diff --git a/solow_model.ipynb b/solow_model.ipynb new file mode 100644 index 0000000..874ff63 --- /dev/null +++ b/solow_model.ipynb @@ -0,0 +1,1215 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": { + "internals": { + "slide_type": "subslide" + }, + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "
\n", + "
\n", + "\n", + "This notebook demonstrates the functionality of the `quantecon.models.solow` module. The code was developed with funding from the Scottish Graduate Programme in Economics (SGPE) and the Scottish Institute for Research in Economics (SIRE). The code has found widespread use in my own research and teaching and it is my fervent hope that others will adapt and contribute to the development of these notebooks for use in their own research and teaching.\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false, + "internals": {}, + "slideshow": { + "slide_type": "-" + } + }, + "outputs": [], + "source": [ + "%matplotlib inline" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false, + "internals": {}, + "slideshow": { + "slide_type": "-" + } + }, + "outputs": [], + "source": [ + "import matplotlib.pyplot as plt\n", + "import seaborn as sns\n", + "import numpy as np\n", + "import sympy as sym\n", + "\n", + "from quantecon.models import solow" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "internals": {}, + "slideshow": { + "slide_type": "-" + } + }, + "source": [ + "# 0. Motivation\n", + "\n", + "The typical economics graduate student places great faith in the analytical mathematical tools that he or she was taught as an undergraduate. In particular this student is likely under the impression that virtually all economic models have closed-form solutions. At best the typical student believes that if he or she were to encounter an economic model without a closed-form solution, then simplifying assumptions could be made that would render the model analytically tractable without sacrificing important economic content. \n", + "\n", + "The typical economics student is, of course, wrong about general existence of closed-form solutions to economic models. In fact the opposite is true: most economic models, particular dynamic, non-linear models with meaningful constraints (i.e., most any *interesting* model) will fail to have an analytic solution. I the objective of this notebook is to demonstrate this fact and thereby motivate the use of numerical methods in economics more generally using the [Solow model of economic growth](http://faculty.smu.edu/tosang/pdf/Solow_1956.pdf). \n", + "\n", + "Economics graduate students are very familiar with the Solow growth model. For many students, the Solow model will have been one of the first macroeconomic models taught to them as undergraduates. Indeed, Greg Mankiw's [*Macroeconomics*](http://www.macmillanhighered.com/Catalog/product/macroeconomics-eighthedition-mankiw), the dominant macroeconomics textbook for first and second year undergraduates, devotes two full chapters to motivating and deriving the Solow model. The first few chapters of David Romer's [*Advanced Macroeconomics*](http://highered.mheducation.com/sites/0073511374/index.html), one of the most widely used final year undergraduate and first-year graduate macroeconomics textbook, are also devoted to the Solow growth model and its descendants.\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "internals": {}, + "slideshow": { + "slide_type": "-" + } + }, + "source": [ + "## 0.1 The basic Solow growth model\n", + "The Solow model can be reduced down to a single non-linear differential equation and associated initial condition describing the time evolution of capital stock (per unit effective labor), $k(t)$.\n", + "\n", + "$$ \\dot{k}(t) = sf(k(t)) - (n + g + \\delta)k(t),\\ k(t) = k_0 \\tag {0.1.1} $$\n", + "\n", + "The parameter $0 < s < 1$ is the fraction of output invested and the parameters $n, g, \\delta$ are the rates of population growth, technological progress, and depreciation of physical capital. The intensive form of the production function $f$ is assumed to be to be strictly concave with \n", + "\n", + "$$ f(0) = 0,\\ lim_{k\\rightarrow 0}\\ f' = \\infty,\\ lim_{k\\rightarrow \\infty}\\ f' = 0. \\tag{0.1.2} $$ \n", + "\n", + "A common choice for the function $f$ which satisfies the above conditions is known as the Cobb-Douglas production function.\n", + "\n", + "$$ f(k(t)) = k(t)^{\\alpha} $$\n", + "\n", + "Assuming a Cobb-Douglas functional form for $f$ also makes the model analytically tractable (and thus contributes to the typical economics student's belief that all such models \"must\" have an analytic solution). [Sato 1963](http://www.jstor.org/stable/2296026) showed that the solution to the model under the assumption of Cobb-Douglas production is\n", + "\n", + "$$ k(t) = \\Bigg[\\bigg(\\frac{s}{n+g+\\delta}\\bigg)\\bigg(1 - e^{-(n+g+\\delta)(1-\\alpha)t}\\bigg)+ k_0^{1-\\alpha}e^{-(n+g+\\delta)(1-\\alpha)t}\\Bigg]^{\\frac{1}{1-\\alpha}}. \\tag{0.1.3} $$\n", + "\n", + "A notable property of the Solow model with Cobb-Douglas production is that the model predicts that the shares of real income going to capital and labor should be constant. Denoting capital's share of income as $\\alpha_K(k)$, the model predicts that \n", + "\n", + "$$ \\alpha_K(k(t)) \\equiv \\frac{\\partial \\ln f(k(t))}{\\partial \\ln k(t)} = \\alpha \\tag{0.1.4} $$\n", + "\n", + "Note that the prediction is that factor shares are constant along both the balanced growth path *and* during the disequilibrium transient (i.e., the period in which $k(t)$ is varying). We can test this implication of the model using data from the newest version of the [Penn World Tables (PWT)](http://www.rug.nl/research/ggdc/data/penn-world-table). \n", + "\n", + "To access the PWT data set we will use the [pyPWT](https://github.com/davidrpugh/penn-world-tables) library. Unless you have run this notebook before, `pypwt` will likely need to be installed on your machine. The easiest way to install `pypwt` is to use `pip` from the command line...\n", + "\n", + "```\n", + "$ pip install pypwt\n", + "```\n", + "\n", + "...now that `pypwt` has been succesfully installed we are ready to import the library..." + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false, + "internals": {}, + "slideshow": { + "slide_type": "-" + } + }, + "outputs": [], + "source": [ + "try:\n", + " import pypwt\n", + "except ImportError:\n", + " raise ImportError(\"Looks like you still need to install pypwt!\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "...if the above did not raise an error, then congrats you have successfully installed `pypwt`! If you get an error, then check that you ran\n", + "```\n", + "$ pip install pypwt\n", + "```\n", + "from the command line (and that the installation returned with success!). Assuming success, now we are ready to load the PWT data!" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "pwt = pypwt.load_pwt_data()" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false, + "internals": {}, + "slideshow": { + "slide_type": "-" + } + }, + "outputs": [ + { + "data": { + "image/png": "iVBORw0KGgoAAAANSUhEUgAAAfcAAAGUCAYAAAAoFWvTAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nCIIgCFeM/x+ZZ10UuXgTJgAAAABJRU5ErkJggg==\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig, ax = plt.subplots(1, 1, figsize=(8,6))\n", + "\n", + "for ctry in pwt.major_axis:\n", + " tmp_data = pwt.major_xs(ctry)\n", + " tmp_data.labsh.plot(color='gray', alpha=0.5)\n", + " \n", + "# plot some specific countries\n", + "pwt.major_xs('USA').labsh.plot(color='blue', ax=ax, label='USA')\n", + "pwt.major_xs('IND').labsh.plot(color='green', ax=ax, label='IND')\n", + "pwt.major_xs('CHN').labsh.plot(color='orange', ax=ax, label='CHN')\n", + "\n", + "# plot global average\n", + "avg_labor_share = pwt.labsh.mean(axis=0)\n", + "avg_labor_share.plot(color='r', ax=ax)\n", + "\n", + "ax.set_title(\"Labor's share has been far from constant!\",\n", + " fontsize=20, family='serif')\n", + "ax.set_xlabel('Year', family='serif', fontsize=15)\n", + "ax.set_ylabel('Labor share of income', family='serif', fontsize=15)\n", + "ax.set_ylim(0, 1)\n", + "\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "internals": {}, + "slideshow": { + "slide_type": "-" + } + }, + "source": [ + "From the above figure it is clear that the prediction of constant factor shares is strongly at odds with the empirical data for most countries. Labor's share of real GDP has been declining, on average, for much of the post-war period. For many countries, such as India, China, and South Korea, the fall in labor's share has been dramatic. Note also that the observed trends in factor shares are inconsistent with an economy being on its long-run balanced growth path. " + ] + }, + { + "cell_type": "markdown", + "metadata": { + "internals": {}, + "slideshow": { + "slide_type": "-" + } + }, + "source": [ + "## 0.2 A more general Solow growth model\n", + "\n", + "While the data clearly reject the Solow model with Cobb-Douglas production, they are *not* inconsistent with the Solow model in general. A simple generalization of the Cobb-Douglas production function, known as the constant elasticity of substitution (CES) function:\n", + "\n", + "$$ f(k(t)) = \\bigg[\\alpha k(t)^{\\rho} + (1-\\alpha)\\bigg]^{\\frac{1}{\\rho}} $$\n", + "\n", + "where $-\\infty < \\rho < 1$ is the elasticity of substitution between capital and effective labor in production is capable of generating the variable factor shares observed in the data. Note that \n", + " \n", + "$$ \\lim_{\\rho\\rightarrow 0} f(k(t)) = k(t)^{\\alpha} $$\n", + "\n", + "and thus the CES production function nests the Cobb-Douglas functional form as a special case.\n", + "\n", + "To see that the CES production function also generates variable factor shares note that \n", + "\n", + "$$ \\alpha_K(k(t)) \\equiv \\frac{\\partial \\ln f(k(t))}{\\partial \\ln k(t)} = \\frac{\\alpha k(t)^{\\rho}}{\\alpha k(t)^{\\rho} + (1 - \\alpha)} $$\n", + "\n", + "which varies with $k(t)$.\n", + "\n", + "This seemingly simple generalization of the Cobb-Douglas production function, which is necessary in order for the Solow model generate variable factor share, an economically important feature of the post-war growth experience in most countries, renders the Solow model analytically intractable. To make progress solving a Solow growth model with CES production one needs to resort to computational methods." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "internals": {}, + "slideshow": { + "slide_type": "-" + } + }, + "source": [ + "# 1. Creating an instance of the `solow.Model` class\n", + "\n", + "We begin by creating an instance of the `solow.Model` class in the IPython notebook. As always, it is a good idea to read the docstrings..." + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false, + "internals": {}, + "slideshow": { + "slide_type": "-" + } + }, + "outputs": [], + "source": [ + "solow.Model?" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "internals": {}, + "slideshow": { + "slide_type": "-" + } + }, + "source": [ + " From the docsting we see that in order to create an instance of the model we need to specify two primitives: the extensive production function, $F$, and a dictionary of model parameters." + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false, + "internals": {}, + "slideshow": { + "slide_type": "-" + } + }, + "outputs": [], + "source": [ + "# define model variables\n", + "A, K, L = sym.symbols('A, K, L')\n", + "\n", + "# define production parameters\n", + "alpha, sigma = sym.symbols('alpha, sigma')\n", + "\n", + "# specify some production function\n", + "rho = (sigma - 1) / sigma\n", + "ces_output = (alpha * K**rho + (1 - alpha) * (A * L)**rho)**(1 / rho)" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false, + "internals": {}, + "slideshow": { + "slide_type": "-" + } + }, + "outputs": [], + "source": [ + "# define model parameters\n", + "ces_params = {'A0': 1.0, 'L0': 1.0, 'g': 0.02, 'n': 0.03, 's': 0.15,\n", + " 'delta': 0.05, 'alpha': 0.33, 'sigma': 0.95}\n", + "\n", + "# create an instance of the solow.Model class\n", + "ces_model = solow.CESModel(params=ces_params)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "internals": {}, + "slideshow": { + "slide_type": "-" + } + }, + "source": [ + "More details on on how to create instances of the `solow.Model` class can be found in the **Getting started** notebook in the [solowPy](https://github.com/davidrpugh/solowPy) repository." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "internals": {}, + "slideshow": { + "slide_type": "-" + } + }, + "source": [ + "# 2. Finding the steady state\n", + "\n", + "Traditionally, most analysis of the Solow model focuses almost excusively on the long run steady state of the model. Recall that the steady state of the Solow model is the value of capital stock (per unit effective labor) that solves\n", + "\n", + "$$ 0 = sf(k^*) - (g + n + \\delta)k^*. \\tag{2.0.1} $$\n", + "\n", + "In words: in the long-run, capital stock (per unit effective labor) converges to the value that balances actual investment, $sf(k)$, with effective depreciation, $(g + n + \\delta)$. Given the assumption made about the aggregate production technology, $F$, and its intensive form, $f$, there is always a unique value $k^* >0$ satisfying equation 2.0.1.\n", + "\n", + "Although it is trivial to derive an analytic expression for the long-run equilibrium of the Solow model for most intensive production functions, the Solow model serves as a good illustrative case for various numerical methods for solving non-linear equations.\n", + "\n", + "The `solow.Model.find_steady_state` method provides a simple interface to the various 1D root finding routines available in `scipy.optimize` and uses them to solve the non-linear equation 2.0.1. To see the list of currently supported methods, check out the docstring for the `Model.find_steady_state` method..." + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": false, + "internals": {}, + "slideshow": { + "slide_type": "-" + } + }, + "outputs": [], + "source": [ + "solow.Model.find_steady_state?" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "collapsed": false, + "internals": {}, + "slideshow": { + "slide_type": "-" + } + }, + "outputs": [], + "source": [ + "k_star, result = ces_model.find_steady_state(1e-6, 1e6, method='bisect', full_output=True)" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "collapsed": false, + "internals": {}, + "slideshow": { + "slide_type": "-" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The steady-state value is 1.82583173149\n", + "Did the bisection algorithm coverge? True\n" + ] + } + ], + "source": [ + "print(\"The steady-state value is {}\".format(k_star))\n", + "print(\"Did the bisection algorithm coverge? {}\".format(result.converged))" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "internals": {}, + "slideshow": { + "slide_type": "-" + } + }, + "source": [ + "More details on on how to the various methods of the `solow.Model` class for finding the model's steady state can be found in the accompanying **Finding the steady state** notebook in the [solowPy](https://github.com/davidrpugh/solowPy) repository." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "internals": {}, + "slideshow": { + "slide_type": "-" + } + }, + "source": [ + "# 3. Graphical analysis using Matplotlib and IPython widgets\n", + "\n", + "Graphical analysis is an important pedagogic and research technique for understanding the behavior of the Solow (or really any!) model and as such the `solow.Model` class has a number of useful, built-in plotting methods." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "internals": {}, + "slideshow": { + "slide_type": "-" + } + }, + "source": [ + "## Static example: the classic Solow diagram" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "collapsed": false, + "internals": {}, + "slideshow": { + "slide_type": "-" + } + }, + "outputs": [ + { + "data": { + "image/png": "iVBORw0KGgoAAAANSUhEUgAAAkYAAAGaCAYAAADqyYylAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAIABJREFUeJzs3XeYFdX9x/H3vbv3bl9AXLGLGj0qxBJFFEVFRVERFSv2\nFhNL1FiSmORnjC2WWBK7RqOJ3aASEbEiICoKYsHytWLXYAG23r1lfn/MLFzXbbBl9t79vJ5nn70z\nc2bmOyy6H845MxPxPA8RERERgWjYBYiIiIj0FgpGIiIiIgEFIxEREZGAgpGIiIhIQMFIREREJKBg\nJCIiIhIoDLsAka7gnNsb+CWwJTAAWAR8CbwBPAc8amafreCxbweODBY/NrN1O11wD3LObQM8n7Vq\nlJlNz9o+CngIuMTMLunp+kREehP1GEnOc85dAEwC3ge2ByqAnwLnAlsANwDHrejxzexoM4sCHwM5\n9+AvM3sxqP/Pwarm17AKUAms1aOFiYj0QuoxkpzmnFsX+D3wuJmdlrXpf8B/nXPzAKNrAk2ki44T\nlkhLK83sPufcs2b2dU8XJCLS26jHSHLdMPxf+K+3tNHMPgWmADU9WVSuUSgSEfGpx0hy3ZLg+4jW\nGpjZAS2td86VAWcBhwCDgTpgFnCxmb24PEU450bg91xtC5QCHwH3ApebWX3Q5mjgtma7Hm1m/wq2\n/xH4E7CKmX0frLudZfObPGBdM/uknVrWBC4BxgDF+KHxvFbaPgvsECxON7NRWdtKgKOBA4CNgJWB\nr/CD5rlmtrCF4xXjD2Eejj9E9zlwJ/4cp8eyrmMUsDpwd9buGwJHBF9rAQXAn83sz865rYBjgZ2C\nbV5wXVeb2X+a1TAV2K3pmoBfANcA2+H/fbkX+C1QDlwN7AUUAY8DvzSzb1r6sxKRvkE9RpLr5uIH\nmu2cc/c45zbqyE5BKHoW+DVwDtAf+BmQAGY45w7qaAHOuUOBGUAtsHlwrD8CZwDTgoCBmd0OrASk\ngDfMLNoUigL74IeBvZpWmNnR+AFnvpkVdCAUDcIPIXsARwXnOwI4FT9U/ICZ7RTMP4IfDxMOAa4D\nXsWf1N4PmABsAzzvnKtodu4I8DDwO+Bv+EFqOBDHDyAA5wXXMcPM7g3OfUew7e/4k+aHAUPxh0Ob\najovuKZfBsfdED+g3e+cO6nZNY3JuqaBwJX4P+fVgVuA04GrgH8BdwHr4IfPvflxcBWRPkY9RpLT\nzGyhc+63+L9UDwYOds69BkwGJpvZ7FZ2vRD/l/0JZvZwsO7jIOS8B9wazLv5X1vnd86thv/L9hPg\nMDNLBZsedM6tDNwInA+cHdS7yDk3A9jZObeumX0UHGdN/CACfkC6M+s0++JPLu+IS4A1gePN7NFg\n3QfOucOBz1i+OVK1wBQzOzNr3fPOuaPww9LP8UNHkyPxe2ruNLMrgnU1wDnOuZFtnKdp7tNnZnZV\n8Plb59xfgE+brgG40cxmBMtfARcHPUkXOOduzvqzzzYEOMTM3gJwzp0PnAKcBJxiZk8E7R5yzj0B\n7Omc629mi9qoV0TymHqMJOeZ2XX4d6NNBhqBzYA/AC84594PhrCWcs4V4t+llgHua3asJDARKMPv\ncWnPkUAJMLGFX8z3Bt+Pd84VZK1vCmL7Zq0bF5z3Q2B351w8qDWC35PRbjAK9jkY/7ruz94W/KKf\nQisTsFtiZm+b2dgWNs0Pvjcfvmwa8ruXH7u7hXXNNa/5b2b2YPD5NDOb3EotA/CH+lrySVMoCo6T\nBhbgB8RHm7V9D///iet3oFYRyVPqMZK8YGYvAOOcc/3xh1zG4Q9JrQfc5pxb08wuDJpvhD+/5HMz\nq27pcMH3rTpw6mHB93daqGmJc+4rYBDggKZf0JPwe7j2wR/SIfh8M7AQf6hnF/w5OVsCUTOb04Fa\nNsKfU/S5mbU02fzTFta1yTm3PfAbYFNgDfyhviYDmjXfAj9wGD/WkXO32sY5Vwn8CjgIWBt/WC9b\n81qafNnCuupWtjXNVyttu0wRyWfqMZK8YmaLzOweM5uAP6R0U7DpD8658uBz0y/V2lYO07S+fwdO\n2ZFjRbLaNd0pNw9/XtQA51w//EnbU4H/Bs32yfr+Xzqmsp1aWgqBrXLOHYY/d2plYD+gNJgX1fT/\njea9T22dvyPnrm+ljmL8h3Sejz9suUFWHU3PZmqtJ6yhtZOZWWMrmzrcqyYi+UfBSHKac66fc27b\nlraZ2RLgZPyegTj+hF3wJ/iCP1zWkqb133eghI4cy2vhWA/j976Mw+/hes7MavEDwCKgaQhrHzo+\nv6i9WipaWd+aP+HXfoKZzQuGGduyuI3zL++5s43Hn4z9kJld2+yuMYUYEelSCkaS67YAnnXOtfh3\n2cwywNf4v0ATweq38XswVguGaJrbOPj+UgfO3zS5e5PmG4JhvVXxA0Pz4aWmsLMPWb1CwTylKcDq\nzrmmxwg83YE6wB/Oq6f161q7g8dpMjj4/l72yqa77FowF//PeeMWti3vudutI9BaLSIiK0TBSPJB\njB9OZF4quNtrE+ALgjk+QVi6Gf/v/yHN2sfxeyhqgH934Nz/wh86Gu+cizXbdnDw/RYz+8HdYGb2\nOv4k4N3wb8fPHi5r+nwFMLUDPTVNx0zhT3KOAgdmb8uae7U8d6V9jB90Nmu2fvtW2jfddn9wC9sO\nXY7ztlQHLdQB/rOJRES6jCZfS65r+kX/D+fcWsAj+A8VHIB/19SF+L/cf9ksnJwLjAQuc84txJ/o\nvAp+GFkN/9b7Hz3AkGZDN2b2P+fccfjPw7nbOXcm/vN39gQuxe9R+lMrtU8CTgPmmtkXWesfw3/W\n0Wp0fBitye+BXYPr+gp4Cn+u1bX4AWPj5tfQ2rXhTwy/FrjFOXc88Cb+ZPMbWmpvZnc55yYAhznn\nXsWfDxTDf1RBi/OH2jl/k4fwQ+QY59zvgH/gD0OejT83q619l3d9e9tEJM9FPC+XX/0kfV3QS7Mj\nfs/Ldvh3Tg3CD0yf4k8evtrM3mxh3xL8J18fCqyL3/MzC7go+/lHWU+fbvqPJQLcbmbHZrXZBj+U\nbIc/x+Yj/N6by82sxQnAzrkdgWnAn8zsgmbbnsB/IOMqy/tMHefc6vihbE/8oaa3gb/iz7FqCmkN\nZlaa9eRrj2WB4DwzOz841sHAmfh3vHnAy/jPSmp6/g/88OndRfgPtzwS/+ewAP8hkW8H+/zezC4J\n2u4EPMMP/1wBdsp6XlHTNa0KXIQf+lbFD78Tg33OCJotMLP1mv28mo55NH4wnNbsfLfjT+D+KFjX\ntM8CM1sPEelzFIxEpNsFD4X8J3Ckmd3ZXnsRkbB0aCjNOTccuCT7PUrB+mH4Qw8R/H/BHdnGLbAi\nkuecc28BO7TwvrG98Ce/P9nzVYmIdFy7wcg59xv8F0LWNFsfwZ/Aur+Zfeic+zn+cERLD3cTkb5h\nI+DfwVyrD/DnSR0L7A/81sy+DrM4EZH2dOSutPfx79JpPiFxQ+Bb4IxgnkJ/M1MoEunbTsB/JckU\n/OcqvYY/yX1/M/trmIWJiHREh+YYOecGA/eY2bZZ67bD7xbfAv9fhpOBS81sWveUKiIiItK9OnO7\n/rfA+029RM65qfjvlmo1GHme50UiuhNWRET6FP3iyyGdCUYfAuXOufXN7AP87vJ/tLVDJBJh4cLl\nel1TTqmqqtD15TBdX+7K52sDXV+uq6rqzBtxpKctTzDyAIIHuJWb2S3Bg+3uDiZizzKzx7qjSBER\nEZGe0KFgZGYL8J8ijJndk7V+GjC8WyoTERER6WF6V5qIiIhIQMFIREREJKBgJCIiIhJQMBIREREJ\nKBiJiIiIBBSMRERERAIKRiIiIiIBBSMRERH5Aedc0Yq0cc4Vd09FPaczrwQRERGRPOCc2xnYG5gO\npIAXgYRzbhxwlpnt0Kz92KY2zQ61pnNusJk91QNldwv1GImIiMivgLuAr4BKM/smWP8e8EJ2Q+fc\natltnHMbO+d+D2Bm7wObOOdKeqzyLqZgJCIiIsVmNgfYGXgoa/22wPPN2h7TrM0oYF7W8qPAhO4o\nsicoGImIiPRhzrkzgRLn3D7AKmZWn7V5a2Cec268c25usG5pG+fcHsBx+ENoqwKY2QfAT3vuCrqW\n5hiJiEjuqakh9vJsYi/MIjb3ZRLjD6ThsCPDrmrFRCKXAwd28VEfwPPO7mDbOUDEzCYFQSfbJsAw\nM5vonHssWLd0grWZPeacO8nMbmm2X87mi5wtXERE+pDaWmIvzyY+ayaxWTMpfPUVIqkUAF40SuPO\no0MuMKcNAd4IPseaVjrnyoOP+znnMmb2UAttVsWfl9RcaXcU2hMUjEREpPepqyM25yVis2YQn/Uc\nhfPmEkkmAfAKCkhtvgXJbbcnud32JLfeBq+iMuSCO8Hv2elo7053GApMCj6ns9YPAyYDU4EDnXMJ\nM5vSQpuXnHPDgDfNrC5Yn+nmmruNgpGIiISvvp7Y3JeJPTeD2PPPEXtlDpHGRsDvEUpttjnJESNJ\nbj8y94NQ77O6mX0efK7LWr8RMA34DCgBFrfQ5gtgS+D9plDknIsA1d1acTdSMBIRkZ7X0EDslTnE\nnpsBL7/Ayi++SCThPxLHi0ZJ/XQzkiO294PQ8G3xKvuFXHD+cc6NB+L4wafJZ865AWb2vZndkLX+\nrFbazAXm8kObArO7p+rup2AkIiLdL5EgNm/ush6hOS8RaWjwt0UipIZuSnK7kf7XNtvi9esfbr19\nQxJYH7gma90twMHAzW3s116bXYCru6LAMCgYiYhI10ulKHz1FeIzpxN7biaxObOJ1C+7Czw15Kc0\nbj+S5IiR9Nt7dxal9Ouop5nZI8AjzdYtds697Zxb28w+aWW/Vts454YAT5uZ5hiJiEgf5nkU2DvE\nZz5LbMazxJ6fRbR6ydLNqY2HLA1CyW1H4K00cNm+AypgYc5OSck7ZjZzRduY2ZtdX1HPUjASEZEV\nEv30E79HaMazxJ6bQcH/vl66LbXueiT2O4DGHXYkud0OeAMHtnEkkd5DwUhERDok8u23/u3zM6YT\nm/kshR99uHRbpmoVGsYfSHKHnWgcuSOZtdYOsVKRFadgJCIiLautJTb7+SAITadw/utEPA+ATHkF\nid33CILQTqTdRhCJhFywSOcpGImIiC+ZpPCVucRnTCM2czqxuS8ve6hiPO7fPh/0CKU2/xkU6leI\n5B/9rRYR6as8j4IP3yf27DPEn32G2HMzidbW+JsiEf+hiiP9IJTcehsozdm3PIh0mIKRiEgfEln0\nPbGZ04kHYajg02V3W6fWW5/EjofQOHInktttjzdgpdDqFAmLgpGISD5LJimcO4f4s08Tn/4MhfNe\nIZLxHzGT6defxN770rjTzjTuOIrM2uuEW6tIL6BgJCKSTzyP6EcfEl86PDaDaI3/jCCvoIDUsOF+\nENppZ3+eUEFBqOWK9DYKRiIiOS6yeBGxmTNYOjz2yYKl21LrrkfiwINp3GkXktuP1MtXZYU554rM\nLLG8bZxzxWbW0Npyb6NgJCKSa9JpCufNJf7MU8SffYbCV+YsGx6r7Edi7D407jjKHx4bvG64tUpO\ncs7tDOwNTDezh51zY4EXgYRzbhxwlpnt0GyfpW2aHW5N59xgM3uqleVeRcFIRCQHRBYuJD7tKeLP\nPEn82WeIfvcdEAyPbbX1D4fHdBu9dN6vgIuAb5xzqwGVZvZNsO094IXsxs3bOOc2BvYzs4vN7H3n\n3J7OuVlmVt98uQevqUP0X4+ISG+UTlP4yhziTz8JM55h5Tlzlm1abXXqDz+Kxp1Hkxy5g95EL92h\n2MzmADjnfg9clbVtW+D5Zu2PadZmFDAva/lRYAJwWyvLvYaCkYhILxH53//8HqGmXqFFi/wNhYU0\nbjeSxp1H07jLaNIbb6KnTEuXcM4NBX4GlAB3mlmtc+5MoMQ5N87M/gus0qxnZ2vgYufceOAPZrZl\ndhvn3B7AccCNzrlVzewrM/vAOXdK0wGaL/cmCkYiImFJpfxb6Z95gvjTTxF7/dWlm9JrrEn93vvR\nuPOu9Bs/lsUJBaF8Fflz5HLgwC4+7APen7yzO9DuWOBeYBOgHKgF5gDRIBQBFDfbZxNgmJlNdM49\n1ryNmT3mnDvJzG5ptl/zzNErM0iHinLODQcuMbNRrWy/GfjWzM7pyuJERPJN5Ouv/blCTz9JfPqy\nXiEvFqNx5I7LeoWy3z1WWQELq0OsWvLYncDfge/M7PZg3RDgjaw2saYPzrny4ON+zrmMmT3UQptV\nga9aOFfzR6f3ykeptxuMnHO/AQ4HalrZ/gtgKPBsl1YmIpIPMhkK33iN+BNTiT85ldiry6ZdpNdc\ni/px42ncJZgrVF4RYqESlqBnpyO9O13KOTcaWMPMtnfOZc/1GQpMylpOZ30eBkwGpgIHOucSZjal\nhTYvOeeGAW+aWV2wPtOshObLvUJHeozeB8YD/26+wTk3An+s8SZgo64tTUQkR9XWEp/xLPEnpxJ/\n8nEKvvb/8ewVFvq9Qrvs5vcKbeg0V0jC9D+gyjl3EHB/1vrVzezzrOW6rM8bAdOAz/DnJS1uoc0X\nwJbA+02hyDkXAZZ2ezZf7k3aDUZm9qBzbnDz9cGteecC+wEHd31pIiK5I/rpJ8SfmErRk1OJzZpJ\nJOE/yiUzcCANBx9KYrcxJHcchVfZL+RKRXxm9hrwWtNyMJk6jh96sn3mnBtgZt+b2Q1Z689qpc1c\nYG6zY2wKzG5judfozMSnA4CVgSnAqkCpc+5tM/tXWztVVeV3V7GuL7fp+nJXj19bOg2zZ8Pkyf7X\nG1lTMjbdFPbeG8aOJTpsGMUFBT+avbq88vlnB/l/fTkiCawPXNNs/S34HSA3t7Fve212Af7WbPnq\nFSuze0U8z2u3UdBjdI+ZbdvK9qOAjTow+dpbmMcTCKuqKtD15S5dX+7qqWuLLF5E/Nln/PlCTz+x\n7CGLRUX+ENnoMTSO3p3Mmmt16Xnz+WcHfeL6cn681Dk3EvjYzD5Z3jbOuSFAYdBD9aPl3mZ5eow8\nAOfcBKC8hdvw2k9YIiI5JrrgI4qmPkr8ianEXnyeSCoFQHrV1ag/4hgadxtD4/Y7QFlZyJWKdB8z\nm7mibczszbaWe5sOBSMzWwCMCD7f08L2O7q2LBGRkHgeha/NIz71UYoem0Lh28v+H5782ZZ+r9Bu\nY0gN3VQTp0XyUK98uJKISI9qbCQ2a6bfM/T4YxR84d+Q4xUVkRi9O41j9iKx2x54gwaFXKiIdDcF\nIxHpkyJLFvsPWZz6KPGnniRavQSATP/+NBx4CIkxe9E4ahcoL2/nSCKSTxSMRKTPiH7xOfGpUyia\n+qh/S30yCUB67XWom3AYjWP2Ijl8W4jF2jmSiOQrBSMRyV+eR8E7b1P02GTiUx/9wVOnk5tuTuOY\nPUmM2Yv0kKGaLyQigIKRiOSbYPJ00eT/Ep88icIPP/BXFxbSuMMoEnvsSePue3b5LfUikh8UjEQk\n92UyFL74AkWPTqLo0Uco+OxTALzSUhJ770tiz7E07robXr/+IRcqIr2dgpGI5KZUitjzz1E0eRJM\nfZQBX/nvI8tU9qPhgINJjN3HnzxdUhJyoSKSSxSMRCR3JBLEZ0wjPvm/FE19lOj33/vrBw6k/rAj\naRw7jsaRO0E8HmqZIrnGOVdkZomw62jinCs2s4blaP+j+pf3GE0UjESkd6urI/7MUxRNnkT8yceX\n3lafHrQq9cf+nMRe4+g/bgw139eHXKhIbnLOjQVeBEIPRs65I4A9gWnOuQ/N7KmsbeOAs8xsh2b7\ntFb/ms65wdnH6AgFIxHpfWpriT/9BMUPP0j86SeI1PuhJ73W2tQddiSJsfuQ2moYRKN++0L9r0xk\nRTjnVgMqzeybDrZfBag2sxX6l0gH9i8xswlB21Odc7Oy2r4HvNBW/c65jYH9zOxiM3vfObdns2O0\nS/83EZHeob6e+NNPUjTpQYqenEqkrg6A1Po/oXHsPiTGjiO16ea6rV6kax0DXLUc7TcGFgAfr+D5\n2tt/uHNuhpm9AzwKTABuC7ZtCzzfrH3z+kcB87KWmx+jXQpGIhKehgbi056maNKDxB9/jGhtDQCp\nddcjse94EuPGk95kiMKQSPdZpak3xTm3OnAs8Ckwwsx+0ZEDOOdGAvsD04NVQ8zswuUtxDm3O/A+\ncAWwl5l94Jw7JavJ1sDFzrnxwB/MbMtm9e8BHAfc6Jxb1cy+auEY7VIwEpGe1dhIfPozFD38IPGp\nU5bNGVp7MHXHnUBin/30glbpUyIRLgcO7OLDPuB5nN2BdsVZn28ADgMqgc2W41xe8P0zM3vZObfv\ncuwLgHPuJ8AwM7vQOTc/a1N2TtkkaDPROfdYsG5p/Wb2mHPuJDO7pdnhlyvrKBiJSPdLJonNfJai\nSQ9RNGUy0cWLAEivuRZ1RxxNYt/xpDbbQmFIpOfFAJxzg4GImdU450aTNZfHObc+MDZY/AnwnXPu\nu2D5LjN7zjn32yAU9QNS2SfowP7f4PdU3Rqs+yhr99LgGE0vLdzPOZcxs4ey6w/arAp81cI1lrb3\nh5BNwUhEukc67b+x/uGJFD3636W31qdXW526Qw7zw9DPtlIYkj4v6NnpSO9Od0gH3/sDFnzeEbis\nqYGZfQD8DcA5tyOwwMyWzhFyzpUATbfF7wk86Zzb1sxe6Mj+gRLgc+fcSvjDaU0ywfdhwGRgKnCg\ncy5hZlOy6m9q85JzbhjwppnVNTtGhygYiUjXaXodx8QHKHp4IgVf+/94Sw9albqf/5LEuPGkhm29\n7G4yEQlbU3h4A0g75/YHhpvZF8txjCEsm19UDawPzFrOOm4AjgIGABcCOOciwfEANgKmAZ/hh6jF\nzeoH+ALYEni/KRQ1O0aHKBiJSKcVfPCeH4YefGDpu8kyAwZQf+SxJMYf4L+xvqAg5CpFpAWfOecG\nAHEz+10wFLZ7G+3T/LCXBjObA8wJPk9u53w/2j/Y713g3WarNwVmB9tvyFp/VvP6zex7M5sLzG3t\nGB2lYCQiKyT69VcUPfQfih58YOlb672SEhr225/E+IP813HoCdQivd0twCHANs65ScAGwHmtNTaz\n5zpzsuXcfxfg6nba3AIcDNzciWP8gIKRiHRYZPEiih59hKKJDxB7bjoRz8MrKCCxy2gS4w8kscdY\nKC9v/0Ai0iuY2WLn3FvAFDP7NOx6mjjnhgBPm1mb84OC+t92zq1tZp+syDGaUzASkbY1NBB/8nGK\nH3yA+FOPE0n4T91PDhtOw/gDSewzHm/llUMuUkRWlJnNDLuG5szszeVo22L9y3OMbApGIvJjnkfh\nS7Mpvv9uiiY9RHSJP88x5TYisf9BNOx3AJl1Bodbo4hIN1AwEpGloh8voPj+eyh+4F4KFviPEkmv\ntjp1RxxNw/4HkR4yVLfXi0heUzAS6eMiSxZT9Mgkiu67m/iL/muIvNJSGg44mIaDJpAcuaPuKBOR\nPkPBSKQvSqWIzZhG8f33UDRlMpEG/9lsjdvvQMNBE2gcOw6vvCLkIkVEep6CkUgfUvDWm34Ymnj/\n0ocvptZbn8TBh9JwwMFk1lo75ApFRMKlYCSS5yLff0fRgw/A/Xez0jz/eUOZ/v2pP/o4Gg6aQGrL\nYZo3JCISUDASyUeZDLGZ0ym++1/+UFkiAYWFJMbsScOBE2jcbQwUFYVdpYhIr6NgJJJHop9+QvG9\nd1F8710UfOo/6yy1wYY0HHok5Scez5Locr1kWkSkz1EwEsl1DQ0UTX2U4rv+RWzGs/7TqEvLqD/s\nSBomHOG/tDUSobyqAhYu17sURSTPOefGAWeZ2Q5Z67bAf5XGAjP7zwoeNwr81czOaGXbBKAeWNXM\nrnfOxYATgGKgv5n9X9D2KuC3wPHARGBh831XpL626BXXIjmqYP4blP3+bAZu5qg84Rji06eRGjac\n6quv45v571Fz1bWkth6u+UMieSIS6OLDvge80ML6CvyQstyCl9KeDuzYSpMxwHwzexD4KghiBwD3\nmNkVwEbOueFB2yOBj4CkmX3dyr5dSj1GIjkkUlNN0X/u93uHXgsmUletQt0pp9Mw4XDSG2wYcoUi\n0tWCMPQksHOw/Aww2vM8rwsOvy3wfPYKM5vnnFt/RXuLzOx74Ern3N6tNKkG/uycOxxYHXgG2Afo\nD9wAfAisEbQ91czuamffLqUeI5EcUPjaPMrPPJWBQzek4je/pnD+6yR234PFd9zDt6++Te255ysU\nieSvJ/GHtiLB1y7Ap5FIZKsuOPbWwDzn3Hjn3NymlSsaijoieLfZd8B8oNbMFgGXAHcETTYDZgef\n13POjXHOndnGvl1KPUYivVVNDcUPT6T4jtuW9g6l11yLhlN/TcOhR5BZdbWQCxSR7hb0Fu3cwqY1\ngIcjkchanew52gQYZmYTnXOPtdfYObcJMLqVzXd0JKg451bD76V6DjjfOfekmX0WbNsJeMbMPgcw\nswuC9es753YHXmtt367SoWAUjPVdYmajmq2fAJwGpIA3gJPMrCu69kT6rIL5b1Dyr9so+s/9RGuq\n8aJR/zb7I4+hcdSuej2HiHQJ51x58HE/51zGzB5qbx8zewt4q5OnPh642MzSzrmPgIOBK5xzA4Ht\nzOyioL5jgAIz+wf+ZOtN8Xu4frRvJ+v5gXaDkXPuN8DhQE2z9SXABcBQM2twzt0NjAUe6coCRfqE\nujqK/vsQJXfcSmzuHMB/eWvtL0+m4bAjyayxZsgFikgYPM/zgjlFuzTb9Dmwbyd7i4YBk4GpwIHO\nuYSZTWlrh3Z6jP4VzC9qbd/BZrYAfziwCKjD71QZFDQ5FPiLc64Qf+L2N8CcYNtgYDqwXda+r2ft\n22U60mP0PjAe+Hez9Q3AtmbWkHWs+i6sTSTvFdg7FN9xK8X330t0yWK8SITELqNpOPJYGkfvDoUa\n7RYRRgOfsmxC8udAZ4fQADYCpgGfASXA4vZ26EiPkXOuDP/W+42dc6cDtwBx4G5gBPB34GTn3JeA\nZ2Z3OedOxO9sORd//vMOwXlOc84tBj4zs6eDeVA/2HcFrrtNkY78uTrnBuPfRrdtK9t/BYwxs73a\nOZS3MI9HBLIZAAAgAElEQVSfo1JVVYGuL3f12PWlUsQff4yS224mPnM6AOlVBtFw2BE0HHYUmbXX\n6ZbT5vPPL5+vDXR9ua6qqqLTt9gHE60fDhb39TxvTlvtZcV16p+jwUOaLgN+AuzfJRWJ5KnIN99Q\nfNcdlNx+KwWf+3MFG7ffgfpjjqdxzF4Qi4VcoYj0Vp7nzYlEImsFnzWXtxt1tp/+Jvwhtf06Oum6\nqqqik6fs3XR9ua1bru/ll+Haa+Hee6GxEcrK4MQT4eSTiQ8ZQrzrz9iqfP755fO1ga5PFIh6yvIE\nIw+W3olWjj8h6lhgBvCMcw7gb2b2cKtHgHzvLtX15bAuvb5EgqJJD1Jy283EXvEfDZJab30ajjuB\nhoMPxavs57frwT/PfP755fO1ga4v1yn05ZYOBaNgFvmI4PM9WZt037BIlujnn1F8x22U3Hk70W++\n8SdT774H9ceeQHLHURDVM1VFRHoz3fIi0gUK575MyU3XUfTIJCLpNJn+/ak7+TTqjz6OzDqDwy5P\nREQ6SMFIZEWlUsSnPELpjdcRm/OSv2rjIdSfcCIN+x0ApaUhFygiIstLwUhkOUWWLKb4zn9RcutN\nFHz6CQCJ0btT/4uTSY7cUW+zFxHJYQpGIh0UXfARJbfcQPHddxKtrcErKaH+6OOoP+Ek0j/ZIOzy\nRESkCygYibTF84jNfoGSG68j/thkIp5HetXVqPn1WTQcfhTeSgPDrlBERLqQgpFIS9Jpf/7QtVcT\nm/cKAMnNtqD+FyeRGLcfxHvy6UMiItJTFIxEstXXU3zf3ZRe/3cKFnzk326/x1jqTzyF5PBtNX9I\nRCTPKRiJAJFF38PNf2fg1X8j+s1CvHic+iOOpv7EX2n+kIhIH6JgJH1a9PPPKLnpeor/fTvU1kBl\nP+pOPYP6n/+SzKBVwy5PRER6mIKR9EkF77xN6XV/o2ji/URSKdKrrgbn/Ynvxk/Aq6gMuzwREQmJ\ngpH0KYWvzKH0qsspevwxAFIbbEjdKaeT2P8gqtYYiJfH72sSEZH2KRhJnxB7YRalV15GfPo0AJJb\nbU3dqWfQuNsYvb9MRESWUjCS/OV5xKZP8wPRi88D0DhyJ+rOOJvkiO11h5mIiPyIgpHkH88j/sRU\nSq+6jNgrcwFI7Lobdb8+m9Sw4SEXJyIivZmCkeSPTIb4o/+l7MrLKXzzDQASe42j7tdnkdp085CL\nExGRXKBgJLkvk6Fo0oOUXnEphe8aXjRKw/gDqTvtTNIbbxJ2dSIikkMUjCR3NfUQXf4XCt95G6+w\nkPoJh1N/6q9Jr6+HMoqIyPJTMJLc43nEp06h7LKLKXzzDb+H6JDDqD3jN2QGrxt2dSIiksMUjCR3\neB7xp5+g9NKLib02Dy8SoWH/g6g767fqIRIRkS6hYCS9X3DbfdmlFxGb+zIADfuMp+7sc0hv6EIu\nTkRE8omCkfRqsRefp/Ti85c+hyix1zhqzz6H9CZDQq5MRETykYKR9EoFb86n7KLzKHrqCQASu+9B\n3W9+T+qnm4VcmYiI5DMFI+lVoh8voOzSi/yXu3oejduNpPaP55HacljYpYmISB+gYCS9QmThQkqv\nuoySO24jkkySHLoptX/8E8lRu+rVHSIi0mMUjCRUkZpqSq6/hpIbriVaW0N6ncHUnvN/JPbdXy93\nFRGRHqdgJOFIJim+41bKrryM6DffkFm5iuo/nkfDEUdDPB52dSIi0kcpGEnPano44/n/R+EH75Mp\nr6D2t3+g7hcnQ3l52NWJiEgfp2AkPabw9Vcp+9MfiM+aiVdQQP2xP6f2rHPwVl457NJEREQABSPp\nAdEvv6Ds4vMpuv8eIp5HYrcx1J57gR7OKCIivY6CkXSfmhpKr/sbpdf/nUh9PalNhlLz54tI7jgq\n7MpERERapGAkXS+Toej+eyi76M8UfP0V6VUGUXfx5TQcchgUFIRdnYiISKsUjKRLFc6bS/nvzyY2\ndw5eSQm1Z/yGulNO18RqERHJCQpG0iUi33xD2UXnUXz3v4l4Hg37jKf2TxeQWXOtsEsTERHpMAUj\n6ZxUiuLb/0HZpRcTXbyI1MabUHPRZSS33yHsykRERJZbh4KRc244cImZjWq2fm/g/4AUcJuZ/aPr\nS5TeKvb8c5SfczaFb79JprIfNRddSv0xP4dC5W0REclN7b5zwTn3G+AWoKjZ+hhwJTAa2BE4wTm3\nSncUKb1L9MsvqPjFMfTfd08K3nmL+sOO5LsXXqH+5ycqFImISE7ryMuo3gfGA83f5Lkx8L6ZLTaz\nJPAcoPGTfJZOU3LLDQzYbhjFD00k+bMtWTT1GWquuhavqirs6kRERDqt3WBkZg/iD5U1Vwkszlqu\nBvp1UV3SyxS+Ng+GD6f8D7+FwgKqr/g7i6Y8TWqLLcMuTUREpMt0ZtxjMVCRtVwBfN+5cqS3iVQv\nofSSCym59WbIZGg48BBqzrtIPUQiIpKXOhOM3gE2cM4NAGrxh9Eub2+nqqqK9prktLy5Ps+DBx+E\nU0+FL76ADTeEG26geOedKQ67tm6UNz+/VuTz9eXztYGuT6SnLE8w8gCccxOAcjO7xTl3BvA4/pDc\nrWb2ZXsHWbiweoUKzQVVVRV5cX3RTz+h/HdnUvTk43jxOHVnn0Pdr35N1VpVeXF9rcmXn19r8vn6\n8vnaQNeX6xT6ckuHgpGZLQBGBJ/vyVo/GZjcLZVJz8tkKP7nPyi/4E9E6mppHLkjNZddSXr9DcKu\nTEREpEfo3moBoODD9yk//RTiLz5Ppn9/qi+5gcTBh0Kk+c2IIiIi+UvBqK9Lpym58TrKLr2QSEMD\niT33pvrSK/EGDQq7MhERkR6nYNSHFbzzNhWnn0TslblkVq5iybU30bj3vuolEhGRPkvBqC9KJin9\n+5WUXnkZkWSShgMOpubCS/BWGhh2ZSIiIqFSMOpjCt41Kk4+gdhr80ivtjo1l19F4257hF2WiIhI\nr9CRV4JIPshkKLn5egbsOpLYa/NoOOQwvp85W6FIREQki3qM+oDoZ59ScdpJxGdOJzNwIEtuvI3G\nPceGXZaIiEivox6jfOZ5FN1/DwN23Jb4zOkkdt+D76bPVigSERFphXqM8lTk22+pOPt0iiZPIlNW\nTvXV19Ew4XDdcSYiItIGBaM8FJs5nYqTfk7B11/RuM0Iqq+5kcw6g8MuS0REpNfTUFo+SSYpvfh8\n+h0wjui331Dzx/NY/NCjCkUiIiIdpB6jPBH95GMqf3kcsTkvkV57MEtuupXUlsPCLktERCSnqMco\nD8QfeZgBO29PbM5LNOy3P98/M1OhSEREZAWoxyiX1dVR/n/nUPLvf+KVlmqCtYiISCcpGOWogg/e\no/LYIyh8+y1SQ37Kkpv/SXqDDcMuS0REJKdpKC0HxSf/l/6jd6Lw7beoP+Z4vn/saYUiERGRLqAe\no1ySTFJ24XmU3nANXmkpS274B4n9Dwq7KhERkbyhYJQjol99SeXPjyY2+wVSP9mAJbfdSXqjjcMu\nS0REJK9oKC0HxGbNZMAuI4nNfoGGfcaz6IlnFYpERES6gYJRb+Z5lNx0Hf0OGEfk+++oufASqm/+\nJ155RdiViYiI5CUNpfVWiQQVZ59O8b13kV5lEEtu/Tep4duEXZWIiEheUzDqhaJff0Xl0YcRm/sy\nyc23YMntd5NZfY2wyxIREcl7GkrrZQrnzaX/bjsRm/syDfsfxKJJUxWKREREeoiCUS9S9MC99B83\nhuhXX1Jz7gVUX38LlJSEXZaIiEifoaG03sDzKL3kAsqu+iuZikqq/3knjbvuHnZVIiIifY6CUdgS\nCSpOO5HiB/9DevC6LL7rAT3FWkREJCQKRiGKfPctlUcfRvzF50kOG87iO+7BW3nlsMsSERHpszTH\nKCTRDz+g/567En/xef+hjRMfUSgSEREJmYJRCApfms2AvXal8MMPqPvVr6m+6TYoLg67LBERkT5P\nQ2k9LD51CpUnHA3JJNVX/J2GI44OuyQREREJKBj1oKJ77qTijF9BURGL77qf5M6jwy5JREREsmgo\nrYeUXPs3Kk87Ca+ykkUTH1EoEhER6YXUY9TdPI+yP/8fpdf/nfTqa7D4vodIu43CrkpERERaoGDU\nnVIpKn59CsX33U3qJxuw+P6Hyay5VthViYiISCvaDEbOuShwPbApkACON7MPsrbvB/we8IDbzOzG\nbqw1tzQ2UvnL4yiaPInkFj9j8d0T8QYODLsqERERaUN7c4z2BeJmNgL4HXBFs+1XAqOB7YAznXP9\nur7EHJRIUHncERRNnkTjiO1ZPPERhSIREZEc0F4w2g6YCmBms4Gtmm1PAv2BEiCC33PUt9XX0++o\nCRQ9/hiNO4xi8d3/wSuvCLsqERER6YD2glElsCRrOR0MrzW5ApgLzAceMbPstn1PbS39Dj+Y+DNP\nkdhlNIvvvA9KS8OuSkRERDqovcnXS4Ds7o6omWUAnHNrA6cA6wB1wJ3OuQPM7D9tHbCqKk97T6qr\nYc89ic+cAfvsQ9F991FVVBR2VV0ub39+AV1f7srnawNdn0hPaS8YzQL2Bh5wzm0DvJ61rRhIAwkz\nyzjn/oc/rNamhQurV7TW3qu2lv6HjCc2+wUSe+/LkutvhSWNQGPYlXWpqqqK/Pz5BXR9uSufrw10\nfblOoS+3tBeMHgJGO+dmBcvHOOcmAOVmdotz7g7geedcA/A+cHv3ldpL1dfT78gJxGa/AAcdxJKr\nb4RCPQVBREQkF7X5G9zMPODEZqvfzdp+FXBVN9SVGxobqTzuCOIznyUxZi+K7rwTFjWEXZWIiIis\nIL0SZEUlk1SecAxFTz1B4867suSW2yEWC7sqERER6QQFoxWRTlNxygkUTXmExu13YPE/74I8nGgt\nIiLS1ygYLS/Po/zs0yl+aCLJrbdh8b/uhZKSsKsSERGRLqBgtJxKL72QkjvvIPnTzVh89wNQXh52\nSSIiItJFFIyWQ/Ftt1B25eWkB6/L4nsm4lXqDSgiIiL5RMGog+KPPEz5OWeRWbmKRfc9hLfKKmGX\nJCIiIl1MwagDYs/NoPLE4/FKy1h870Qy664XdkkiIiLSDRSM2lHwzttUHnUoeB5L7rib1Kabh12S\niIiIdBM9orkNkYUL6Xf4QUSrl7Dkhn+Q3GGnsEsSERGRbqQeo9Y0NNDvqAkUfPIxtWefQ2L/g8Ku\nSERERLqZglFLPI+K008mNuclGsYfQN1Zvwu7IhEREekBCkYtKL3iUooffIDkVltTffX1EImEXZKI\niIj0AAWjZoomPUjZZReTXnsdFt9xDxQXh12SiIiI9BAFoywFb79FxWknkSkrZ/G/78Orqgq7JBER\nEelBuistEFm8iMqjDyVSV8eS2+4kvfEmYZckIiIiPUw9RgCZDBUnn0DhRx9Sd+oZNI4dF3ZFIiIi\nEgIFI6D0yssoemIqjTuMovac/wu7HBEREQlJnw9G8aefoPTyv5Becy2W3HQbFBSEXZKIiIiEpE8H\no+iXX1Bx8gkQi7Hkn3fiDRwYdkkiIiISor47+TqdpuLE44l+9x3Vf/krqc22CLsiERERCVmf7TEq\nvepy4s8/R2LPvWk49udhlyMiIiK9QJ8MRrEXZlH610tIr7kW1Vdfqydbi4iICNAHg1Hk+++o+OVx\nEImw5IZb8foPCLskERER6SX6XDAq/+0ZFHz5BXW/+T2p4duEXY6IiIj0In0qGBU9PJHihx8kudXW\n1J16RtjliIiISC/TZ4JR9OuvKP/tGXilpVRfe6OeVyQiIiI/0jdu1/c8ys/4FdHvv6f6L38lvd5P\nwq5IREREeqE+0WNUfM+dFD35OI0jd6LhmOPDLkdERER6qbwPRtEvv6Dsj78jU1FJ9d+ug2jeX7KI\niIisoLwfSis/52yiNdVU//VvZNZcK+xyREREpBfL6+6T+JTJFE15hOTwbWk4/KiwyxEREZFeLm+D\nUaR6CeXnnIUXi1F9xd81hCYiIiLtytu0UPqXC/wHOZ56BukNXdjliIiISA7Iy2BU+OorlNx6M6mf\nbEDdaWeGXY6IiIjkiDYnXzvnosD1wKZAAjjezD7I2j4MuAKIAJ8DR5pZY/eV2wGeR/nvf0PE86i5\n9EooLg61HBEREckd7fUY7QvEzWwE8Dv8EASAcy4C3AwcbWYjgaeBdbur0I4qmng/sTkvkRi7D8mR\nO4ZdjoiIiOSQ9oLRdsBUADObDWyVtW1D4FvgDOfcs0B/M7PuKLLDamooO/9cvOJias67MNRSRERE\nJPe0F4wqgSVZy+lgeA1gZWAEcA2wK7CLc25U15fYcaXXXEnBV19Sd9KpZNZeJ8xSREREJAe194DH\nJUBF1nLUzDLB52+B95t6iZxzU/F7lKa1dcCqqoq2Nq+4jz6C66+BNdek7PxzKSsr657ztKPbrq+X\n0PXltny+vny+NtD1ifSU9oLRLGBv4AHn3DbA61nbPgTKnXPrBxOyRwL/aO+ECxdWr2itbao482yK\nEwmW/PHPJOoyUNc952lLVVVFt11fb6Dry235fH35fG2g68t1Cn25pb1g9BAw2jk3K1g+xjk3ASg3\ns1ucc8cBdwcTsWeZ2WPdWWxrCt94jeKHJpLcbAsS+x0QRgkiIiKSB9oMRmbmASc2W/1u1vZpwPBu\nqGu5lF14HgC1fzwPIpEwSxEREZEclvMPeIw9N4P4tKdp3GEUyR1DnfstIiIiOS63g5HnUXbReQDU\n/uHccGsRERGRnJfTwSj++GPE5s4hsfe+pLbYMuxyREREJMflbjDyPEqvuBQvEqH2t38IuxoRERHJ\nAzkbjGLTniL22jwSe+9LekMXdjkiIiKSB3IzGHkeZVdcBkDd6WeFXIyIiIjki5wMRrFZM4m9PJvE\n7nuQHvrTsMsRERGRPJGTwaj0qssBqPv12SFXIiIiIvkk54JR4dyXic+cTuNOO5P62VZhlyMiIiJ5\nJOeCUclN1wFQd8rpIVciIiIi+SanglH0888oemQSqY2HkBy5Y9jliIiISJ7JqWBUcuvNRNJp6n9x\nkt6JJiIiIl0ud4JRbS3F/76dzMpVNIw/MOxqREREJA/lTDAqvu9uoosXUX/0cVBcHHY5IiIikody\nIxh5HiW3/wMvFqP+qOPCrkZERETyVE4Eo8I5L1H4ztsk9hiLN2hQ2OWIiIhInsqJYFR85x0ANBxx\ndLiFiIiISF7r9cEosmQxxQ9PJL32YN2iLyIiIt2q1wejookPEKmvp/6IoyDa68sVERGRHNa7k4bn\nUfzv2/EKCkgccljY1YiIiEie69XBqODN+cTmv07jbnuQGbRq2OWIiIhInuvVwah44v0ANBx4SMiV\niIiISF/Qe4NRJkPRQ/8hU9mPxl13C7saERER6QN6bTCKvfg8BV98TmLsOD3pWkRERHpErw1GRcEw\nWmL/g0KuRERERPqK3hmMGhspeuRh0oNWJTli+7CrERERkT6iVwaj2HPTiS5aRGLf8VBQEHY5IiIi\n0kf0ymBUNOVRABr3GhdyJSIiItKX9L5glMkQn/oomYEDSQ4bHnY1IiIi0of0umBUOPdlCv73NYnd\n99QwmoiIiPSoXheMih4LhtH2GBtyJSIiItLX9K5g5HnEpzyCV1pG4w47hV2NiIiI9DG9KhgVvP8e\nhR9+QOOoXaCkJOxyREREpI/pVcEoPu0pABpH7x5yJSIiItIXFba10TkXBa4HNgUSwPFm9kEL7W4G\nvjWzczpTTGza0wA07rRzZw4jIiIiskLa6zHaF4ib2Qjgd8AVzRs4534BDAW8TlWSSBB//jlSbiMy\nq6/RqUOJiIiIrIj2gtF2wFQAM5sNbJW90Tk3AtgauAmIdKaQ2OwXiNTX07jTLp05jIiIiMgKay8Y\nVQJLspbTwfAazrnVgHOBU+hkKAKIP/sMAI2jNIwmIiIi4WhzjhF+KKrIWo6aWSb4fACwMjAFWBUo\ndc69bWb/auuAVVUVLW+YNR3icfrvPQZKSztSe6/U6vXlCV1fbsvn68vnawNdn0hPaS8YzQL2Bh5w\nzm0DvN60wcyuAa4BcM4dBWzUXigCWLiw+kfrIksWM/DVV0kO35bFtWmo/XGbXFBVVdHi9eULXV9u\ny+fry+drA11frlPoyy3tBaOHgNHOuVnB8jHOuQlAuZnd0qztCk++jr08m4jnkdxmxIoeQkRERKTT\n2gxGZuYBJzZb/W4L7e7oTBGxF18AILnNtp05jIiIiEin9IoHPMZefB4vGiU1bHjYpYiIiEgfFn4w\namigcN5cUkN+ildRGXY1IiIi0oe1N8eo+wt4dR6RxkYNo4mIyHL5/nt4880CzKJsv30a5zLt7yTS\njtCDUeylFwFIDlcwEhGRH/M8+OSTCPPnFzB/fpQ334wyf34Bn322bNDj4IOTXHNNQ4hVSr4IPxi9\nNg+A1M+2aqeliIjku0QC3n03yvz50awgVMCSJT98jvDKK2cYNSrF0KFphg7NMHp0KqSKJd+EHowK\nX32FzMork1ljzbBLERGRHtQ0FLZgAbz4YjHz50d5990oqdSyEBSJeKy/foadd84wdGiGoUPTDBmS\nYdCgzr2eU6Q1oQajyDffUPDpJyR2GQ2RTr9VREREeqGODIVBjJISj802yzBkSHppCNp44wxlZaGV\nLn1QqMGo8PVgGG3zn4VZhoiIdJEVGQobMaKItdeuZb31MhQUhFS4SCDUYBSb9wqgYCQikosWLfKH\nwrJD0LvvRkkml28orKqqiIULdUeZ9A4h9xi9BkBqs83DLENERNrQ0lDYm28W8OmnP3wUXkmJx6ab\naihMcluowajgnbfIrLQSmUGrhlmGiIgEVvSusKFDMxoKk7wQXjCqq6NgwUckt91OE69FRELQVUNh\nIvkktGBU+J4R8TzSG20cVgkiIn2ChsJEOi60YFTw9lsApDYeElYJIiJ5R0NhIp0TXo9RUzDaaJOw\nShARyWkaChPpeuEFo3f8YJTeaKOwShARyQnNh8KaeoE0FCbS9cIbSnvXSK++Bl6//mGVICLS6zQ2\ngtmyp0P7IQgWLy7/QTsNhYl0j3CCUX09BZ9/RuP2O4RyehGR3qCjQ2EbbgijRiU1FCbSA0IJRgWf\nfAxAevC6YZxeRKRHeR58+umKD4UNHlzBwoUNIVUv0reEE4wWfAQoGIlI/mlpKGz+fN0VJpIrQgpG\nHwKQXne9ME4vItIldFeYSP4JJxh95AejjHqMRCQHdHYoTHeFieQODaWJiGTRUJhI3xZKMIou+IjM\nwIF4FZVhnF5EBNBQmIj8WM8Ho1SKgk8+JrXZ5j1+ahHpmzQUJiId1ePBKPrlF0RSKdLrDO7pU4tI\nH6ChMBHpjBCC0ZcAZFZfs6dPLSJ5pmkobMECePHFYg2FiUin9Xww+uoLADKrrdbTpxaRHNWxobCY\nhsJEpNN6PBgVfOkHo/Sqq/f0qUUkB6zIUNiIEUWsvXathsJEpNPCG0pTj5FIn9dVd4VVVRWxcGEm\njEsQkTwT4lCaeoxE+grdFSYiuSKUHiMvEiGzyqCePrWI9ADdFSYd4XkeiXSChlQ9jUuW8Nmi/1GX\nqqc+VUd9qt7/Svqf65auy/qeDL6nG2hI1XPkJscydv1xYV+W5IFQ5hhlqlaBWKynTy0iXUwPSMxP\nyXRyaQj5USj5UVipp6EpyDTtk2weZH4YauqCUOPRdX8HfrbKlgpG0iV6PBhFFi7Uy2NFcoyGwnqP\npp6WulQtdck6/6vp89LvddQma6lL1VGXXLauLln7456XVD11zcJNKpPqsnojRCgpLKU0VkJxQQkD\nilZi9fJSSgpLgq9SBpRXEk3Fli6XxPzvxYXFlBb+sG12m6ZtxYUlFBUUdVnN0re1GYycc1HgemBT\nIAEcb2YfZG2fAJwGpIA3gJPMrPV/AiQSRGtrSA1YqQtKF5HuoKGwzst4maU9Jy2FlmVhpa1AE7RL\n1ZHI1FOdqFnaNuN1zUTz7MBRGa9kldJBS5dLs8NIrFkoKfRDSXFhcQth5YdtiwqKiEQibdZRVVXB\nwoXVXXJNIp3VXo/RvkDczEY454YDVwTrcM6VABcAQ82swTl3NzAWeKTVo337LQCZgQpGIr1BXx8K\n8zyP+lQ9NckaapM11CZrg6/s5WXfaxprguDSLOSkmvfc1HVJfYXRQkoLyygvKqM8Vs4qpYMoLSyl\nNFZKaWHZD78Hn8t+sK2U0ljZsu+x0iD0+KEmGom2X4RIH9NeMNoOmApgZrOdc1tlbWsAtjWzhqxj\n1bd5tCAYeeoxEulRngcLFsD06YU5OxTWFGKWhpSswFK4MMMX3y78UZhpCjK1yRpqU7XBuuofBKDO\nznMpKihaGjwGFK3EGuVrtRBKWggywfayNrbFC+KAelREelJ7wagSWJK1nHbORc0sEwyZLQRwzv0K\nKDOzp9o8WlOPkYKRSLdpfSgMoGRpu54YCkukE1Q3VlPTWE11spraxhqqG5dQnaymprHG35b0tzf1\n2tQ0LgsxPww4nQ8xZbFyymJllMXKWKX0/9u78+g4qjvR419JlmQtrcVavEnesP0DY7wEAoR4wTBk\nwkBCgJk8QuKwZAFmmDcB53E45CWTzJBkJgkTlhDIABmbhCUHAgEmj6w4BAjgMcF2jOEHBoxtLFuy\nbEmWLMmy1O+Pui2V2r1JarW6W7/POTqtvlVddW/fkvrXd6k7uf/3kvxSSvu3DexTWhDo/73Yl14y\nYaD1ZUJu6tfiNsaMnnh/0W1AwPc8V1X7O7fdGKTvAHOBi+OezQVGJTOmUVITiLNzZqrJ0nKFWPlS\nIxj0AoB4YzMOHoTNm2HTpoGfbdugp2dgn5wcmD8fzj0XliwZ+JkyJRfIJfzfQE9vD4eOHKKtu41D\n3d5jW3db7LQjvrTugbQjvUeG/R6UFpR6P4WlTAlMJlAQGEhzPxHTCiPvV5RflNFdR+lybY6WbC+f\nyRzxAqMXgI8Bj4jI6cCWsO0/wutSuzDmoOsQFxi15RfTnYXNwtne3G3lG33BYJC//duP89xzzwKw\nfL9JAKYAABk/SURBVPlKHn30SSAnoVlhEyf2ISd2MVsOUTe3mclzGqiYsZuuvGb6JnSz52ATb7S3\ncc8zbf2tOO2uFae9p532I4fo6u2KkLP4csghUFBGoCBA9cQaZpXNoTS/tD/N+z1ASUGAQH7ABTXe\n76UFrsXGtdAUTygeUhATte56gU443NnHYTqGVa50kA7X5mgaD+UzmSNeYPQ4cI6IvOCeX+FmopUC\nG4ErgT8Cz4gIwG2q+ouoRwuNMZpkXWnG+AWDQTp62rnkkxez4U8v9ac/99yzTJ0+n9y8RznavWzQ\nayYEDlBy/DZyp27haO1GOqtfpKvqTbbm9rE1tNMu9xNDiQtYKgsrqQ/UU1pQ1h/EeAHNQBATCnTC\nt5cWBCieUBy3hcsYY9JdzMDItQJdE5b8pu/3oY1G2L8fsDFGJjt1He2itbuFFvfT2n3QPbYMemzr\nbqX1SCtt3W20tsDBnTM4vGsewT2LYMtLxxy37+g++novhgW3wtTNMGUTTNlEb6CRvIIyygvLCRSU\nUVYwibKCjxBwaWUF5QQKyygr8H7qa6YQ7Mr30l1QU5JfmtHdS8YYk2ypHTVog69NGgsGgxzuOXxM\nINPSffCYtEiP3b3dMQ4OtMyEvUtg7wdh7xJy9i0l2DIzbKcrI768orqH+x+sorzwQsoKLqOssGzI\nQU22d1cYY0wyjElgZF1pZrR193ZzsOsAB7oOhD029/8eSu8Pbo60DGmwcG5OLhWFFZQXVjC9dDrl\nhRVUFFZQkltF3z6hY/dcDu6YSeM7U9j1VhWH2wcvg1NV3cdJYbPCbrxxZf/4opApU6aybt2DLJ12\nclLeG2OMMdGlNjBqbQUgGChL6WlN5goGg7QdaT0mmDnYdYAD3f60g4O2Hz6a2EDbvJy8/uBm9qRZ\nlOQG+p9XFFb2BzvlhRVUTKzof15RWEFpfoDW1pyEb5C4cGFP3BskPvrokyxefDx79zYAXlC0efMb\nNnbHGGNSJLWB0aFD9JWUQq6NaRiv+oJ9tHQfpLmzmebO/TR1NtHcuZ/9nU00d+13vw88HuhqpjfY\nm9CxiyeUMGniJI6rmEvlxElMmlhJ5cRJ3u+F7tE9D/1eVlDeH3TE6mrqXytsQx5Pj+INEnNycli3\n7kEuu+xSANate9CCImOMSaHUBkbt7QTT4Ra6JmlCLTqNhxv7g5lQkLPfBT3Nnc3s72waUqBTXlhB\ndVE1s8pnDwQzhccGNv7HZC0iOdZrhS1dejKbN78BxL+PkTHGmORKfWBUWprSU5rh6TraRVNnI42H\n99F42HvsoIV39+9yaXv702MOOnbKCyuomljF7PI5VBVVU+1+qiZWu+c1VBVVU1NUw6SJVeTn5cc9\nZjL41wrbvh02bixOi7XCLCAyxpixkfrAqGZySk9pBms/coiGjgYaOvbQ0L6Hxs5GGjv2DgqAGjsb\nae1uiXmc/Nx8aosns6DqRGqLJ1NTVEt1UY0X7BQNBDvVRdVMmljVv+bTWOnvCotzg8Sioty0XSvM\nGGPM6EttYNTRYV1po6Qv2Mf+zv00tL/fH/js7djDnvY9NHQ0sLfDezx0pC3mcaomVjGtZBqLa5ZS\nW1xLbfFk91PL/KmzKegJMLl4MhWFlWnbqjHcrrAVK4qoqGhP6lphxhhjMktqA6Ng0AKjYQgGg7R2\nt7CrfRe7D+1i96Gd7D60m/fbd7On/X32djSw7/Beevp6oh6jsrCSutJ6ppZOZWrJNO+ndBqT+wOf\nyVQX1cRs2UnH++D4u8LizQqL1xVWUwNNTakugTHGmHSS8mWhgyU2xihcX7CPfR172e0Cn139wc8u\nl7ab9p7IAcmE3AlMLp7CopolLuCZytTS6d5jyTSmuECoaEJRxNdnisS7wkY2K8wYY8z4NgaB0fj8\nhOo82snOtvfY0fYuO1rfcY/vsqPtXXa17eRIX+QbC5YVlDOjbCZ1pXXUBeqpC8ygPlBPXaCe6aV1\n1BTVkpebXX0/Yz0rzBhjzPiV8sCI/LEdhDuaDvccZuv+v7D94Ju8Gwp+XADU0LEn4msmTZzEwuqT\nqA/MdIFPHXWBGdSV1lMfqKessDzFpUitZHaFGWOMMSOV+sBoQmZ/nQ8GgzR1NrH94Ju81fKm7/Et\ndh3aSZDBH9Y55DC9tI5l01cwq2w2s8pnD3rM9sAnxLrCjDHGZILUd6VlUD/Hwa4DvN68jW3NW3n9\nwDa2Nb/G9pa3Ik5lry2ezMpZK5lZchxzK+Yyp/w4ZpXPYUbZzKTdeDBTWFeYMcaYTJX6FqO81J8y\nnt6+Xra3vMXW/VvY1vwarze/xrbm19jT8f6g/SbkTmB22RzOmLaMeRXzmVs5j3mV85lbMY/ywoq0\nnLU12qwrzBhjTDYZg660sQ2MgsEg77a9w6bGP7Op8VU2Nf6ZLU2bj1l0dGrJNM6ecQ4nVJ3IgqoT\nWVC1kLkV88b8RoVjJRiEHTvg2WcnWFeYMcaYrJX6rrQUB0YdPR28su9/eLnhRTY0vMSmplcHdYXl\n5uQilcezuHYpJ1UvYkHVQk6oWsCkiVUpzWc6id4VBjAw7d+6wowxxmSbMehKG91PzdbuFl54/3le\navgTLzf8iS1NmwctWjqn/DjOnnEOS2qXsqT2ZBZWn0Rp/vi9t9JQusLOPTePefO6rSvMGGNM1sr4\nrrSjfUd5tfEV1u/8PX/Y9Qx/btxIX7DPO1XuBJbUfoDTp57B6dPO4INTTh23LUHJmBXmjaGKfL8l\nY4wxJhtkZFdae087z7z3W375zpM8s+v3/V1jeTl5nDL5VFbWr+KMactYWnsyxfnFIz5fprFZYcYY\nY8zwZMystI6eDp5+97956u0nWL/zd3T1dgEwIzCTC467iFUzzmbZ9OWUF1YkM7dpz2aFGWOMMcmT\n1mOMgsEgG/dt4KHXf8ovtj/Wv16YVB7Pecd9nPPmfJyFVSel7SrvyWQ3SDTGGGNGX1re+fpI7xEe\ne+sR7tp0B68f2AbA9NI6vrj4Gi6e90nmVc4f7VyOKesKM8YYY8bGGNz5Ovopu3u7Wbv1Xu7cdDt7\nOxrIy8njguMu4tITVrOi7sysWywVrCvMGGOMSSdpMSstGAzyi+0/55svfYOdh96jJL+UqxdfyxcX\nXUNdoD7lWRwN1hVmjDHGpL8xD4wa2vdw/R/+kd/v/C0FuQVcvfhavnTymoyeVm9dYcYYY0xmGtNF\nZJ/Z+Vuu+u3naO1u4cz6s/juyluZWTYr1VkaEX9X2PbtsHFjsXWFGWOMMRlqzFqM1m69jxufW0N+\nbj7fW3kbqxdcntazyxLvCsu1rjBjjDEmQ43JdP2H33iAG/54HdVFNdx/7kOcMuXUlGcjluF2ha1Y\nUURFRbt1hRljjDEZKuWB0YajO7hu/c1UFlby+AW/RCYdn+osDJLMWWE1NdDUlOoSGGOMMSZZUhoY\nHc2Faw7+J33BPu776E9SGhTZrDBjjDHGxJPSwOiBk2B7TwOfXXAly6avGLXz2KwwY4wxxgxHSgOj\nO06DCeRx3clfTtox7QaJxhhjjEmWmIGRiOQCPwQWAd3A51X1bd/2jwFfBY4CP1bVe2Md75VpcFbp\nIqYH6oacUesKM8YYY8xoi9di9AmgQFXPEJHTgFtcGiKSD/wHcApwGHhBRJ5U1cZYBzypeG7cTFlX\nmDHGGGPGQrzA6MPArwBU9WUROcW37QRgu6q2AojI88AK4NFYB5xcMPiO1tYVZowxxph0ES8wKgPa\nfM97RSRXVfvctlbftkNAecyjtcxgT8tyvvNGgXWFGWOMMSbtxAuM2oCA73koKAIvKPJvCwAHYx7t\n1vf4ge+pdYUZY4wxJp3EC4xeAD4GPCIipwNbfNveAOaJSCXQgdeN9t1YBwsGCVvzI9f9pP4G3KOl\npiYQf6cMZuXLbNlcvmwuG1j5jEmVnGAw+jgdEclhYFYawBXAyUCpqt4jIucDX8OLbu5T1btGOb/G\nGGOMMaMmZmBkjDHGGDOe5MbfxRhjjDFmfLDAyBhjjDHGscDIGGOMMcaxwMgYY4wxxhmVefLJXmMt\n3SRQvuuAzwFNLukqVX0z5RkdAbcEzL+p6qqw9Iyuu5AY5cvounNL9fwYmAkUAjer6lO+7RldfwmU\nL9PrLw+4B5gPBIGrVfU13/aMrb8EypbRdRciIrXAK8DZ/vxnct2NN6N1A6Gkr7GWZqKWz/kAsFpV\nXx2T3I2QiNwAfAZoD0vPhrqLWj4no+sO+DTQpKqr3T3GNgFPQdbUX9TyOZlef+cDfaq6TERWAt8k\ne/53Ri2bk+l1F6qjH+Hd2y88PZPrblwZra60QWus4V0MIf1rrKlqDxBaYy2TxCofePd6uklEnhOR\nG1OduSTYDlwE4TfkzIq6g+jlg8yvu0fw7i0G3t/3Ud+2bKi/WOWDDK8/VX0CuMo9ncXg1QQyuv7i\nlA0yvO6c7wJ3AQ1h6Rldd+PNaAVGEddY820b2hpr6SdW+QAewvsHcBawTETOS2XmRkpVH+PYDxzI\njrqLVT7I/LrrUNV2EQngBRFf8W3O+PqLUz7I8PoDUNVeEVkL3A486NuUDfUXrWyQ4XUnIpfjtWb+\nxiX5v3hlfN2NJ6MVGCV3jbX0E6t8ALep6gH3zeCXwNKU5m70ZEPdxZPxdSci9cAzwP2q+rBvU1bU\nX4zyQRbUH4CqXo43FuceESlyyVlRf1HKBplfd1cA54jIemAJsM6NN4IsqbvxYrTGGCV1jbU0FLV8\nIlIObBGRBXh9yWcB941JLpMvG+ouqmyoOxGZDPwG+HtVXR+2OePrL1b5sqT+VgN1qvptoBPowxuo\nDBlef7HKlg11p6orQ7+74Ogq3xiijK678Wa0AqPH8SLnF9zzK0TkUwyssXY98GsG1lgL749Nd/HK\ndyOwHm/G2u9U9VdjldERCv3Tyqa684tUvkyvu5vwmui/JiKhsTj3ACVZUn/xypfp9fcosFZEngXy\ngX8CLhSRbPj7i1e2TK+7cDlZ/L8zq9laacYYY4wxjt3g0RhjjDHGscDIGGOMMcaxwMgYY4wxxrHA\nyBhjjDHGscDIGGOMMcaxwMgYY4wxxrHAyBhjjDHGscDIGGOMMcaxwMhkJLdeljEZLVXXsYh8JMa2\nchFZnop8GJMJRmtJEJNiInIR8EWgAK9eC4C3gSeA/1bVw0k+3wV4K2Qfr6qdIrIEuEBVvzHE41wN\nXA0sAmap6s44++cA38dbgHFI50pn4e+nSxvWexrnPBcBXwVagErg34Aj4WkRFmcdzrki5j9SWUfD\nUK+tkb5umO4WkQdV9YHhvFhEfgB8AfiEqj4dZZ9LgHeiHUNVW0XkdBHpUNU/DycfxmQTazHKAiJy\nO3Aj8HlVPUtVV+AtwngAeBg4ZxRO24y3MGKXe74E+OehHkRV78ZbMylRNwG1yQwW0kT4+wnDfE+j\nEZEC4KfAraq6CliNt6DlT3xpn3VpyRAt/5HKmnTDuLZG9Lph+jvg6yJyxjBff4N7fDHSRrfo7qmq\nuiEs/XQRecKX9D3gKyJinwlm3LMWowwnIp8GrgLmqeruULprIfpHEVnJwOrcSaOqzwN/naTD5SSy\nk4hMA74OHJ+k86aNJL+f0UwFJgI73Dn/IiJtQJEvbQuwZTQzkaKyhiR0bSXxdUOiqodF5BbgbrwW\nqqE6A3hbVVuibL8R+FGE9PPwWpRD+QiKyG/wArWfDSMfxmQNC4wy3xrgDzGa+y8D9gGIyPluf/Dq\nvhP4svswDO9CuBK4BKgCSoGbVPVxt9/HgK8ApwKrgIXAtW7benf8/1LV++Odc4guAXaoav8/9ETz\n7Pa9AfgU0Oby8jPgDveh4C/TFcBHgVnAacCS8PyKyHV4Ael8Vc11ad/Ae7+Dqjo7wnt1BfAR4Dig\nBLhGVZ8P2+dMVf2jiFwL/EPYe7pWVddFe3MSKN9NbtdbRaQF+A933kFpqvqU67L8P9GO5zvnGrxW\npjagGPgL8G3grzj2mliL14rZX1ZgA/AMcDrwOvB9Vb1XRFa7/QqBNar6WKJ5imeI1+QpInInMIUI\n15Q73g3AZ/Ba2kqAdap6i9sW67paqqqbgV8BPxSRRcP4u1gOvBClnDnAYlV9I8LmFXj17/ck8J9Y\nYGTGOWs2zWAiUgIsBrZG20dVX1XVPe7pxcDPVHWVqi7H62Z7WkQCbl9/F8LFwPmq+kHgm8AjIrLI\n7fcU8L/cfkFVvRNvrAru2KtU9f5EzjlEK4C3wsqXUJ5F5Ft4gcxfqepK4OPAl/A+aMPL9GngSlX9\nkMtvb3hGVPX7eAGAP+2fgf/C10IXdtxPAper6unAs8CPI+wTet0POPY9jRUUJVK+S9zu/+SO5z+v\nPw33/kU9njvnzcD1wN+4ul0GnAD8tbsm/j08/+FlVdUuVT0D2I4X4N/r0n+C1z10pao+lmieEjSU\na/JTwIWRrin3HnzL5eFcd72cB6xxQXK86+qoS38Pb5zXiiGWA7z3/AURyRGRq0Tk/7qgErz/DYPG\nFonIpa7rfRmwQkSuD21T1Qa8oM2Ycc0Co8xWgdfk357g/l8B7vM9fwCve+VUX1qoC+FWVT0KoKo/\nBfYw8C3bv1+050M5Z6Km4o1PCRczzy6AvA64S1Wb3fZm4BEil+mB0KBgVb1UVV+Lkp9IZc6JkB56\n/rCq9rjffwfM9X0YRztWXCJSytDKF/MciRzP7bMG+LGqvu/26cSr721xshwpH/cCnxaRInf8cuBk\nVV0/xDImYijX5N3R/g58efK/B7vwWsa+HCoLca4r19p1wOUhYSKSj9fy9CJeq91DeOMJT3C7LOTY\nLxIP4gVlb6jqGlUNbzVqFJFZQ8mHMdnGutIy20G81onSBPcvxpsFI3jfVkMtG9Mi7Lsj7Pk7wInD\nyONQzhlPBQPfsiPZEfY8lOcFeF0yl4vIeb7tZUC7iJSoqn/A8WjNQtrt+73VPVYAh0Z43KGWb8TH\n8+0T/sH7u+EUAC+Y+Fe81pW1eK0r/playSxjsv4OQnl6M2yfN/HGbS0AXvGlx7queoBJ8TIe5gNA\nN17rz/9T1TYR+d8M1Ek1A9eZ3zLguSjHPADUcGy5jRk3LDDKYG7g5mbgpHj7ikgxXvfN/wBnq2q3\nS+9jlAaajsI5m4H8EWTpe6q6NoH9juk6iyLSuJZYf1P+44Zem8z3PtHyjfh4XkyRPKraKCJP4U09\nXwtcDpw/lDwlYiz+DnxiXVf5RG4NjWU5Xln2ApeKyO1uzFJIIZFbk5cTfRzREVI08NyYdGVdaZnv\nO8DKSDeKE5ESEWkWkUvxmtenAo/6PgwKYhx3tu84OXgDhqOOZQL6ws5dPIxzxtOA9202mmh53oY3\nNXxQi5eIzBKRH44gP63uOP4Wu3qSNwsw0nsaSbLLl8jxQvtI2D4r3eDmoeQ/5B7gQyJyGbBbVRuH\nmKdEJPPvIJSn8FmSAhwmfpei/7hVeNf3UCwDfqGqvwQ+BHxBRPJEZK7bvh/vvlTh5/oQ8Lx7virs\nmJUMPUAzJqtYYJTh1LsR3x14g0LrQukiMgmvK+JlvLEHb+N9e/RPk/6Ue4z0DfELIhJq/fgM3ofJ\nLRH2C712rztvpYicBqzHG1A7lHPG+6a6HpgXY3vEPLsulu/hdcPMd/nMxxs8vTvCcRL9xrwJ78N/\nlTvmTLz7R0V7fSJl9j+P9J4eQ1XbGXn5+tMSOV7YPtPdPmXAbQy0UsTLf3g+foPX3XQX3uyokZQx\nWvmG+ndwbbS/g7A81bs81ePNTLxFj715ZbTrYg5ei9HvQwkiMl9E+kRkcaQXuADnwwzMSCsAmvBm\nA050ae8BtWEvrQVyVXWHiHyYY7umJ+GNozJm3MoJBpN+ixszBkTkE8Df4/2DBK8Z/efAbaEBvyJy\nDl4LUwGgwEbgZryb7d2lqneIyJl406cvxpv+fsw0ZRmY+n0q3j1v7sSbjfVzoA6vy+Drqvp0nHPe\njdd0fxXedPuXgW/7ZkaFl3Ey3gfnElV93ZceN89uv+uBz+G19PQBT6nqv7ttq4Bv+cr0kqpek8D7\n/g94s5J2401V73DPX8T7gJzrO+5m4F/c+/MvrswbgKeBc3373KWq94hIXqT3NEZeYpUvvM4agR+E\npe1T1Y8mcjzfPmtcOVvxvmjd6Qb4Epb/o3h3Kp/gO2d/WX3H+yrejUpnDrWMEfa9moFrawPwLfVu\nRTCUa/JyvPFOEW8BEfYeHMabrr9WB6brx72u3Ligz6rqKb60i/AGpE8NtWyFvWYy8GtVXeKeXwis\nBLaGZva5FronVPWcsNf+DG+M0UH13XHbDRb/tXo3iDVm3LLAyAziCzJGeymEYRHv/kErVPVCX9qZ\npHGejYnGzb57Ffg7VX3FpQXwxg6tVdXbR3j8x4HPJDIw3QWMp6nqzSM5pzGZzrrSTDRpOQBTvfsH\n/UW8+8eES8s8GxPDw8B1oaDImQL8cKRBkXML8PkE912N14pozLhmgZHp57oevo83ePghEfmbMc5S\nRKr6NeBWyJw8GxPFalX1r1mGqr4V6g4bKfWWX6l3Yw6jcuONNmn0pUWMGTesK80YY7KYm3X3JVX9\nTpTt5XitVl9PacaMSVMWGBljjDHGONaVZowxxhjjWGBkjDHGGONYYGSMMcYY41hgZIwxxhjjWGBk\njDHGGONYYGSMMcYY41hgZIwxxhjjWGBkjDHGGOP8fyQ+jCK3LHpmAAAAAElFTkSuQmCC\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig, ax = plt.subplots(1, 1, figsize=(8,6))\n", + "ces_model.plot_solow_diagram(ax)\n", + "fig.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "internals": {}, + "slideshow": { + "slide_type": "-" + } + }, + "source": [ + "## Interactive example: the classic Solow diagram" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "collapsed": false, + "internals": {}, + "slideshow": { + "slide_type": "-" + } + }, + "outputs": [], + "source": [ + "from IPython.html.widgets import fixed, interact, FloatSliderWidget" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "collapsed": false, + "internals": {}, + "slideshow": { + "slide_type": "-" + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 13, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": "iVBORw0KGgoAAAANSUhEUgAAAkYAAAGaCAYAAADqyYylAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nQmCC\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# wrap the static plotting code in a function\n", + "def interactive_solow_diagram(model, **params):\n", + " \"\"\"Interactive widget for the Solow diagram.\"\"\"\n", + " fig, ax = plt.subplots(1, 1, figsize=(8, 6))\n", + " model.plot_solow_diagram(ax, Nk=1000, **params)\n", + " \n", + "# define some widgets for the various parameters\n", + "eps = 1e-2\n", + "technology_progress_widget = FloatSliderWidget(min=-0.05, max=0.05, step=eps, value=0.02)\n", + "population_growth_widget = FloatSliderWidget(min=-0.05, max=0.05, step=eps, value=0.02)\n", + "savings_widget = FloatSliderWidget(min=eps, max=1-eps, step=eps, value=0.5)\n", + "output_elasticity_widget = FloatSliderWidget(min=eps, max=1.0, step=eps, value=0.5)\n", + "depreciation_widget = FloatSliderWidget(min=eps, max=1-eps, step=eps, value=0.5)\n", + "elasticity_substitution_widget = FloatSliderWidget(min=eps, max=10.0, step=0.01, value=1.0+eps)\n", + "\n", + "# create the widget!\n", + "interact(interactive_solow_diagram, \n", + " model=fixed(ces_model),\n", + " g=technology_progress_widget,\n", + " n=population_growth_widget,\n", + " s=savings_widget, \n", + " alpha=output_elasticity_widget,\n", + " delta=depreciation_widget,\n", + " sigma=elasticity_substitution_widget,\n", + " )" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "internals": {}, + "slideshow": { + "slide_type": "-" + } + }, + "source": [ + "There are number of additional plotting methods available (all of which can be turned into interactive plots using IPython widgets). See the **Graphical analysis** notebook in the [solowPy](https://github.com/davidrpugh/solowPy) repository." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "internals": {}, + "slideshow": { + "slide_type": "-" + } + }, + "source": [ + "# 4. Solving the Solow model\n", + "\n", + "Solving the Solow model requires efficiently and accurately approximating the solution to a non-linear ordinary differential equation (ODE) with a given initial condition (i.e., an non-linear initial value problem). \n", + "\n", + "## 4.1 Solow model as an initial value problem\n", + "\n", + "The Solow model with can be formulated as an initial value problem (IVP) as follows.\n", + "\n", + "$$ \\dot{k}(t) = sf(k(t)) - (g + n + \\delta)k(t),\\ t\\ge t_0,\\ k(t_0) = k_0 \\tag{4.1.0} $$\n", + "\n", + "The `quantecon` library has its own module `quantecon.ivp` for solving initial value problems of this form using [finite difference methods](http://en.wikipedia.org/wiki/Finite_difference_method). Upon creation of our instance of the `solow.Model` class, an instance of the `quantecon.ivp.IVP` class was created and stored as an attribute of our model..." + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "collapsed": false, + "internals": {}, + "slideshow": { + "slide_type": "-" + } + }, + "outputs": [], + "source": [ + "ces_model.ivp?" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "internals": {}, + "slideshow": { + "slide_type": "-" + } + }, + "source": [ + "...meaning that we can solve this initial value problem by applying the `solve` method of the `ivp` attribute!" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": { + "collapsed": false, + "internals": {}, + "slideshow": { + "slide_type": "-" + } + }, + "outputs": [], + "source": [ + "ces_model.ivp.solve?" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": { + "collapsed": false, + "internals": {}, + "slideshow": { + "slide_type": "-" + } + }, + "outputs": [], + "source": [ + "# need to specify some initial conditions\n", + "t0, k0 = 0.0, 0.5\n", + "numeric_soln = ces_model.ivp.solve(t0, k0, T=100, integrator='dopri5')" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "internals": {}, + "slideshow": { + "slide_type": "-" + } + }, + "source": [ + "We can plot the finite-difference approximation of the solution as follows..." + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": { + "collapsed": false, + "internals": {}, + "slideshow": { + "slide_type": "-" + } + }, + "outputs": [ + { + "data": { + "image/png": "iVBORw0KGgoAAAANSUhEUgAAAgMAAAGWCAYAAADlmIA6AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nNdz/Bzlft7raL1QsAAAAAElFTkSuQmCC\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig, ax = plt.subplots(1, 1, figsize=(8,6))\n", + "\n", + "# plot the finite-difference-approximation\n", + "ax.plot(numeric_soln[:,0], numeric_soln[:,1], 'bo', markersize=3.0)\n", + "\n", + "# equilibrium value of capital stock (per unit effective labor)\n", + "k_star = ces_model.steady_state\n", + "ax.axhline(k_star, linestyle='dashed', color='k', label='$k^*$')\n", + "\n", + "# axes, labels, title, etc\n", + "ax.set_xlabel('Time, $t$', fontsize=15, family='serif')\n", + "ax.set_ylabel('$k(t)$', rotation='horizontal', fontsize=20, family='serif')\n", + "ax.set_title('Finite-difference approximation',\n", + " fontsize=20, family='serif')\n", + "ax.legend(loc=0, frameon=False, bbox_to_anchor=(1.0, 1.0))\n", + "ax.grid('on')\n", + "\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "internals": {}, + "slideshow": { + "slide_type": "-" + } + }, + "source": [ + "Finite-difference methods only return a discrete approximation to the continuous function $k(t)$. To get a continouous approximation of the solution we can combined finite-difference methods with [B-spline interpolation](http://en.wikipedia.org/wiki/B-spline) using the `interpolate` method of the `ivp` attribute." + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": { + "collapsed": false, + "internals": {}, + "slideshow": { + "slide_type": "-" + } + }, + "outputs": [], + "source": [ + "ces_model.ivp.interpolate?" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": { + "collapsed": false, + "internals": {}, + "slideshow": { + "slide_type": "-" + } + }, + "outputs": [], + "source": [ + "# interpolate!\n", + "ti = np.linspace(0, 100, 1000)\n", + "interpolated_soln = ces_model.ivp.interpolate(numeric_soln, ti, k=3)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "internals": {}, + "slideshow": { + "slide_type": "-" + } + }, + "source": [ + "We can graphically compare the discrete, finite-difference approximation with the continuous, B-spline approximation as follows." + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": { + "collapsed": false, + "internals": {}, + "slideshow": { + "slide_type": "-" + } + }, + "outputs": [ + { + "data": { + "image/png": "iVBORw0KGgoAAAANSUhEUgAAAgMAAAGWCAYAAADlmIA6AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\niIiIJJySARERkYT7/48AIM4O8QS6AAAAAElFTkSuQmCC\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig, ax = plt.subplots(1, 1, figsize=(8,6))\n", + "\n", + "# plot the interpolated and finite difference approximations\n", + "ax.plot(ti, interpolated_soln[:,1], 'r-')\n", + "ax.plot(numeric_soln[:,0], numeric_soln[:,1], 'bo', markersize=3.0)\n", + "\n", + "# equilibrium value of capital stock (per unit effective labor)\n", + "k_star = ces_model.steady_state\n", + "ax.axhline(k_star, linestyle='dashed', color='k', label='$k^*$')\n", + "\n", + "# axes, labels, title, etc\n", + "ax.set_xlabel('Time, $t$', fontsize=15, family='serif')\n", + "ax.set_ylabel('$k(t)$', rotation='horizontal', fontsize=20, family='serif')\n", + "ax.set_title('B-spline approximation of the solution',\n", + " fontsize=20, family='serif')\n", + "ax.legend(loc=0, frameon=False, bbox_to_anchor=(1.0, 1.0))\n", + "\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "internals": {}, + "slideshow": { + "slide_type": "-" + } + }, + "source": [ + "## Accuracy of our numerical methods\n", + "\n", + "When doing numerical work it is important to understand the accuracy of the methods that you are using to approximate the solution to your model. Typically one assesses the accuracy of a solution method by computing and evaluatin some residual function:\n", + "\n", + "$$ R(k; \\theta) = sf(\\hat{k}(\\theta)) - (g + n + \\delta)\\hat{k}(\\theta) - \\dot{\\hat{k}}(\\theta) $$\n", + "\n", + "where $\\hat{k}(\\theta)$ is out computed solution to the original differential equation. We can assess the accuracy of our finite-difference methods by plotting the residual function for our approximate solution using the `compute_residual` method of the `ivp` attribute." + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": { + "collapsed": false, + "internals": {}, + "slideshow": { + "slide_type": "-" + } + }, + "outputs": [], + "source": [ + "# compute the residual...\n", + "ti = np.linspace(0, 100, 1000)\n", + "residual = ces_model.ivp.compute_residual(numeric_soln, ti, k=3)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "internals": {}, + "slideshow": { + "slide_type": "-" + } + }, + "source": [ + "We can then plot the residual as follows. Our approximation is accurate so long as the residual is everywhere \"close\" to zero." + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": { + "collapsed": false, + "internals": {}, + "slideshow": { + "slide_type": "-" + } + }, + "outputs": [ + { + "data": { + "image/png": "iVBORw0KGgoAAAANSUhEUgAAAgcAAAGZCAYAAAAdJZKVAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n/AAAABNJREFUFwdmZmZW4OLAzMzMCv4/xQDg7nnYjawAAAAASUVORK5CYII=\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# extract the raw residuals\n", + "capital_residual = residual[:, 1]\n", + "\n", + "# typically, normalize residual by the level of the variable\n", + "norm_capital_residual = np.abs(capital_residual) / interpolated_soln[:,1]\n", + "\n", + "# create the plot\n", + "fig = plt.figure(figsize=(8, 6))\n", + "plt.plot(interpolated_soln[:,1], norm_capital_residual, 'b-', label='$k(t)$')\n", + "plt.axhline(np.finfo('float').eps, linestyle='dashed', color='k', label='Machine eps')\n", + "plt.xlabel('Capital (per unit effective labor), $k$', fontsize=15, family='serif')\n", + "plt.ylim(1e-16, 1)\n", + "plt.ylabel('Residuals (normalized)', fontsize=15, family='serif')\n", + "plt.yscale('log')\n", + "plt.title('Residual', fontsize=20, family='serif')\n", + "plt.legend(loc=0, frameon=False, bbox_to_anchor=(1.0,1.0))\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "internals": {}, + "slideshow": { + "slide_type": "-" + } + }, + "source": [ + "For more details behind the numerical methods used in this section see the the **Solving the Solow model** notebook in the [solowPy](https://github.com/davidrpugh/solowPy) repository." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "internals": {}, + "slideshow": { + "slide_type": "-" + } + }, + "source": [ + "# 5. Impulse response functions\n", + "\n", + "Impulse response functions (IRFs) are a standard tool for analyzing the short run dynamics of dynamic macroeconomic models, such as the Solow growth model, in response to an exogenous shock. The `solow.impulse_response.ImpulseResponse` class has several attributes and methods for generating and analyzing impulse response functions. \n", + "\n", + "### Example: Impact of a change in the savings rate\n", + "One can analyze the impact of a doubling of the savings rate on model variables as follows." + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": { + "collapsed": false, + "internals": {}, + "slideshow": { + "slide_type": "-" + } + }, + "outputs": [], + "source": [ + "# 50% increase in the current savings rate...\n", + "ces_model.irf.impulse = {'s': 1.5 * ces_model.params['s']}\n", + "\n", + "# in efficiency units...\n", + "ces_model.irf.kind = 'efficiency_units'" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": { + "collapsed": false, + "internals": {}, + "slideshow": { + "slide_type": "-" + } + }, + "outputs": [ + { + "data": { + "image/png": "iVBORw0KGgoAAAANSUhEUgAAAfsAAAGUCAYAAAAyKYtdAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nB4PDIBoN7EwOAAAAAElFTkSuQmCC\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig, ax = plt.subplots(1, 1, figsize=(8,6))\n", + "ces_model.irf.plot_impulse_response(ax, variable='output')\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "internals": {}, + "slideshow": { + "slide_type": "-" + } + }, + "source": [ + "### Example: Interactive impulse reponse functions\n", + "Using IPython widgets makes it extremely easy to analyze the various impulse response functions." + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "metadata": { + "collapsed": false, + "internals": {}, + "slideshow": { + "slide_type": "-" + } + }, + "outputs": [ + { + "data": { + "image/png": "iVBORw0KGgoAAAANSUhEUgAAAgEAAAGUCAYAAACspfEMAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nHHeJxC7ZBQAAAABJRU5ErkJggg==\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "def interactive_impulse_response(model, shock, param, variable, kind, log_scale):\n", + " \"\"\"Interactive impulse response plotting tool.\"\"\" \n", + " # specify the impulse response\n", + " model.irf.impulse = {param: shock * model.params[param]}\n", + " model.irf.kind = kind\n", + " \n", + " # create the plot\n", + " fig, ax = plt.subplots(1, 1, figsize=(8,6))\n", + " model.irf.plot_impulse_response(ax, variable=variable, log=log_scale)\n", + " \n", + "\n", + "irf_widget = interact(interactive_impulse_response, \n", + " model=fixed(ces_model),\n", + " shock = FloatSliderWidget(min=0.1, max=5.0, step=0.1, value=0.5),\n", + " param = ['g', 'n', 's', 'alpha', 'delta' , 'sigma'],\n", + " variable=['capital', 'output', 'consumption', 'investment'],\n", + " kind=['efficiency_units', 'per_capita', 'levels'],\n", + " log_scale=False,\n", + " )" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "internals": {}, + "slideshow": { + "slide_type": "-" + } + }, + "source": [ + "For more details and examples see the accompanying **Impulse response function** notebook in the [solowPy](https://github.com/davidrpugh/solowPy) repository." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "internals": {}, + "slideshow": { + "slide_type": "-" + } + }, + "source": [ + "# 6. The Solow model, declining labor's share, and secular stagnation\n", + "\n", + "Recently there has been much discussion about the reasons for the decline in labor's share of income (see [Elsby (2013)](http://www.brookings.edu/~/media/Projects/BPEA/Fall%202013/2013b_elsby_labor_share.pdf) for an analysis using U.S. data); as well as much debate about whether or not developed economes are experiencing some sort of [secular stagnation](http://www.economist.com/blogs/buttonwood/2014/11/secular-stagnation) more generally.\n", + "\n", + "Let's see if the Solow model can match the following stylized facts:\n", + "\n", + "1. A decline in labor's share of output/income (note this implies rising capital's share)\n", + "2. A slow-down in the growth rate of per capita output/income.\n" + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "metadata": { + "collapsed": false, + "internals": {}, + "slideshow": { + "slide_type": "-" + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 27, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": "iVBORw0KGgoAAAANSUhEUgAAAsUAAAGWCAYAAACQOf7cAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAABJRU5ErkJggg==\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "def awesome_interactive_plot(model, iso3_code, **params):\n", + " \"\"\"Interactive widget for the my awesome plot.\"\"\"\n", + " \n", + " # extract the relevant data\n", + " tmp_data = pwt.major_xs(iso3_code)\n", + " actual_labor_share = tmp_data.labsh.values\n", + " actual_capital_share = 1 - tmp_data.labsh\n", + " \n", + " output = tmp_data.rgdpna\n", + " capital = tmp_data.rkna\n", + " labor = tmp_data.emp\n", + " \n", + " # need to update params\n", + " model.params.update(params)\n", + " \n", + " # get new initial condition\n", + " implied_technology = model.evaluate_solow_residual(output, capital, labor)\n", + " k0 = tmp_data.rkna[0] / (implied_technology[0] * labor[0])\n", + " \n", + " # finite difference approximation\n", + " T = actual_labor_share.size\n", + " soln = model.ivp.solve(t0, k0, T=T, integrator='dopri5')\n", + " \n", + " # get predicted labor share\n", + " predicted_capital_share = model.evaluate_output_elasticity(soln[:,1])\n", + " predicted_labor_share = 1 - predicted_capital_share\n", + " \n", + " # get predicted output per unit labor\n", + " predicted_intensive_output = model.evaluate_intensive_output(soln[:,1])\n", + " technology = implied_technology[0] * np.exp(ces_model.params['g'] * soln[:,0])\n", + " predicted_output_per_unit_labor = predicted_intensive_output * technology\n", + "\n", + " # make the plots!\n", + " fig, axes = plt.subplots(1, 2, figsize=(12,6))\n", + " axes[0].plot(soln[:,0], predicted_labor_share, 'b')\n", + " axes[0].plot(soln[:,0], predicted_capital_share, 'g')\n", + " axes[0].plot(actual_labor_share)\n", + " axes[0].plot(actual_capital_share) \n", + " axes[0].set_xlabel('Time, $t$', fontsize=15, family='serif')\n", + " axes[0].set_ylim(0, 1)\n", + " axes[0].set_title('Labor share of income in {}'.format(iso3_code),\n", + " fontsize=20, family='serif')\n", + " axes[0].legend(loc=0, frameon=False, bbox_to_anchor=(1.0, 1.0))\n", + " \n", + " axes[1].set_xlabel('Time, $t$', fontsize=15, family='serif')\n", + " axes[1].set_title('Growth rate of Y/L in {}'.format(iso3_code),\n", + " fontsize=20, family='serif')\n", + " axes[1].legend(loc=0, frameon=False, bbox_to_anchor=(1.0, 1.0))\n", + " axes[1].plot(soln[1:,0], np.diff(np.log(predicted_output_per_unit_labor)),\n", + " 'b', markersize=3.0)\n", + " axes[1].plot(np.log(output / labor).diff().values)\n", + "\n", + " \n", + "# define some widgets for the various parameters\n", + "technology_progress_widget = FloatSliderWidget(min=-0.05, max=0.05, step=5e-3, value=0.01)\n", + "population_growth_widget = FloatSliderWidget(min=-0.05, max=0.05, step=5e-3, value=0.01)\n", + "savings_widget = FloatSliderWidget(min=eps, max=1-eps, step=5e-3, value=0.2)\n", + "output_elasticity_widget = FloatSliderWidget(min=eps, max=1.0, step=5e-3, value=0.175)\n", + "depreciation_widget = FloatSliderWidget(min=eps, max=1-eps, step=5e-3, value=0.02)\n", + "elasticity_substitution_widget = FloatSliderWidget(min=eps, max=10.0, step=1e-2, value=2.0+eps)\n", + "\n", + "# create the widget!\n", + "interact(awesome_interactive_plot, \n", + " model=fixed(ces_model),\n", + " iso3_code='USA',\n", + " g=technology_progress_widget,\n", + " n=population_growth_widget,\n", + " s=savings_widget, \n", + " alpha=output_elasticity_widget,\n", + " delta=depreciation_widget,\n", + " sigma=elasticity_substitution_widget,\n", + " )" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false, + "internals": { + "slide_helper": "subslide_end" + }, + "slide_helper": "slide_end", + "slideshow": { + "slide_type": "-" + } + }, + "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": "3.5.1" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +}