlhrOZG3h3NblhNQWkAAYMOiiBo9l9ihY7SCRZqUwoeISDt37tQRTuQsxXUpzxc6QroQnnI/g9PuwhUQ4HR50gYpfIiItFOXL54jP2s5nNmJCwuBoXQcMpXE8dMJCg51ujxpwxQ+RETambLSKxzKfhvP0SyM9YAJIGRQBgnpD9ChU1eny5N2QOFDRKSdqKqq4NDmdVQefB/jqcQFuPqPIj59Pl0iejldnrQjCh8iIm2c1+Ph0KcbKNm7FldVCQYgMoGY9IVE9YtzujxphxQ+RETaKOv1cnT/Ni5uX4Gr/ILvcuhd+tF33Hz6J4x0ujxpxxQ+RETaoDPHDnBq0zJcRcd9oaNDd3qkzWHQiHQtmxXHKXyIiLQhl86d4mjWUji/r7bxWxidh99HwpipavwmrYbCh4hIG3Cl6BL52W/hObm1tvFbEKEJU0iYOIvQDmFOlyfyJQofIiJ+rLK8jIM5q6k5/CF43WBcBMRMICFjHp279XC6PJF6KXyIiPghd001uVvfpWz/ekxNuW9jr2TiMhYQ0au/s8WJNEDhQ0TEj1ivl/w9WRTuXIWr4jIGsOGx9J+wkL4Dk5wuT6RRFD5ERPzEydzdnNu6DFNyBhfgDetJ1Oh5DBw6SitYxK8ofIiItHLnT+dzInspXDqMAbwhXeiWMpOEtClq/CZ+SeFDRKSVKr54jvzsZdiCnQDYgFA6DJ1G0rjpBIeEOFydyK1T+BARaWXKS4vIzVlFzZEssB6sK4CguEkkTpxDWGc1fhP/p/AhItJK1FRVkLt5HeWH3gN3FWAw/dKIz8gkXI3fpA1R+BARcZjX4yF/xwcU7XkHU1Xi2xaRREx6Jr37q/GbtD0KHyIiDrFeLycObuX8thWYqxd9J5N27kfvcZnEJKY4XZ5Is1H4EBFxwLljBzi9aSm26AQG8HToQfc7ZpOQosZv0vYpfIiItKDCz09xLGsp3s/3AeANCqPT8OkkjrmbIDV+k3ZC4UNEpAWUFl8kP+st3Ce3Yq3FBgQTNPibDJk4iw4d1fhN2heFDxGRZlRVUUpezmoqD3+E9dSAcUHMBJLS59E1vLvT5Yk4QuFDRKQZeNw15G1dT+m+9VDb+M3bawRxGZlEqfGbtHMKHyIiTch6vRzb8wmXdq6GissAuLsNpP+EBUTHqfGbCCh8iIg0DWs5lbeLc1uXQ8lZADxhPYkcPZ9BQ9O0gkXkGgofIiK36eyJPE5tWoYpzAfAE9yVzikzGTLqmwSo8ZvIVyh8iIjcogufF3Asexnm3B4MYAM7EJo0laTx9xESEup0eSKtlsKHiMhNKiq6TG7WW7hObcZYL7gCCR48mYSJs+kY1sXp8kRavQbDhzHmNWA6cMFaO6yexycDa4DjtZtWWmufbcoiRURag8qKcg5kr6b68Ie4vNUYYwiMGcugjPl06RbpdHkifqMxRz7+DLwIvPE1Y7KttdObpCIRkVbG63aTu/19rnz2Dq7qMlxAYO9hDMxYSHjPaKfLE/E7DYYPa22WMSam+UsREWldrNfLiQNbuLB9BVy9hAuw3QYwYEImveOGO12eiN9qqnM+xhlj9gJngX+x1h6ob5Ax5gngCYDoaP1rQURar7NH93N601IoPgn4Gr9FjZ5L3PDxWjYrcpuaInzsAgZYa8uMMfcCq4HB9Q201r4CvAKQlpZmm+C9RUSa1KVzJziWtRR73vdvKE9QJzon30/S6LsIDApytjiRNuK2w4e1tuSa2+uNMX80xkRYay/d7muLiLSUK0UXyf9kGZ7T26G28Vtwwl2MmDCD0A4dnS5PpE257fBhjOkFnLfWWmPMaMAFFN52ZSIiLaDiaim52SupPvIxeN1gXAQMTCc+/QG6dFXjN5Hm0JiltkuAyUCEMaYAeBoIArDWvgzMBb5vjHEDFcACa62+UhGRVq2muoq8resp2/8uxl0BgO2TwqD0BUT07OtwdSJtW2NWuyxs4PEX8S3FFRFp9bweD/m7P6Jo1xpMZTEG8HYfzICJmfSJSXC6PJF2QVc4FZF2wXq9nMzdyedb38KUnfOFjk596DV2HjGJqVrBItKCFD5EpM07eyKP0zlL4PJRX+gIDSc8dRbxIyfjClDoEGlpCh8i0mYVni/gaPZS7Nm9ANjAjoQNu4fEsfcQFBzicHUi7ZfCh4i0OWUll8n95C08JzZDbeO3oMHfIGnibDqEdXa6PJFYyPx1AAAa2ElEQVR2T+FDRNqMyoqr5G1aS2XeBvBUgzG4oscSn5FJ1+4RTpcnIrUUPkTE73ncNeRue5/Sz97B1Fz1bew5jIHpC4jsM8DZ4kTkKxQ+RMRvWa+Xo3tzuLRzJaa80HcyabcY+o3PpP+gYU6XJyI3oPAhIn7p9OE9nNm8HFNyGgPYjpFEjJ5L3LCxWjYr0sopfIiIX7lQcIzj2UvgYq7vSEdwZ7qOuJ/E0XfjCghwujwRaQSFDxHxCyWF58nLWo634NPaxm8hdEi6m8Tx0wkJVeM3EX+i8CEirVpFWQm5OSupPvLJPxq/xU0iMeMBOnXu5nR5InILFD5EpFWqqa4ib8v/cvXAu+Cu9G3seweD0ufTI6qPs8WJyG1R+BCRVsXr8ZC/a6Ov8VvVFd+2HvEMmLiAPgMGO1ydiDQFhQ8RaRWs18vJQ5/6Gr9dPY8BPJ360HtcJjGJIzHGOF2iiDQRhQ8RcdzZ44c4tWkZ5trGb3fMJj5lkhq/ibRBCh8i4phLn5/mWPZS7LnPfNfqCOpI2LB7fY3fgoKdLk9EmonCh4i0uJLiQg5nvYXn5JZ/NH6Ln0LShFl0COvkdHki0swUPkSkxVRWXCU3ZzVVeR+CtwaMC9eA8cRnzKNruBq/ibQXCh8i0uzcNdXkbvs7ZfvW1zV+s72SGZSeSUTvaIerE5GWpvAhIs3Ger0c3pPN5Z0rcVVc9p3X0S2G/hMX0HfgUKfLExGHKHyISLM4mbuLs1uW4yo9gwvwhvWk55i5xA4ZrcZvIu2cwoeINKlzp/I5mbMMcynPFzpCuhCeMpP4tClq/CYigMKHiDSRyxfOkp/9FpzZ4ft6JTCUjkOmkjR+OkHBoU6XJyKtiMKHiNyWstJicrPexn08G+P1gCuQ4LgMEtLn0LFTV6fLE5FWSOFDRG5JVVUFuZvWUXHoPYynCmMMrv6jiM+YT9cevZwuT0RaMYUPEbkpXo+H3E8/oGTPWkx1KQYgMpHY9IVE9RvodHki4gcUPkSkUazXy7H9W7nw6du4rl7wndfRpT99x8+nf3yK0+WJiB9R+BCRBp05doDTOUsxxSdwAbZDd3qkPcCgERO1bFZEbprCh4jc0KVzJzmavRQ+31/b+C2MTsn3kTh6KoFq/CYit0jhQ0S+oqT4EoezluM9uRWsxQYEE5JwJ0kTZhDaIczp8kTEzyl8iEidyvIycjd90fjNDcZFQOwE4jPm0aVrd6fLE5E2QuFDRHDXVJO37V3K9q2HmnIAbK8RxGXMJ7KXGr+JSNNS+BBpx6zXy5Hdn1C4axWmoggAb/hA+k9YQL+BSQ5XJyJtlcKHSHtkLafydnFu63IoOYsBPGG9iBozl7gho7SCRUSalcKHSDtz/tRhTuQshUv5AHhDutI1ZSaJad9U4zcRaREKHyLtRPHFc+RnLcWe2QWAN7ADHYZMZci46QSHhDhcnYi0JwofIm1ceWkRuVlvU3MsB6wH6wogMG4ywybOJqyzGr+JSMtT+BBpo6orK8jdvJbyQx9gPFWAgf5jSEifR3hET6fLE5F2TOFDpI3xut3k7fiAK3vfwVT5Gr95I5KIzVhALzV+E5FWQOFDpI2wXi/H92/hwva3MeUXfaGjS3/6jM9kQPwIp8sTEamj8CHSBpw5uo/Tm5Zjik/4ls126EFE2gMMHjFBy2ZFpNVpMHwYY14DpgMXrLXD6nncAL8D7gXKgUettbuaulAR+apLZ09wNHsZnPc1fvMGdaJz8nQSR99NYFCQ0+WJiNSrMUc+/gy8CLxxg8fvAQbX/hkDvFT7XxFpJleKLnIkaxnuU9vrGr8Fx9/JkIkzCe3Q0enyRES+VoPhw1qbZYyJ+ZohM4E3rLUW2GqM6WaM6W2tPddENYpIrcryUg5lr6I6/6O6xm+u2IkkZMxV4zcR8RtNcc5HX+D0NfcLard9JXwYY54AngCIjlazKpHGcldXkbd1PaX738W4KwCwvVMYlJFJRM9+DlcnInJzmiJ8mHq22foGWmtfAV4BSEtLq3eMiPyD9Xo4vOsjinatwVQW+04mDR/EgIkL6Bub4HR5IiK3pCnCRwHQ/5r7/YCzTfC6Iu2XtZw8tINzW9/ClJ3zhY5Ovek5Zh4Dk+7QChYR8WtNET7WAj8wxizFd6LpFZ3vIXLrzp3M41TOUig84lvBEtKN8NRZxKdOVuM3EWkTGrPUdgkwGYgwxhQATwNBANbal4H1+JbZHsG31PbbzVWsSFtWdOEMR7KW4j27BwAb2IGOQ+8hady9BAWr8ZuItB2NWe2ysIHHLfB/mqwikXamrOQyeVlv4z6eA9aLdQUSPGgyiemz6RjWxenyRESanK5wKuKQqsqr5G1aS0XuBvBUgzEQPYbE9Pl06xHldHkiIs1G4UOkhXncbvK2v0fJZ+sw1WUA2KghxKYvoGffWIerExFpfgofIi3Eer0c/SyHSztWYcov+VawdB1Av/HziR6c7HR5IiItRuFDpAUU5O+lYPNyzJVTvhUsHSOJSHuAQcnjtGxWRNodhQ+RZnTxzDGOZy/FXjjkCx3BneicPIOkMXcToGWzItJOKXyINIOSwgsczlqGp+DT2sZvIYQk3kXS+PvV+E1E2j2FD5EmVFFWQm7O21QfyfpH47eBGSSmz6GzGr+JiAAKHyJNoqa6itzN67h68O8Yd6VvY59UBmVk0iOqj7PFiYi0MgofIrfB6/GQv2ujr/Fb1RXfeR094hkwMZM+A+KdLk9EpFVS+BC5Bdbr5eShT/l82wpM2ee1jd/60HvsfGKSUjGmvmbPIiICCh8iN+3s8UOc2rQMc/mo70hHaLiv8dvIybgCtGxWRKQhCh8ijVR4/jRHs5Zhz+3FADawI2HD7yVx7D0EBQU7XZ6IiN9Q+BBpQGlxIYez38J9YgtYL7gCCRr8TZImzqZDWCenyxMR8TsKHyI3UFlxlbxNq6nM21jX+M0MGE9C+jy6do9wujwREb+l8CFyHY+7htytf6d03/9iaq4CYHsOJy49k8g+AxyuTkTE/yl8iNSyXi9H9+ZwacfbmIrLvpNJu8XQb8IC+scNdbo8EZE2Q+FDBDh9eA9nNi/HlJyubfwWReToucQNG6PGbyIiTUzhQ9q18wVHOJG9FC7m+UJHSBe6JN9P4ui71PhNRKSZKHxIu3Sl8HMOf7IMW7ADABsQQoekqSROmE5ISAeHqxMRadsUPqRdKS8rJjd7JTVHs8HrxroCCKxt/NapczenyxMRaRcUPqRdqKmuJHfzOsoP/h3cVYCBvmnEZ8yne2Rvp8sTEWlXFD6kTfN6PBzesYGiPWtxVZX4tkUkEDMxk97Rgx2uTkSkfVL4kDbJer0cP7idC9tWYK6exwV4O/el97hMYhJHOl2eiEi7pvAhbc7ZYwc5vWkJFJ2obfzWne53zCZ+ZIaWzYqItAIKH9JmFJ47xdHsJdjP9wPgDQqj8/D7SBwzlUA1fhMRaTUUPsTvlRRf4nDWW3hPbsFai3UFEZwwhSETZxHaIczp8kRE5DoKH+K3KsvLOJSzmurDH4LXDcaFK2Y88Rnz6Nqth9PliYjIDSh8iN9x11STt/VdSvevx9SUA2B7jSAufT6RvaMdrk5ERBqi8CF+w3q9HNn9CYW7VmEqinwnk4YPJHpCJn0HDnG6PBERaSSFD/ELJ3N3cW7rckzJGQzgCetFz9FzGTh0lFawiIj4GYUPadXOnzrM8ZxlmEuHaxu/daXbyJkk3PFNXGr8JiLilxQ+pFUqvniO/KyleM/swgA2IJQOQ6eRNG46wSEhTpcnIiK3QeFDWpWrJUXk5ryN+2gOWA+4AgmMm0TixNmEde7qdHkiItIEFD6kVaiurODQlneoOPg+xlMFxmD6jSI+Yz7dIno5XZ6IiDQhhQ9xlNftJu/TD7iy9x1MdanvK5bIJGImZtKrf5zT5YmISDNQ+BBHWK+XY/u3cHH725jyi76TSbv2p8/Y+QxISHG6PBERaUYKH9Lizhzdx+lNyzHFvsZvng49iBz1AIOSJ2jZrIhIO6DwIS3m0tkTHM1eCucP+I50BIXROXk6iaOnEhgU5HR5IiLSQhQ+pNldKbpIftZyPKe2gbXYgGBCEu4kacIMNX4TEWmHFD6k2VSWl3IoexXV+R/9o/Fb7EQSM+bSuWt3p8sTERGHKHxIk3NXV5G79V3K9q/HuCt8G3unEJeRSUTPfs4WJyIijmtU+DDGTAN+BwQAr1prn7vu8UeBXwFnaje9aK19tQnrFD9gvR4O7/qYol2rMZXFvvM6uscRPWEhfWMTnC5PRERaiQbDhzEmAPgDcBdQAHxqjFlrrT143dBl1tofNEON0spZr5eTuTs5t20FrtKzvtDRqRc9x8wjNilNK1hERORLGnPkYzRwxFp7DMAYsxSYCVwfPqQdOncyj5M5SzGFR3AB3pBuhKfOIj51shq/iYhIvRoTPvoCp6+5XwCMqWfcA8aYDOAw8CNr7enrBxhjngCeAIiOjr75aqXVKLpwhvysZdizu31XJQ3sQMeh00gadx9BwWr8JiIiN9aY8GHq2Wavu/8OsMRaW2WMWQz8BfjmV55k7SvAKwBpaWnXv4b4gbKSIvKyVuA+ngPWC65AggZNJjF9Nh3DujhdnoiI+IHGhI8CoP819/sBZ68dYK0tvObufwO/uP3SpDWpqiwnd9NaKnM/AE81GIMregzxGfPp2j3K6fJERMSPNCZ8fAoMNsbE4lvNsgB48NoBxpje1tpztXdnAIeatEpxjMftJm/7e5R8tg5TXQaAjRrCwPSFRPWNcbY4ERHxSw2GD2ut2xjzA+A9fEttX7PWHjDGPAvssNauBX5ojJkBuIHLwKPNWLO0AOv1cvSzTVzasRJTfqm28Vs0fcdnEj042enyRETEjxlrnTn1Ii0tze7YscOR95avdzr/M85sXoq54jtn2NsxkshRc4gbPl7LZkVEpF7GmJ3W2rTGjNUVTqXOxTPHOZ69BHvhkG8FS3BnOo+4n8RRdxEQqF8VERFpGvobRSgpvEBe9jK8pz8FayEgmJDEu0iaMIOQ0I5OlyciIm2Mwkc7VlFWQm7OSqqPfFLX+C1gYDoJ6Q+o8ZuIiDQbhY92qKa6itzN67h68L1/NH7rm8qg9Pn0iOrrbHEiItLmKXy0I16Ph8M7P6Jo9xpcVb7Gb7bHYKInZNInRo3fRESkZSh8tAPW6+XEoR2c3/YWpuxzXw+Wzn3oPXYeAxJStYJFRERalMJHG3f2eC6nNi3FXD7qu1ZHaLiv8dvIybgCFDpERKTlKXy0UYXnT3M0axn23F7f1ytBHQkbei+J4+4hKCjY6fJERKQdU/hoY0qvXOZw1nLcJ7b8o/Hb4CkkTZxFh7BOTpcnIiKi8NFWVFZcJTdnDVWHP7ym8du42sZvEU6XJyIiUkfhw8+5a6rJ2/4+pZ+tw9Rc9W3sOYyB6QuI7DPA2eJERETqofDhp6zXy5G9OVzasRJXRaHvZNJuMfQbn0n/QcOcLk9EROSGFD780KnDezi7eTmm5LRv2WzHKCJHzyVu2BgtmxURkVZP4cOPnC84yvHspZiLub4jHSFd6DpiBomj7sQVEOB0eSIiIo2i8OEHii99Tn7WMrxndmKsxQaE0CFpKokTphMS0sHp8kRERG6KwkcrVl52hdzsldQczapr/BY4aBIJ6Q/QqXM3p8sTERG5JQofrVBNdSWHNq+j/OB7GHclAKZfGoPT5xMe2dvh6kRERG6Pwkcr4vV4OLzjQ4r2rMFVVeK7MmlEAjHpC+jVf5DT5YmIiDQJhY9WwHq9HD+4nfPbVuC6er628Vtf+oybz4DEVKfLExERaVIKHw47e+ygr/Fb0XFf6AjtTve0OcSnpGvZrIiItEkKHw659PkpjmYthc/3+ZbNBoXRefi9JI6ZRqAav4mISBum8NHCSoovcTjrLTwnt4L1Yl1BhMR/k6T02YR2CHO6PBERkWan8NFCKsvLOJSzmurDH9Ytm3XFTCA+Yx5du/VwujwREZEWo/DRzNw11eRufZey/esxNeW+jb2SGZiRSWSvaGeLExERcYDCRzOxXi/5e7Io3LkKV8Vl33kd4bFET1hA34FDnC5PRETEMQofzeBk7i7ObVmGKT3rW8ES1pOo0fMYOHSUVrCIiEi7p/DRhM6fyud4zlLMpcN1jd/CU2YSnzZFjd9ERERqKXw0gaKL58jPWoY9s9N3VdLAUDoMmUbSuOkEh4Q4XZ6IiEirovBxG66WFJGbsxL30SywXnAFEhiXQVL6HDp26up0eSIiIq2SwsctqKosJ3fzOioOvY/xVIExmP6jiE+fT7eIXk6XJyIi0qopfNwEr8dD7qcfULJnLaa61PcVS2QSsemZ9OwX53R5IiIifkHhoxGs18ux/Vu4uP1tTPlFX+jo0p/e4+YzICHF6fJERET8isJHA84c3c/pTcswxSd8K1g69CAibQ6DRkzUslkREZFboPBxA5fOnuRo9lI4v993pCMojM7J95Mw+i41fhMREbkNCh/XuVJ0kcOfLMd7ehtYCwHBhCTcSeKEGWr8JiIi0gQUPmpVXC3lUM5qavI31jV+Cxg4kYT0uXTu2t3p8kRERNqMdh8+3DXVHNryLlcPXNP4rXcKcRmZRPTs52xxIiIibVC7DR/W6yVv10cU7VqDq7LId15H9ziiJy6kT0yC0+WJiIi0We0ufFivl5N5uzi39S1cXzR+69SLXmPnE5N4h1awiIiINLN2FT7OnczjZM4yTGG+L3SEdCM8dSbxqd9Q4zcREZEW0i7Cx+ULZziStQx7dndt47cOhA2dRuK4+wgKVuM3ERGRltSo8GGMmQb8DggAXrXWPnfd4yHAG8AdQCGQaa090bSl3ryykiJys1fgOZZT1/gtaNBkktLn0CGss9PliYiItEsNhg9jTADwB+AuoAD41Biz1lp78Jph3wGKrLWDjDELgF8Amc1RcGNUVZZzaNNaqnI/AE81GIMregzxGZl07R7pVFkiIiJC4458jAaOWGuPARhjlgIzgWvDx0zgmdrbK4AXjTHGWmubsNYGedxucre/T+ln6zDVpb6NPYcSO3EBUX1jWrIUERERuYHGhI++wOlr7hcAY240xlrrNsZcAXoAl64dZIx5AngCIDo6+hZLvrGykiLKdr2F8brxdo2m3/j59B88osnfR0RERG5dY8KHqWfb9Uc0GjMGa+0rwCsAaWlpTX5UpGv3SMJGzCK0Sw/iho/XslkREZFWqDHhowDof839fsDZG4wpMMYEAl2By01S4U0alj7TibcVERGRRmrMoYFPgcHGmFhjTDCwAFh73Zi1wCO1t+cCG1v6fA8RERHxDw0e+ag9h+MHwHv4ltq+Zq09YIx5FthhrV0L/An4H2PMEXxHPBY0Z9EiIiLivxp1nQ9r7Xpg/XXbfnbN7UpgXtOWJiIiIm2RzsgUERGRFqXwISIiIi1K4UNERERalMKHiIiItCiFDxEREWlRCh8iIiLSohQ+REREpEUZpy5Eaoy5CJxsppeP4Lqmdm2Q5tg2aI5tg+bYdrSHeTbXHAdYayMbM9Cx8NGcjDE7rLVpTtfRnDTHtkFzbBs0x7ajPcyzNcxRX7uIiIhIi1L4EBERkRbVVsPHK04X0AI0x7ZBc2wbNMe2oz3M0/E5tslzPkRERKT1aqtHPkRERKSVUvgQERGRFuXX4cMYM80Yk2eMOWKMeaqex0OMMctqH99mjIlp+SpvTyPm+Kgx5qIxZk/tn8edqPNWGWNeM8ZcMMbsv8HjxhjzQu38PzPGpLZ0jberEXOcbIy5cs0+/FlL13i7jDH9jTEfGWMOGWMOGGP+bz1j/HpfNnKOfr0vjTGhxpjtxpi9tXP8eT1j/PpztZFz9OvP1S8YYwKMMbuNMevqeczZ/Wit9cs/QABwFBgIBAN7gSHXjfn/gJdrby8AljlddzPM8VHgRadrvY05ZgCpwP4bPH4v8C5ggLHANqdrboY5TgbWOV3nbc6xN5Bae7szcLie31W/3peNnKNf78vafdOp9nYQsA0Ye90Yf/9cbcwc/fpz9Zp5/BPwt/p+J53ej/585GM0cMRae8xaWw0sBWZeN2Ym8Jfa2yuAKcYY04I13q7GzNGvWWuzgMtfM2Qm8Ib12Qp0M8b0bpnqmkYj5uj3rLXnrLW7am+XAoeAvtcN8+t92cg5+rXafVNWezeo9s/1qxL8+nO1kXP0e8aYfsB9wKs3GOLofvTn8NEXOH3N/QK++kFQN8Za6wauAD1apLqm0Zg5AjxQexh7hTGmf8uU1mIa+zPwd+NqDwO/a4wZ6nQxt6P28O1IfP+ivFab2ZdfM0fw831Ze6h+D3AB+MBae8P96Kefq42ZI/j/5+pvgX8FvDd43NH96M/ho76Edn16bcyY1qwx9b8DxFhrk4EN/CPJthX+vg8bYxe+nggjgN8Dqx2u55YZYzoBbwNPWmtLrn+4nqf43b5sYI5+vy+ttR5rbQrQDxhtjBl23RC/34+NmKNff64aY6YDF6y1O79uWD3bWmw/+nP4KACuTaP9gLM3GmOMCQS64l+Hvxuco7W20FpbVXv3v4E7Wqi2ltKY/ezXrLUlXxwGttauB4KMMREOl3XTjDFB+P5SftNau7KeIX6/LxuaY1vZlwDW2mLgY2DadQ/5++dqnRvNsQ18rk4AZhhjTuD7uv6bxpi/XjfG0f3oz+HjU2CwMSbWGBOM74SZtdeNWQs8Unt7LrDR1p5d4ycanON135nPwPc9dFuyFlhUu1JiLHDFWnvO6aKakjGm1xfftRpjRuP7/7LQ2apuTm39fwIOWWt/c4Nhfr0vGzNHf9+XxphIY0y32tsdgDuB3OuG+fXnamPm6O+fq9ban1hr+1lrY/D9vbHRWvvQdcMc3Y+BLfVGTc1a6zbG/AB4D9+qkNestQeMMc8CO6y1a/F9UPyPMeYIvkS3wLmKb14j5/hDY8wMwI1vjo86VvAtMMYswbdCIMIYUwA8je8EMKy1LwPr8a2SOAKUA992ptJb14g5zgW+b4xxAxXAAn/6MK81AXgY2Ff7XTrAT4FoaDP7sjFz9Pd92Rv4izEmAF9wWm6tXdeWPldp3Bz9+nP1RlrTftTl1UVERKRF+fPXLiIiIuKHFD5ERESkRSl8iIiISItS+BAREZEWpfAhIiIiLUrhQ0RERFqUwoeIiIi0qP8feKUtHe1GpG4AAAAASUVORK5CYII=\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig, ax = plt.subplots(figsize=(9, 5))\n", + "\n", + "ax.plot(y_grid, get_greedy(v_solution), lw=2,\n", + " alpha=0.6, label='Approximate policy function')\n", + "\n", + "ax.plot(y_grid, σ_star(y_grid, α, β),\n", + " lw=2, alpha=0.6, label='True policy function')\n", + "\n", + "ax.legend()\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The figure shows that we’ve done a good job in this instance of approximating\n", + "the true policy" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Exercise 1\n", + "\n", + "Here’s one solution (assuming as usual that you’ve executed everything above)" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": {}, + "outputs": [], + "source": [ + "def simulate_og(σ_func, og, α, y0=0.1, ts_length=100):\n", + " '''\n", + " Compute a time series given consumption policy σ.\n", + " '''\n", + " y = np.empty(ts_length)\n", + " ξ = np.random.randn(ts_length-1)\n", + " y[0] = y0\n", + " for t in range(ts_length-1):\n", + " y[t+1] = (y[t] - σ_func(y[t]))**α * np.exp(og.μ + og.s * ξ[t])\n", + " return y" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig, ax = plt.subplots(figsize=(9, 6))\n", + "\n", + "for β in (0.8, 0.9, 0.98):\n", + "\n", + " og = OptimalGrowthModel(f, np.log, β=β, s=0.05)\n", + " y_grid = og.y_grid\n", + "\n", + " v_solution = solve_model(og, verbose=False)\n", + "\n", + " σ_star = get_greedy(v_solution)\n", + " σ_func = lambda x: interp(y_grid, σ_star, x) # Define an optimal policy function\n", + " y = simulate_og(σ_func, og, α)\n", + " ax.plot(y, lw=2, alpha=0.6, label=rf'$\\beta = {β}$')\n", + "\n", + "ax.legend(loc='lower right')\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "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": "3.6.5" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/optimal_savings/toda_crra.ipynb b/optimal_savings/toda_crra.ipynb new file mode 100644 index 0000000..c995735 --- /dev/null +++ b/optimal_savings/toda_crra.ipynb @@ -0,0 +1,421 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Optimal Savings with Stochastic Financial Returns" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### John Stachurski \n", + "\n", + "Prepared for the fall semester 2018.\n", + "\n", + "Thanks to Natasha Watkins for help putting this together." + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "from numba import njit, prange\n", + "import quantecon as qe\n", + "import matplotlib.pyplot as plt" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The code below solves for the optimal savings and consumption rates by first obtaining the fixed point of the operator\n", + "\n", + "$$ Sg(z) = \\left\\{ 1 + (Kg(z))^{1/\\gamma} \\right\\}^\\gamma $$" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [], + "source": [ + "z_size = 20 # size of state space" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [], + "source": [ + "class OptimalSavings:\n", + " \n", + " def __init__(self,\n", + " γ=4,\n", + " β=np.linspace(0.9, 0.96, z_size),\n", + " R=np.linspace(1.05, 1.15, z_size),\n", + " mc=qe.tauchen(0.95, 0.1, n=z_size)):\n", + "\n", + " self.γ = γ\n", + " self.β = β\n", + " self.R = R\n", + " self.mc = mc\n", + " \n", + " Π = self.mc.P\n", + " self.K = β * R**(1 - γ) * Π\n", + "\n", + " r_K = max(abs(np.linalg.eigvals(self.K)))\n", + " print(f'Spectral radius is {r_K}\\n')\n", + "\n", + " if r_K >= 1:\n", + " raise ValueError('Spectral radius not less than one')" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [], + "source": [ + "def S_factory(op):\n", + " \"\"\"\n", + " Here `op` is an instance of OptimalSavings\n", + " \n", + " \"\"\"\n", + " γ = op.γ\n", + " K = op.K\n", + " \n", + " @njit\n", + " def S(g):\n", + " return (1 + (K @ g)**(1 / γ))**γ\n", + " \n", + " return S" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [], + "source": [ + "def solve_model(op,\n", + " use_parallel=True,\n", + " tol=1e-4,\n", + " max_iter=1000,\n", + " verbose=True,\n", + " print_skip=25):\n", + " \n", + " S = S_factory(op)\n", + "\n", + " # Set up loop\n", + " i = 0\n", + " error = tol + 1\n", + "\n", + " # Initialize g\n", + " g = np.ones(z_size)\n", + "\n", + " while i < max_iter and error > tol:\n", + " g_new = S(g)\n", + " error = np.max(np.abs(g - g_new))\n", + " i += 1\n", + " if verbose and i % print_skip == 0:\n", + " print(f\"Error at iteration {i} is {error}.\")\n", + " g[:] = g_new\n", + "\n", + " if i == max_iter:\n", + " print(\"Failed to converge!\")\n", + "\n", + " if verbose and i < max_iter:\n", + " print(f\"\\nConverged in {i} iterations.\")\n", + "\n", + " return g_new" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's solve the model and see in particular how the parameters affect the state contingent savings rate, which is\n", + "\n", + "$$ 1 - g^*(z)^{-1/\\gamma} $$" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Spectral radius is 0.7154363875415961\n", + "\n", + "Spectral radius is 0.6438927487874369\n", + "\n", + "Error at iteration 25 is 1104.584903146846.\n", + "Error at iteration 50 is 202.83508007034834.\n", + "Error at iteration 75 is 25.58057464905869.\n", + "Error at iteration 100 is 3.072077351695043.\n", + "Error at iteration 125 is 0.36624615878099576.\n", + "Error at iteration 150 is 0.04360801046277629.\n", + "Error at iteration 175 is 0.005190996147575788.\n", + "Error at iteration 200 is 0.0006178897165227681.\n", + "\n", + "Converged in 222 iterations.\n", + "Error at iteration 25 is 306.38461814922994.\n", + "Error at iteration 50 is 24.311201606284158.\n", + "Error at iteration 75 is 1.5277156051452039.\n", + "Error at iteration 100 is 0.09380224678534432.\n", + "Error at iteration 125 is 0.005738016423492809.\n", + "Error at iteration 150 is 0.0003507113378873328.\n", + "\n", + "Converged in 162 iterations.\n" + ] + } + ], + "source": [ + "op_1 = OptimalSavings()\n", + "op_2 = OptimalSavings(β=op_1.β * 0.9)\n", + "\n", + "g_star_1 = solve_model(op_1)\n", + "g_star_2 = solve_model(op_2)" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig, ax = plt.subplots()\n", + "\n", + "ax.plot(range(z_size), (1 - (g_star_1)**(-1/op_1.γ)), \n", + " label=\"high $\\\\beta$\")\n", + "ax.plot(range(z_size), (1 - (g_star_2)**(-1/op_2.γ)), \n", + " label=\"low $\\\\beta$\")\n", + "\n", + "ax.set_xlabel(\"$z$\")\n", + "ax.set_ylabel(\"savings rate\")\n", + "\n", + "ax.legend()\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now let's try with the interest rate." + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Spectral radius is 0.7154363875415961\n", + "\n", + "Spectral radius is 0.8344497886474358\n", + "\n", + "Error at iteration 25 is 1104.584903146846.\n", + "Error at iteration 50 is 202.83508007034834.\n", + "Error at iteration 75 is 25.58057464905869.\n", + "Error at iteration 100 is 3.072077351695043.\n", + "Error at iteration 125 is 0.36624615878099576.