{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Economics Simulation" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This is a simulation of an economic marketplace in which there is a *population* of actors, each of which has a level of wealth. On each time step two actors (chosen by an *interaction function*) engage in a transaction that exchanges wealth between them (according to a *transaction function*). The idea is to understand the evolution of the population's wealth over time. I heard about the problem when I visited the Bard College Computer Science Department. \n", "\n", "\n", "\n", "Why is this interesting? \n", "- It is an example of using simulation to model the world. The model is simple but captures some aspects of a complex world.\n", "- Many students will have preconceptions about how economies work that will be challenged by the results shown here.\n", "- It reveals subtle differences between computational thinking, mathematical thinking, and statistical thinking." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Population Distributions" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We will model a population as a list of N numbers, each number being one actor's wealth. We'll start with a Gaussian distribution (also known as a *normal* distribution or *bell-shaped curve*), with a mean wealth of 100 [simoleons](http://en.wiktionary.org/wiki/simoleon) and a standard deviation of 1/5 the mean:" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": true }, "outputs": [], "source": [ "import random\n", "\n", "N = 5000 # Default size of the population\n", "MU = 100. # Default mean of the population\n", "\n", "population = [random.gauss(mu=MU, sigma=MU/5) for actor in range(N)]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Population Statistics and Visualization\n", "\n", "How evenly is the wealth in a population distributed? The traditional measure is the [Gini coefficient](http://en.wikipedia.org/wiki/Gini_coefficient), which Wikipedia says is computed by this formula (which assumes the *y* values are sorted):\n", "\n", "![Gini](https://upload.wikimedia.org/math/b/b/5/bb50601acc135c45a24bb0493f7555b4.png)\n", "\n", "A Gini index of 0 means total equality (everyone has the same amount), and values closer to 1 mean more inequality (most of the money in the hands of a few individuals). Here's a table of Gini coefficients for several countries:\n", "\n", "\n", "
 Sweden 0.250\n", " Canada 0.326\n", " Switzerland 0.337\n", " United States 0.408\n", " Chile 0.521\n", " South Africe 0.631\n", "
\n", "\n", "\n", "The Gini coefficient is traditionally computed over *income*, but we will be dealing with *wealth*. Here is the computation:" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def gini(y):\n", " \"Compute the Gini coefficient (a measure of equality/inequality) in a population, y.\"\n", " y = sorted(y)\n", " n = len(y)\n", " numer = 2 * sum((i+1) * y[i] for i in range(n))\n", " denom = n * sum(y)\n", " return (numer / denom) - (n + 1) / n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We'll define the function hist to plot a histogram of a population. Our hist wraps plt.hist, but with some specific keyword values:" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": true }, "outputs": [], "source": [ "%matplotlib inline\n", "import matplotlib.pyplot as plt\n", "\n", "def hist(population, label='pop', **kwargs):\n", " \"A custom version of hist with better defaults.\"\n", " label = label + ': G=' + str(round(gini(population), 2))\n", " h = plt.hist(list(population), bins=30, alpha=0.5, label=label, **kwargs)\n", " plt.xlabel('wealth'); plt.ylabel('count'); plt.grid(True)\n", " plt.legend()" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "hist(population)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Transactions" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In a transaction, two actors come together and exchange some of their wealth. For now we will use a wealth-conserving transaction function in which all the wealth from both actors is put into a pot, which is then split randomly and uniformly between the two actors:" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def random_split(A, B):\n", " \"Take all the money uin the pot and divide it randomly between the two actors.\"\n", " pot = A + B\n", " share = random.uniform(0, pot)\n", " return share, pot - share" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "(95.3251239711815, 104.6748760288185)" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "random_split(100, 100)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Interactions" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "How do we decide which parties interact with each other? We will define an interaction function that, given the size of the population, randomly selects any two actors in the populations (denoted by their index numbers in the list). We'll call this function anyone, meaning that any actor can interact with any other actor:" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def anyone(N): return random.sample(range(N), 2)" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[3405, 116]" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "anyone(N)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Simulation" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The function simulate takes an initial population, calls an interaction function to select two actors, and a transaction function to split their wealth, and repeats this T times. After each transaction, we yield the population, so simulate yields the complete history of the simulation." ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def simulate(population, T, transaction=random_split, interaction=anyone):\n", " \"Run simulation on population for T transactions; yield (t, pop) at each time step.\"\n", " population = population.copy()\n", " yield population\n", " for t in range(1, T + 1):\n", " i, j = interaction(len(population))\n", " population[i], population[j] = transaction(population[i], population[j]) \n", " yield population" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here is a simple example of simulating a population of 4 actors for 8 time steps:" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[100, 100, 100, 100]\n", "[100, 139.34514344135886, 100, 60.65485655864116]\n", "[170.2563182135521, 139.34514344135886, 29.743681786447894, 60.65485655864116]\n", "[105.13376035310705, 139.34514344135886, 29.743681786447894, 125.7774144190862]\n", "[105.13376035310705, 222.24697868451042, 29.743681786447894, 42.875579175934625]\n", "[105.13376035310705, 222.24697868451042, 53.493944819559275, 19.125316142823255]\n", "[105.13376035310705, 182.09114633291017, 53.493944819559275, 59.28114849442351]\n", "[105.13376035310705, 221.7092394595479, 53.493944819559275, 19.663055367785798]\n", "[264.84710771935215, 61.995892093302835, 53.493944819559275, 19.663055367785798]\n" ] } ], "source": [ "for pop in simulate([100] * 4, 8):\n", " print(pop)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# SImulation Visualization\n", "\n", "If we want to do larger simulations we'll need a better way to visualize the results.\n", "The function show does that:" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": false }, "outputs": [], "source": [ "import statistics\n", "\n", "def show(population, k=40, percentiles=(1, 10, 50, 90, 99), **kwargs):\n", " \"Run a simulation for k*N steps, printing statistics and displaying a plot and histogram.\"\n", " N = len(population)\n", " start = list(population)\n", " results = [(t, sorted(pop)) # Sort results so that percentiles work\n", " for (t, pop) in enumerate(simulate(population, k * N, **kwargs))\n", " if t % (N / 10) == 0]\n", " times = [t for (t, pop) in results]\n", " # Printout:\n", " print(' t Gini stdev' + (' {:3d}%' * len(percentiles)).format(*percentiles))\n", " print('------- ---- -----' + ' ----' * len(percentiles))\n", " fmt = '{:7,d} {:.2f} {:5.1f}' + ' {:4.0f}' * len(percentiles)\n", " for (t, pop) in results:\n", " if t % (4 * N) == 0:\n", " data = [percent(pct, pop) for pct in percentiles]\n", " print(fmt.format(t, gini(pop), statistics.stdev(pop), *data))\n", " # Plot:\n", " plt.hold(True); plt.xlabel('wealth'); plt.ylabel('time'); plt.grid(True)\n", " for pct in percentiles:\n", " line = [percent(pct, pop) for (t, pop) in results]\n", " plt.plot(line, times)\n", " plt.show()\n", " # Histogram:\n", " R = (min(pop+start), max(pop+start))\n", " hist(start, 'start', range=R)\n", " hist(pop, 'end', range=R)\n", " \n", "def percent(pct, items):\n", " \"The item that is pct percent through the sorted list of items.\"\n", " return items[min(len(items)-1, len(items) * pct // 100)]" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " t Gini stdev 1% 10% 50% 90% 99%\n", "------- ---- ----- ---- ---- ---- ---- ----\n", " 0 0.11 19.7 55 74 100 125 145\n", " 20,000 0.50 98.2 1 11 70 230 440\n", " 40,000 0.51 102.6 1 10 69 232 489\n", " 60,000 0.50 98.2 1 11 70 232 453\n", " 80,000 0.50 99.1 1 11 68 230 459\n", "100,000 0.50 99.6 1 11 69 227 472\n", "120,000 0.49 98.3 1 11 71 224 459\n", "140,000 0.50 99.7 1 11 69 229 469\n", "160,000 0.50 101.1 1 11 68 228 484\n", "180,000 0.50 100.4 1 10 68 230 465\n", "200,000 0.50 99.8 1 10 69 230 456\n" ] }, { "data": { "image/png": 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wwAdZHxzSbs40h4MRMs0Ii8BeamfynyZjL9EmKEHtA9KIWDOg5oFmrCar8YwP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\ne+DYf9KPd7cX7x4vPUd6zOI1kenKvJV5zPj5jHG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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "show(population)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "There are three parts to this output:\n", "\n", "**The printout:** For the starting population and for every 10,000 transactions along the way, we \n", "print the Gini coefficient and standard deviation of the population, and the wealths at five percentile points in the population: the 1%, 10%, 50% (median), 90% and 99% marks.\n", "\n", "**The plot:** This shows the same information as the printout (except for the Gini index), but with more data points along the way. The leftmost (blue) line is the 1% mark, the rightmost (purple) is the 99% mark, and the inner lines are the 10%, 50% and 90% marks, respectively. For the plot, time goes from bottom to top rather than top to bottom. So, the 99% (purple) line starts at around 150, and over time increases to over 400, indicating that the richest 1% are getting richer. The fact that the lines are going more or less straight up after about 50,000 transactions suggests that the system has converged.\n", "\n", "**The histogram:** The starting and ending populations are plotted as histograms. \n", "\n", "The results show that income inequality is increasing over time. How can you tell? Because the Gini coefficient is increasing over time, the standard deviation is increasing, and the 1% and 10% marks are decreasing (the blue and olive lines are moving left as time increases) while the 90% and 99% marks are increasing (the aqua and purple lines are moving right as time increases).\n", "\n", "Would the population continue to change if we let the simulation run longer? It looks like only the 1% line is changing, the other lines remain pretty much in one place from about T=15,000 to T=25,000. This suggests that running the simulation longer would not have too much effect." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Effect of Starting Population\n", "\n", "What happens to the final result if we vary the starting population? I'll introduce the function samples to sample from a distribution function n times, normalizing the result to have the specified mean:" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def samples(distribution, *args, n=N, mu=MU):\n", " \"Sample from the distribution n times, then normalize results to have mean mu.\"\n", " numbers = [distribution(*args) for _ in range(N)]\n", " return normalize(numbers, mu)\n", "\n", "def normalize(numbers, mu):\n", " \"Make the numbers non-negative, and scale them so they have mean mu.\"\n", " numbers = [max(0, n) for n in numbers]\n", " factor = len(numbers) * mu / sum(numbers)\n", " return [x * factor for x in numbers]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we can easily make an initial population from a distribution function. I'll start with a uniform distribution:" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " t Gini stdev 1% 10% 50% 90% 99%\n", "------- ---- ----- ---- ---- ---- ---- ----\n", " 0 0.34 58.7 2 20 99 182 199\n", " 20,000 0.49 95.7 1 11 72 228 443\n", " 40,000 0.50 100.5 1 10 69 231 460\n", " 60,000 0.50 99.3 1 11 70 232 465\n", " 80,000 0.50 100.1 1 11 69 229 464\n", "100,000 0.50 99.1 1 11 71 233 465\n", "120,000 0.50 100.8 1 11 68 236 471\n", "140,000 0.50 101.1 1 11 67 228 479\n", "160,000 0.50 99.5 1 10 69 230 455\n", "180,000 0.51 102.3 1 11 67 233 475\n", "200,000 0.50 98.7 1 10 71 227 455\n" ] }, { "data": { "image/png": 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Wp7P0FjFhUTMghiYjtRqt+mRAOEhKCqxbp9/9Rwi+UIjPbN3Kpr4+7hw9Wq1UUhyGlJKg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\ndrJzO5OvgI5MUjXGhIHDk1T7FWPMKqCh3ekrgefix88BV8W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OiomIiORMxSQBmjOJJ8RMEGYuZYpHmZKjYiIiIjlTMUmA5kziCTEThJlLmeJR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\nD5nZaWb2gpktMLO/RFdnxcx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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "show(samples(random.uniform, 0, 200))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "And try a constant distribution, where everyone starts out the same:" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " t Gini stdev 1% 10% 50% 90% 99%\n", "------- ---- ----- ---- ---- ---- ---- ----\n", " 0 0.00 0.0 100 100 100 100 100\n", " 20,000 0.49 94.7 1 12 71 228 425\n", " 40,000 0.50 100.0 1 11 70 226 457\n", " 60,000 0.50 100.5 1 11 69 230 458\n", " 80,000 0.50 99.6 1 11 70 229 450\n", "100,000 0.49 99.3 1 11 70 231 445\n", "120,000 0.50 98.8 1 11 71 231 461\n", "140,000 0.51 101.7 1 10 69 231 472\n", "160,000 0.50 99.0 1 11 68 232 458\n", "180,000 0.50 99.4 1 11 70 229 460\n", "200,000 0.49 99.0 1 12 69 229 449\n" ] }, { "data": { "image/png": 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FDKPbYuedO+l+rRt7hZ3CqwupfqSa9NnpugcbjIZyQMR3QA1dDcbdkK6iAv75\nT71VKI6DNLOZL5aVUZuWxuMtLez1epnocOgtS3GCUPNEDZ2vdOLe5KZ/RT8HfnMAxyQHOefkUHh1\nIRnzMwy1CFrNARF/CM5qshozCwJAfT2con2IeCqOb48X42ULkxBcWVjIg1VVACxtbR3jCv1R7SKG\n0W1hL7NTdksZJ/3iJOYum8sZXWdw0q9PwpxuZu2CtXS/qu0uyh8W5YCI3wOqza9la8fW5ItJhP/8\nJ9ILUqQs+3w+AJyjpWJXKDTAZDWRuSCTirsrcJ7kZNMlm1g5fSWe3caY31ZDcMR3QDu6d1CdW518\nMYlw++3w9NNw7bWaVmv08e1kMt62eLunhzMyM7m9bNSNeg2DahcxUskW27+wnZbHW0aUD9UP4d3l\nxVnl1EHV4ajbL+I7oJq8GrZ3bk++mERoaYFZI/b3U6QQC7Oy8ITDuMxmvaUoTlAmfnMiGfMP38ts\nYfNClsgl5JyTo5Oqw1EOiPgOKMeZgydojG7qCBobYepUzas1+vh2MhlvWxRYrTT5fARG24zKQKh2\nESOVbNG3vC+yG9owNpy/QR8xo6CG4IjvgAZ8A2TYDLgTalsbvPkmfOUreitRfAgmORy0BwJcsHEj\n/5w9G7OBIpMUqUtwMMj+H+6n770+et/upeJrFUz+6WQclQ5sRTaEyVjtTDkg4kfBOa1OhgKj7FSn\nJzt3Qn4+zJmjedWpNL493oyXLba63fy1s/PQWqChUIiQlIZ2QKpdxDC6LWRQ4m/142/zY3Ka6Pp7\nFwOrBw4lILUWWTFZTZTeUorZpf/wr3JAxHdAGbYMer299Hp7yXbonzPpEPPmQU8PrFkzLqHYivFh\nKBTi1DVr6A0G+URBAY9UV3NWVhYWFQWn0BBrtpWaJyJJlIN9Qbz7vQTaAoec0u7/2U3YEyZ7STYZ\np+g/wqNaPzApznrTfX37KMkoIdOemXxBR8Nuh6oqiN5Ba0kqjW+PN1rbwgQ0eDx8pbycawsLWZKd\nnTLOR7WLGKlkC0uWhfQZ6eSck0PRtUVU3FVB5X2VAKyZt4Z3c99l1exVbLp0E979+mTlUD0gIN7e\nYBKJw+Iw3o6oPp/aAygFcZjN/GHqVK6qrwdg3SmnMCdD/ztQxYmNZ7eHVdNXEfaEMbkiv2Vp09Nw\nVDiwV9ixT7DjmODAmqfPBolCSjn2WScwQgj55S9LfvKTw8vdfjclj5aw5bYtVGQZbNHnpz8NU6bA\nAw/orUTGfDWIAAAgAElEQVSRIB1+P1fV15NjsfDrk06i0BY/Xb5CcTyEfWF8B3z4mn34mnz4m/34\nmn0MrB6g752+Q+ed2Xcmlkxt+h1CCKSUH2ryUvWARsFmtjEpZxIrm1cazwHdcw+ccw5ceSWobMop\ngTsUYsfQEHdXVCjno/hQSCkJtAfw7vPS/Wo3zb9oJtgXxFZsw15mjxzldmxlNkpvLaXqwSrsZXZs\npTbMTv0DD4ajHNAo7OrZRetgK5fWXKq3lJHMmgUPPQS33qrpcJwe+90bFa1tUWCz0RMMUpaCO6Kq\ndhFDT1tsvWErbc/Gds90zXThmu5i7vtzcU5yGi7EOhGUAxqFovQi3AE3VrM+Y6NjcuWVcNdd4PeD\nuqM2LFJKPt/QwHPt7UxwOLiysFBvSYoUpfxL5YS9YYa2Rvb4Gdo6hL/Vj7veja3ERtqUNHLOyyH7\nY9lY0lPjpz01VOqA0+LEG/QipTRU+vJDmEyR+HENU7mou9wYWtnCGw5T19vLYCjEtSnqfFS7iKGn\nLTJOzmD6c9MPvZYhib/Dj78lcvSv7GfrtVsJDYaoXVpL8fXFumlNFIOFeOlDvHVAg/5BHBYH8shc\nFkZh926YMEFTB6TQHpMQXFlQAMBjzc06q1GcSAizwF5sJ2NuBq6ZLvY9vI/QYCStS/c/jbXtwmgo\nBwQMxUl4kJeWh81so2uoK/mCEsFuj2zLrSGptMZhvNHKFnaTiYcmTeJrFRVUpujGc6pdxDCqLRwV\nDk6tP5Wi6yPbbYe9xs8xCGoIDoDRdkauyKygsaeRAldBcgUlQnk5dHXB3r0wcaLeahSjMBQK8a+e\nHkJSUu926y1HcYIRHAyy+dLNuLe4CbRHbkgrvlFB9Q8MupXMEage0FGwmCy0DbaNfaIepKfDokXw\nj39oVqUa64+hlS1e6+7m0/X1/LipibtSdBNB1S5iGM0WMijJvSgX10zXobLh636MjuoBjYIv6GND\n2wYumHyB3lLi88QTUFcHTz6ptxLFUfhkQQGlNhunr1vHxbm5estRnCCE/WG237ydzr924qh0YJ9g\np/TWUuwT7GQvMlDuyjFQPaBRsFvs1OTVsKltk95S4rN1K1xyCRRoNzxo1PFtPdDKFi93dnLxpk1c\nU1jIrPR0TepMNqpdxDCKLYa2DdH1chc1T9Yw9XdTqX2qlik/m8LEeyaSdXqW3vISRvWAiL+MZm/v\nXtrcbUwt0H7jN01YuBC++129VSiOwpqBAS7bvJlrCwt5dPJktfupQjNsJTbyLsuj5cmWSKbrFj/B\n3iAmh4myL5cx6cE4GZYNiHJARJbUHMmm9k2cUnIK6TaD3rX+4Q9wzTWaVmm08W090cIWs10u/jJ9\nOi90dDBh+XJmp6ezMgW30FDtIoZRbGErsDF1aeTmeHDzIINrBxlYO0Dr0tYRu6AaGeWAAE+cnbfX\nHFjD3OK5yReTKMuWwaOP6q1CcRQsJhNXFBRwRUEB7/b2ctb69Tzb2sr1xcZfIKgwHmFfmEBngEBP\ngGBPkGBPEO8+Lzvv2HnonMrvVjLxf1InKlbNARF/HZDEoBkQDjJrFmzQdn93o4xvGwGtbXFmdjZb\n5s/n9oYGujVevzXeqHYRQ09bLHMuY3n5clbPXM2ue3Zx4PEDDKwYoOyOMkpuLiH34lyKrys29u/W\nESgHRHwHdGnNpTyx9onki0mUU06BFSv0VqFIkLCU/LmjAyGEobffVhgXYYm1G2uBFXtpZD8fZ7WT\nouuKmPWPWTgmptZiZ7UfkBDyrLMky5YdXh6WYSzftRD4dgCzyYCTx+eeC9deC5/9rN5KFAngC4dx\nLFvGQ1VV3KsWDiuOg+BAEP8BP/4OP4H2AP52P97dXtyb3HS/1s28jfNIn5m8OWu1H5BGxFugbhIm\nJuVMYl3rOuaVzku+qLG44Qb49a+VA0oR7CYTVxUU8Kf2duWAFMeFJcPC7l/upn95P4GOAP42Pwiw\nFdlIPzkdky31BrRST/E4EArFLz+78mxe2f5KcsUkypVXwsaN0NqqWZVqrD+G1rZ4saODf/f0cEdZ\nmab1JgPVLmLobYvmnzZTeX8ls/81m9PbT2eRexGn7TqNeWvmkVaTpqu240H1gIDRFqhn2DNwWAw6\npmq3RwIR1q2Diy7SW41iFP7fvn280dPDWz09vDVnDouzU2eVusJ4uGa62PLJLVhyLFiyLSMePQ0e\nSj5fQuGnUmPrD+WAiL8dA8DErInUd9QnV0yieDyRbAi1tZpVaZQ1DkZAK1t0BYP0BoM4TCb2j5b1\n1uCodhFDb1vM2zCPsCccCcPuDUZCsnsjIdnbrtsGQFptmnJAqURmZvxyiSQYDiZXTKK8917E+VRV\n6a1EcRQenjSJe4JBztuwgYZ4C84UimNACIE5zYw5zYy97PDt3XM+lsPub++m7Q9t9L3TR94leeSc\nl4Oj0oGt2GbIOSLjKdKB0RzQzu6dzCqalVwxiZKXB/v3j76XxHGg9/i2kdDSFiv6+9nkdnN3imbD\nVu0ihpFtYS+zU/t0Lae3nc7kn00mHAjT+PVGPpj0Acvsy3iv6D1Wz13Nxks24tljjJuhMR2QEOIk\nIcS/hRCbo69nCSH+Z/ylJY+MjPjl27u2Mzl3cnLFJMrcuTB7Njz+uN5KFGPQ7vczw+VSueAUScFk\nMZF9ZjbVP6hm0vcnQTTISlgEabVp5P1XHrbCOAkwdSCRHtATwL1AAEBKuRHQNgmZzsTLBQdQmVXJ\nzu6d8d/Um+5uWLMGpkzRrEq9x7eNhFa2GAgG2eP1ssXtJpiia+5Uu4iRarZIn5tO1YNVlNxUgmu6\ni4G1AzTe1cjK2pVsOH8DG87fgK/Zp5u+ROaA0qSUK49I72DQiZHjo7c3frndYscTNEZXdQT19ZGu\n24UX6q1EMQr/6u7mvI0buTA3l3/Ono19tDsdhWKcsOZamfityLqzQHeAjj934N7spuvvXfT8sweI\nLHC1Yz9aNeNGIn8RnUKIaqI5VoUQnwJaxlVVkmloiF9+4eQLeX3n68kVkyhOZ2QOyKfd3YuRx7eT\njRa28ITD5FutrBsY4IWODg5o+H+VTFS7iJHKtuj8WycNtzTg3e9lyq+msLB5IUvkEly1rrEvHicS\ncUC3A78BaoUQzcBXgFsTqVwI8ZQQok0IsXFYWY4Q4k0hxHYhxBtCiKxh790rhNghhNgqhDh/WPnJ\nQoiNQogGIcRPhpXbhBDPRa9ZLoSYMOy966PnbxdCXHdUI4xihc6hTkoyShL5qsnn0UfhiivAYdB1\nSgo+np9Pxxln8O7cufykqYlfHzigtyTFRxD3Njd7vreH5p83A+Dd5SXvwjzspfr0eoYzpgOSUu6S\nUp4LFAC1UsozpZR7Eqz/GeDIPa3vAf4lpawB3iIyv4QQYhpwFTAVuAj4pYiN+/0K+JyU8iTgJCHE\nwTo/B3RLKacAPwF+FK0rB/gOMB9YANw33NEdyWgOaF/fPiZkToj/pt6sXQsaj0en2vj2eKKlLR5v\naaHMZuPrKRoFp9pFjFS0xaqpq9jznT0Mrh0kY0EGGadk0PlKp96ygATmgIQQ2cB1QCVgOegTpJRf\nGutaKeW7QogjE19dBiyOPn8WqCPilC4FnpNSBoE9QogdwKlCiL1AhpRyVfSa3wKXA29E67ovWv4C\n8LPo8wuAN6WUfdHv8CZwIfB/8XSOFpzU4e5gUo5BdxYcHNTcASnGhxKbjVa/nx0eD3NHC7lUKMZA\nhiWBjgC+Fh/+luguqH1BwkNhQkOhUR8z5mUQ6Arg3e1lYMUAAysGCPvD5H88X++vlFAQwqvAB8Am\nYJScAcdEoZSyDUBK2SqEOLhktwxYPuy85mhZEGgaVt4ULT94zf5oXSEhRJ8QInd4+RF1xWXUKLjs\nSvb17UvsWyWb6mp4+WW46y7Nqqyrq0vJO7zxQEtb3FlRwVA4zCe3bGHXaadpUmcyUe0ihh62cG91\ns2pa5P7bmm/FVmLDVmrDXmLHkmPB5DRhTjNjzbdiTjNjSjMd/dFpwpxujCUBiTggh5RSu1+5kWgZ\nm3pcqcF37LiB+++vBCA7O5s5c+awZMkSnFYnu9btos4Ra3QHJyF1f/2lL8EDD1B38snG0HOCvT6I\nVvXdvWgRP2lq4oGXXmJxdrbu3+9YXq9fv95QevR8vX79+qR/fqAvQPbMbIa2DrHetJ4p357C+Vee\nn3h9blgy/8PrqaurY+nSpQBUVlaiBWPuBySEuBMYBP4OHArjkVJ2J/QBkSG4V6SUs6KvtwJLpJRt\nQohi4G0p5VQhxD2RauUPo+e9TmR4be/Bc6Ll1wCLpZS3HjxHSrlCCGEGWqSUhdFzlkgpb4le8+to\nHSOG4IQQcsECyQcfjNT+9LqneWffOzxz2TOJfNXk0tgIp50GL74IZ52ltxrFKGxzu3m+o4Pn29sZ\nCIV4c/ZsatJSL2uxQj/8nX4abm6g560eQv0hFuxegLPSqbcsTfYDSiQKzg88QmR4bE30WH0MnyE4\nvGfyMnBD9Pn1wN+GlV8TjWyrAiYDK6WUrUCfEOLUaFDCdUdcc330+ZVEghogMj90nhAiKxqQcF60\nLC5dXfHL2wbbyHfqP04al+pqeOQR+OEP9VaiGIWhUIjT1q7lvj17OCs7mx0LFijnozhmvHu89P6n\nl+pHqlnYstAQzkcrEnFAXwUmSykrpZRV0SOhmXkhxB+B94lEru0TQnwW+AER57AdOCf6GillPfA8\nUE9k3uk2Geue3Q48BTQAO6SUBxfnPAXkRwMWvkIkmAEpZQ/wPSKOcgXwgJRylOWmMGfOyLKwDPNK\nwyvMLp6dyFdNPlLCsmXg0i6G/8jhp48yWtgizWymaeFCHps8mV8fOMBXdho0q8YYqHYRQw9bpNWm\nUfL5Ejr+3MGq6at4v/R9Nl6ykd3f3o2n0aAL5RMkkTmgncDQ8VQupfz0KG+dO8r5DwMPxylfA8yM\nU+4jErodr66lwNJEdKbH2cXWH/KztmUtl9ZcmkgVyScchvXr4cYb9VaiOArpFgunRCPffjDJoBGV\nCkMT6gvh2enB3+5H+iXhcBj/AT9uuxvfAR/O6tTtESXigNzAeiHE2xw+BzRmGHaqMBTHvTosDjLt\nmQz4Bsi0j5IuW0/MZrjmGti2TbMqD048KrS1Rb3bzZz0dDItqbn7iWoXMfSwRd97fXT+JbJux5Jn\nIevMLDLmZUSOk1M7rD+Rv4iXoscJy2hxGIWuQloGWyjLNOg2ym++CZcatIemOESB1UqaSeWBUxwf\nhVcVUnhVIeFAGE+jB/dGNwNrBtj2mW0U31BM9SPVeks8bhLJhPBsvCMZ4pLFwED88hmFM9jRtSO5\nYhKltxeWL4fzzx/73ARRY/0xtLTFqoEBThtt06kUQLWLGHrawmQ14ap1UXhVIVUPVjHx2xM58Hhq\np3catQckhHheSnmVEGITI9fqSCmlQWfnjx37KCmRvEEvZpMxFmyNoLERioqgpkZvJYoxmOZy8bjK\nA6fQAO9eL61LW2n+eTP2CXYm/SC15xVHXQckhCiRUrYIIZ4Hvjb8LeBHUsq4k/+phhBCXn215Lnn\nDi+XUlLwSAHrb1lPeWa5PuKORlcXlJXBN74BDzygtxrFUThvwwZmulz8eLJBNzdUpAQrZ6xkaEtk\nwjr/k/lkL8nG7DKTf1k+1lxr0vVosQ5o1B6QlPLglguTpZR7j/jg2g/zoUYj3q7Wvd5ehgJDlGaU\nJl9QIuTlwdlng4qsMjzZFgsBKfGHw9jUXJDiOJn5t5kMbRvC3+7H1+xj5x2RsH7ry1ZD5HU7Hkb9\naxBC3BodfquJboVw8NgNbBztulTE7x9ZluXIojSjlLUta5MvKBF274bVq+ETn9CsSjXWH0NLWzhM\nJn7e3Mzy/n7N6kwmql3E0NMWzmonuRfnkn95PtmLswGwl9tT1vnA0aPg/gi8RmRdzj3DygcSTcOT\nKuTH+f8LhUPs7dvL5FyDDpvk5ESiJ5ypuwbgo0Jdby9P1tSwODtbbykKgxL2hdly1RZ8TT4cEx2Y\nnCaCfUFC/SGC/UFCfdHH/hAmh4m06WkUfaaIzAWpG9wCRx+C6wP6gP8veXL0ISdnZJnVbCXdlo4/\nFKd7ZASys6GgADZvhrlzNalSrfeIoZUtOv1+mnw+0kfb8yMFUO0ixnjYIjgYZGD1AF0vR3KCDa4d\nBGDG32ZgybJgzjRjyYw9muwnzjBuaq6M05h4Q3AQScdjFgb+4cjMjD+BpTAM+TYbkxwOgmMk/VV8\n9HBvcbPpsk14GyN/w9ZCK+VfKidjfgbpc9OxFdh0Vjj+nDiu9EMwWhj2xKyJ7O7dnVwxx8KnPgUP\nj8hcdNyosf4YWtnid62t7PJ6OT9eNztFUO0ihpa2cNY4qflNDVN+MYWyL5UR7A7iqHKQe37uR8L5\ngOoBAfFzwQH0+fpwWBzJFXMsXHQR/OMfeqtQHIWF0QWoL3Z28oVSg0ZUKnTBZDGRc04OOedEbk4G\nVg7Q+ttWAh0BLHkWrHnWQ4cl14Ily4IwfaioZ8OhHBAQDMYvr86ppnWwlRmFM5IrKFE6OuJPYB0n\naqw/hla2mJyWxq2lpXQHAprUpweqXcQYT1tUfreS/vf78TR6CKwMEOgKEOyKzA8d5PS207EWWIns\nTJP6KAcE9PTELy/NKOXAgIFXsNfXq3VAKcDUtDSeamnh3okT9ZaiMDC55+WSe17uiPKWZ1pouKWB\ntNo0Vk5bSdgbxl5qj/SMhvWULDkWAl0BMudnUnRtkQ7f4NhRDojRHZDFZGHAN0qiOCPw+uvwJe2S\nktfpsN+9UdHKFn3BIP+zezc3l5R8eFE6odpFDD1sUfLZEko+G2s/gd4A/lY/wa4g/g4/TY820fbb\ntkPv987oTRkHpIIQAMco0zzv7HuHMyackVwxiVJfD1u3apqMVKE9mWYzD1ZV8YsDB/CGQnrLUZwA\nWLOtuGpdZJ2Rhb3MTt+7fQDMfns2S+QS5m+ar7PCxFE9IEaPgpNSYhIG9dE7dkTmf0YTfxyou9wY\nWtlCCIFfSq4pLMSRomuBVLuIYQRbSCkJD4UJdAdYuzCWqWXD2RsAKLymkGl/mqaXvGNCOSAg3nxe\nt6eb1sFWphUY9D/y0kvhi1+E116Dj39cbzWKo/DL5maeVFnLFceJDEsCHQF8zT58zT623bCNYHcQ\nW5kN1zQXliwLYW+YkDtEaDCEfYJ2N6XjjXJAxB+C63B3kJeWZ9wekBBw553wzDOaOSA11h9DK1v0\nBgI0+3wpvRBVtYsYybRFyBviHec7cd8r+UIJjgmOQ9kRbMU2cs7LSbnoOOWAiD+KVZFVQa+3l9bB\nVuNmxF62DK64Qm8ViqOwy+tFCMEMl0tvKYoUw+wwM2/jPEIDIcK+cCwvXH+I7je6aX26FRmQCLsg\n59zoeqIUG+VVDoj4W3L/veHvzCudR0m6QaOXfD7Yvz+Sjkcj1F1uDK1scXJGBsU2G691d3NdURGW\nFNyOQbWLGMm2RfrMkavkfa0+dn51J+V3lZNzbg5ZZ2RhdqaY54mSen8N40C8XHBOi5NQOGTcLu1L\nL0WG4dT8j6Fp8flYlJXF57Zv56XOTr3lKE4AZFBicpjIXJCJs9qJyZG6P+Opq1xD4mVCWFK5hOVN\nywmFDRo6u20bnH46aBhZpXJ+xdDCFk+3tFC6fDm/bWujyuFI2e0YVLuIYQRbhAZChPpCbLliCysm\nrWDjRam7PZsagiO+A9rTu4ccRw5mk0G7tkKMnsROYQhuKC7mjKws1g0McHdjIz9tbuZ7VVV6y1Kk\nOIGOw9M69bzRw/sl72Mvt2OvsB96tBXZyLskT5ftuhNFOSDidyLe3/8+iysXJ19MophMoHF+MTXW\nH0MLW5iEoCYtjWyLhWa/nwf37uWT+fnMycj48AKTiGoXMYxgi+xF2SyRMR3hYJhAWwDvfi++Jh++\n/T68e7zs+vouzOlmij9XjDXfetjhnOTEMUH/RMvKAQHxFqifXHIyv17z6+SLSZTsbNi3T28VigT4\n+KZNADxcVcVJaWk6q1GcaJgsJuxlduxlh4fz5l+ej6/JR6AzQKAzwOC6QQIdATr/GpmLrLy/cmTW\n7TwLtgIbZldyRn6UAyL+nm7Lm5ZTllGWfDGJ8uabsGiRplWq9R4xtMwFt2FwkLo5c1J6Dki1iwip\nZIucsw/PlB/2hQl0BSi8ppCWJ1voeKGDoR1DSN/IMODhPazxRDkgwOMZWWY322kZbEFKacxIuL17\n4bTT9FahGIMf7dvHgszMlHU+itRGSsmue3bR/ItmpF8e2lvImmvFUe0gY34GllwL9lI7ruku0qan\njehJjSdCpvAKbS0QQsjLL5f89a+Hl0spyfxBJvvv3E+2w4A/Hjk58O67MH263koUoyCl5Kr6elb0\n97Nv4UK95Sg+grT9qY3tN29nwY4F2Iptmt5MCyGQUn6oClUYNvHn8kMyhFmY8QV9yRc0FuEwWCya\nByEotKU3GOSFjg72+3yIujp61f+XIsn0r+gn7A6zvHQ5noY4Qz06oxwQ8ZORvrfvPSZkTaDQVZh8\nQWPR1BRxPrNna1qtEdY4GAUtbJFjteJftIg0k4k0kwlnimbDVu0iRirYItgfZM2CNayoXUHL4y24\nZrso+UKJIZOUKgdEpDNxJFU5VbQMthCW4eQLGoutW6G2Nr7nVBgKq8nEzgULODMri683NuotR/ER\nwOQw4Wv24dnuweQ0IUwC3z4fO27fwa57d9H8q2Z63u7Bd8CH3lMwag5ICPnJT0peeOHwciklju87\n6Pp6F+k2gy349Pth4sRIMtIpU/RWo0iAd3t7uXDjRpbW1vKpQgP2qhUpT//qftwb3JFtGdwhgj1B\nvLu9eBo9eBo9hPrjZ3U5s/dMLFnHHo+mxRyQioIjfg9ICEFpRint7nbjOSCbDc46C955RzmgFOGM\nrCy+Ul7OzQ0NygEpNENKiXuTm5137sS7y0v2kmxMLhPmdDPmDDOZCzPJOTcHc7o5Uu4yR470yKMp\nzXRczkcrlAMiElAWj0AogFkYdNz+v/4LXnkFbrxRsypTaY3DeKO1LS7ZtInVAwP8fupUzepMFqpd\nxNDbFu56N4MbB3FvduPe4KZveR+WTAtlt5dR9uUyTJbUmlVRDohIVpsj2du7F3/IT3lmefIFJcKU\nKbB8OfT2RrIiKAzJXTt38peODvb5fLQsXEixhluoKz5aeBo9rJq+CkeVg+Lriym+oZiTfnMS9tLU\nbVPKAQFDQyPLhBAIIYy7I2pXVyQIQcMfNHWXG0MLW7zT28v/NjVxS2kpv5gyBVOKBo2odhFDT1s4\nJjmY9Mgkmn/ezP5H92MrtR1KwWMrtZF7Qe6I7AdGRzkgYGBgZJnFZKHP24c36MVpdSZf1Fj09sLC\nheA0oDYFAH+N7v9jhpR1PgrjIIRgwt0TqPhqBaH+EC1PttD5t07aftcGwNDWoZRzQAa9vU8ufX0j\ny0rSS1g0cREv1L8w8k0j0N4ef+zwQ5AKaxyShRa28IfDWIVgh8fDP7u7P7wonVDtIoYRbCGEwJJl\nofHuRoa2D1H9v9XMXT6XaX+cpre0Y0Y5IOInFBBCUOgqxBcyYCYEgD/8Ac48U28ViqPwsylT+NuM\nGWx2uzl/40YCYQOuKVOkLHPq5pAxL4M9397Dtuu30fJMi96Sjhm1DkgIuXixJN6NzT3/ugerycr3\nPva9pOsakwsvjMwBvfaa3koUo7B2YIAz1q3DG3U8nWecQZ7VuJuDKVKTcDBM2+/a2H7jdlyzXeR8\nLIcJ907AVmAb189VueA0YrTh+WA4iNVs0B8MkwnOOENvFYqjcHJGBv1nnslZWVkAhxyRQqElJouJ\nks+WsKBxAe5Nbpr+t4lNH9+kt6yEUA4IGO2m9JWGV7h4ysXJFZMov/oVPPJIZFsGjTDC+LZR0MoW\nVpOJ12bN4pT0dL63Z4/uqU+OB9UuYhjZFiF3CKL3OMHeIOvOWsfGSzZS/+l6Gm5toPGeRvY+tJfm\nXzTT+rtWBjcP6isYFQUHQHqcRAeBUIADAweoyq5KvqBEsNkie4kXF+utRDEGDpOJaqeT//T14ZcS\nu4qIU4wD6TPTWSKX4GvxEWgPsHrO6hHnCIsgbVoa1jwreV15pM/QN8uLckBARsbIMospYhrDrgPa\nvz+yBkjDHzO13iOGlrb4fVsbz3d00HDqqdg1jlxMBqpdxEgFW9hL7NhL7FhyLAR7goe9V35XOdU/\nrNZJ2UhS769hHIg3BCeEoDi9mJZBg0aWbN4MkyePPn6oMAyLsrK4uaSEM9atw6/mgRRJouCTBYcX\niMi23EZCOSDAFyfSOizD7OndQ3WOce4WDtHbC/feGzk07AEZeXw72Whpiyqnk69WVKRsEIJqFzFS\nyRYyHJtvdM1wUXJTCfYSO62/baXrtS76V/fj3eslNBQ/S3Yy0G0ITgixB+gjMm0WkFKeKoTIAf4P\nmAjsAa6SUvZFz78XuBEIAl+WUr4ZLT8ZWAo4gFellF+JltuA3wKnAJ3A1VLKffG0DMaZixMIphdM\n583GN/l4zce1+dJa8ctfwgUXwMUGDZBQHMYL7e18oaGBR6ursaXgEJwiNal5vIaq71bha/JFjmYf\nvv0+3Jvd+Dv8BDoCBDoC+Nv9CLPAVmSj5KYSSm4qwVY4viHcB9FtHZAQYhdwipSyZ1jZD4EuKeWP\nhBDfAHKklPcIIaYBfwDmA+XAv4ApUkophFgBfFFKuUoI8SrwmJTyDSHErcBMKeVtQoirgU9IKa+J\no0Nefrnkr38dqfGOV+9gUs4k7lx4p/YGOF6kjAQe/PvfMGOG3moUCbBo3TpuKinhOhUwojAgUkpC\ngyG8u73se3gfXa914ZzkJK0mLZJvrtR+6NE124U1OzLsn+r7AQlGDgFeBiyOPn8WqAPuAS4FnpNS\nBoE9QogdwKlCiL1AhpRyVfSa3wKXA29E67ovWv4C8PPRhOTlxS/v9fWS7TBYpmkhImOG+fl6K1Ek\nyMAq04wAAB74SURBVIW5uXy1sZHzc3JUNmyF4RBCYMmwkD4rnWl/msbAugF23LaD9ufaYyeZwFZs\no+KuCiq+WqHZZ+vpgCTwTyFECPiNlPJJoEhK2QYgpWwVQhzcuasMWD7s2uZoWRBoGlbeFC0/eM3+\naF0hIUSvECJXSjkiKVe8VDwA5RnlNA80H+fXGyfc7siOqGlpmlet914nRkIrW3xn925+1tzMbaWl\nZMXb+TAFUO0iRqrbIuwLExwIEuoPEewPEhoIRZ5Hyzw7Pex/ZD8Tvz2RCd+ccKj3Yyu0IczaLx/Q\n8y/iDCllixCiAHhTCLGdiFMajpbjg6Nar67uBu6/vxKA7Oxs5syZw5IlS3AH3PRu66UuHGt0Bych\ndX8dndA2jJ4T7PVBPmx979bVkeHx8F8zZ+I0mw3z/Y7l9fr16w2lR8/X69evN5SeeK97/tPDtAPT\nEGbBuxvfJdARYObgTAKdAdaF1mF2mZmfOx9zppl14XWY08ycVnkalkwLq3tXY7vDxpLvDqt/Oywp\nWUJdXR1Lly4FoLKyEi0wRC44IcR9wCBwE7BEStkmhCgG3pZSThVC3ANIKeUPo+e/TmR4be/Bc6Ll\n1wCLpZS3HjxHSrlCCGEGWqSUI/ZCFkLIhQsl778/Utd/v/jfLJ64mJtPuXlcvvdxc8MNUFUF9903\n5qkKfQmEw1yxZQu1aWk8Um3AiErFCcfWz2yl7fdtWHIt1DxRE9kvqMyGNd+KyW5CaBQ5m7K54IQQ\naUKI9OhzF3A+sAl4Gbghetr1wN+iz18GrhFC2IQQVcBkYKWUshXoE0KcKiJWve6Ia66PPr8SeGs0\nPaNtqbPqwCoWViw8nq84vphMkWAEheGxmkzs83pxh0K0+/16y1F8BJj0g0mU31lOsDuIOd1M5oJM\nHOUOzA6zZs5HK/SKCS0C3hVCrAM+AF6JhlX/EDgvOhx3DvADACllPfA8UA+8CtwmY12324GngAZg\nh5Ty9Wj5U0B+NGDhK0SCGeISLwwboGuoi/w0A072CzEuDujI4aePMlra4unaWoZCIYref587duzQ\nrN5kodpFjFSwxYYLNuDZ4WHSjyaRMS9OmhcDocsckJRyNzAnTnk3cO4o1zwMPBynfA0wM065D7gq\nET3xghA63B2EZIgiV1EiVSSXhgb49Kf1VqFIkFMyMlg6der/396Zh8lRXYf+d3qdmW7Nqtk0Qhti\ntAspEpaEEBIWm/HDEJZAzPNCDE6ebTAmwQKTgMEkgXzE8YKJSQgY8MPgxDEICM8CgT4QSICQRjtC\nsvZZNWtrZnq6u7ru+6N61DPStDRCPVM13ff3ffXVrVvVpVNHd+rUvffcc2g1DI7oXpDmDKl9vJZ9\n9+7DFXDhznPjynNBHGJtMYxWA1xw7qpz8Y9xvsflyHTLSTNjxpxYdyh0yHku2AB1dbB1K8yYkfZb\n905katKvi5hpsjsc5pfV1Wm973Cg20USJ+gifjSO0W5A+4nnfFU+fKU+tv/ZdtwBN+6AZaB6y8cf\nF19ejL/KPkOlDRBWUOnjGVcwjiNdR5yXE6igwBp+6+jQkbAdjlKKVW1tvNnWxqstLUzOzeXCRG4g\njeazMm7FOMatGNevzggZGCEDs8sk3hU/tpndyePec0aHQbQuSu1j1hKTsi+X4av04a+0XK7zpuYx\nau7wDN1pA4Q1p388OZ4cRIRIPOIsAxQIwL33wgMPwPPPp/XWa0b4God0kg5dhOJxLt+yhVsrK/m3\n6mouKChw3CTwYNDtIolTdeHJ9+DJP/nr3DRMorVRunZ20b29m5KrSmh9rZWm560Fp648F/4qP8G5\nQWa8mP4RloHQBoiBDVDQF2RG6Qw21G1g2YRlwy7TSZk3D155xW4pNKdgW1cXAN+orGRBfr7N0miy\njdCHIQ7/7DCRgxF6DvQQrY/iLfOSNyWPwIwAJV8ooeo7Vfir/PjH+HHnD7+XnDZAJ2Fe5TzWHVrn\nPAMUCqX2HT8DnPhlZxfp0MWT9fWM9/up8A1PYMehQreLJCNJF54CDyqiCK0LUbCkgPkb5+MtcdBo\nDtoAAak9mhWKfL8Dv1xnz4aNG2HXLpgyxW5pNAMQM02eb2ykZv58xufk2C2OJoPpOdBDaH2IWHPM\n8oRrM45tsbYYnhIP7W+3c/TjoxRfWmy3uP3QBgiIp0iH8d6h97hm2jXDK8xgOPtsWLEC7roLVq5M\n222dOr5tB+nQRaXPR4dhnPpCh6PbRRIn6SLaFOX98hNDuORMyiH37FxyJ+dS8RcV+Mf68RZ78Y9z\nnlu2NkCkNkATCidwpOvI8AozWG66CR55xG4pNClYFwpxIBJhb08PU/PyKNSZazVpxlvqZdars1CG\nsno+LQax1hixFms9UOvrrcSPxpn6zFTE5UznF22AgFSJKmPxmDOH4AAOH4Zx40593WnglC87J3Cm\nujhv1Ch+Nnkyzzc2cvvu3bw6axYLR6gLtm4XSZykCxGh5IspcskAHes72HT+JppebMJb5sU72kus\nKUa0PsrctXMpWGx/e9TpGU9CJB7B73FetxWwkhg1NZ36Oo0t5Lrd3DZ2LK/Ons2SwkJ+sG+f3SJp\nsoyChQUsM5exuGUxVf+niq7NXUTrrUgcroAzXv3OkMJmUjkhlAfKORw6PPBJu9m/f+AVtGfASIhz\nNVykSxchw+Cl5mbebm/nuYYGoqm62w5Gt4skI0EXPYd6qH28lt237abm4hrWT1xP29ttzHl3DsvU\nMpapZYya44wYcXoIjtQGqCJYQUt3y/AKM1j++7/h5pvtlkJzCvI9HjbPn8877e0809DAo4cO8ey0\naZwbDNotmiZDqX2slo73Oii9tpTiLxYTnBW0NdzOydAGiNQdiVxPLmEjPLzCDBafz0rNnUacNL5t\nN+nUxexgkNnBIN+uquKZhgYu3byZ56ZN45KiohERGUG3iyR260IpRc/+Hiu8TocVVqd36z2u/Vkt\nZo/JnNVzcPmdPcilDRBQmCLmaDQepSDH/om6AdFrS0YcIsJXKipY2dLCZVu2sH/hQr1GSHNahNaF\n2LR4U7+6/MX5BKYH8BR4cBe4mfRPk3CPciNe53/cONs8DhOpDFDYCON3O7PryqJF8FbKHHufiZEw\nvj1cDIUuwvE4l23eTEM0yrq5c0eM8dHtIonduig4v4ALoxdy3vbzmPabaVR+s5LuHd1E6iIEZgco\nva6Uqm9XUfn1Sse6XvdFGyCgqGjg+pZwC25Xeif608bFF1vREFItYtI4hk7D4Je1tczZsIExfj/v\nzp07Yl2yNfbj8roITA9QfmM5U56YwqJDiyi9tpSWlS1svWIrawvXsufOPXTt7MI0nO30IirLUzuL\niPrhDxX339+/vivaRdmjZdTeWevMvEAA8+fDww9bxkjjSN5obeXa7duZGwxy34QJfL6wcETM+2hG\nLtHGKHvv3kvH2g4ihyOYPSbzNsxj1Lz0er6JCEqpM2rMugcENDefWGcqE1OZBLyB4RdosFx5Jaxe\nbbcUmpMQVYqj8TiFHo82PpphwVfuY+rTU1mwewEL9iwAoPnlZtpWtxFtdFZGXm2AgIaGE+v2tu2l\nMliJx+VgP42mJigtTdvt7B7fdhLp0sWcYJClBQWsbGnhrfYBUliOAHS7SOJ0XRhHDfb+7V52fXMX\n267Zxo4bdwBw4EcH2HzxZt6vODF2nJ04+O06fOTlnVhnmAZFuQ52k+3uhmefhZoauyXRnIQqv5//\nmjGDCzZt4un6epanmnDUaD4jpmESrYsSORSh/Z12Dv79QaqfqMZbYoXf6d08xR5cXmf1ObQBYuDM\n1h6XB8N0cCRjvx/KymD7dis6dhqwe42Dk0inLkb7fPx+5kwu27IlbfccTnS7SOIkXbStbuOTr39C\npC4CCV8DV56LyT+dTOl1pXiKPM79gE6gDRADByMtyi2isbMRpZQz/xPdbmsxalmZ3ZJoBkFcKQyl\nnNueNCOOggsLmP7b6ccynvYc6CFyMEL9k/Xsu28fxME/3k/B4gKmPOHMvGHO6o/ZRCJzcj/y/fl0\nRDqIxNMbbSCtnH8+fPBB2m7n9PHt4STdupgZDNJmGHSNQLd53S6SOEkX4hbypuQx6rxRFF1SROn1\npVTeUslZf30WEx+cSOVfVuIr89H8+wG8rByC7gEBrgHMsN/tpzi3mO1N25k3Zt7wCzUYenqsXpBm\nRDApJ4c329q4Oo2OI5rswThqcPDhg3Tv6ib8aZjwnjDiEzyFHmsrSGyJsrvATfEVxYz93li7RU+J\nNkAMHAsu15vL8onLeffgu840QFu3wqpV8JOfpO2WThrftpt06qI9FuO2PXsImyYzAw5260+BbhdJ\nhkMXylTEWqy8PdH6KD2Heuis6aTl1RYiByJMf2E6udVWxlPPqJH9Ch/Z0qeJWGzg+mumXcPPP/w5\ndyy8Y3gFGgzjx4PHA42NaXXF1qSXzZ2dXLttG5cVF7P1vPMIpDmFhiZz2PfDfdQ/WU+sMYYykgEC\n8mbkUfmNSqb+aiqj/mQUnvzMeW3rOSBSGyC3uPG5HTrElZ8PgcDAq2g/I04a37abdOniii1bmBUM\n8tg554xY46PbRZKh1EXVt6qY+qupTHlqCpMemUTFzRV4Sjx0b++m6rYqipYVZZTxAd0DAlIbIFOZ\nuMXBL42KCujosFsKzUl4cOJEbtm1i0/DYaYMtOBMk1WouCLaGCXaYA2vRRuiROojyeNEXbQhiriF\n3OpczvrpWbg8mdlX0AYIMFIs96kIVjg3IyrAddfBypVw1VVpuZ0e60+SLl3ku91cWFAwoo2PbhdJ\nzlQXW67YQtuqNgLnBvBX+vFV+PBV+sirzqNwaSG+Sp9VV+HDE8z813PmP+EgOFkPKMfj4JD5N9wA\n//AP8J//Cddfb7c0muPY3tXFE3V1IybtgmZoiTZHaVvVxuirR1N2UxlFy4vwFnntFstWMrNfd5qk\nMkChSIigz8Gpkysr4bnn4PbbIRQ649vpsf4kZ6KLrnicL+/YwfKaGr5QUsKTU5y5CHCw6HaR5Ex0\n4RvtY96meXgKPez88528N/o9tt+4PX3CjUB0D4jUBqixq9G5+YB6ufRSuOgiePRRePBBu6XJegzT\n5MJNmzg3GGTfwoXkjlDHA016+eOKP9L8UjORgxFyJuRQekMp+QvzKbo4u2MDagNE6jmg8QXjqQ3V\nDq8wp4sIzJ2blogIeqw/yWfVRVMsxsbOTi4vLs4Y46PbRZLT1YVSit3f2U3d43Wc+/a55C/Mx52T\nGe0iHeghOFKPXk0rncbh0GEihoPD8QAsWAAffggjNNx/pnCwp4ertm2j2OOhXEeoyHrMqEnDUw20\nvNbC4pbFFC0r0sbnOLQBIvUQHCQT0zmaJUvg2mvhwgvP6DZ6rD/J6epCKcVLzc1sOHqUvxs/ntvH\nOjf8yemi20WSU+nCjJrs+d4eNi3dxPtj3qfh2QamvzAdb3F2OxukQg/BAbm5A9cX+AsIG2FnJ6UD\naxju0UchGIR9+2DiRLslyipMpaj+4AP8LhdPVFfzv8vL7RZJYxNGm8HhnySXbvjP8pP/uXwbJXI2\nopQ69VUZjIio889XvPfeieciRoSKf67gna+/w6zyWcMv3Onyi1/Aj38M77wDVVV2S5MVdBgGLzc3\n87VPPiG8ZAk5GTLvoxk8SinaVrdx+MeHrUWm9VFiR5LhdBa3Ls5Id2sRQSl1RrlFHP5pPzykGoLz\ne/xcPfVqXtv92sgwQN/+thWa55Zb4PXX7ZYm42mIRFhWU0N1Xh4vzZypjU8GEmuPETnQJ9/OoQjR\npiixppi1PxIj1hTD7DEpu7GMCQ9MsBaTlvscl33UiWgDRGovOIDm7maumpKeSAPDwve/D/Pnwz/+\nI9xzz2n9dM2aNdrjKcHJdPFRKMTPamt5raWF71RV8WCGD3lmY7tQccW2a7fR8nILgZkB/OP85IzP\nYWNsI0uXLsVb6sVX5sNb5sVX6sMd0B8fnwVtgBg4HUMv1cXVbG7YzNVTrx4+gc6E3Fx4801YuBBm\nzoQrr7RboozihcZG7tizh3vGj+fRs8/W3m4jDDNqYrQZxFpjGG0GRpuRjM3WZwvvDeMf62dR7SL8\nY/zHfl+3po7KZZU2PkFmoeeARNSCBYr16wc+/8SGJ3hx+4us/urqkZVKee1aK1bclVfCQw+Bnhg/\nI7Z3dfHVnTtpjsX49bRpLCkstFskzQAopYg1xeis6aTt7TaOfniUWHPsmNFRUYWnyIOn2IO3yIun\nyIOvPBl/7dg2xkfu5NyR9Tc/zKRjDkgbIBE1ebJi9+6Bzxumwef+/XPcc8E9XD9jhMVba2+HBx6A\nX/3KClh6442wfDl4M29CdCgwleIPra38a10dazs6eGTSJL5RWYlLv5SGnXhXnOiRKEaLQaw5Rqwl\nuRkthtVr2WNlCXXluMibkUfhskIKzi/AV+7DU+zBU+TBHXBro5ImtAFKAyKiJkxQ7NuX+ppVf1zF\nba/fxoZbNzDKP2r4hEsXzc3w7LNW0NLDh+HOO+Gb37TyCfUhG8f6U/HGW2+xftIk7tu/nx9NmMD3\nzjprxObzOVOGs13Ew3G2fnErRoeBp8BDtD5KpC6Ciiq8ZV68JdbmKfEcK3tLvHjLveROtrKEeguH\n7gNL/40k0V5waSIcPvn5SyZdwvwx8/nW/3yL5/70ueERKp2MHm0ZnTvvhI8/hocfhh/9CC67zBqi\n+8IXoCi7Y1IBfHz0KL8/coS1HR18sHUrU0aN4n+VlPCXY8ZkrfE5U5RSdH/STWhdCKPdIN4Vt7bO\nOGaXeazcWx9rtrzOAIouLmLG72bgG+PDU+DRPZcMRPeARFQgoKirs5KMpuLD2g+59rfX8tqXX2N2\n+ezhE3CoqKuD116DV16BNWtg0SL4wQ9g6VK7JRs2TKXYEw6zqrWV55uaqI1E+Ep5OUsKC1mYn0+B\nR3+fnQ6x9hjdO7vp3tlN144uund201nTiXiEwgsL8Y724gq4cAfduAN9tqDbqk+Ue+s9hR7ErY2O\nU9FDcGlARFRVleKtt6C6+uTXPrXpKVa8uYKb59zMfUvvc3aqhtMhHLbmiR56CGodHnz1DAkZBq+2\ntPB/GxtZFwpZCeMKC/mz0lIuKy7G69JrN/oSa4kR3hc+5jFmtBkY7QaxtqQXWexIjO5d3Rghg7yp\neQSmB8ibZu0DswLkTMzRvZcMRBugQSAilwM/wYp79x9KqUeOO68WLFDcf781EnUqGjsbueuNu1iz\nfw0rFq/ghpk3MDpv9JDIPqw0NrJm6lSWtbXZLUna6O3hrAuFeL+jg3WhEHvDYZYUFvK18nIuKipK\n6UadyWP9ZsS0DEh70qAcX442RTn6wVEidRF2lO9gwbgFeAqTnmOeIg+eQmvvLfGSNyUP/1g/4sps\nQ5PJ7eJ00XNAp0BEXMBjwHKgDvhIRF5WSn3S97ovfQmefnpwBqg8WM6zf/osaw+u5fGPHufu1XdT\nmlfKrPJZzCqbxezy2cwqm8U5Jec4P4bccdTEYiyzW4jToNMw+GNPD3vCYfaEwxzq6aEuGqUuEqE2\nGqUxGqXS52NRfj6LCgq4pbKSc4NBfIPo5dTU1DjuRaOUwoyYA8+fJPZml3msHGuNWR5jR/rvzR7T\n8gorTG7eIm+yXOIltzqXsd8dS2BWgI8f+5g5d8yx+/EdgRPbxUhmZL0hT5/PAbuVUgcAROQF4Cqg\nnwG69VZr+O3tt63cboPhgnEXcMG4C4ibcfa07mFr01a2Nm7lhW0vcG/TvdSGaqkcVcmYUWOoDFZS\nGbTK5cFygr4gQV+QgDdAwBfoVw54A3jd9rhJtw9jb1gpRdg06YzH6YrH6Uxsfcsd8TitsRithkFr\nLEZL37Jh0BmPc3ZODpNzczk7N5dz8vJYVljIGL+fKr+fCp8P/2ccUmsfZGoL0zBREcsw9G6DOY6H\nU0zEd558kl480m/upN8cSrB/va/cR2BmAO9oL97R1op972gv7vzTc0UerC6yAa2L9JLpBqgKONTn\n+DCWUepHaSn87ndw/fVw/vmWMaquhgkTwOcDl8uKluBy9S9bezcu1xRmuqcwu+o6XGdZ9RGzmyM9\ntRzpqedIuJ6mnjoOt9ZTU7uDLqOTsNFFt9FFV7STrt59rIuuaBdul7ufccrx5OB1efG5fXjdib3L\n26/cb+/2Du76PtcF2jo5UFzM6y0tRJUiYppETZOoUifsIynqo6aZ8lzENOlOGJzOeJzueByfy0XQ\n7SaQ2AfdbgJuN0GXiyBuilweit0exru8zPHkUuS3jotwU+j2UOL2IiYoU4EJKqZQPYmyGceIh4n1\nnjMVKp4sY9Lv2Ow2k+tLmmM0/6GZbVu2HVvEmMqgALj8Llx+F+KXY+V+x74Tz7nykgbDO9pLzvic\nAY3I8UbG5dFzVJrMIdMN0KD5/OctD+WNG+HTT60Eo7/9rRUnLh4H07S23vJAdf3P52Ga52Ca5wz6\nN0qBuBR4I3TmdNHt76IlpxPx9uDyxhBPFJcnhniSZdxRxG3V4UmU3VFwxxB3DOWOIu5ulDsKLut6\nXDGUKwauqLV3RymLRPD1zOCCqz/BbYLbBJeCPCUETXAljt0mSKLsUiDxxN4ESRyLUtZxPFFnAqZK\n7BPHcXfCEMRRpgHxpGEAwIXlAeUCccmxMi6hzQXtbmH/cefEJSf8rvf4VOdcOS68pYk1JaO9NPma\nKL+pHO9oa2jKlZPCwGSBQdi/f7/dIjgGrYv0ktFOCCKyEPihUuryxPHdgOrriCAimasAjUajGUK0\nF9xJEBE3sAvLCaEe+BD4c6XUTlsF02g0Gk1mD8EppeIi8h1gFUk3bG18NBqNxgFkdA9Io9FoNM4l\n82dQT4KIXC4in4jIpyKywm55hhoR+Q8RaRSRLX3qikRklYjsEpE/iEhBn3P3iMhuEdkpIpfaI/XQ\nICJjReQtEdkuIltF5PZEfdbpQ0T8IvKBiGxK6OL+RH3W6QKs9YMislFEViaOs1IPACKyX0Q2J9rG\nh4m69OlDKZWVG5bx3QOMB7xADTDVbrmG+JkvAOYAW/rUPQJ8P1FeATycKE8HNmEN005I6ErsfoY0\n6qICmJMoB7HmCqdmsT7yEns3sB5ruUK26uJ7wK+BlYnjrNRD4hn3AkXH1aVNH9ncAzq2SFUpFQN6\nF6lmLEqptcDxsXauAp5JlJ8BelO/fgl4QSllKKX2A7sZYA3VSEUp1aCUqkmUO4GdwFiyVx/diaIf\n6wWiyEJdiMhY4ArgyT7VWaeHPggnjpSlTR/ZbIAGWqRaZZMsdlKmlGoE66UMlCXqj9dPLRmqHxGZ\ngNUzXA+UZ6M+EsNOm4AG4A2l1Edkpy7+BbgLywD3ko166EUBb4jIRyJyS6IubfrIaC84zWciq7xS\nRCQI/BfwXaVU5wDrwrJCH0opE5grIvnA70VkBic+e0brQkS+CDQqpWpEZNlJLs1oPRzHYqVUvYiU\nAqtEZBdpbBfZ3AOqBcb1OR6bqMs2GkWkHEBEKoCmRH0tcFaf6zJOPyLiwTI+zymlXk5UZ60+AJRS\nIWANcDnZp4vFwJdEZC/wG+DzIvIc0JBlejiGUqo+sT8CvIQ1pJa2dpHNBugjYLKIjBcRH3AjsNJm\nmYYDSWy9rAS+nih/DXi5T/2NIuITkYnAZKyFvJnEU8AOpdRP+9RlnT5EZHSvJ5OI5AKXYM2JZZUu\nlFI/UEqNU0pNwnofvKWU+grwClmkh15EJC8xQoCIBIBLga2ks13Y7WVhs4fH5VjeT7uBu+2WZxie\n93mstBQR4CBwM1AEvJnQwyqgsM/192B5suwELrVb/jTrYjEQx/J+3ARsTLSH4mzTBzAr8fw1wBbg\n3kR91umiz/MtJekFl5V6ACb2+fvY2vuOTKc+9EJUjUaj0dhCNg/BaTQajcZGtAHSaDQajS1oA6TR\naDQaW9AGSKPRaDS2oA2QRqPRaGxBGyCNRqPR2II2QBrNCEJEnhaRaxLl74pITp9zR+2TTKM5fbQB\n0mhGLncAgT7HelGfZkShDZBGM4SIyN8k0sIjIv8iIqsT5YtE5NcicomIvC8iG0TkRRHJS5z/u0SS\nuC0i8ssB7nsbMAZ4q/eeVrU8JCI1iXuWDtNjajSfCW2ANJqh5V1gSaI8DwiIiDtRtwX4W2C5Umo+\n8DHw14lrf66UWqCUmg3kJSI1H0Mp9XOssErLlFLLE9UB4H2l1JzEv3vrED6XRnPGaAOk0QwtHwPz\nRGQUVgy+dcB5WAYojJVF8r1ELp6vkozQvlxE1ouVPv0iYEaK+/cNLBtRSv1Pn393QjofRKNJNzof\nkEYzhCilDBHZjxU9+D2sXs9FwNlY6Y5XKaVu6vsbEfEDvwD+RClVJyL3Azmcmlifchz9961xOLoH\npNEMPe8CfwO8A6wF/gorwvAHwGIRORuOhb8/B8vYKKAlEQ7/uhT3DQH5fY4lxXUajSPRBkijGXre\nBSqAdUqpJqyht3eUUs1YPaPfiMhm4H1gilKqA3gS2A68Tv+cKn093f4d+H99nBC0F5xmRKHTMWg0\nGo3GFnQPSKPRaDS2oA2QRqPRaGxBGyCNRqPR2II2QBqNRqOxBW2ANBqNRmML2gBpNBqNxha0AdJo\nNBqNLWgDpNFoNBpb+P9iXd+FDST+lwAAAABJRU5ErkJggg==\n", 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LS0oBqr+/23JpcWa5YFiNy2VlpRQXF1f/NlPVh83V8tSpUxk0aFCTvV9TLmf3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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def constant(mu=MU): return mu\n", "\n", "show(samples(constant))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The resulting histogram looks different, but only because the starting distribution is so narrow and tall; the end distribution has a Gini coefficient of about 1/2 and standard deviation of about 100, just like we get from the other starting distributions.\n", "\n", "Here is one that statisticians call the [beta distribution](https://en.wikipedia.org/wiki/Beta_distribution) (with carefully chosen parameters):" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " t Gini stdev 1% 10% 50% 90% 99%\n", "------- ---- ----- ---- ---- ---- ---- ----\n", " 0 0.50 99.2 1 10 69 236 430\n", " 20,000 0.50 99.8 1 11 68 230 467\n", " 40,000 0.50 101.2 1 11 70 228 490\n", " 60,000 0.49 96.4 1 11 70 230 433\n", " 80,000 0.50 99.8 1 10 70 227 469\n", "100,000 0.50 98.6 1 10 69 232 459\n", "120,000 0.49 96.3 1 11 71 228 443\n", "140,000 0.50 99.3 1 11 69 232 447\n", "160,000 0.50 101.2 1 10 69 234 460\n", "180,000 0.50 98.6 1 10 69 235 444\n", "200,000 0.50 99.2 1 11 69 230 467\n" ] }, { "data": { "image/png": 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Pe2t76V/Zj2enh2B3LBnpdrazWC7WT/DDoAwQkKhCckVWhTH3Ab3xxqiEYBvB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\nIw3dwcQLTlrfup6phQaf4ub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peBTGZPMXNtP2ZKSgmclpIu+CPMq+WkbhZYVYi6yYrMae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\n8Mdbt9Idj1Oj93/UKOr6zy7aH2u3rnD2DZGKpkA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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def beta(): return random.betavariate(0.9, 12)\n", " \n", "show(samples(beta))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Surprise:** We can confirm that the starting population doesn't matter much. I thought it would make a real difference, but we showed that three very different starting populations—Gaussian, uniform, and beta—all ended up with very similar final populations; all with G around 1/2 and standard deviation around 100. The final distribution in all three cases looks similar to the normalized beta(0.9, 12) distribution." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Effect of Transaction Function\n", "\n", "Does the transaction function have an effect on the outcome? So far we've only used the random_split transaction function; we'll now compare that to the winner_take_all function, in which the wealth from both actors is thrown into a pot, and one of them takes all of it:" ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def winner_take_all(A, B): return random.choice(([A + B, 0], [0, A + B]))" ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " t Gini stdev 1% 10% 50% 90% 99%\n", "------- ---- ----- ---- ---- ---- ---- ----\n", " 0 0.11 19.7 55 74 100 125 145\n", " 20,000 0.89 282.9 0 0 0 374 1411\n", " 40,000 0.94 403.7 0 0 0 111 1946\n", " 60,000 0.96 473.6 0 0 0 0 2627\n", " 80,000 0.97 555.7 0 0 0 0 2986\n", "100,000 0.97 611.4 0 0 0 0 3485\n", "120,000 0.98 694.3 0 0 0 0 3592\n", "140,000 0.98 762.0 0 0 0 0 3670\n", "160,000 0.98 799.5 0 0 0 0 3603\n", "180,000 0.99 844.0 0 0 0 0 3603\n", "200,000 0.99 890.0 0 0 0 0 3677\n" ] }, { "data": { "image/png": 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Zwvd37OC+PXtYcuAAL7W2kkmDVFzmkZUzXCebc+1719LT3MPIK0f2y0CU7f3Z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\nGyXj9XurVwC/CO7/AnhvcP9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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "show(population, transaction=winner_take_all)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now the results look **very** different: most of the wealth goes to the 99th percentile (purple line on the far right of the plot), with everybody else getting wiped out (although the 90th percentile holds out until around 50,000 transactions). The Gini coefficient is all the way up to 0.99 and the standard deviation is over 800, and still rising.\n", "\n", "That makes sense: any time two actors with non-zero wealth interact, one of them will end up with zero—the number of actors with zero wealth increases monotonically until all the wealth is with one actor, and from then on the wealth just gets swapped around.\n", "\n", "At the other end of the spectrum, let's try a transaction function, redistribute, that taxes both parties 31% (the average income tax rate in the US) and splits that tax revenue evenly among the two parties; the non-taxed part is split with random_split:" ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def redistribute(A, B, rate=0.31):\n", " \"Tax both parties at rate; split the tax revenue evenly, and randomly split the rest.\"\n", " tax = rate * (A + B)\n", " Arand, Brand = random_split(A + B - tax, 0)\n", " return tax / 2 + Arand, tax / 2 + Brand" ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " t Gini stdev 1% 10% 50% 90% 99%\n", "------- ---- ----- ---- ---- ---- ---- ----\n", " 0 0.11 19.7 55 74 100 125 145\n", " 20,000 0.33 60.2 17 36 86 182 288\n", " 40,000 0.33 62.2 17 35 86 186 302\n", " 60,000 0.33 60.7 17 35 87 185 289\n", " 80,000 0.33 61.8 17 35 86 183 291\n", "100,000 0.33 61.0 18 35 85 182 293\n", "120,000 0.33 61.1 17 34 87 185 288\n", "140,000 0.33 60.8 17 35 86 183 295\n", "160,000 0.33 61.4 16 34 86 185 297\n", "180,000 0.33 61.4 17 36 86 184 292\n", "200,000 0.33 61.9 18 34 85 187 288\n" ] }, { "data": { "image/png": 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SL0kl5/kcIuZGkD8/n9q/1eJPiwJlgAwQHw8nnADvvKN/jLSoNHY17NLd3xI+8Lw8WLhQ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\n/3ltgOzqq+HgQVr7UT11MOiKRvmws5PqYJCDweAZj03hMEV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q13g5lvLycsqib9mSkhIGDRrU8OHVT34VYnnC5AnMf3M+AL379gagZlXNXssb\nPt7A+eefz6Rxk1pd//z5VfTuXd7wRV8/Ud7U8ty5I1t8Pne5XnPLuf0//XRdi8/nLtfUZPb4n6OQ\n2zeU5aqqqqDy5AolT6jLVVVVQeUJ6e+psrKSiooKgIbvy3yYe7u+r/N7U7NewGvu3j9aHkq2mBwH\nDHP3tWbWG3jJ3QeY2VjA3X1K1H8OcLu7v9HEuj2p36n8lnLKRpbF6puZnqHinorW11k+kbKyibHW\n+eijIxk1anqqfTOZiVRUTIzVV0TCZWa4e7vnolPZM4mKxYdmdqK7rwDOApZGj3JgCnAVMCN6yTPA\n76I9mD7A8cD8xIPnYVHVIspvKW+939vvxy4mIiKhSPNorpvJFogqsvMmd5ItIueY2TtkC8xd0HD5\n+yfJXgJ/FnBDYrsfBZCpyrCtdhtlI8tafWyr25xMJp1nEluIuZQpHmVKTmq33nX3xcBXm3jq7Gb6\nTwYmFzWUiIi0i+7jnoCyQWXMfXJurL7rN9QwvbI8Xt+/LW9/psCO5IJwj78PMZcyxaNMyVExCUyd\n1VIyrCxW3/fee7G4YUREYtK1uRKQqcqkHWEvmjOJL8RcyhSPMiVHxURERPKmYpKAskFlaUfYi+ZM\n4gsxlzLFo0zJUTEREZG8qZgkQHMm8YQ6lhxiLmWKR5mSo2IiIiJ5UzFJgOZM4gl1LDnEXMoUjzIl\nR8VERETypmKSAM2ZxBPqWHKIuZQpHmVKjoqJiIjkTZdTSUBbrs3VFjtqN7f7Ol6aM4kvxFzKFI8y\nJUfFpAPbfWCdruMlIkHQMFcCNGcST6hjySHmUqZ4lCk5KiYiIpI3DXMloFhzJvko1JzJokWLKS+f\nGKtvv34lTJp0S7PPhzqWHGIuZYpHmZKjYtLIhMkTqF5bHavvoiWLKBtZVtxAgdu2zWPfsz6TiddP\nRDoeDXM1Ur22Ota92stGlrFt+7ZY69ScSTyhjiWHmEuZ4lGm5KS6Z2JmnYCFwCp3v8jMSoHfA8cA\nGeA77r456jsO+AegDviBuz+XTuqOqfFhxJ9sqqEqU9Fk33xuBywi+6e0h7l+ACwDukfLY4EX3H2q\nmY0BxgFjzWwg8B1gANAXeMHMTnB3TyN0W4UwZ9L4MOISyprtm9ZhxKGOJYeYS5niUabkpDbMZWZ9\ngQuB3+Q0jwAejn5+GBgZ/XwR8IS717l7BlgJDE4oqoiItCLNOZO7gR8DuXsXvdx9LYC71wA9o/Y+\nwIc5/Vaf+K55AAAOt0lEQVRHbR1CiHMmmzKZtCPsJdSx5BBzKVM8ypScVIa5zOx/AWvdvcrMhrXQ\ntV3DWOXl5ZSVlQFQUlLCoEGDGnYt6z/I5pZrVtVA1WeXja8vBPks17xb05Cttf51n+5kUyZDSZS/\n/ks/3+V6zS3n9q/bvv2zvNFEff2hxI2XP/10HZlMZbPPN15ubfuHuFxVVRVUnlyh5Al1uaqqKqg8\nIf09VVZWUlFRAdDwfZkPS2PawczuBEaRnUz/HNANeBr4CjDM3deaWW/gJXcfYGZjAXf3KdHr5wC3\nu/sbTaw7r6mU8lvKYx/u++j4Rxl156iC9v35Nb/gy6NvjrXOuf/xM4Ze9+OC931z2oP80zXxDo9+\n9NGRjBo1PVbfTGYiFRUTY/UVkWSZGe5u7X19KsNc7j7e3fu5e3/gcuBFdx8NzATKo25XATOin58B\nLjezLmZ2LHA8MD/h2CIi0ozQzjO5CzjHzN4BzoqWcfdlwJNkj/yaBdzQUY7kAs2ZxBXqWHKIuZQp\nHmVKTtqHBuPuLwMvRz9vAM5upt9kYHKC0UREJKbQ9kz2SSHeA76kABNuhRbq8fch5lKmeJQpOSom\nIiKSNxWTBGjOJJ5Qx5JDzKVM8ShTclRMREQkbyomCdCcSTyhjiWHmEuZ4lGm5KiYiIhI3lI/NHh/\nEOqcSXN7J40vV9+SQl6uvrKyMsh/tYWYS5niUabkqJjIXhpfrr4laV2uXkTComGuBGjOJJ5Q/7UW\nYi5likeZkqM9E8lLW4bEfPv7wMRixhGRlGjPJAGhzpkUQv2QWJzHtrrNLa4r1OPvQ8ylTPEoU3JU\nTEREJG8qJgnQnEk8oY4lh5hLmeJRpuSomIiISN5UTBKwL8+ZFFKoY8kh5lKmeJQpOSomIiKSNx0a\nnICyQWXMfXJu2jH2kMacyfoNNZTfUt5in4rpFQD069WPSeMmFT9UDCGOcStTPMqUHBUTSUyd1VI2\nsixW38z0TFGziEhhaZgrAZoziSfE7QRhjnErUzzKlJxUiomZ9TWzF81sqZm9ZWY3R+2lZvacmb1j\nZs+a2WE5rxlnZivNbLmZnZtGbhERaVpaeyZ1wK3ufjLwdeBGM/sCMBZ4wd1PAl4ExgGY2UDgO8AA\n4ALgfjOzVJK3g84ziSfE7QRhjnErUzzKlJxU5kzcvQaoiX7+xMyWA32BEcC3om4PA5VkC8xFwBPu\nXgdkzGwlMBh4I+HokpBFVYtanayHsCbqRfZnqc+ZmFkZMAh4Hejl7muhoeD0jLr1AT7MednqqK1D\nCHEuIPQ5k2212ygbWdbqo3ptddFzhTjGrUzxKFNyUj2ay8y6Av8F/CDaQ/FGXRovx1JeXk5ZNIxT\nUlLCoEGDGnYt6z/I5pZrVtVA1WdDLvVfcPks17xb05Cttf51n+7c48ZV9V/6+S7Xa245t7/v2NXi\n87nLvmNXm/LG3X71Wutfs6pmj5sNtfb5tme5qqqqqOtvz3K9UPKEulxVVRVUnpD+niorK6moqABo\n+L7Mh7m36/s6/zc2OxD4b2C2u98btS0Hhrn7WjPrDbzk7gPMbCzg7j4l6jcHuN3d9xrmMjPP53cq\nv6U89uGrj45/lFF3jipo359f8wu+PPrmWOuc+x8/Y+h1P+4wfd/87S/4p2nxfre42yszPUPFPRWx\n1ikizTMz3L3dc9Fp7pk8CCyrLySRZ4ByYApwFTAjp/13ZnY32eGt44H5yUXN3/r1m5g+vbLVfjt2\n1BY/jIhIgaV1aPAQ4LvAmWa2yMz+ZGbnky0i55jZO8BZwF0A7r4MeBJYBswCbshr9yNhmaoMdXW7\nKSkZ1upjd0K/VuhzJiEJcYxbmeJRpuSkdTTXPOCAZp4+u5nXTAYmFy2UiIi0W+pHc+0PQjx/QueZ\nxBfieQHKFI8yJUfFRERE8qZikoAQ5wI0ZxJfiGPcyhSPMiVHVw2WDi3umfIAf1n5F/qf0D9WX51Z\nL9I2+3wxWb58Ob+b8btYfTsf0JlPP/204BlCnAvYV+ZM6s+Uj2Pu+LmcOfLMWH1zL4Ef4hi3MsWj\nTMnZ54vJh6s+5H17n6NOOqr1vos/ZPv27QmkEhHZt+wXcyZdDu7CoSWHtvo4sEtxamuIcwGaM4kv\nxDFuZYpHmZKzz++ZiLRH7lxMzaqahtsJN0XzKyIqJonQnEnWjh07Wr2kTFW0x7R+/abiB2pB7lxM\nGWUt9k3jFsMhjrsrUzwhZioEFRNJzG6HkpJhsfq+V7ekuGFEpKD2izmTtIU4FxDinEmImSDMzy/E\ncXdliifETIWgYiIiInlTMUmA5kziCTEThPn5hTjurkzxhJipEDRnIpKntpyFryO/ZF+lYpKAEMfc\nc2+1G4oQM0H282tp76QtZ+EX6sivypxbFYdCmeIJMVMhqJiIJEh7MbKvUjFJQIhj7iHuAYSYCQr7\n+bVlL+bpiU9Tvba62edzT6QMofCE+K9tZUqOiolIoNIYPhNprw5VTKL7xN9D9ii0ae4+JeVIsWjO\nJJ4QM0HrcyZpaJwp7vBZMfdgQpwLUKbkdJhiYmadgH8HzgL+Ciwwsxnu/na6yVpX825N2hH28klN\nTXBf3CFmguznF1oxaZwp7l5Ma0NnudpaeKqqqoL7klSm5HSYYgIMBla6+wcAZvYEMAJIrZisX7+p\n1WtNAdQszLBjR23xA7VBXYCX2g8xE8D2T8LL1d5MxRw627Qp3eupNUWZktORikkf4MOc5VVkC0xq\n6up2x7rW1KaDK9ntHxc/0D4kzkUhIf0LQu7L2noXyy3rt5DZlInVV3e83Pd0pGLSLgd0OoC3X32b\n9xe/32pf+9T461/W8cH0zbHWHXdvY3uA/xIJPVPci0ImcUHITTXhbaskMrX1LpZdS7rG6t+WO162\nZViuqSI197m5TRa4uEVqwuQJBR8WzBTxGnTFyBuXuXvBVlZMZvY1YKK7nx8tjwW88SS8mXWMX0hE\nJDDubu19bUcqJgcA75CdgF8DzAf+t7svTzWYiIh0nGEud99lZv8IPMdnhwarkIiIBKDD7JmIiEi4\n9plL0JvZ+Wb2tpmtMLMxKebImNliM1tkZvOjtlIze87M3jGzZ83ssARyTDOztWa2JKet2RxmNs7M\nVprZcjM7N8FMt5vZKjP7U/Q4P+FMfc3sRTNbamZvmdnNUXtq26qJTDdF7altKzM7yMzeiP6u3zKz\n26P2NLdTc5lS/ZuK3qdT9N7PRMup/r+Xk2lRTqbCbid37/APskXxXeAYoDNQBXwhpSx/AUobtU0B\nfhL9PAa4K4EcQ4FBwJLWcgADgUVkhz3Lom1pCWW6Hbi1ib4DEsrUGxgU/dyV7LzcF9LcVi1kSntb\nHRL99wDgdbKH5qf9N9VUplS3U/RePwQeBZ6JllPdTs1kKuh22lf2TBpOaHT3nUD9CY1pMPbe4xsB\nPBz9/DAwstgh3H0usDFmjouAJ9y9zt0zwEqKcA5PM5kgu80aG5FQphp3r4p+/gRYDvQlxW3VTKY+\n0dNpbqu/RT8eRPaLxkn/b6qpTJDidjKzvsCFwG8avXdq26mZTFDA7bSvFJOmTmjs00zfYnPgeTNb\nYGbXRm293H0tZL8ogJ4pZev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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "show(population, transaction=redistribute)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Another surprise:** This transaction function does indeed lead to less inequality than split_randomly or winner_take_all, but surpprisingly (to me) it still increases inequality compared to the initial (Gaussian) population.\n", "\n", "Here's one more interaction function, status_quo, in which both actors keep half of their wealth out of the transaction, and the other half is randomly split using a triangular distribution in such a way that the most likely outcome is that each actor keeps what they started with, but from there probability falls off on either side, making larger and larger deviations from the status quo less and less likely:" ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def status_quo(A, B):\n", " \"A transaction that is most likely to leave things unchanged, but could move any amount of wealth around.\"\n", " a = random.triangular(0, (A + B) / 2, A / 2)\n", " return (A / 2 + a), (A + B) - (A / 2 + a)" ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " t Gini stdev 1% 10% 50% 90% 99%\n", "------- ---- ----- ---- ---- ---- ---- ----\n", " 0 0.11 19.7 55 74 100 125 145\n", " 20,000 0.21 38.5 33 55 95 151 209\n", " 40,000 0.22 40.3 31 53 94 154 219\n", " 60,000 0.22 40.3 31 53 94 154 214\n", " 80,000 0.23 41.0 31 52 94 155 220\n", "100,000 0.23 40.8 30 52 94 156 216\n", "120,000 0.23 40.9 31 53 94 154 220\n", "140,000 0.23 41.3 31 52 95 153 223\n", "160,000 0.22 40.5 32 53 95 153 213\n", "180,000 0.22 40.3 32 53 94 155 213\n", "200,000 0.23 40.9 32 52 94 156 216\n" ] }, { "data": { "image/png": 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cnBEezsb6erYNoDNB7l4X4aeFM61wGjPqZjD+q/H4D/Fn3bB17LhkB22VbW6V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\ndBjchkUDhk02QRAMgSRkIWQn6XTnvD9uIy0mIND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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "show(population, transaction=status_quo)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The status_quo transaction increases inequality from the initial population, but not as much as the other transaction functions." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Effect of Interaction Function" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We have been using anyone as our interaction function: anyone can enter into a transaction with anyone else. Suppose that transactions are constrained to be *local*—that you can only do business with your close neighbors. Will that make income more equitable, because there will be no large, global conglomorates? " ] }, { "cell_type": "code", "execution_count": 23, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def neighborhood(n, width=5): \n", " \"Choose two agents in the same neighborhood\"\n", " i = random.randrange(n - width)\n", " return random.sample(range(i, i + width + 1), 2)" ] }, { "cell_type": "code", "execution_count": 24, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " t Gini stdev 1% 10% 50% 90% 99%\n", "------- ---- ----- ---- ---- ---- ---- ----\n", " 0 0.11 19.7 55 74 100 125 145\n", " 20,000 0.48 93.2 1 11 72 224 415\n", " 40,000 0.48 93.6 1 11 71 227 423\n", " 60,000 0.49 95.7 1 11 72 225 432\n", " 80,000 0.49 96.2 1 11 71 226 442\n", "100,000 0.49 95.4 1 12 71 229 430\n", "120,000 0.49 96.0 1 10 70 229 432\n", "140,000 0.50 97.5 1 11 70 235 430\n", "160,000 0.50 97.5 1 11 70 234 448\n", "180,000 0.50 98.3 1 11 71 232 453\n", "200,000 0.49 96.5 1 11 71 229 442\n" ] }, { "data": { "image/png": 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zkjI1hWn/nqazwoGj9gENIUIIvAEvVpNBa3dNnw5/+UtoE5PDobcaRQxcfj+v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\n2hEEgkmSnuY6cgnHThMil24aGyEQUPEZwdw1cSK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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "show(population, interaction=neighborhood)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Surprise:** The neighborhood interaction is not too different from the anyone interaction. \n", "\n", "Let's get even more local, allowing trade only with your immediate neighbor (to either side):" ] }, { "cell_type": "code", "execution_count": 25, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " t Gini stdev 1% 10% 50% 90% 99%\n", "------- ---- ----- ---- ---- ---- ---- ----\n", " 0 0.11 19.7 55 74 100 125 145\n", " 20,000 0.45 84.0 1 13 79 217 364\n", " 40,000 0.47 90.1 1 11 75 223 399\n", " 60,000 0.47 90.8 1 12 74 226 401\n", " 80,000 0.49 94.9 1 11 72 229 437\n", "100,000 0.48 93.0 1 12 73 222 431\n", "120,000 0.48 93.0 1 12 73 228 424\n", "140,000 0.48 93.3 1 10 73 228 421\n", "160,000 0.48 94.2 1 11 72 226 430\n", "180,000 0.49 93.2 1 11 72 231 416\n", "200,000 0.48 92.7 1 11 72 225 412\n" ] }, { "data": { "image/png": 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mxnuBO0VYMTE2lgtSU8mLiqLWbCbXaAy2JEUYceS1I+y5dM9XxpLOTiLjvzIY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\n5S9w883guMA0UGU5ZTxx9RM8cfUTHGo9xNtVb7OrcRfvHni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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def adjacent(n): return neighborhood(n, 1)\n", " \n", "show(population, interaction=adjacent)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "It is still surprising that we still have no efect from restricting trade." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# United States Distribution\n", "\n", "We've drawn from mathematical distributions; let's look at the actual distribution of family income in the United States. Each row in the following table is a tuple giving the lower bound and upper bound (in thousands of dollars of income), followed by the cumulative percentage of families in the row or a previous row. The table I got this from actually had \"\\$250,000 or above\" as the final row; I had to cut it off somewhere, and arbitrarily chose \\$300,000." ] }, { "cell_type": "code", "execution_count": 26, "metadata": { "collapsed": false }, "outputs": [], "source": [ "USA_table = [ \n", " (0, 10, 7.63),\n", " (10, 20, 19.20),\n", " (20, 30, 30.50),\n", " (30, 40, 41.08),\n", " (40, 50, 49.95),\n", " (50, 60, 57.73),\n", " (60, 70, 64.56),\n", " (70, 80, 70.39),\n", " (80, 90, 75.02),\n", " (90, 100, 79.02),\n", " (100, 110, 82.57),\n", " (110, 120, 85.29),\n", " (120, 130, 87.60),\n", " (130, 140, 89.36),\n", " (140, 150, 90.95),\n", " (150, 160, 92.52),\n", " (160, 170, 93.60),\n", " (170, 180, 94.55),\n", " (180, 190, 95.23),\n", " (190, 200, 95.80),\n", " (200, 250, 97.70),\n", " (250, 300, 100.0)]\n", "\n", "def USA():\n", " \"Sample from the USA distribution.\"\n", " p = random.uniform(0, 100)\n", " for (lo, hi, cum_pct) in USA_table:\n", " if p <= cum_pct:\n", " return random.uniform(lo, hi) " ] }, { "cell_type": "markdown", "metadata": { "collapsed": false }, "source": [ "Let's see what it looks like:" ] }, { "cell_type": "code", "execution_count": 27, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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MEGcuZcpHpgXD3S+q8tJpVdrfCNyYXSIREdlVMQx67zFiPL9AmcLEeMx8jJkg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\nU1YD2AAAAABJRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "hist(samples(USA), label='USA')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Hey—that looks like the beta distribution. Let's compare:" ] }, { "cell_type": "code", "execution_count": 28, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "hist(samples(beta), label='beta')\n", "hist(samples(USA), label='USA')" ] }, { "cell_type": "code", "execution_count": 29, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " t Gini stdev 1% 10% 50% 90% 99%\n", "------- ---- ----- ---- ---- ---- ---- ----\n", " 0 0.46 89.5 2 17 74 219 422\n", " 20,000 0.50 100.0 1 11 69 227 478\n", " 40,000 0.50 99.9 1 11 69 229 463\n", " 60,000 0.50 101.5 1 11 68 232 465\n", " 80,000 0.50 99.7 1 11 69 230 463\n", "100,000 0.50 101.0 1 10 70 228 472\n", "120,000 0.50 100.0 1 11 68 236 448\n", "140,000 0.50 100.7 1 10 70 233 479\n", "160,000 0.50 100.7 1 11 69 228 455\n", "180,000 0.50 100.3 1 10 69 233 457\n", "200,000 0.50 100.3 1 11 69 228 468\n" ] }, { "data": { "image/png": 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Tz9RfZVa1XbUGRLSw6Ml0+bqwGC3oMlv40qXRYnQvvpjUbpWvP06qdHFHSQmfLCykORjk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\nizIo+OMC/GV+7ZI/znQvQOXA+PaPU9F9H3KpiQQ+Vfspbqm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lVTsDa8SIEQwfPpwDDzyQP/zhD5u0efPNN2PfTKuQJ5ZWVFQwadIkgLqxoVwU/Ax4M0sB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\nANhiuVbtp5jaftZ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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "show(samples(USA))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The USA distribution is indeed similar to the beta(0.9, 12) distribution, and to the stationary ending distribution." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# A Mathematician, a Statistician, and a Programmer walk into a problem ..." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In 2013, mathematician George Andrew's editorial *[Drowning in the Data Deluge](http://www.ams.org/notices/201207/rtx120700933p.pdf)* complains of an \"overblown enthusiasm for data analysis.\" The tone was that this new fad for \"big data\" was taking away from traditional mathematics.\n", "\n", "Two Stanford professors, mathematician Persi Diaconis and \n", "statistician Susan Holmes, were more accepting of new ideas. The three of us got to discussing Andrew's editorial and the differences between mathematical, statistical, and computational thinking. At the time, I had just heard about the economics problem covered in this notebook, and I suggested the three of us work on it, and compare approaches and results.\n", "In the end, all three of us found similar results, in that we all identified the shape of the final distribution. But there were differences in how we got there:\n", "\n", "**Mathematical thinking** (Persi):\n", "\n", "- **Tool:** Paper and pencil.\n", "- **Notes:** The process can be modeled by a Markov chain, using the same techniques as in [this paper](http://statweb.stanford.edu/~cgates/PERSI/papers/kac10.pdf). In the limit, there is a difference between the continuous case (where money is a real number, and the distribution is stationary), and the discrete case (where money comes in integer amounts and the distribution is not ergodic as there is an absorbing state). \n", "\n", "**Statistical thinking** (Susan):\n", "\n", "- **Tool:** Simulation in R, with N=10 actors for T=1,000 transactions.\n", "- **Notes**: this is extremely similar to what happens for random genetic drift in generations, that also gives clumping (and extinction of some of the alleles).\n", "\n", "**Computational thinking** (Peter):\n", "\n", "- **Tool:** Simulation in IPython, with N=5000 actors for T=200,000 transactions.\n", "- **Notes**: Results are very similar to Susan's, but with more variations explored and more pretty pictures." ] } ], "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 }