\n", + "Error at iteration 150 is 0.04360801046277629.\n", + "Error at iteration 175 is 0.005190996147575788.\n", + "Error at iteration 200 is 0.0006178897165227681.\n", + "\n", + "Converged in 222 iterations.\n", + "Error at iteration 25 is 8527.396701902107.\n", + "Error at iteration 50 is 6967.974429636553.\n", + "Error at iteration 75 is 2840.624110790435.\n", + "Error at iteration 100 is 969.6588715630933.\n", + "Error at iteration 125 is 314.1662402781076.\n", + "Error at iteration 150 is 100.17206293356139.\n", + "Error at iteration 175 is 31.78101348137716.\n", + "Error at iteration 200 is 10.067230146320071.\n", + "Error at iteration 225 is 3.1874166965135373.\n", + "Error at iteration 250 is 1.009021653328091.\n", + "Error at iteration 275 is 0.31940443464554846.\n", + "Error at iteration 300 is 0.10110548365628347.\n", + "Error at iteration 325 is 0.03200415556784719.\n", + "Error at iteration 350 is 0.010130651120562106.\n", + "Error at iteration 375 is 0.003206772613339126.\n", + "Error at iteration 400 is 0.001015076762996614.\n", + "Error at iteration 425 is 0.00032131391344591975.\n", + "Error at iteration 450 is 0.00010170903988182545.\n", + "\n", + "Converged in 451 iterations.\n" + ] + } + ], + "source": [ + "op_1 = OptimalSavings()\n", + "op_2 = OptimalSavings(R=op_1.R * 0.95)\n", + "\n", + "g_star_1 = solve_model(op_1)\n", + "g_star_2 = solve_model(op_2)" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig, ax = plt.subplots()\n", + "\n", + "ax.plot(range(z_size), (1 - (g_star_1)**(-1/op_1.γ)), \n", + " label=\"high $R$\")\n", + "ax.plot(range(z_size), (1 - (g_star_2)**(-1/op_2.γ)), \n", + " label=\"low $R$\")\n", + "\n", + "ax.set_xlabel(\"$z$\")\n", + "ax.set_ylabel(\"savings rate\")\n", + "\n", + "ax.legend()\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now let's see what happens in the last exercise if $\\gamma$ is a smaller number." + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Spectral radius is 0.9817880675015813\n", + "\n", + "Spectral radius is 0.9569286384125347\n", + "\n", + "Error at iteration 25 is 0.10939053068125215.\n", + "Error at iteration 50 is 0.044445013716073234.\n", + "Error at iteration 75 is 0.017980448973453633.\n", + "Error at iteration 100 is 0.007362855078422825.\n", + "Error at iteration 125 is 0.003043374285336853.\n", + "Error at iteration 150 is 0.0012642687681339027.\n", + "Error at iteration 175 is 0.0005264397738962145.\n", + "Error at iteration 200 is 0.00021943908838295556.\n", + "\n", + "Converged in 223 iterations.\n", + "Error at iteration 25 is 0.040711350108816546.\n", + "Error at iteration 50 is 0.005589487898059353.\n", + "Error at iteration 75 is 0.0007084105533428087.\n", + "\n", + "Converged in 99 iterations.\n" + ] + } + ], + "source": [ + "op_1 = OptimalSavings(γ=0.5)\n", + "op_2 = OptimalSavings(R=op_1.R * 0.95, γ=0.5)\n", + "\n", + "g_star_1 = solve_model(op_1)\n", + "g_star_2 = solve_model(op_2)" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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GpzD2gtO4omc0ETZxn6kE3AyLxUAbEYnDOWMYCVzjv4OIRAKZqloEPIBzZdTh5zYQkUaquhMYBPx2xJ0xFVxRkfLzhl28t2AT36/ZjgKD2jVmVJ+WDGjbiKq2NoSpRFwLC1UtEJHbgOk4l85OUtXVIjIeSFDVKcBZwBMiojjNULf6nlsoIvcCP4hzXp4IvOFWrcaUpawD+XyamMYHizaTuiuHhuE1+PPAU7mmV4xNvWHKXlEhHNgNtRu7+jZBPd2HMeVpRfpe3luwiSnLMzhUUER8ywZc17clQzo1oWY1u6LJlJH8g7AlETYvgE0LIO0XaNoF/jDthF7OpvswphwcKijkm+VbeW/BRpanZ1GrRlUu6xnNqN4t6dCsrtflmWBwcA9sXgSb58PmhbBlCRTlO9satYcuV0DcQNfLsLAw5gTsycnjg0WbeGfBJnZmH6JN49qMH96RS7o3t4WEzMnJSndCYdN85+xhh29oWpXq0Kw79LkZWvaDFr2hVsNyK8vCwpjjkLorh0nzUvk0MY3c/CIGtm3En66M48zWkXbZqzkxmSmQ8qMvIBZA1mbn8Rq1oUUv6DgCYvpA855Qw7s+LwsLY0qhqizeuIc35qbw/ZrtVK9ShUu6N+NP/VvRNsqmAjfHSdU5W1jzjfO1fZXzeHgjiOkLfW9xwiGqM1StOL+iK04lxlQwBYVFTFu1jbfmprA8PYsGtapz+9mtGdW3JY3r2Bxb5jgUFUHGElgzxQmIzBRAnFA4/5/Q5nyIOBUq8NmphYUxxWTn5vPJ4jQm/7yRLXsP0ioynMcu6cRlPaI5pYZd1WQCVFjgdEqv+QbWfAvZGVClGsQNgH63Q7sLoU6U11UGzMLCGJ8tew8yeV4qHy9OY/+hAnrHNeSRizsy6LTGVLEBdCYQBYec/oc1U2DtNDiYCdXCoPW50P5haHs+nNLA6ypPiIWFCXkr07OYODeFaSu3AnBh56b8qX8cXaLre1yZqRTyciB5pnMGsW465GVDzbpOMLQf5gRFjXCvqzxpFhYmZP2SmslLs5KZm7yLOjWr8ccz47ihXyzNbcZXU5qiItj0Myz7EJK+hvwcqBUBnS6F9hc7TU3VgmvOLwsLE1JUlbnJu3h59np+Sc0ksnYNxl5wGtf2jqGOjY8wpclMgeUfw/KPYO9mqFEHOl8Gna90rmSqQFcvlbXg/ZcZ46eoSPlh7Q5enpXM8vQsmtYLY9ywDlx1eox1WptjO5QNq79yziI2zwcEWp0Fgx6C0y70dOxDebKwMEGtsEiZtnIrr8xez9pt2cQ0rMUTIzozokdzm6/JHF1REaT+5JxBJE2BgoMQ0RrOeQi6XAX1Qm/FSQsLE5TyC4v4aukWXv1xAym7cmjduDbPXdWVYV2aUa1qFa/LMxXV7g3OGcTyj2FfOtSsB11HQrdrITq+Qo+DcJuFhQkqufmFfJqYzms/bmDL3oN0aFqXV6/twfkdm9jlr6ZkuVmw+ksnJNIWgVSBU8+BweOdsRDVbQAmWFiYIHEgr4APF21m4pwUdmQfontMfR69pCNnt2tsczaZkmUsg4S3YOVnkH8AGp0G5413OqvrNvW6ugrHwsJUajmHCnh7/kbempdKZk4e/U6N4PmrutH31AgLCfN7+Qeds4jFb8GWBKh2CnS+HHr+AZr3COlmptJYWJhKKTe/kPcXbuLVHzewOyePs9s14rZBrenZsvymbDaVyO4NkDAJln3grA8R2RaGPOX0R5xigy8DYWFhKpW8giI+SUjj5VnJbN93iP5tIrlncDu6tbAfeFNMYQGs+845i0iZ7czLdNpFcPqfIPZMO4s4Tq6GhYgMAV7AWYP7TVV9stj2lsAkoBGQCYxS1XS/7XWBNcCXqnqbm7Waiq2gsIgvlm7hxR+SSd9zkNNjG/DCyO70aRXhdWmmotm3FZa8C4lvO5P31W0OZz8IPa6DOk28rq7Sci0sRKQq8ApwHpAOLBaRKaqa5LfbM8C7qvqOiAwCngCu89v+KPCTWzWaiq+oSPl25Vaen7mOlF05dImux+OXdmZAG1tsyPhRdcZFLH4L1k4FLXSuaLrwGWf67yAeWV1e3DyCvYD1qpoCICIfA8MB/7DoANztuz0b+OrwBhHpCUQB/wVKXUzcBBdVZUbSdp6buY6127JpF1WH16/ryeAOURYS5n8OZcPSD2Dxm7A72ZnRte8tTod1xKleVxdU3AyL5kCa3/10oHexfZYDl+E0VV0K1BGRCGAPMAHnLOOco72BiIwBxgDExMSUWeHGO6rKnORdTJjxKyvSs2gVGc6LV3fnos5NbZyE+Z+9m2HR605z06F9EH06XPo6dLjExkW4xM2wKOknW4vdvxd4WURGA3OALUABcAswTVXTjvVXpKpOBCYCxMfHF39tU8ksTNnNhBm/snjjHprXP4WnL+/CiO7NbcS1+Z+0X2DBK856EQh0vAT63ArRPb2uLOi5GRbpQAu/+9FAhv8OqpoBjAAQkdrAZaqaJSJ9gf4icgtQG6ghIvtVdayL9RqPLEvby4QZvzI3eRdRdWvy6CWduCq+BTWqWUgYnKua1nwNC/7tjI0Iq+esNNdrTEjO0eQVN8NiMdBGROJwzhhGAtf47yAikUCmqhYBD+BcGYWqXuu3z2gg3oIi+GzclcPT09cybeU2GobX4MEL2zOqT0vCqtsEfwY4uBeWvAOLJjrzNDVsBUOfga5XQ83aXlcXclwLC1UtEJHbgOk4l85OUtXVIjIeSFDVKcBZwBMiojjNULe6VY+pODJz8njxh2Q+WLSJalWqcOc5bbhpQCtq17QrVgzOALpFrzkd1/k5ENv/f1c1VbGzTa+IanA09cfHx2tCQoLXZZhjyM0vZNLPqbw6ewM5eQVcdXoMd5/bhsZ1rUMy5Kk6K88t+Df8Os0ZQNf5CuhzMzTt4nV1QU1EElW11CtO7U8547rCIuXLpVuYMONXtmblcm77xtw/5DTaRNXxujTjtcICWP0FzH8Jtq2AUxrCgHudUdY2gK5CsbAwrpqzbidPfLeWNVv30TW6Hs9d1c1GXRvIO+DM0zT/Recy2Mh2MOwFZ2Gh6rYGekVUaliISFvgVSBKVTuJSBfgYlV9zPXqTKWVlLGPJ75bw9zkXbRoeIqNlTCOg3ucAXQLX4MDu6BFb7jgX9BmsPVHVHCBnFm8Afwf8DqAqq4QkQ8BCwvzOxl7DzJhxjq+WJpO3bDqPHhhe67r29KWMA11+7bCwlcgYTLk7Xc6q8+8G1r29boyE6BAwqKWqv5SbHBcgUv1mEpqX24+r/64gUnzUlFgTP9W3HJWa+rVqu51acZLu9bD/BecZUqLCqDTZXDGXdCkk9eVmeMUSFjsEpFT8Y2+FpHLga2uVmUqjfzCIj5YuIkXfkhmz4F8Lu3enHsGtyW6QS2vSzNeylgK856DpClQrSb0uB763gYN47yuzJygQMLiVpwpNU4TkS1AKnDtsZ9iQsGcdTsZ/20S63fsp9+pEfxtaHs6Na/ndVnGK6qQOgfmPQspP0LNetD/r9D7L1C7sdfVmZMUSFioqp4rIuFAFVXN9o3KNiEqdVcOj09N4vs1O2gZUYs3r4/nnPa21nXIKiqCtd86ZxIZS6B2FJz7CMT/wZmawwSFQMLic6CHqub4PfYZYDN3hZjs3HxenrWeST+nUrNaVR644DRGnxFrndeh6vAYiTn/gl3roEEcXPS8Mx2HzfwadI4aFiJyGtARqCciI/w21QXskxBCioqUz5ak8/R/f2XX/kNc0TOa/xvSjsZ17GMQkgoLYOWnTkhkboDGHeDySc704FXsD4dgdawzi3bARUB9YJjf49nATW4WZSqOxE2ZjJuSxMotWfSIqc9bN8TT1da7Dk2F+bDiE5jzDOxJhajOcOV7zrrWNkYi6B01LFT1a+BrEemrqgvKsSZTAWzNOsiT363l62UZNKkbxgsju3Fx12bWLxGKCvJg+UcwdwLs3QRNu8LID6HdULDPQ8gIpM9iqYjcitMkdaTdQVVvdK0q45nc/EImzknh1R83UKjK7YNac/NZp1Krhs0ME3IKDjlTcsx9DrI2Q7MeMNQ32tpCIuQE8hvgPWAtcD4wHuey2TVuFmXKn6oybeU2/jltDVv2HmRo5yY8cEF7WjS08RIhJz8Xlr4H85531pGIPh0ueg5an2MhEcICCYvWqnqFiAxX1Xd8U31Md7swU36SMvbxyDerWZSayWlN6vDRTX3oe6pN9hdy8nOdxYbmPQ/ZGdCiDwx/CVqdbSFhAgqLfN/3vSLSCdgGxLpWkSk3WQfzeXbGr7y3cBP1TqnOY5d0YuTpLWzN61CTdwAS34afX4D926DlGXDpaxA3wELCHBFIWEwUkQbAg8AUnDWx/+FqVcZVqsoXS7bwxHdryMzJY1SfltxzXjubxynUFBxyQmLuBNi/3VmR7vK3IPZMryszFdAxw0JEqgD7VHUPzrKnrY7nxUVkCPACzrKqb6rqk8W2t8RZd7sRkAmMUtV0EemGMy16XaAQeFxVPzme9zYlW7ttH//4ahWLN+6hW4v6vP2HXjZFR6gpzIdlH8JPTzt9ErH94Yq3oWU/ryszFdgxw0JVi3zraP/neF9YRKoCrwDnAenAYhGZoqpJfrs9A7zr6wsZBDwBXAccAK5X1WQRaQYkish0Vd17vHUYR3ZuPs9/n8zb8zdSN6waT47ozJXxLWx9iVBSVAirPocfn4DMFGgeD5e8AnEDrbnJlCqQZqiZInIv8AlwZMoPVc0s5Xm9gPWqmgIgIh8DwwH/sOgA3O27PRv4yvfa6/zeJ0NEduCcfVhYHCdVZcryDB6fuoad+w8x8vQY7ju/HQ3Ca3hdmikvqrDmG5j9T9i5xhlMd/Un0PZ8CwkTsEDC4vB4ilv9HlNKb5JqDqT53U8HehfbZzlwGU5T1aVAHRGJUNXdh3cQkV5ADWBDALUaP8nbs3no69UsSNlN5+b1mHh9PN1s9HXoUIXkmTD7Mdi6HCLbOs1N7YfbiGtz3EoNC1U90RlmS/qTRYvdvxd4WURG4/SJbMFvYSURaYozzuMGVS363RuIjAHGAMTExJxgmcEn51ABL85K5q25qYTXrMZjl3Ti6l4xVLUmp9CROgdmPQZpi6B+S7jkNehypc3dZE6Ym8Ny04EWfvejgQz/HVQ1AxgBICK1gctUNct3vy4wFXhQVReW9AaqOhFnrQ3i4+OLB1HIUVW+W7WNR79NYmtWLlfGR3P/kNOIqF3T69JMeUn7BWY96oRFnWbOYLru10FVu9LNnBw3w2Ix0Ma39sUWYCRwjf8OIhIJZPrOGh7AuTIKEakBfInT+f2pizUGjZSd+3l4ymrmJu+ifdO6vHxNd3q2bOh1Waa8bF0Osx6H5OlQKxLOfwLib7Spwk2ZcS0sVLXAdyXVdJxLZyep6moRGQ8kqOoU4CzgCRFRnGaow/0iVwIDgAhfExXAaFVd5la9lVVufiEvz1rPxDkp1KxWhXHDOjCqT0sbWBcqdq13ziSSvnIWGjrnIej1Z6hZ2+vKTJAR1WO33ojIGcAyVc0RkVFAD+AFVd1UHgUGKj4+XhMSErwuo1zN/nUHD329irTMg1zavTkPDD3N1pgIFdnb4KenIPEdqBYGfW91vk6xCxjM8RGRRFWNL22/QM4sXgW6ikhX4D7gLeBdYODJlWhO1LasXMZ/u5ppK7fRqlG4zeUUSnL3wfwXYcErUJjnNDUNvM/WuDauCyQsClRVRWQ4zhnFWyJyg9uFmd8rKCzi3QWbmDDjVwqKlHsHt+WmAa1sWdNQUHAIEiY5q9Md2A0dR8CgByHiVK8rMyEikLDIFpEHgFHAAN/IbLu0opwtS9vL379cyeqMfQxs24jxwzvSMiLc67KM24qKYNVnTr/E3s3O5H7nPgLNe3hdmQkxgYTFVThXMf1RVbeJSAzwL3fLModlHcznmem/8v6iTTSqXZNXrunB0M5NbMW6YKcKG36AmeNg+0po0hlGfQGnDrJR18YTgQzK2wY863d/M06fhXHR4Wk6Hv12DZk5h7ihbyz3DG5LnTA7qQt6W5bA9w87YyXqt4QRb0Kny2zUtfFUqWEhItn8fuR1FpAA3HN47idTdlJ35fCPr1Yxb/0uukTXY/LDziRaAAAY8klEQVTo0+kcbTPDBr3dG5zmptVfQq0IuOBp6PkHqGbzeBnvBdIM9SzOyOsPcabwGAk0AX7FGUR3llvFhZrc/EJe+2kD//5xAzWrVmH88I5c27ulTdMR7Pbv8F0G+zZUrQkD74e+t0FYXa8rM+aIQMJiiKr6TwA4UUQWqup4EfmbW4WFmnnJu/jH16tI3ZXDsK7N+MeF7Wlc18ZMBLW8A84lsD8/DwW50HM0DLgP6kR5XZkxvxNIWBSJyJXAZ777l/ttC/n5mE7Wjn25PD5tDV8vy6BlRC3evbEXA9o28ros46aiIljxidPktG8LnHaRc4VTZGuvKzPmqAIJi2txphD/N044LARGicgpwG0u1hbU8guLeGf+Rp7/Ppm8giLuGNSaW85uTVh1GzMR1DbOg+l/c+ZyatYdRrwBsWd4XZUxpQrkaqgUYNhRNs8r23JCw6KU3Tz09Wp+3Z7NWe0a8fCwjsRF2piJoLZrPcx8CH6dCnWjnZDodLld4WQqjUCuhmoE3ATE+u+vqjce7TmmZDv25fLPaWv4alkGzeufwsTrenJehygbMxHMDmQ6ndeL33TmcDrnIehzC1Q/xevKjDkugTRDfQ3MBb4HCt0tJzgVb3K6fVBrbjmrNafUsCanoFVwCH6Z6EzPcSgbetwAZ//N5nAylVYgYVFLVe93vZIgZU1OIUYVkr52BtXt2Qitz4PBj0Lj9l5XZsxJCSQsvhWRoao6zfVqgog1OYWg9ASY/ndIWwiNO8J1XzrTcxgTBAIJizuBv4nIISAfZ2CeqqqNGCpBQWER7yzYxHMz11mTU6jYswl+eARWfQ61o2DYi9B9lK13bYJKIFdD1SmPQoKBNTmFmLwcmPsszH8JpIozoO6MO22VOhOUjhoWInKaqq4VkRLnQlbVJaW9uIgMwRmjURV4U1WfLLa9Jc6UIY2ATGCUqqb7tt0APOjb9TFVfSeAf48nrMkpxKjCyk9h5sOQnQGdr4Rzx0G95l5XZoxrjnVm8VdgDDChhG0KHLMx1rfuxSvAeUA6sFhEpqhqkt9uzwDvquo7IjIIeAK4TkQaAg8D8b73SvQ9d0+A/65ysScnjzfnpfD2zxvJL1RrcgoFWxLhu7GQ/oszqO6KtyGmd6lPM6ayO2pYqOoY3/ezT/C1ewHrD89KKyIfA8MB/7DoANztuz0b+Mp3+3xgpqpm+p47ExgCfHSCtZSpvQfyeHNuKm/P30hOXgEXdm7KPYPbWZNTMMveBj+Mh2UfOP0Sl7wKXUbaoDoTMgIZlLcc+Bj4j6puOI7Xbg6k+d1PB4r/CbYcuAynqepSoI6IRBzluZ6f4xcPiaGdm3LnOW1oG2XdOkErPxcW/hvmTnDWvD7zbuh/D9S0/3MTWgK5GupinNXy/iMiRcAnOMGxuZTnldRgX3ziwXuBl0VkNDAH2AIUBPhcRGQMTlMZMTExpZRz4vYeyOOtealM/nkj+w85ZxJ3nNOGdk3sF0bQUoW1U2HG353xEu0uhPMfg4atvK7MGE8EcjXUJuBp4GkRaQP8A3gKp9P6WNKBFn73o3HWxfB/7QxgBICI1AYuU9UsEUnnt+tkRAM/llDbRGAiQHx8fJnPgJt1IJ+35qUw+eeNZPtC4vZzWnNaE7tqOKhtT4L/joXUn6DRaTZewhgCO7NARGKBK3HOMAqB+wJ42mKgjYjE4ZwxjMRZy9v/dSOBTFUtAh7AuTIKYDrwTxFp4Ls/2Le9XGQdyOetn1OZPC+V7EMFDO3chDvOaWMhEewOZMKPT8Dit5xmpgv+BfE3QtWAfkyMCWqB9FksAqoDnwJXBLqMqqoWiMhtOL/4qwKTVHW1iIwHElR1Cs7ZwxMiojjNULf6npspIo/iBA7A+MOd3W4qHhIXdHJCon1TC4mgVlgAiZNh9uOQuw9O/yOc9QDUauh1ZcZUGKJ67Nabw+MtyqmeExYfH68JCQkn9Nysg/lMmpfKpJ9Tyc4tYEjHJtx5roVESEidC9/dBzuSIG4ADHkKojp4XZUx5UZEElU1vrT9AumzWCsiFwIdgTC/x8efXIkVQ+quHC5+ed6RkLjjnDZ0aGYhEfT2ZcCMB50pOurHwFXvOyvW2UBKY0oUSDPUa0At4GzgTZxlVX9xua5yExtRi6t7xTC8WzM6NqvndTnGbQV5zqWwPz0NRQUwcCyceZetL2FMKQLpueunql1EZIWqPiIiE4Av3C6svIgIfxtq00eHhA2zYNp9sDsZ2g2F8/8JDeO8rsqYSiGQsDjo+35ARJoBuwH7CTOVx940mP4ArPnGGSdxzafQdrDXVRlTqQS6nkV94F/AEpzBcW+6WpUxZSE/Fxa8BHN805sN+gf0ux2q1fS2LmMqoUA6uB/13fxcRL4FwlQ1y92yjDlJ66bDd/fDnlToMBwGPw71W5T+PGNMiUqdBU1ErhCRw/Na/B8wWUS6u1uWMScoMxU+HAkfXglVqzujr69814LCmJMUSDPUP1T1UxE5E2c22GeA1/j9pIDGeCfvAPz8PMx73gmJ8x6F3n+BajW8rsyYoBBIWBT6vl8IvKqqX4vIOPdKMuY4HJ7w778PQNZm6HwFnDce6jbzujJjgkogYbFFRF4HzgWeEpGaBNB8ZYzr9mx0LoVNng6NO8DoqRB7ptdVGROUAgmLK3EWHnpGVfeKSFOcvgtjvFFwCOa/CHOegSrVnM7r3n92mp+MMa4I5GqoA/gNwlPVrcBWN4sy5qhSfoSp9zoD6zoMh/OfsLWvjSkHNveyqRyyt8H0v8Oqz6BBHFz7ObQ51+uqjAkZFhamYisqhMVvwqzHoCAXBt7vLG1qczkZU64sLEzFlZ4I394F21ZAq7PhwgkQcarXVRkTkiwsTMVzcA/8MB4SJkPtKLh8MnS81KYPN8ZDFham4lCF5R8760wczIQ+Nzsr1oXZ+iLGeM3CwlQMO9bA1Htg088QfTpc+CU07eJ1VcYYH1cH14nIEBH5VUTWi8jYErbHiMhsEVkqIitEZKjv8eoi8o6IrBSRNSLygJt1Gg/l5cDMh+G1M2H7ahj2Atw4w4LCmArGtTMLEakKvAKcB6QDi0Vkiqom+e32IPAfVX1VRDoA04BY4Aqgpqp2FpFaQJKIfKSqG92q13ggeSZM/Svs3QzdRsF5j0B4pNdVGWNK4GYzVC9gvaqmAIjIx8BwwD8sFDjcIF0PyPB7PFxEqgGnAHnAPhdrNeUpexv8dyys/hIi28LoaRB7htdVGWOOwc2waA6k+d1P5/cz1Y4DZojI7UA4zvxTAJ/hBMtWnPW/71bVzOJvICJjgDEAMTExZVm7cUNRESROgu8fcabsOPvvcMadthiRMZWAm30WJV3nqMXuXw28rarRwFDgPRGpgnNWUgg0w1nC9R4RafW7F1OdqKrxqhrfqFGjsq3elK3tq2HSYKcTu1k3uHk+DLzPgsKYSsLNM4t0wH/FmWj+18x02B9xJilEVReISBgQCVwD/FdV84EdIvIzEA+kuFivcUPeAfjpKVjwMoTVg0tfhy5X2ZgJYyoZN88sFgNtRCRORGoAI4EpxfbZDJwDICLtgTBgp+/xQeIIB/oAa12s1bgh+Xv4dx9nUaKuI+G2BOe7BYUxlY5rZxaqWiAitwHTgarAJFVdLSLjgQRVnQLcA7whInfjNFGNVlUVkVeAycAqnOasyaq6wq1aTRnL3u7rwP4CItrYOhPGBAFRLd6NUDnFx8drQkKC12WEtqIiWPI2zBwHBQeh/71w5l3WL2FMBSYiiaoaX9p+NoLblI3tSfDNnZD+C8T2h4ueg8g2XldljCkjFhbm5OQfdDqw578ENevCJa9Zv4QxQcjCwpy4lJ+cKcQzU6DbtXDeoxAe4XVVxhgXWFiY43cgE2b8A5a976xad/0UaDXQ66qMMS6ysDCBU4VVnztXOh3IdFasG3i/rVpnTAiwsDCB2ZvmjL5Ong7NesB1X0KTzl5XZYwpJxYW5tiKCuGXifDDo4DC+U9A7z9DlapeV2aMKUcWFubotq+GKbfDlkRofS5c+Cw0aOl1VcYYD1hYmN/Lz4U5T8PPL0BYfRjxJnS+3C6HNSaEWViY30qd6wyuy9wAXa+B8x+HWg29rsoY4zELC+M4uMe5HHbpe9AgFq77Ck492+uqjDEVhIVFqFOFpK9g2n1wYLezGNHAsVCjlteVGWMqEAuLULYvA6beC79OhabdYNRn0LSr11UZYyogC4tQdGR22IehMN+ZpqPPLVDVPg7GmJLZb4dQs2u904G9aZ4zO+zFL0LD361Ya4wxv2FhESoK852ZYX98EqqFwcUvQffr7HJYY0xALCxCQcYyZ3DdthXQfhgMfQbqNPG6KmNMJeLmGtyIyBAR+VVE1ovI2BK2x4jIbBFZKiIrRGSo37YuIrJARFaLyEoRCXOz1qCUf9Dpl3hjEOzfDle+C1e9b0FhjDlurp1ZiEhV4BXgPCAdWCwiU1Q1yW+3B4H/qOqrItIBmAbEikg14H3gOlVdLiIRQL5btQaljfNgyh3O4Lruo2DwY3BKA6+rMsZUUm42Q/UC1qtqCoCIfAwMB/zDQoG6vtv1gAzf7cHAClVdDqCqu12sM7jkZsHMhyDxbWdw3fVfQ6uzvK3JGFPpuRkWzYE0v/vpQO9i+4wDZojI7UA4cK7v8baAish0oBHwsao+7WKtwWHtVGca8f3boe9tcPbfbXCdMaZMuBkWJV1mo8XuXw28raoTRKQv8J6IdPLVdSZwOnAA+EFEElX1h9+8gcgYYAxATExMWddfeezfAdP+zxmJHdUJRn4AzXt6XZUxJoi4GRbpQAu/+9H8r5npsD8CQwBUdYGvEzvS99yfVHUXgIhMA3oAvwkLVZ0ITASIj48vHkTBTxWWfQjT/wb5B2DQg3DGXVC1uteVGWOCjJtXQy0G2ohInIjUAEYCU4rtsxk4B0BE2gNhwE5gOtBFRGr5OrsH8tu+DpOZCu9dAl/fAo3bw19+hgH/Z0FhjHGFa2cWqlogIrfh/OKvCkxS1dUiMh5IUNUpwD3AGyJyN04T1WhVVWCPiDyLEzgKTFPVqW7VWqkUFsCiV2HW41ClGlw4AXreCFVcvQraGBPixPndXPnFx8drQkKC12W4a9sqmHIbZCyFtkOcoKgX7XVVxphKzNcfHF/afjaCuzIovnLd5ZOg4wibqsMYU24sLCq6TfOdwXW7k23lOmOMZywsKqrcLPh+HCRMgvoxcN2XcOogr6syxoQoC4uKaO003+C6bb7BdX+DGuFeV2WMCWEWFhXJ/h3w3X2w+kto3NGZ9C/aBtcZY7xnYVERlDS4rt+dUK2G15UZYwxgYeG93Rtg6l8h5UeI6QvDXoRGbb2uyhhjfsPCwiv5uTDvWZj3nLNynQ2uM8ZUYBYWXlj/PUy9F/akQucrYPDjUCfK66qMMeaoLCzK074M+O9YSPoaIlrbWhPGmErDwqI8FBbAL6/D7H9CUQGc/SCccQdUq+l1ZcYYExALC7el/QLf/hW2r4Q2g+GCp6FhnNdVGWPMcbGwcMuBTPj+YVjyLtRtDle+B+2H2XxOxphKycKirBUVwfIPnXWwD+51RmCf9QDUrO11ZcYYc8IsLMrS9tXONB2bF0CLPnDRsxDV0euqjDHmpFlYlIVD++GnJ2HBvyGsHlz8MnS71sZMGGOChoXFySjIg6XvwZxnIDsDelwP5z5iU4gbY4KOhcWJKMiDZR/A3AmQlQbRveCKtyGmt9eVGWOMK1xtJxGRISLyq4isF5GxJWyPEZHZIrJURFaIyNAStu8XkXvdrDNghfmQ+A681BO+vQtqR8Goz+GPMywojDFBzbUzCxGpCrwCnAekA4tFZIqqJvnt9iDwH1V9VUQ6ANOAWL/tzwHfuVVjwArzYfnHMOdfsHcTNOvhdF63PtcuhTXGhAQ3m6F6AetVNQVARD4GhgP+YaFAXd/tekDG4Q0icgmQAuS4WOOxFRbAyv/AT0878zg17QZD/+UMrrOQMMaEEDfDojmQ5nc/HSjeVjMOmCEitwPhwLkAIhIO3I9zVnLUJigRGQOMAYiJiSmrup2QWPWZExKZG6BJF7j6Y2g7xELCGBOS3AyLkn6rarH7VwNvq+oEEekLvCcinYBHgOdUdb8c45ezqk4EJgLEx8cXf+3jV1QIqz6Hn56C3euhSWcY+SG0G2ohYYwJaW6GRTrQwu9+NH7NTD5/BIYAqOoCEQkDInHOQC4XkaeB+kCRiOSq6suuVFpU6Cxl+tNTsGsdRHVyljRtd6GNlTDGGNwNi8VAGxGJA7YAI4Friu2zGTgHeFtE2gNhwE5V7X94BxEZB+x3LSj2bIQPr4Kda6FxB7jiHWh/sYWEMcb4cS0sVLVARG4DpgNVgUmqulpExgMJqjoFuAd4Q0TuxmmiGq2qJ9+cdDzqNocGsTDwfuhwiYWEMcaUQMr7d7Nb4uPjNSEhwesyjDGmUhGRRFWNL20/+zPaGGNMqSwsjDHGlMrCwhhjTKksLIwxxpTKwsIYY0ypLCyMMcaUysLCGGNMqSwsjDHGlCpoBuWJyE5g00m8RCSwq4zKcYPVd3KsvpNj9Z2cilxfS1VtVNpOQRMWJ0tEEgIZxegVq+/kWH0nx+o7ORW9vkBYM5QxxphSWVgYY4wplYXF/0z0uoBSWH0nx+o7OVbfyano9ZXK+iyMMcaUys4sjDHGlCqkwkJEhojIryKyXkTGlrC9poh84tu+SERiy7G2FiIyW0TWiMhqEbmzhH3OEpEsEVnm+3qovOrzq2GjiKz0vf/vFhARx4u+Y7hCRHqUY23t/I7NMhHZJyJ3FdunXI+hiEwSkR0issrvsYYiMlNEkn3fGxzluTf49kkWkRvKsb5/icha3//flyJS/yjPPeZnwcX6xonIFr//w6FHee4xf95drO8Tv9o2isiyozzX9eNXplQ1JL5wVuvbALQCagDLgQ7F9rkFeM13eyTwSTnW1xTo4btdB1hXQn1nAd96fBw3ApHH2D4U+A4QoA+wyMP/720415B7dgyBAUAPYJXfY08DY323xwJPlfC8hkCK73sD3+0G5VTfYKCa7/ZTJdUXyGfBxfrGAfcG8P9/zJ93t+ortn0C8JBXx68sv0LpzKIXsF5VU1Q1D/gYGF5sn+HAO77bnwHniIiUR3GqulVVl/huZwNrgObl8d5lbDjwrjoWAvVFpKkHdZwDbFDVkxmoedJUdQ6QWexh/8/ZO8AlJTz1fGCmqmaq6h5gJjCkPOpT1RmqWuC7uxCILuv3DdRRjl8gAvl5P2nHqs/3u+NK4KOyfl8vhFJYNAfS/O6n8/tfxkf28f2wZAER5VKdH1/zV3dgUQmb+4rIchH5TkQ6lmthDgVmiEiiiIwpYXsgx7k8jOToP6ReH8MoVd0Kzh8JQOMS9qkox/FGnDPFkpT2WXDTbb5msklHacarCMevP7BdVZOPst3L43fcQiksSjpDKH4pWCD7uEpEagOfA3ep6r5im5fgNKt0BV4CvirP2nzOUNUewAXArSIyoNj2inAMawAXA5+WsLkiHMNAVITj+HegAPjgKLuU9llwy6vAqUA3YCtOU09xnh8/4GqOfVbh1fE7IaEUFulAC7/70UDG0fYRkWpAPU7sFPiEiEh1nKD4QFW/KL5dVfep6n7f7WlAdRGJLK/6fO+b4fu+A/gS53TfXyDH2W0XAEtUdXvxDRXhGALbDzfN+b7vKGEfT4+jr0P9IuBa9TWwFxfAZ8EVqrpdVQtVtQh44yjv6/XxqwaMAD452j5eHb8TFUphsRhoIyJxvr88RwJTiu0zBTh81cnlwKyj/aCUNV/75lvAGlV99ij7NDnchyIivXD+/3aXR32+9wwXkTqHb+N0hK4qttsU4HrfVVF9gKzDTS7l6Kh/0Xl9DH38P2c3AF+XsM90YLCINPA1swz2PeY6ERkC3A9crKoHjrJPIJ8Ft+rz7wO79CjvG8jPu5vOBdaqanpJG708fifM6x728vzCuVJnHc5VEn/3PTYe54cCIAyn6WI98AvQqhxrOxPnNHkFsMz3NRT4C/AX3z63AatxruxYCPQr5+PXyvfey311HD6G/jUK8IrvGK8E4su5xlo4v/zr+T3m2THECa2tQD7OX7t/xOkH+wFI9n1v6Ns3HnjT77k3+j6L64E/lGN963Ha+w9/Dg9fIdgMmHasz0I51fee77O1AicAmhavz3f/dz/v5VGf7/G3D3/m/PYt9+NXll82gtsYY0ypQqkZyhhjzAmysDDGGFMqCwtjjDGlsrAwxhhTKgsLY4wxpbKwMMYYUyoLC2OMMaWysDDGRSIyy29tg1wRucLrmow5ETYoz5hyICI3A2cDV6tqodf1GHO8qnldgDHBTkSux5nc8DILClNZWVgY4yJfs9O1wHBVzfe6HmNOlIWFMS4RkYtwluq9SFVzva7HmJNhfRbGuEREduOsh5Lje+glVX3Lw5KMOWEWFsYYY0pll84aY4wplYWFMcaYUllYGGOMKZWFhTHGmFJZWBhjjCmVhYUxxphSWVgYY4wplYWFMcaYUv0/b5VEoN0NQXcAAAAASUVORK5CYII=\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig, ax = plt.subplots()\n", + "\n", + "ax.plot(range(z_size), (1 - (g_star_1)**(-1/op_1.γ)), \n", + " label=\"high $R$\")\n", + "ax.plot(range(z_size), (1 - (g_star_2)**(-1/op_2.γ)), \n", + " label=\"low $R$\")\n", + "\n", + "ax.set_xlabel(\"$z$\")\n", + "ax.set_ylabel(\"savings rate\")\n", + "\n", + "\n", + "ax.legend()\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "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": "3.6.5" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +}