{
 "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 in 2008. *Update:* In 2017, a version posed by Uri Wilensky [became popular](http://www.decisionsciencenews.com/2017/06/19/counterintuitive-problem-everyone-room-keeps-giving-dollars-random-others-youll-never-guess-happens-next/). We cover his version [below](#Uri-Wilensky-Version).\n",
    "\n",
    "![](money.png)\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 _ 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",
    "<table>\n",
    "<tr><td>Sweden <td> 0.250\n",
    "<tr><td>Canada <td> 0.326\n",
    "<tr><td>Switzerland <td> 0.337\n",
    "<tr><td>United States<td> 0.408\n",
    "<tr><td>Chile <td> 0.521\n",
    "<tr><td>South Africa <td> 0.631\n",
    "</table>\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": true
   },
   "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": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.11285526402866708"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gini(population)"
   ]
  },
  {
   "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": 4,
   "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": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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Md98MfMTd3wdMAU4zs+OBecAD7n4ksAS4EMDMjgbOBI4CTgOuNTMrMqOIiKRTeEvK3f+a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\nq0OMAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1021c9b70>"
      ]
     },
     "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": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def random_split(A, B):\n",
    "    \"Take all the money in 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": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(39.32170492026867, 160.67829507973133)"
      ]
     },
     "execution_count": 7,
     "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": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def anyone(N): return random.sample(range(N), 2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1593, 1439]"
      ]
     },
     "execution_count": 9,
     "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": 10,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def step(population, transaction=random_split, interaction=anyone):\n",
    "    \"Modify the population by doing one transaction.\"\n",
    "    i, j = interaction(len(population))\n",
    "    population[i], population[j] = transaction(population[i], population[j]) \n",
    "    return population\n",
    "    \n",
    "def simulate(population, T, step=step, transaction=random_split, interaction=anyone):\n",
    "    \"Run simulation on population for T transactions; yield population at each time step.\"\n",
    "    population = population.copy()\n",
    "    yield population\n",
    "    for t in range(T):\n",
    "        yield step(population, transaction, interaction)"
   ]
  },
  {
   "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": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[100, 100, 100, 100]\n",
      "[100, 100, 166.07034848304477, 33.92965151695522]\n",
      "[100, 129.37411310873642, 166.07034848304477, 4.555538408218797]\n",
      "[100, 21.916292438917807, 166.07034848304477, 112.01335907803742]\n",
      "[100, 21.916292438917807, 89.32137618847126, 188.7623313726109]\n",
      "[88.88749715846127, 33.028795280456535, 89.32137618847126, 188.7623313726109]\n",
      "[88.88749715846127, 0.008026672184755057, 122.34214479674304, 188.7623313726109]\n",
      "[88.88749715846127, 0.008026672184755057, 147.86216819550745, 163.24230797384647]\n",
      "[88.88749715846127, 54.73884147345122, 147.86216819550745, 108.51149317257999]\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": 12,
   "metadata": {
    "collapsed": true
   },
   "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, T=k * N, **kwargs))\n",
    "               if t % (N / 10) == 0]\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 % (k * N // 10) == 0: # Print 11 report lines (initial plus 10 as t varies)\n",
    "            data = [percent(pct, pop) for pct in percentiles]\n",
    "            print(fmt.format(t, gini(pop), statistics.stdev(pop), *data))\n",
    "\n",
    "    plt.title('/'.join(map(str, percentiles)) + ' Percentile Plots')\n",
    "    times = [t for (t, pop) in results]\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",
    "    \n",
    "    plt.title('Histograms')    \n",
    "    R = (min(pop+start), max(pop+start))\n",
    "    hist(start, 'start', range=R)\n",
    "    hist(pop, 'end', range=R)\n",
    "    plt.show()\n",
    "\n",
    "    plt.title('Ordered Curves')\n",
    "    order = list(range(len(pop)))\n",
    "    start.sort()\n",
    "    pop.sort()\n",
    "    plt.plot(sorted(start), order, label='start')\n",
    "    plt.plot(sorted(pop), order, label='end')\n",
    "    plt.xlabel('wealth'); plt.ylabel('order'); plt.grid(True)\n",
    "    plt.legend()\n",
    "\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": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   t    Gini stdev   1%  10%  50%  90%  99%\n",
      "------- ---- ----- ---- ---- ---- ---- ----\n",
      "      0 0.11  20.1   54   75  100  126  148\n",
      " 20,000 0.50  99.4    1   11   71  231  454\n",
      " 40,000 0.49  98.0    1   11   71  231  452\n",
      " 60,000 0.50  99.1    1   10   69  233  441\n",
      " 80,000 0.49  96.6    1   11   71  230  442\n",
      "100,000 0.50 100.4    1   11   69  230  465\n",
      "120,000 0.50 101.1    1   10   69  230  468\n",
      "140,000 0.50 101.8    1   10   69  230  466\n",
      "160,000 0.50 102.7    1   11   68  227  477\n",
      "180,000 0.49  98.4    1   11   72  229  450\n",
      "200,000 0.49  99.0    1   11   70  231  464\n"
     ]
    },
    {
     "data": {
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3M2LpUm4oLuamkpL+L9RookigO0Dn2k461nTQ+E4jja83kjY1jaLri0g/Oh2LIz5jEe2C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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10a077e80>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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zP8bT/wH8985uVEREdi1J72cyheiijKvixznu/kAhg+1K1DNJJsRMEGYuZUpG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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10b18a128>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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IfCgit+N0YQ10q8AaEfkQWANkAPe5LxJgOGceGjw9wtkL5bN1n9G7aW8qlD7z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\nyKyYGGOMCdn/A1TJNEPpch64AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10b362198>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "show(population)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There are four parts to this output:\n",
    "\n",
    "**The printout:** For the starting population and for every 20,000 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 plots:** 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 histograms:** The starting and ending populations are plotted as histograms. \n",
    "\n",
    "**The ordered curves:** Here the initial (blue) and final (green) populations are sorted, and the curves show wealth versus ordinal number. The poorest actor (ordinal number 0) has wealth 0 in both the initial and final populations. The 2000th poorest actor (a bit below the median; at the 40th percentile) has wealth of almost 100 in the initial population, but only about 50 in the final population.\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",
    "\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": 14,
   "metadata": {
    "collapsed": true
   },
   "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": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   t    Gini stdev   1%  10%  50%  90%  99%\n",
      "------- ---- ----- ---- ---- ---- ---- ----\n",
      "      0 0.33  57.9    2   19  102  181  200\n",
      " 20,000 0.49  97.1    1   11   72  224  447\n",
      " 40,000 0.50 102.7    1   10   69  229  486\n",
      " 60,000 0.50 101.1    1   11   68  233  460\n",
      " 80,000 0.50 101.0    1   10   69  229  490\n",
      "100,000 0.51 101.7    1   10   67  234  465\n",
      "120,000 0.50  99.7    1   10   70  229  462\n",
      "140,000 0.50  99.5    1   11   71  229  444\n",
      "160,000 0.51 102.6    1   10   66  235  469\n",
      "180,000 0.50 102.3    1   10   68  229  455\n",
      "200,000 0.51 102.3    1   10   70  232  472\n"
     ]
    },
    {
     "data": {
      "image/png": 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8o333j3O6gkG+tncvYzwe7pg4EWeMH82tiR4JzgSSS5LJOT+Hwv8pZNxN45jw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\n0QAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10b41e048>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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LSxkzZgz//d//zc6dOzn++OO5+OKLGTlyZL1vSV9cXMydd97J8uXL6dWrF48//njF7Viq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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10afd23c8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x10b4b27b8>"
      ]
     },
     "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": 16,
   "metadata": {},
   "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 0.48  94.0    1   11   72  226  424\n",
      " 40,000 0.49  97.3    1   11   71  235  446\n",
      " 60,000 0.50  98.1    1   11   68  233  443\n",
      " 80,000 0.50  99.1    1   11   69  227  472\n",
      "100,000 0.50  99.2    1   11   68  229  452\n",
      "120,000 0.50 100.9    1   11   67  235  444\n",
      "140,000 0.50 100.9    1   11   70  228  472\n",
      "160,000 0.50 101.3    1   10   70  229  474\n",
      "180,000 0.50 100.4    1   11   70  226  455\n",
      "200,000 0.51 101.6    1    9   68  233  471\n"
     ]
    },
    {
     "data": {
      "image/png": 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ah/hoqJn1DwNPKaWCSqkKYC+wVEQKgXSl1NvmeY8Dl0Zc85j5/hngPPP9hcDL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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10b4304a8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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ySoUlh2n+OFAWgbIIlEU8VFhERCSjVFhymOaPA2URKItAWcRDhUVERDJKhSWH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\n/5Ieek/2qQ0nAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10a8f4710>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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GTh3I5xs+5w9X/6FM6+teYSKSiVJ5r7DjHrG4u5vZaHc/G3g3FR+aSd5b+h73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\nyIPw0QAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10ad4d0b8>"
      ]
     },
     "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": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   t    Gini stdev   1%  10%  50%  90%  99%\n",
      "------- ---- ----- ---- ---- ---- ---- ----\n",
      "      0 0.50  97.5    1    9   71  230  442\n",
      " 20,000 0.50 101.2    1   10   68  237  474\n",
      " 40,000 0.50  98.8    1   11   70  230  451\n",
      " 60,000 0.50 100.6    1   11   68  232  460\n",
      " 80,000 0.50  98.3    1   10   71  229  444\n",
      "100,000 0.50  99.1    1   11   71  228  457\n",
      "120,000 0.50  99.3    1   11   70  232  450\n",
      "140,000 0.51 100.7    1   10   68  232  465\n",
      "160,000 0.49  98.2    1   11   70  232  445\n",
      "180,000 0.51 101.7    1   10   69  233  480\n",
      "200,000 0.51 103.2    1   10   67  233  494\n"
     ]
    },
    {
     "data": {
      "image/png": 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wTkpP56ysLBauX8++JUvsFkdjEa3vtVL3XB0dmzvwbfYR9odx57px5R4MufX+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\nSfElq1bGAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10b423080>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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Z2ctm9jszaw90c/e18T7XAPvH7XsAKzLevype1yyE2EeqTMmFmEuZklGm9CTu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\nZw84H/h9xvJPgR8BbzRVrpb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      "text/plain": [
       "<matplotlib.figure.Figure at 0x10b829da0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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tWgCndzFDNd/17a60LtyGf/eJZejQ0G/P5m3e5m0+O/OpqakMGjQI4NT3ZY6o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\nY1ZMjDHG5Nj/A7ZZGGmuh3MDAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10a0b76a0>"
      ]
     },
     "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&mdash;Gaussian, uniform, and beta&mdash;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": 18,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def winner_take_all(A, B): return random.choice(([A + B, 0], [0, A + B]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   t    Gini stdev   1%  10%  50%  90%  99%\n",
      "------- ---- ----- ---- ---- ---- ---- ----\n",
      "      0 0.11  20.1   54   75  100  126  148\n",
      " 20,000 0.89 287.7    0    0    0  364 1448\n",
      " 40,000 0.94 398.9    0    0    0  111 2135\n",
      " 60,000 0.96 475.2    0    0    0    0 2576\n",
      " 80,000 0.97 560.1    0    0    0    0 3066\n",
      "100,000 0.97 629.9    0    0    0    0 3346\n",
      "120,000 0.98 683.4    0    0    0    0 3569\n",
      "140,000 0.98 729.2    0    0    0    0 3843\n",
      "160,000 0.98 800.1    0    0    0    0 4144\n",
      "180,000 0.99 859.6    0    0    0    0 4140\n",
      "200,000 0.99 902.2    0    0    0    0 4140\n"
     ]
    },
    {
     "data": {
      "image/png": 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YEmZUY4wxHgqnZvR3YDqwnGNrRiec2h0PrGZkTPxRVV5NeJWFutDrKH2WFzWj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\nOWuMjDHGeM4aI2OMMZ6zxsgYY4zn/j8c9+i4EKGKKQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10b863908>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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JYmpvDikWIcUipFhET0lGREQioz4ZERFRn4yIiGQeJZkspvbmkGIRUixCikX0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\nIiISGSUZERGJjJKMiIhE5n8BlZDfGh2zKuwAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10b97ce48>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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xxzqy67uskEmmSyGPysxqXZcuXfj973/P0qVL2WuvvRg+fDhnn302b775ZovbK/2LuXv3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\ns9z8fxaFwGo/qVU+AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10a830e10>"
      ]
     },
     "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&mdash;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": 20,
   "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": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   t    Gini stdev   1%  10%  50%  90%  99%\n",
      "------- ---- ----- ---- ---- ---- ---- ----\n",
      "      0 0.11  20.1   54   75  100  126  148\n",
      " 20,000 0.32  59.8   18   36   88  183  285\n",
      " 40,000 0.33  62.1   16   34   86  187  289\n",
      " 60,000 0.33  61.9   18   35   85  185  297\n",
      " 80,000 0.33  60.8   17   35   87  181  287\n",
      "100,000 0.33  61.7   17   34   87  183  297\n",
      "120,000 0.33  61.2   18   35   88  183  291\n",
      "140,000 0.33  61.1   16   35   87  185  291\n",
      "160,000 0.33  61.6   17   35   86  186  294\n",
      "180,000 0.33  61.6   17   35   86  183  301\n",
      "200,000 0.33  61.3   17   34   87  187  295\n"
     ]
    },
    {
     "data": {
      "image/png": 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33yyEuLAzPl9ysrYNjhkHFOuOZW3xWlbvXR04YVaQnKxtivT001Yr6TH4pGRr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\nAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10b0145f8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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MvhQkp7OAlcAzQHnQZiKxy7YQ1I8zswPM7CjgGGBpCvsXEZE0Svaqwd9OeFxo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\niKRMyURERFL2/wADhG6UOyIKCQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10ba51908>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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i3TJjTKyK6ftMTHR8sPoDsjWbG5vdCDjPfbeZXMYYP1kyKWGyNZvnFjzHiE4j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\n9v9HM64ItJCNRQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x107028470>"
      ]
     },
     "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 surprisingly (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": 22,
   "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": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   t    Gini stdev   1%  10%  50%  90%  99%\n",
      "------- ---- ----- ---- ---- ---- ---- ----\n",
      "      0 0.11  20.1   54   75  100  126  148\n",
      " 20,000 0.21  38.5   34   56   95  152  210\n",
      " 40,000 0.22  40.5   31   53   95  155  222\n",
      " 60,000 0.22  40.3   31   53   95  155  217\n",
      " 80,000 0.23  41.3   31   52   95  154  222\n",
      "100,000 0.23  41.8   32   52   94  158  224\n",
      "120,000 0.23  41.0   32   53   95  157  223\n",
      "140,000 0.23  40.9   31   53   94  155  216\n",
      "160,000 0.23  41.2   31   53   94  156  223\n",
      "180,000 0.23  40.9   31   52   95  156  219\n",
      "200,000 0.22  40.6   31   53   95  155  219\n"
     ]
    },
    {
     "data": {
      "image/png": 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KqdUi8hnwuFLqSxG5ChillLpaRM4HzlZKXSAiccAaYDxaEfO1wHil1M9Wcfly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\nCoVCYQjKASkUCoXCEJQDUigUCoUh/H9cVOA/N4vwxQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1011ce4a8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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Jz4HLAc+Z18/dFwO4ezXQN5m/C/BBTruFybzNTsz9rjrPJCzlDyv2/GkFKSZm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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10b041518>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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+UFkxMWG1aucqNh/cTMUjd1O3LuS100uMyRFszMSE1aOTHqVKiSrkXvhXdu+G\nt9/2OpExJhg2ZmJixt6je5nwwwSeaPQE8+ZBixZeJzLGRIsVkxjj537XfsP6cc9V91CmcBmWLsV3\ng+9+3vZg+b3m9/yhsjstmrBQVaasn8L0+6bzyy+QJw/ExXmdyhgTLZccMxGR3MAnqvpgdCKFxsZM\nvDF1/VT6zOzDmp5rGDVK+PJLGDfO61TGmGBFfMxEVU8BlUUkX1ZXYrK/ocuH0qd5H0SExERo0MDr\nRMaYaAp2zGQjsFBE/k9E/nz6J5LBcio/9rv+sv8XFm1dRNwep1/Lr8XEj9s+kOX3lt/zhyrYMZMN\n7k8uoEjk4hg/em/pezxS/xEK5i2IKqxeDfXre53KGBNNmTrPREQK6dk7J8YkGzOJrgMpB6j6blUS\nn0jkimJXsG4dtG4NycnYBR6N8ZGonGciIteLyFrgB/d5PREZnNWVmuzj/aXv065GO64odgUA8+ZB\ny5ZWSIzJaYIdM3kHuB34FUBVVwM3RipUTuanftcTp04waOkg+jTvAzjZ58/378mKftr2F2P5veX3\n/KEK+qRFVd1y3qRTYc5ifGbSD5OoUqIKtcvUPjPNz8XEGJN1QY2ZiMgXwFvAe8C1QG+gsap2jmy8\nzLMxk+ipO6Qub9z2Bq2rtQZgxw645hrYs8e6uYzxm2hdm+tJnDsdVsC593p997nJodbuWcv2w9tp\nVbXVmWmnDwm2QmJMzhNUMVHVvar6oKrGqWpZVe2qqr9GOlxO5Jd+1xdmv8BzzZ4jl5z9E/rvfxO4\n9loPQ4XIL9s+PZbfW37PH6oMzzMRkUFAun1Gqmo3ZM2Bdh7ZydzkuYy+d/Q50xMT4fe/9yiUMcZT\nGY6ZiEh392FzoDYwxn1+H7BWVZ+MbLzMszGTyBu8bDAJyQmMvW/smWlHjkD58rBrFxQq5GE4Y0yW\nhDpmkuGeiaqOdFfyB+AGVU11nw8F5md1pca/VJXBywYzqM2gc6YnJUHNmlZIjMmpgh2ALwEUDXh+\nmTvNhFms97vO3TSXk2knaRnf8pzpS5ZAhQoJnmQKl1jf9pdi+b3l9/yhCvbaXAOARBGZAwjOCYsv\nRSqUiV2vLXiNZ69/FjnvkK3Vq6F6dY9CGWM8F8z9TASoCJzEOccEYImq7oxwtiyxMZPImblhJr2m\n9WJNzzXkzZ33nNcaNoQhQ/D10VzG5GShjpkEe9Lid6p6TVZXEk1WTCIjTdNo9GEjXmjxAh1rdzzn\ntZQUKFWb7dx1AAAYrElEQVQKdu+GwoU9CmiMCUm0TlpcKSJNsroSE7xY7Xed/ctsjpw4wr217r3g\ntUWLoF49WLYsIfrBwihWt32wLL+3/J4/VMGOmVwLdBWRZOA3nHETVdW6kQpmYsunSZ/yVNOnLhgr\nAVi+HJrYVw1jcrRgu7kq4xy9dfoSfvOAA6q6KYLZssS6ucLv16O/Um1QNdb2XEv5IuUveP2BB5x7\nmHTvfpGFjTG+EK1urruBT4HSQBn3cfusrtT4y7CVw7ir5l0XLSTgnGNSr16UQxljYkqwxeRR4DpV\nfVFV/wZcDzweuVg5V6z1u6ZpGh+t/IgnG1/8YgcHD8KmTVCrVuxlzyzL7y3L72/BFhPh3PuXnHKn\nmWxu9i+zKZyvMNdWuPgxv/PmwXXXQf78UQ5mjIkpwY6Z/BnoDkx0J90NjFDVdyKYLUtszCS87h59\nN62rtU53z6RfPyhYEF58McrBjDFhFZUxE1V9C3gY2Of+PByLhcSE17Jty1i8dTHd6nZLd56FC6FZ\nsyiGMsbEpMzctnelqr7r/iRGMlROFkv9rq/Me4VXbn6FwvkufibiiROwcuXZs95jKXtWWH5vWX5/\nC7qYmJxl55GdLNi8gAeveTDdeRITnetxFS2a7izGmBwiqDETP7Exk/B4c+Gb/LD3Bz6+6+N053nr\nLfj5Zxg8OIrBjDEREa3zTLJERCqKyGwRWSMi34nI0+70EiIyQ0R+FJGvRaRYwDL9ReQnEVknIq0C\npjcUkSQRWS8iNl4TQarK8FXDebjBwxnO9+230Lx5lEIZY2JapLu5UoE/q2odnHNTeonIVUA/4BtV\nrQnMBvoDiEhtoBNQC2gDDJaz1+8YAjyqqjWAGiJye4SzeyIW+l3nb55PaloqzSulXylULxx8j4Xs\nobD83rL8/hbRYqKqO1V1lfv4CLAO53L2dwEj3dlG4hxqDM5Z9aNVNVVVk4GfgKYiUg4ooqrL3Pk+\nCVjGhNlbi97iuWbPXfQ6XKclJzv/xsdHJZIxJsZFbcxEROKBBOBqYIuqlgh4bZ+qlhSRQcAiVR3l\nTh8GTAM2Aa+pait3+g1AH1W94JIuNmYSmp1HdlL7/dps7L2R4gWKpzvfuHHw2WcwaVIUwxljIiam\nx0xOE5HLgC+A3u4eyvmf9vbpHyM+/+5z2tdsn2EhAedIrgYNohTKGBPzgr0EfZaJSB6cQvKpqp7+\nHrtLROJUdZfbhbXbnb4NqBSweEV3WnrTL6pHjx7Eu/0vxYsXp379+rRs2RI4268Zq8/feecdT/MO\nmzCM7vXPXv43vfmXL2/J00+f+3pgn3GsbM/MPLf8lj8n5U9ISGDEiBEAZz4vQ6KqEf3BGd9467xp\nrwN93cd9gQHu49pAIpAPqAL8zNmuuMVAU5xrgk0DWqezPvWzOXPmeLbu5P3JWur1Uno89XiG86Wm\nqpYsqbpt27nTvcweDpbfW5bfW+5nZ5Y/6yM6ZiIizXHuffIdTleWAs8DS4GxOHsbm4BOqnrAXaY/\nzlWKT+J0i81wpzcCRgAFgGmq2juddWok31N29vqC19m4fyMftPsgw/mWLIFHHoE1a6IUzBgTcVG5\nB7yfWDHJGlWl5ns1GX7XcJpfkfHJI//4B+zb55y0aIzJHnwxAG+CF9jvGk0rdqwAoFmlS1+1cd48\ncLtgz+FV9nCx/N6y/P5mxcQAMOb7MXSq0ynDc0sATp6ExYvhhhuiFMwY4wvWzWVQVeIHxjP1galc\nE3dNhvMuX+6MlyQlRSmcMSYqrJvLhGzptqUUzluYq8tefcl5ExLs/iXGmAtZMYkxXvS7JiQncNuV\nt12yiwtg0SK46aZ02vF5n7Hl95bl9zcrJoapP03ltqq3BTXvihXQqFGEAxljfMfGTHK4pF1JtP1v\nWzY8vYH8efJnOO/evVC1KuzfD7nsa4gx2YqNmZiQfLjiQx5v+PglCwnA6tVQt64VEmPMhexjIcZE\ns9/1xKkTfLH2C7pc0yWo+WfPhhtvTP91v/cZW35vWX5/s2KSg435fgw1S9ekeqnqQc2f3smKxhhj\nYyY52LXDruVvN/6NO2rcccl5Dx+Gyy+H7duhSJEohDPGRJWNmZgsSdyRSPKBZFpVbRXU/LNnw7XX\nWiExxlycFZMYE61+17/P+zsvtHiBvLnzBjX/+PFw110Zz+P3PmPL7y3L729WTHKgHYd3MPuX2Tza\n4NGg5k9JgSlToGPHCAczxviWjZnkQH1n9iUlNYWBbQYGNf+YMTBsGMycGeFgxhjPhDpmEvHb9prY\nciDlAMMSh7Hy9yuDXmbKFOjUKYKhjDG+Z91cMSbS/a5Dlg3hjup3ULl45aDmV4W5c4M7JNjvfcaW\n31uW399szyQHOXbyGAOXDOSbh74JeplNm5x7mFSrFsFgxhjfszGTHGTIsiF89fNXTH5gctDLfPqp\n0801dmwEgxljPGdjJiYoqWmpvPntm3x2z2eZWm7ePGjRIkKhjDHZho2ZxJhI9buO+X4MFYpWCOoe\n74Hmz8/4elyB/N5nbPm9Zfn9zYpJDvHu0nfp06xPppbZtcv5ufrSN2A0xuRwNmaSA6zds5ZbP7mV\nzX/aTJ5cwfdsjh8Pw4fD1KkRDGeMiQl2bS5zSSNXjaRb3W6ZKiQAS5c61+MyxphLsWISY8Ld75qa\nlsqnSZ/So36PTC+7dCk0aRL8/H7vM7b83rL8/mbFJJubsWEGVxS7glplamVqub17ITERrr8+QsGM\nMdmKjZlkc+0/b0/b6m15svGTmVpu9Gj473+dc0yMMdmfjZmYdC3cvJDVu1ZnqYtr4UK46abwZzLG\nZE9WTGJMuPpdVZV+s/rxcsuXKZCnQKaXX70aGjbM3DJ+7zO2/N6y/P5mxSSbmrp+KvuP7adb3W6Z\nXjYlxSkm9epFIJgxJluyMZNsKE3TqDO4Dv/83T+5p9Y9mV5+4ULo3RuWL49AOGNMTLIxE3OBj1d+\nTME8BelwVYcsLb9wIVx3XZhDGWOyNSsmMSbUftdDxw/x1zl/ZeTdIxHJ2peM6dPh9tszv5zf+4wt\nv7csv79ZMclm3lj4Bq2rteaauGuytPzhw7BsWXA3wzLGmNNszCQb2f3bbqoPqs6qJ1ZRpUSVLLUx\naRK8+y7MmhXmcMaYmGZjJuaMV+e/SqfanbJcSAAmToQ77ghjKGNMjhDRYiIiH4vILhFJCphWQkRm\niMiPIvK1iBQLeK2/iPwkIutEpFXA9IYikiQi60XknUhm9lpW+11T01IZ/f1o+t7QN8vrVoVp0+De\ne7O2vN/7jC2/tyy/v0V6z2Q4cP5Qbj/gG1WtCcwG+gOISG2gE1ALaAMMlrMjyEOAR1W1BlBDRLIw\nPJy9TV0/lSolqlCtZNZv1r5mDRQpApUrhzGYMSZHiPiYiYhUBqaoal33+Q/ATaq6S0TKAQmqepWI\n9ANUVV935/sKeAnYBMxW1dru9M7u8n9IZ305csyk5YiW9GzSk051OmW5jUGDnJMVhw0LYzBjjC/4\nccykrKruAlDVnUBZd3oFYEvAfNvcaRWArQHTt7rTjGv9r+v5Ye8PWT6v5LQ5c+Dmm8MUyhiTo2Tu\nbkmREfbdiB49ehAfHw9A8eLFqV+/Pi3dY11P92vG6vN33nkn03k/WP4BXet2JW/uvFlef4sWLZk7\nF7p0SSAhIWv5A/uMY2V7Wv7YyWf5Y+t5QkICI0aMADjzeRkSVY3oD1AZSAp4vg6Icx+XA9a5j/sB\nfQPmmw5cGziPO70zMCSD9amfzZkzJ1PzJ+1M0jJvlNHk/ckhrXf2bNUGDUJqItPZY43l95bl95b7\n2Znlz/pojJnE44yZXOM+fx3Yp6qvi0hfoISq9nMH4P/rFpAKwEyguqqqiCwGngaWAf8D3lXV6ems\nTyP9nmJJu8/b0bJyS55t9mxI7TzzDJQoAS++GKZgxhhfCXXMJKLdXCIyCmgJlBKRzcCLwABgnIg8\ngjO43glAVdeKyFhgLXAS6BlQFXoBI4ACwLT0CklO8/XPX/PTrz8xvtP40Nv6Gj77LAyhjDE5UkQH\n4FW1i6perqr5VfUKVR2uqvtV9VZVramqrVT1QMD8r6lqNVWtpaozAqavUNVrVLW6qvaOZGavBfa7\nXsrHiR/zVNOnyJc7X0jrXL0afvsN6tcPqZlMZY9Flt9blt/f7Ax4n1qzew0JyQl0rds15LaGDIHH\nH4fcucMQzBiTI9m1uXyqx5c9qFmqJv1b9A+pnZQUqFQJliyBK68MUzhjjO/E9JiJiYzDxw8zft14\nNj69MeS2xo93ureskBhjQmHdXDEmmH7XV+a+QsfaHSlTuEzI6xs0CJ56KuRmAP/3GVt+b1l+f7M9\nE5/ZcXgHHyd+zPc9vw+5raQk2LYN2rYNQzBjTI5mYyY+0/3L7lyW9zLev+P9kNt6+WU4cADefjsM\nwYwxvmZjJjlI4o5Evtn4Dev/uD7ktk6dgv/8x7l/iTHGhMrGTGJMRv2ug5cN5rEGj1E4X+GQ1zNt\nGpQvDw0bhtzUGX7vM7b83rL8/mZ7Jj7x+XefM3n9ZH7o9UNY2hs8GHr2DEtTxhhjYyZ+cPTkUa54\n+wqmd51O48sbh9zehg1w3XWwZQsUKBCGgMYY3/Pj/UxMJn244kNuir8pLIUEYOhQePhhKyTGmPCx\nYhJjzu93PZhykAELBvBCixfC0v6xYzBiBDzxRFiaO4ff+4wtv7csv79ZMYlxAxYM4Laqt9GwfHhG\nyseNg0aNoGrVsDRnjDGAjZnEtF+P/kqVgVVY12sdFYqGfqdiVeforX/8A+64IwwBjTHZho2ZZGMT\nf5hIm+ptwlJIAObOdS7s2KZNWJozxpgzrJjEmNP9rqrKqO9G0a5Gu7C0qwr9+0OfPpArQr91v/cZ\nW35vWX5/s2ISo8atHcfOIzu5v879YWlv2TLYvRseeigszRljzDlszCQG7T+2n2qDqjGtyzSurXht\nWNp87jnInx/++c+wNGeMyWZCHTOxYhJjVJUek3pQJF8R3mv7XljaPHAAqleHxYvtKC5jzMXZAHw2\n8/SQp1m+fTkvtXwpbG1+8AHcemvkC4nf+4wtv7csv7/ZtbliyOaDmxmxagSrBqyidKHSYWnz4EF4\n6y345puwNGeMMRdl3VwxIk3TaPxhY+6pdQ9/vfGvYWv3+edh507ncvPGGJMeu59JNjFi1Qjy58kf\ntsumAGza5HRxrV4dtiaNMeaibMwkBqzauYq+3/RlcNvBzJ07N2ztvviic5n5ihXD1mSG/N5nbPm9\nZfn9zYqJx7Ye2kr7z9vzXpv3aFC+QdjaHTsW5syBZ58NW5PGGJMuGzPx0O7fdnPj8Bt5vOHjPNss\nfJ/6SUlwyy0weTJcf33YmjXGZGN2aLBP7Ti8g1aftuL+OveHtZDs2wedOsHbb1shMcZEjxUTD/y8\n72eafNSEDld1uOB8klD6XY8fh/btnSsCd+0aWsas8HufseX3luX3NzuaK8p2/7abDmM68PS1T9On\neZ+wtv3001CuHLzxRlibNcaYS7Ixkyg6dPwQzT5uxh3V72DArQMQyXL35AXGjoVnnoF166BYsbA1\na4zJIezaXOeJ1WJy+Phh2n3ejqolqvJR+4/IJeHrYfzlF2jSBGbPhrp1w9asMSYHsQF4Hzieepy2\no9pSvWR1Pmz3YYaFJLP9rlu2wD33OPcp8bqQ+L3P2PJ7y/L7mxWTCDt8/DBdJ3YlrnAcH7T7gNy5\ncoel3RMn4N//hgYN4P774S9/CUuzxhiTJdbNFSGqyierP+FvCX/jxso38sGdH1Aob6GwtP399/DH\nP4IIDB4MtWqFpVljTA5m1+aKMSdPnWTCugm8t+w9DqQc4NMOn3Jj5RvD0vbRo84Z7ePHO3sif/oT\n5LHfoDEmBviqm0tEWovIDyKyXkT6ep0nkKoyYd0Erh5yNe8seYenmj7Fyt+vzHQhSa/fdft2+N3v\n4Ndf4YcfnGISa4XE733Glt9blt/ffFNMRCQX8B5wO1AHeEBErvI2lePIiSM8OOFBnp/1PG/f/jbf\nPvItnep0Im/uvJlua9WqVWceb9gAH38MDz8MV13lXCLl88+hZMlwpg+fwOx+ZPm9Zfn9Lca+22ao\nKfCTqm4CEJHRwF3AD16E2XxwM+PWjGPR1kVMWDeBbvW6sfKJlVkeFzlwABITYfr0AyQlwZIlzn1I\nWreGxo3h1VehfPkwv4kwO3DggNcRQmL5vWX5/c1PxaQCsCXg+VacAhMRqWmpHDp+iAMpBy74mfTj\nJBZsXkDHWh25+6q7ebfNu1xe5PIM2zt1yikOGzc654UkJ5/77+7d0KgRpKRAhw7OpeMbNIDc4Tn4\nyxhjIspPxSQihi4fyqQfJ5Galsrx1OPs+m0X2w9v5+jJoxTLX4ziBYpTvEBxihUoxu5NxTm4uzhF\nfruFhrtGkzyrIL8ojFRISwNV5+fUKec6WSkpsH+/83P0qNM9Vb06VKkC8fHQvLlzDa34eKhUCfLl\ngx49knniCa+3StYkJyd7HSEklt9blt/ffHNosIhcB7ykqq3d5/0AVdXXz5vPH2/IGGNiTI64nIqI\n5AZ+BG4BdgBLgQdUdZ2nwYwxxvinm0tVT4nIH4EZOEehfWyFxBhjYoNv9kyMMcbELt+cZ3IpsXxC\nY3pEJFlEVotIoogsdaeVEJEZIvKjiHwtIjFzQXkR+VhEdolIUsC0dPOKSH8R+UlE1olIK29Sn5VO\n/hdFZKuIrHR/Wge8FjP5RaSiiMwWkTUi8p2IPO1O98X2v0j+p9zpftn++UVkift/9TsRedGd7pft\nn17+8G1/VfX9D05R/BmoDOQFVgFXeZ0riNwbgRLnTXsd6OM+7gsM8DpnQLYbgPpA0qXyArWBRJyu\n1Hj39yMxmP9F4M8XmbdWLOUHygH13ceX4YwfXuWX7Z9Bfl9sfzdTIfff3MBinFMTfLH9M8gftu2f\nXfZMzpzQqKongdMnNMY64cK9w7uAke7jkcDdUU2UAVVdAOw/b3J6edsDo1U1VVWTgZ+I4HlBwUgn\nPzi/h/PdRQzlV9WdqrrKfXwEWAdUxCfbP538FdyXY377A6jqUfdhfpwPWcUn2x/SzQ9h2v7ZpZhc\n7ITGCunMG0sUmCkiy0TkMXdanKruAuc/IFDWs3TBKZtO3vN/J9uI3d/JH0VklYgMC+imiNn8IhKP\ns4e1mPT/XvyQf4k7yRfbX0RyiUgisBOYqarL8NH2Tyc/hGn7Z5di4lfNVbUh0BboJSItOPtt4TS/\nHSHht7yDgStVtT7Of7J/e5wnQyJyGfAF0Nv9hu+rv5eL5PfN9lfVNFVtgLNH2FRE6uCj7X+R/LUJ\n4/bPLsVkG3BFwPOK7rSYpqo73H/3AF/i7EbuEpE4ABEpB+z2LmFQ0su7DagUMF9M/k5UdY+6ncTA\nR5zdlY+5/CKSB+eD+FNVneRO9s32v1h+P23/01T1EJAAtMZH2/+0wPzh3P7ZpZgsA6qJSGURyQd0\nBiZ7nClDIlLI/ZaGiBQGWgHf4eTu4c7WHZh00Qa8I5zbx5pe3slAZxHJJyJVgGo4J5p67Zz87gfA\nafcA37uPYzH/f4C1qjowYJqftv8F+f2y/UWk9OkuIBEpCNyGM+7ji+2fTv4fwrr9vTy6IMxHKrTG\nOULkJ6Cf13mCyFsF56izRJwi0s+dXhL4xn0vM4DiXmcNyDwK2A4cBzYDDwMl0ssL9Mc5CmQd0CpG\n838CJLm/iy9x+sBjLj/QHDgV8Dez0v2bT/fvxSf5/bL9r3Ezr3LzvuBO98v2Ty9/2La/nbRojDEm\nZNmlm8sYY4yHrJgYY4wJmRUTY4wxIbNiYowxJmRWTIwxxoTMiokxxpiQWTExxiMiMlxE7nEf9xaR\nAgGvHfYumTGZZ8XEmNjwDFA44LmdAGZ8xYqJMUESkefEuXU0IvK2iMxyH98sIp+JyG0i8q2ILBeR\nMSJSyH39/9wbEyWJyNCLtPsUcDkw+3SbzmT5h3s1129FpEyU3qYxWWLFxJjgzQdauI8bAYVFJLc7\nLQn4K3CLqjYGVgDPuvMOUtVrVbUuUEhE7ghsVFUH4VzmpaWq3uJOLgx8q87VXOcDj0fwfRkTMism\nxgRvBdBIRIrgXN9rEdAEp5gcw7m73kL3nhEPcfZK1reIyGJxbhd8M1AnnfYDL6B5XFWnBaw3Ppxv\nxJhwy+N1AGP8QlVTRSQZ5yqxC3H2Rm4GquLcgnmGqj4YuIyI5AfeBxqq6nb33tsFuLSTAY9PYf9X\nTYyzPRNjMmc+8BwwD1gAPIlzFdwlQHMRqQpnbjFQHadwKPCre8uBjum0ewgoGvD8YrdSNSZmWTEx\nJnPmA+WARaq6G6d7a56q7sXZY/lcRFYD3wI1VfUgMAxYA3zFufeECDxi6yNgesAAvB3NZXzFLkFv\njDEmZLZnYowxJmRWTIwxxoTMiokxxpiQWTExxhgTMismxhhjQmbFxBhjTMismBhjjAmZFRNjjDEh\n+399JexSzHrZVgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10a09eb00>"
      ]
     },
     "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*&mdash;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": 24,
   "metadata": {
    "collapsed": true
   },
   "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": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   t    Gini stdev   1%  10%  50%  90%  99%\n",
      "------- ---- ----- ---- ---- ---- ---- ----\n",
      "      0 0.11  20.1   54   75  100  126  148\n",
      " 20,000 0.48  94.6    1   12   73  223  431\n",
      " 40,000 0.49  96.2    1   11   71  232  428\n",
      " 60,000 0.49  95.4    1   11   73  226  426\n",
      " 80,000 0.50  98.6    1   11   69  234  449\n",
      "100,000 0.49  98.4    1   11   71  228  465\n",
      "120,000 0.49  96.7    1   11   72  233  445\n",
      "140,000 0.50  99.3    1   10   70  229  460\n",
      "160,000 0.49  97.8    1   11   70  231  442\n",
      "180,000 0.50  98.3    1   11   70  233  461\n",
      "200,000 0.49  96.4    1   11   72  226  437\n"
     ]
    },
    {
     "data": {
      "image/png": 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Q3D/2/oOzxpyVemWGigiMHWskI1iErvmVYDhsISL8eOJE7qqp4YING9gbCFj+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\nRmMJ2gFpNBqNxhK0A9JoNBqNJfx/uN8w+Dtj5foAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x107bfb5f8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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iyFO9XFpaysSJEwFIpVLElffb9ppZCpjs7odEy7cAK939FjMbCZS4+6hoAP4R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\nxKZiIiIisamYiIhIbComIiIS2/8HR12GVUi6jfYAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10b34ebe0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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sOGbPnh3vCOViOb1lOb0Vlpzu784K/773+8ykFTDWHTepBnyoqpNFZCHwkYgM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\nbHddG2BzxPrN7roKm5s5lz7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      "text/plain": [
       "<matplotlib.figure.Figure at 0x10b3d5be0>"
      ]
     },
     "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": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   t    Gini stdev   1%  10%  50%  90%  99%\n",
      "------- ---- ----- ---- ---- ---- ---- ----\n",
      "      0 0.11  20.1   54   75  100  126  148\n",
      " 20,000 0.45  85.3    1   13   79  218  373\n",
      " 40,000 0.47  90.1    1   11   76  224  407\n",
      " 60,000 0.48  92.0    1   12   73  228  404\n",
      " 80,000 0.48  92.5    1   12   73  231  406\n",
      "100,000 0.48  94.3    1   12   71  227  421\n",
      "120,000 0.48  94.1    1   12   73  226  437\n",
      "140,000 0.49  95.7    1   12   71  236  421\n",
      "160,000 0.49  97.5    1   11   71  231  454\n",
      "180,000 0.48  95.0    1   12   72  227  434\n",
      "200,000 0.50  97.8    1   11   70  235  442\n"
     ]
    },
    {
     "data": {
      "image/png": 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0LWzC3eyOtjhhZ6BnQI8Cpwdp/71Sarp5vAUgIhXAJUAFcCbwZ/EHtj8EfFsp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\ny22dYSmKlT/JlimlGkWkBFgrIrsxRCmWRKYOjvv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0X06j7jt15DkHmbWabPj9RqG6w4fh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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10b03e4e0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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A7l5pZj3isQcAc/LeuyKet1OsXr2WqVPLmxy3sfpDOp9UVtAy/77giYLGzZv3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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10aa5ac18>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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VtSLyDrAWOAb8wv2QAPdx6qXBn/ic3RNZB7N4beVrrL9v/fffC3g3lzHGFJfN\nzeWze6fcS43KNXi+9/OntOfmOs9+/+47qGAPAjDGxJk9zyTAdh3exTtr32Hdfeu+997OnVC3rhUS\nY0zpYBN5+OjfK/9N/7b9aXzO9/uypk5NCXwXV/5gXdBZTm9ZTm+FJWe07Pdin+Tk5vDKklf44LYP\nCn1/zx4bLzHGlB42ZuKT99a+xytLXuGzoZ8V+v64cTBnDowfX+jbxhgTU4Gem6sse3HRi6fc7V6Q\nXclljClNrJj4YOH2hWR+m8mN7YqePmzpUhsz8Yrl9Jbl9FZYckbLiokP/rLwLzx42YNUKFf0kJSN\nmRhjSpMzjpmISHlggqreEZtI0Yn3mMk3e77hstcvY8vwLZxT6Zwi1+vZE55+GsrItD3GmIDzfcxE\nVXOBRBGpVNKDlCUvLHyBn1/089MWErAxE2NM6VLcbq7NwOci8oSI/Cr/y89gYfTt0W9548s3uL/b\n/WdcNy3Nxky8Yjm9ZTm9FZac0SrufSbfuF/lgBr+xQm3d9e+S3JSMk1qnP6JV4cPw7FjUKtWjIIZ\nY4zPzuo+ExGppiefnBhI8Rwz6TmuJyMuHcFN7W867XqbN8PVV0NqamxyGWPMmcTkPhMR6S4ia4H1\n7vKFIvJqSQ9aGm3Zu4W1O9dyXZvrzriujZcYY0qb4o6ZvAT0AXYDqOoXwA/8ChVG/1j2DwZfMJhK\n5c98nUJWFlSokOJ/qCiFpa/XcnrLcnorLDmjVey5uVR1u8gpZ0C53scJp2O5xxj/xfgip04pKCvL\nmTHYGGNKi2KNmYjIe8ALwF+BS4HhwMWqOtDfeGcvHmMmH67/kD8v+DPz75pfrPV/9zsoXx6efNLn\nYMYYU0yxmptrGM6TDhNwnr3e2V02wOsrX+dnXX5W7PVtzMQYU9oUq5io6i5VvUNVG6lqQ1X9iaru\n9jtcGGzcvZFFaYu4teOtxd4mMxN27kzxL5RHwtLXazm9ZTm9FZac0TrtmImIvAIU2Wekqg94nihk\nXlz4Ij/veuY73iPZmIkxprQ57ZiJiAxxX14BdAAmucu3AmtVdZi/8c5eLMdM0g6kccHfL2D9/etp\nWL1hsbdr1gw+/xwSE30MZ4wxZyHaMZPiDsAvAq5U1ePuckVgnqpeVtID+yWWxeQ3s37DoWOHeKnv\nS8XeJi8PKleGQ4egks12ZowJiFgNwNcBakYsn+O2lVnHco/x71X/5t6u957Vdnv3wjnnwIIFKX7E\n8lRY+nr5Zkb1AAAXYElEQVQtp7csp7fCkjNaxb3P5FlgpYjMAQTnhsWn/AoVBlM2TuG8uufRvkH7\ns9pu505oWPweMWOMCYXiPM9EgGbAMZx7TAAWq2qWz9lKJFbdXD9680fc1vE2Bl84+Ky2mzsXHn8c\n5hfvlhRjjImJaLu5znhmoqoqItNUtRPwYUkPVJocOHqAuVvn8ubNb571ttnZdo+JMab0Ke6YyQoR\nucTXJCEyed1kfpD4A2pWrnnmlQvIzHSKSRj6UcOQESyn1yynt8KSM1rFHTO5FPiJiKQCh3DGTVRV\nL/ArWFDlaR7Pzn+WV/q9UqLts7OhUSOPQxljTJwV99LgRJyrt3q4TXOBfaq61cdsJeL3mMncrXO5\nb9p9rB62mgITXxbLPffAxRfDvWd3EZgxxvgqVpcG3whMBOoDDdzX/Ut60DD7eOPH3ND2hhIVErAz\nE2NM6VTcYvIz4DJVfVJVfwd0B+7xL1YwqSofbPiAG9vdWOJ9ZGZCkybh6EcNQ0awnF6znN4KS85o\nFbeYCKc+vyTXbStTZnwzg8rlK9O1SdcS7yMjA5o29TCUMcYEQHHHTH4FDAH+6zbdCIxT1eLPIxIj\nfo6ZDHh3AL1a9uLei0s24JGbC1WrwsGDNpWKMSZYYjI3l3ugi4Ar3cV5qrqypAf1k1/F5GDOQZq9\n0IyvH/ia+tXql2gf2dlw/vnOXfDGGBMksRqAR1VXqOrL7lcgC4mfPtrwEd2bdy9xIYGT4yUQjn7U\nMGQEy+k1y+mtsOSMVrGLSVk3ed1kBnQYENU+bLzEGFNaFbubKyz86OY6lnuMhs83ZP1962l0Tsmv\n6339dWdOrrFjPQxnjDEeiFk3V0mISDMRmS0iX4nIlyLygNteR0RmiMgGEflURGpFbPOYiGwSkXUi\n0jui/SIRWS0iG0UkpgP/UzZOoVPDTlEVEji1m8sYY0oTv7u5jgO/UtWOOPem3Cci7YCRwP9UtS0w\nG3gMQEQ6AAOA9kA/4FU5eXfg34GfqWoboI2I9PE5+wmT103mto63Rb0fGzPxh+X0luX0VlhyRsvX\nYqKqWaq6yn19EFiHM539DcB4d7XxOJcag3NX/duqelxVU4FNQDcRaQzUUNWl7noTIrbxlaoybdM0\nbmp/U9T7sjMTY0xpFbMBeBFJAjoDi4BGqpoNTsEB8h8XlQBsj9gs3W1LANIi2tPcNt+t2bGGOlXr\n0LRG9CPnkQPwycnJUe/Pb2HICJbTa5bTW2HJGa2YFBMROQd4DxjunqEUHCEP7FUAH6z/gOvOu86T\nfe3YYU9ZNMaUTsWdgr7ERKQCTiGZqKr5D9fKFpFGqprtdmHtcNvTgeYRmzdz24pqL9TQoUNJSkoC\noHbt2nTu3PnEbwf5/ZfFXX5jyhunPOf9bLfPX+7ZM5nMTNi0KYU09xwrOTm5xPuLxXJkX28Q8hS1\nvGrVKkaMGBGYPEUt2/fTvp9ByJO/nJKSwrhx4wBO/LyMiqr6+oUzvvFCgbZRwKPu60eBZ93XHYCV\nQCWgJfA1Jy9fXgR0w5kTbBrQt4jjqVd2HNyhtZ6ppUePH416X3v2qNaseXJ5zpw5Ue/Tb2HIqGo5\nvWY5vRWWnO7PzhL/rPf1PhMRuQLn2Sdf4nRlKfA4sAR4B+dsYyswQFX3uds8hjNL8TGcbrEZbntX\nYBxQBZimqsOLOKZ69Zn+vvTvzE6dzbu3vhv1vtasgVtvhXXrPAhmjDEe8/0Z8NFQ1c+B8kW8fU0R\n2zwDPFNI+3Kgk3fpzuydte/wUPeHPNlXaip4cSZpjDFBZNOpFOHI8SMsTlvMVUlXebK/9HRo1uzk\ncmR/b1CFISNYTq9ZTm+FJWe0rJgUYf62+Zzf8HyqV6ruyf4yM21eLmNM6WVzcxVh2NRhtKrTikeu\neMSDVM6z37t2hWHDPNmdMcZ4KtBzc4VVbl4uH6z/gJvb3+zZPjMyICEmt1kaY0zsWTEpxOfbP6fx\nOY1pXbe1Z/ssOP18GPpRw5ARLKfXLKe3wpIzWlZMCvHe2vc8PSsByMqCxo093aUxxgSGjZkUkKd5\ntHixBTMGz6BDgw6eZFKFypXh22+dP40xJmhszMRjKzJXcE6lczwrJAC7d0P16lZIjDGllxWTAuZs\nmcPVLa/2dJ9btkDLlqe2haEfNQwZwXJ6zXJ6Kyw5o2XFpICpm6Z6NktwvsKKiTHGlCY2ZhJh73d7\nSXwpkeyHs6lasapnmUaNgp074fnnPdulMcZ4ysZMPDR361wua3aZp4UEnDMTm5fLGFOaWTGJMHPz\nTHq06OH5fm3MxF+W01uW01thyRkt3x+OFRaqyn/X/5fPhn7m+b5TU23MxBhTutmYiWvDrg30/k9v\nUoenIlLibsPvycuDatVgzx7nT2OMCSIbM/HI7C2zubrl1Z4WEnBmC65d2wqJMaZ0s2Limp0627Nn\nl0Qq6rLgMPSjhiEjWE6vWU5vhSVntKyY4IyXzN06lx8k/sDzfdtswcaYssDGTID1u9bT9z99SR2R\n6nmel1+GDRvgb3/zfNfGGOMZGzPxwILtC7iixRW+7HvbNmjRwpddG2NMYFgxwS0mzf0pJtu3F15M\nwtCPGoaMYDm9Zjm9FZac0bJiglNMLm9+uS/7tueYGGPKgjI/ZrLr8C5ajW7Frkd2Ual8Jc/ztGsH\nkydDB+9mtDfGGM/ZmEmU5m2dx+XNL/elkABkZ0OjRr7s2hhjAqPMF5OZm2fSq2UvX/Z98CAcOQJ1\n637/vTD0o4YhI1hOr1lOb4UlZ7SsmGyeSe/WvX3Z99atkJgIHt9Ub4wxgVOmx0y27N1C99e7k/FQ\nBuXE+7o6fTq89BJ8+qnnuzbGGE/ZmEkUZm2ZRc+knr4UEoD0dLv73RhTNpTpYjLjmxmeP6I3UlZW\n0YPvYehHDUNGsJxes5zeCkvOaJXpYrIwbaFvNytC0TcsGmNMaVNmx0y2799O1zFdyX442/Np5/P1\n7Qu//CVc59/JjzHGeMLGTEoo/653vwoJOPNyJSb6tntjjAmMMl9M/KLqXBpcVDdXGPpRw5ARLKfX\nLKe3wpIzWmW3mKT5W0x274ZKlaBmTd8OYYwxgVEmx0wO5RyiwZ8bsPuR3VStWNWXHCtWwF13wapV\nvuzeGGM8ZWMmJbAsYxmdGnXyrZDAybvfjTGmLPC1mIjI6yKSLSKrI9rqiMgMEdkgIp+KSK2I9x4T\nkU0isk5Eeke0XyQiq0Vko4i8FG2uhWkLubyZf11ccOaHYoWhHzUMGcFyes1yeissOaPl95nJWKBP\ngbaRwP9UtS0wG3gMQEQ6AAOA9kA/4FU5eanV34GfqWoboI2IFNznWfF78B0gLQ2aNfP1EMYYExi+\nj5mISCIwRVUvcJfXAz1VNVtEGgMpqtpOREYCqqqj3PWmA08BW4HZqtrBbR/obv9/RRzvtGMmqkqD\nPzdg1bBVNKvp30/7gQOhf38YNMi3QxhjjGfCOGbSUFWzAVQ1C2joticA2yPWS3fbEoC0iPY0t61E\nvtr5FbWq1PK1kABkZkKTJr4ewhhjAqNCvAMAnp8aDR06lKSkJABq165N586dSU5OBuBf7/+Ltgfa\nnlg3vz8z/32vltPTk2natOj389v8Or4XywWzxjtPUcurVq1ixIgRgclT1LJ9P+37GYQ8+cspKSmM\nGzcO4MTPy6ioqq9fQCKwOmJ5HdDIfd0YWOe+Hgk8GrHeJ8Clkeu47QOBv5/meHo6A94doONXjT/t\nOtHKyVGtXFn1yJGi15kzZ46vGbwQhoyqltNrltNbYcnp/uws8c/6WIyZJOGMmXRyl0cBe1R1lIg8\nCtRR1ZHuAPwbbgFJAGYC56mqisgi4AFgKfAx8LKqflLE8bSoz6SqNPlLExbdvYik2klefsxTbNoE\nvXvDli2+HcIYYzwV7ZiJr91cIvImkAzUE5FtwJPAs8C7InIXzuD6AABVXSsi7wBrgWPALyKqwn3A\nOKAKMK2oQnImm/ZsolL5SiTW8vcGkE2boE0bXw9hjDGB4usAvKoOUtWmqlpZVVuo6lhV3auq16hq\nW1Xtrar7ItZ/RlXPVdX2qjojon25qnZS1fNUdXhJ88zdOpeeST19ndwRYOPGMxeTyP7eoApDRrCc\nXrOc3gpLzmiVqTvg526dS48WPXw/zqZNcN55vh/GGGMCo8zMzaWqtHipBbN+Oos29fztg/rhD+Gh\nh5znmRhjTBiE8T6TuNi4eyOqynl1/T1lUIUvvoBOnXw9jDHGBEqZKSYpqSn0atXL9/GSrCzIzYWm\nTc+QJwT9qGHICJbTa5bTW2HJGa0yU0w+3/65r897z7dqFXTpAj7XLGOMCZQyM2bS+uXWfDTwIzo2\n7Ojr8f/8Z8jIgBdf9PUwxhjjKRszKYasg1ns/W4v7Ru09/1Ya9bA+ef7fhhjjAmUMlFMPt/2Od2b\nd6ec+P9xv/qqeMUkDP2oYcgIltNrltNbYckZrTJRTGLxMCxwBt7XrYMOHXw/lDHGBEqZGDP54cQf\n8uBlD3Ltedf6euyvv3buMbE5uYwxYWNjJmeQp3ksz1hOl8ZdfD/WmjXQ0d/xfWOMCaRSX0zW7lxL\nnap1aFLD/ydVnc3gexj6UcOQESyn1yynt8KSM1qlvpgsSlvk+/Pe8xV38N0YY0qbUj9m8ouPf0Gb\nem0YcdkI34/dqRNMnAidO/t+KGOM8ZSNmZzB6uzVdG7s/0/3Awecgff2/t/KYowxgVPqi8mG3Rto\nV7+d78eZPx+6doXKlYu3fhj6UcOQESyn1yynt8KSM1qlupjsOLSDY7nHaFS9ke/HWr0aunXz/TDG\nGBNIpXrM5OONH/PS4peYOXim78e9+264+GIYNsz3QxljjOdszOQ0lqQv4ZKml8TkWMuWObMFG2NM\nWVS6i0nGErol+N/3tH8/fPPN2RWTMPSjhiEjWE6vWU5vhSVntEptMVFVlqYvjUkx+fxzZ7ykUiXf\nD2WMMYFUasdMNu/dTI+xPUj/Vbrvxxw5EqpWhSef9P1QxhjjCxszKcJnqZ9xZYsrY3KsuXOhZ8+Y\nHMoYYwKp1BaTFZkruCzhMt+Pc/iwc1nwpZee3XZh6EcNQ0awnF6znN4KS85oldpisip7FRc0usD3\n4yxc6EyfUrWq74cyxpjAKpVjJrl5udR+tjZbhm+hXrV6vh7vnnugdWtn3MQYY8Iq2jGTCl6GCYrU\nfanUrlLb90Ly3Xfw/vvO1PPGGFOWlcpurlVZq7iw8YW+H2fqVOeu96ZNz37bMPSjhiEjWE6vWU5v\nhSVntEplMVmavpSuTbr6fpw33oA77vD9MMYYE3ilcsykz8Q+/OKSX9C/bX/fjnP4MCQkwNq10MT/\nhzgaY4yv7D6TQqzIXOH7M98//RQuusgKiTHGQCktJhXKVaBZzWa+HmPCBPjxj0u+fRj6UcOQESyn\n1yynt8KSM1ql8mqui5tejEiJz9bOaNo0+OILePNN3w5hjDGhUirHTJ6a8xRPJvszUdbOnXDBBU4h\nueoqXw5hjDExZ2MmhbioyUW+7FcV7rrLuYLLCokxxpwUqmIiIn1FZL2IbBSRR4tar0sTfwbfZ86E\nr7+GP/4x+n2FoR81DBnBcnrNcnorLDmjFZpiIiLlgL8CfYCOwO0i0q6wdRNqJHh+/BkznEfz/uEP\nULly9PtbtWpV9DvxWRgyguX0muX0VlhyRitMA/DdgE2quhVARN4GbgDWF1zRq8F3VZg/H0aPhsWL\n4aWX4OabPdk1+/bt82ZHPgpDRrCcXrOc3gpLzmiFqZgkANsjltNwCoynjh+HBQucK7Y++giOHoXh\nw2HcODjnHK+PZowxpUOYioln1qyBRx+F3NyTXzk5zpVamzdDx45w/fXw+uvO43jLl/c+Q2pqqvc7\n9VgYMoLl9Jrl9FZYckYrNJcGi8hlwFOq2tddHgmoqo4qsF44PpAxxgRMNJcGh6mYlAc2AL2ATGAJ\ncLuqrotrMGOMMeHp5lLVXBG5H5iBcxXa61ZIjDEmGEJzZmKMMSa4QnOfyZkU94bGGGV5XUSyRWR1\nRFsdEZkhIhtE5FMRqRXx3mMisklE1olI7xjmbCYis0XkKxH5UkQeCFpWEaksIotFZKWb8cmgZSyQ\nt5yIrBCRj4KaU0RSReQL93u6JMA5a4nIu+5xvxKRS4OWU0TauN/HFe6f+0XkgaDldI/7oIisEZHV\nIvKGiFTyNKeqhv4Lpyh+DSQCFYFVQLs45rkS6AysjmgbBTzivn4UeNZ93QFYidPlmOR+DolRzsZA\nZ/f1OThjUu2ClhWo5v5ZHliEc0l4oDJGZH0Q+A/wUYD/3jcDdQq0BTHnOOBO93UFoFYQc0bkLQdk\nAM2DlhNo6v69V3KXJwFDvMwZs2+0z9+oy4DpEcsjgUfjnCmRU4vJeqCR+7oxsL6wrMB04NI4Zf4A\nuCaoWYFqwDLgkiBmBJoBM4FkThaTIObcAtQr0BaonEBN4JtC2gOVs0C23sC8IObEKSZbgTpugfjI\n6//rpaWbq7AbGr2fUyU6DVU1G0BVs4CGbnvB7OnEIbuIJOGcTS3C+ccVmKxu19FKIAuYqapLg5bR\n9SLwayByIDKIORWYKSJLReTugOZsCewSkbFuF9IYEakWwJyRbgPyH0wRqJyqmgH8BdjmHnO/qv7P\ny5ylpZiEUWCufBCRc4D3gOGqepDvZ4trVlXNU9UuOL/5dxORjoVkimtGEbkOyFbVVcDprtUPwt/7\nFap6EXAtcJ+I9CBg30+c354vAv7mZj2E89ty0HICICIVgf7Au25ToHKKSG2c6acScc5SqovIHYXk\nKnHO0lJM0oEWEcvN3LYgyRaRRgAi0hjY4ban4/Sx5otpdhGpgFNIJqrqh0HOqqoHgBSgbwAzXgH0\nF5HNwFvA1SIyEcgKWE5UNdP9cydO12Y3gvf9TAO2q+oyd/l9nOIStJz5+gHLVXWXuxy0nNcAm1V1\nj6rmAv8FLvcyZ2kpJkuBc0UkUUQqAQNx+gTjSTj1N9SPgKHu6yHAhxHtA90rK1oC5+LckBkr/wbW\nquroiLbAZBWR+vlXmIhIVeCHwLogZQRQ1cdVtYWqtsL59zdbVQcDU4KUU0SquWeiiEh1nH7+Lwne\n9zMb2C4ibdymXsBXQcsZ4XacXyLyBS3nNuAyEakiIoLz/Vzrac5YDlD5PMDUF+dqpE3AyDhneRPn\nqo6j7l/inTgDX/9zM84Aakes/xjO1RLrgN4xzHkFkItz9dtKYIX7fawblKxAJzfXKmA18Bu3PTAZ\nC8nck5MD8IHKiTMWkf/3/WX+/5Wg5XSPeyHOL4qrgMk4V3MFMWc1YCdQI6ItiDmfdI+5GhiPc+Wr\nZzntpkVjjDFRKy3dXMYYY+LIiokxxpioWTExxhgTNSsmxhhjombFxBhjTNSsmBhjjImaFRNj4sSd\nd+rH7uvhIlIl4r1v45fMmLNnxcSYYBgBVI9YthvATKhYMTGmmETkYXEeHY2IvCgis9zXV4nIf0Tk\nhyKyQESWicgkd5ZbROQJcR7wtVpE/lHIfn+JM/ne7Px9Os3y/0RklbvPBjH6mMaUiBUTY4pvHtDD\nfd0VZ+bV8m7bauC3QC9VvRhYDjzkrvuKql6qqhcA1dwZhk9Q1Vdwpt9JVtVebnN1YIGqdnaPe4+P\nn8uYqFkxMab4lgNdRaQGzrxrC3Ee1NUD+A7n6XSfu89e+SknZ7LuJSKLxHmM81VAxyL2Hzkx6FFV\nnRZx3CQvP4gxXqsQ7wDGhIWqHheRVJxZVj/HORu5CmiN80jUGap6R+Q2IlIZ+BtwkapmiPMM+yqc\n2bGI17nY/1UTcHZmYszZmQc8DMwF5gPDcGbgXQxcISKt4cRU7+fhFA4FdrtTv99SxH4P4DyqNt/p\nHrBlTOBYMTHm7MzDeVb2QlXdgdO9NVedhyINBd4SkS+ABUBbVd0PvIbzLI7pnPpMiMgrtv4FfBIx\nAG9Xc5lQsSnojTHGRM3OTIwxxkTNiokxxpioWTExxhgTNSsmxhhjombFxBhjTNSsmBhjjImaFRNj\njDFRs2JijDEmav8fUiIRclxMBf8AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1011b2fd0>"
      ]
     },
     "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": 27,
   "metadata": {
    "collapsed": true
   },
   "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": {},
   "source": [
    "Let's see what it looks like:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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4BHgc+Cowyd03mtlw4AV3H2dmMwB39/nR+58BZrv7y3tt12fP7rzfdXU/Zvfuzxg7dm6n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\nVDBERCQWFQwREYnl/wP9xzRf/8enkwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x102101080>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "hist(samples(USA), label='USA')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Hey&mdash;that looks like the beta distribution. Let's compare:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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TapcNlfLHS/nDFnsxyYd27Rt/LGuni/1FRPJFf2ELjPpM4qP88VL+sKmYiIhI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\nbGySAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10b690a20>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "hist(samples(beta), label='beta')\n",
    "hist(samples(USA), label='USA')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   t    Gini stdev   1%  10%  50%  90%  99%\n",
      "------- ---- ----- ---- ---- ---- ---- ----\n",
      "      0 0.45  88.3    2   18   75  217  420\n",
      " 20,000 0.50 100.3    1   10   69  228  451\n",
      " 40,000 0.50 102.5    1   11   69  229  468\n",
      " 60,000 0.50 101.6    1   11   69  231  481\n",
      " 80,000 0.50 100.6    1   10   71  223  480\n",
      "100,000 0.50 100.5    1   11   69  229  457\n",
      "120,000 0.50  99.0    1   11   70  228  465\n",
      "140,000 0.50  99.2    1   10   71  225  462\n",
      "160,000 0.50 101.5    1   10   67  232  461\n",
      "180,000 0.50 100.1    1   10   70  237  448\n",
      "200,000 0.49  98.1    1   12   71  228  455\n"
     ]
    },
    {
     "data": {
      "image/png": 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K+HX4NfBppdRqEXlGRN6rlHoO+DTQopSaKiIfAe4ALheRPOC7wEJAgLUi8oRS\nqn0wIfsnPrWGWsnz2ewB/fWvRjXsnJykukn3OHQy+r0dDFLi8aAwviSpiB6/kWXKj6cw6TuTiNRF\nCB8IEzkQIVIXIVIboWlDE+F9YUL7QkSbo3jLvLgL3DiznGQtyGLyrZNxuA5/D2+3bscDI2qAlFKv\nisjEQV4a7P/9EuBhpVQM2Csiu4AlIrIPyFJKrTbPewC4FHjOfM/3zPbHMIwdwHuB//QaHBH5D3Ae\n8MhgcpqL4d+hI9xBhufYy69byrvfDd/7HjQ1WZaSrTlIRyzGms5OGk87DYeugHDCIiK4cly4clwE\nphtzgUopenb00Lm6k+6N3TiznfRs6yG0O0Rot5Gy3/Z8GxP+dwKOvNQO4aY6diUhfElEPgGsAb5m\nGopxwMo+59SYbTGgb12a/WY75t9qAKVUXETaRSS/b3u/voZEYaCQHc07jk0jq5k82XDN+lvHY2TF\nihVpfSc2XP1+UVPD+8aMISPF09z1+I0MiUiC0N6Q4e30Pg4YXlDHax0kwglyTjO25B73pXEEpgXw\nlnlxZgz9+5LuY2cFdhige4AfKqWUiPwf8FPgfyzqe1i3sv/979V8//uTAMjNzaXSU0nOZCP01TuR\n2PtFGrXjU08Fl4sVf/sbzJ077P42mFsMjLr8o3Q8HP3u3r+fVeXlvDh/vu3y6/EbXf2e+e0z1N1f\nx9TNU3EXudkY2Ig7383pc0/HU+Jha+FW/F/3c/5nz0dEDr5/emp8XnYer1ixgvvvvx+ASZMmYQUy\n0hOwZgjuX0qpuUd6TURuBJRS6nbztWcxwmv7gBeVUjPN9suBM5VSX+g9Rym1SkScwAGlVJF5znKl\n1OfN9/zG7GNACE5E1LXXKu6662DbHa/dwYHOA/z8vJ9b+lkcM6edBl/7Glx2mb1ypBmf27GDzd3d\nvDB/Pl6HDqGcSHRv66b6J9W0/qeVaGsUT6EHd4Ebd+HBh6fQw5iLx5Axy+YwfIojIiilkopfj8Z/\nn9DHMxGRkj6vXQZsNp8/iZFA4BGRyUAF8KZSqg5oF5ElIiLAlcATfd5zlfn8Q8AL5vPngHNFJMdM\nSDjXbBtcwH4fYSQesbcYaS/NzUY2nMZSfj1tGpu6u/nyrl10JBni1BxfZMzMYMa9M1hatZRTa09l\n3n/nUfGLCkqvKSV3eS6eIg/hA2HWLllLz64eu8VNe0Y6Dfsh4HVgmohUicgngTvMlOoNwJnAVwCU\nUluBR4EDM5CLAAAgAElEQVStwDPANeqge/ZF4F5gJ7BLKfWs2X4vUGAmLFwP3Gj21QrcjDHHtAr4\ngVLqsPnM/RfAO8SB2D0xvW4dtLfDjBlJddPrQqcrw9HPIcLaRYv4e2Mj81N823M9fiODiODKduGf\n4idnaQ4FFxVQ9OEi3EVuRASHz4HDk9zPY7qPnRWMdBbcFYM033eE828Fbh2kfS1w0iDtYYzU7cH6\nuh+4fyhy9p+HzvJkUdNRM5S3jhytrYbxybM5HTxN8TsctMRifGP8eLtF0aQIrf9tZccnjeSj7FOz\nOfDHA0Z4rs/DlefCN9Fn/w1qmqBL8WA4Gn0pySzhhb0vDH7yaOH3W7IItXcyMV0Zjn6t0SiL163j\nC6WlfLa01HqhLESP3+hRcEkB7+p5F20vtBHcEyTaFKVnRw/136on3hl/57wFKxeQs/To6/NSSbdU\nRRsgwOc79Hh20WzWH1hvjzC9nHyy4QWtW2csSNVYxud27mSSz8c906bZLYomhQjuDbL9yu04vA6c\nWU5irTEidRHinXFKryml9LOlBGYGkg7NaQ6iP0mgfyJgZ7iTfH++PcL04vHABRfASy8l1U26x6GH\no99Xysp4o6ODSIrt/TMYevxGj2hDlPZX2mn9bytN/2yibUUb/ul+lmxfwrRfTSNzXuYxGZ9U0i1V\n0QaIgQYo15dLWygFarAtWQKrVtktRdrxt8ZGriktxaNTsDV9yF6SzXK1nOVqOWdEzmDR2kVEG6PU\n/anObtHSFv0fyEADVNVexYScFNiaubUVCgqS6iLd49DD0W+C10vwOPB+QI+fHcS6YgR3BgnXhPGW\neqm6tYrO9Z3H3E8q6pZq6DkgBhqghu4GijOL7RGmL/n5sHLl0c/THBMTfT6ea221WwyNzWz5yBba\nXmrDO9aLw+cgUh8h0hCBOHgnevGX+/GV+5jwvxPwjvPaLW5aog0QAw3Q1satTMtPgQnqykqoSG4D\nrBVpXo9qOPpN8vl4o6ODL+/axc+mTEnpbbj1+FlD64pWutZ1EW2JEmuOEW2J0vhoIwDR+igAS3Yu\nwVPswZnltCTNOt3Hzgq0AWKgAcr0ZNLY02iPMH055xy44gr4/veNpASNJbSY1Q9+WVPDzZMmkZvC\nBkhjDTs+uYPQ3tA7x+4CN/nn5TPph5PeKb9zLIVGNdag//MYaIAKMwppCbbYI0xfTjnF2J57/fBT\nwtP9Dmw4+l21bRsdsRj3Tp9Od4rPBenxS46OVR2skBWHGB+AaFOUlmdbCFeFURE1IsYn3cfOCrQH\nxEADtL9jP6VZKbBA8b77oKwMThpQBEKTBG8sXMjfm5q4p6aGO6qq2H7KKXaLpBkhAjMCjP/6eFRC\nIW5BHEK8M060NUqsNcaWD24B4JQ9p+Cf5LdZ2hMP7QEx0ADNL5nP07ueJp6ID/6G0eL+++HssyEQ\nGHYX6b4WYTj6lfl8lHg8NEWjfKw4BZJNjoAev+Rw5biY8uMpVPy0gim3TaH8lnKm/mIqs/48i7lP\nz2XOk3MAqL69+ig9HTvpPnZWoA0QAw3QJdMvYXvTdoKxoD0C9fLjH8MTTxz9PM0xUxMOsy8c5qqS\nkqOfrEkLlFLEu+OED4Tp2dFDx5sdtL9i1OHKO0fXXLQDHYJjoAGKqzgJlcAhNttnvx+CyRnBdI9D\nD1e/DxUW8rXKSia+8Qadp59OZv+S6CmCHr/hEW2NUv/neur+WEe0NUq8I06sI4bD48CZ7cSVbWzD\n7cx24vAbKdhWk+5jZwWp+V83yvQ3QC6HizlFc3ir7i2WjV9mj1AANTWQoTfFGgnG+3w8PGsWl2/d\nyurOTt6tq46nBW2vtLH9yu1Em6LkLs+l4u4KvGVeXNkunFlOXcctxdCjwUADBEYqdjgeHn1h+vLU\nU0nvhprucehk9HtvXh4X5OezoavLOoEsRo/fsRFrjRHaG2LBqws46V8nkfuuXPyT/bjHuEfd+KT7\n2FmBNkAMEoJLxFl3YB0zCpLbDC5pTj0VXnhhcAupSZpl69cjwEeKiuwWRWMRGXMycOW6WDN/DZ0b\njr18jmZ00QaIgb/vIoLH6WFf2z57BOrl4x+HjRthz55hd5Hucehk9Mt0Ojk7L49Sb+qWWdHjN3Sq\nbq9i1ZRV+Cb7mPufuWTNz7Ks7+GQ7mNnBdoAAf3XIjrEwbVLruXhzQ/bI1AvbjeUlMDf/mavHGmK\nR4S1nZ10mZURNMc3pZ8vpeCyAro2dlH/QD2V36xk/937qX+ono7VHXaLpxkEbYAOQ11XHRNzJ9ot\nBlRVwRlnDPvt6R6HTka/B2bO5K8NDazuTN1QjR6/oePKcTHzwZnM/fdc8s7Jw+F38PZ1b7PtY9vY\neN5Gy64zVNJ97KxAZ8EBg61FfGrXU1y/9PrRF6Y/LlfSBUk1A9nW3c2lmzdzeVGRzoBLI5wBJ/nn\nGptJKqWINkapvaeWBS8vsFkyzWCIOsEnuEVE3XKL4qabDm2ffNdknr/yecrzyu0RrJeyMnj8cWOL\nbo0l7AkG+eT27Yz1evnLzJk4LKh8rElNet7u4c2pb+Kf7je2V5jswz/FT/bSbLJOztJp2UkgIiil\nkvrn0R4Q4PMdetxrlEOx0CBnjzJZWaDnKCzjsYYGLt+6la+MH88PJ03SxifNCVQEeFfXuwjtDRHc\nEyS0O0RwV5DKr1UCsGDlAnKW5tgs5YmLNv9AuN9yn4RK0BJsIdubbY9Avbz2mrEYdfLkYXeR7nHo\nY9XvPfn5LM7OJtPpxO9M/fL7evySx5nhJGN2BgUXFVB2bRnjvzmezPmZAKxftp4VsoJExPqq6Ok+\ndlagDRAQ6ufoKBRKKTLcNlchKC6GSATGjLFXjjQi2+Wi2O3m7SRLHGmOX/bfuZ/w/oN3neIWOLFn\nImxDGyAGGqCq9ipyfDnk+W2enH7qKfjgB41EhGGS7msRhqPfBWPG8HRzM5/fsYPt3d3WC2Uhevys\np+InFVTcXUHOGUboTUUVibD1HlC6j50VaAPEwBCc1+klHLO5DE8kAt/+Nnz5y/bKkYZ8trSUzYsX\n80xLCzNXr2a39oZOOGp+WUP+efmc8vYpnBk/E1e2ng63A22AGFhw2ufy2V8Hzu2GeBzmzEmqm3SP\nQw9XvwK3G6/DwfVlZZT7U3cjMj1+1tPwSAMdr3dQeFkh/il+xDEyiSjpPnZWoA0Q0L8WZSQewSkp\nMEHtdEJTk91SpCUeh4Pn5s7lofp61nToVfInEj07egBYu3gtr+S+wgpZQfsb7TZLdWKiDRAwc+ah\nx5meTEKxkL07okajxk6oa9cm1U26x6GT0e+Rhga643FKPB7rBLIYPX7WM+m7k1iulnN6++ksfH0h\nAOtPW8/GCzYSrLQuHJvuY2cFOvAJ9P/98bv9xBIxQrEQGR6bMuFEDNds7lx7rn8CkOty0Z1IUBuJ\nUNZ/MZgm7RERMmZlsFwtJ1wTZuvHtrKqYhXOLCfuMW5c+a6Df/Pd+Cb6GH/DeESvHbMM7QExcJ2n\ny+FiesF01h5IzvtIiq4uS8rwpHscerj6hRMJ7qmt5e6KCpZk27ze6wjo8RsdvOO8LFixgDPjZ7K0\nainznp9H+W3loKDp8SZqf13L7ht3oyJDz9dOFd1SGW2AGLzQwNstb7OgxMb6UU8/rcvvjCChRIKq\nUIgL9RorTR/EIbhz3fjL/fin+nHmOPFP9oMTvGVeau6pQcX1oiGr0CE4jGSz/hQGCqnprGGG16ZN\n6To7obAw6W7SPQ49XP1yXC7K/X629/SkdBacHr/RI94Tp3tTN7G2GNHmKNGWKJknZeIt9ZIxJ4O2\nFW3sv3M/RR8twlty9D2kUkm3VEUbIAZ6QEopAu4AkXjEHoEATjkFbr3VvuufACzKzOTbe/awMDOT\nkhTelE4zOjT8tYEd/7MDcQsFlxXgznfjHuPGV+4ja3EWYz87ltzluTjcOnBkFfqTZKABWl+3nnA8\nzMyCmYO/YTT4wx/g6quT7ibd49DJ6Pf76dM5Jy+P927cyNs9PdYJZSF6/EYWpRThA2FanmshUm/c\ncJbfUc7sh2cz7Z5pTL55MuOvH0/JJ0rIPzf/mIyP3bodD2gPiIEGKMuTRTAaRNlVICoSgRUr4Kc/\ntef6Jwgiwu3l5RS43Vy6eTMvL1hAvtttt1iaUeT1kteJNkRxjXGR/5585r8yn5zTdHXs0ULvBySi\nrr9e8fOfH2xLqAQ5t+Ww97q9jAnYMEn98MNwzz3w4ovGYlTNiKKU4jM7dpDtcvEzvfnfCUXljZV0\nrukkWh8lfCBMvCOOu8iNf4qf/PPyKbmyBO84HZ4dDL0fkEX0D/+HY2HiiTgOsSlCOXYsVFZCczMU\nFdkjwwmEiHBlSQnX7tpltyiaESZcGyZSFyHWHiPeESdjVgbeMi/x9jix9hjRpig9O3voXN1J1/ou\n3IVuSv+n1G6x0xY9B4RRdKAvsUSMaCKK321TdtSZZ8K8efDyy0l3le5xaKv0q/D72ZGCRUn1+FnL\npgs3sXbRWt466y02X7qZ7Z/cTt19dUQaIrjyXWQtzmLcNeM46ZmTOK3ptKSMT7qPnRVoD4iBadhZ\n3ixyfbm0BlsZmzXWHqGqqpJehKoZOq+3tzPV70cppVe6pzELVy2k660ump9spumJJro3ddO1rotI\nfYRT959qt3gnHNoAAY5+fmA8ESeeiNv7Q+R2gwWZWem+FsEq/c7Lz+emPXt4pqUlpRan6vFLjngw\nTsPDDbS92Eb7q+2Ea8J4x3nxTTJSq4s/UUzOaTlkLsy0/NrpPnZWoA0QA+f5tzZuZUxgDCWZJfYI\nBLB8uRGCO1XflY0GfqcTAcalcGFSzbGhEopXAq+8c1xwaQGlXyjFW+o1Eg0q/Pgm+bTHayN6DoiB\nHlBhRiGtwVZ7hOmlqMhIQkiSdI9DJ6tfJJHgrv37KX/jDUo9HuZmWn8nnAx6/IaPOIRF6xYx54k5\nTPv9NLIWZxGuCdP8dDNVt1Wx/l3reS3/NTactYEDfzxAImbtrqjpPnZWcFQPSESmAb8GipVSc0Rk\nLvA+pdT/jbh0o0R/D6g4o5iuSBc90R4C7oA9Qi1YALfcYs+1TyC+VlnJ5u5u/jFnDouysuwWR2Mx\nWQuyyFpw+HGNNEToWNVB9U+qqftTHdPumUbGbJsq4J+ADMUD+j1wExAFUEptBC4fSaFGm/4eUEe4\nA4c48DptzP/PzR24V/gwSPc4dLL6/b+WFi4tKEhZ46PHb2TxFHkouLiA+S/MZ8zFY9hw1ga2fGgL\nkabky3DZrdvxwFDmgAJKqTf7xUkHqR99/NLfA8ryZhGKhexbBwQwZQrs2GEkIgRs8sLSnG3d3ewI\nBvHoOYATikQ4YawHqo0Qrgkbz2sihGvD+Cb6aHyskaKPFlF4WfLFgDVHZii/sE0iMgWMujQi8kHg\nwIhKNcr094Ac4sDj9BCKhewRCIxK2JmZSc8DpXscOhn9XmtvJ9vp5AMWVB0fKfT4WUPri62skBW8\nWvAqr2S9woblG6j8eiUNjzYQ2h0ySvGcl0/5reUs3raYgvcXJH3NdB87KxiKB/RF4HfADBGpAfYA\nHx9K5yJyL3ARUK+Ummu25QGPABOBvcCHlVLt5ms3AZ/C8LCuU0r9x2xfCNwP+IBnlFLXm+0e4AFg\nEdAEfEQpVWW+dhXwLQzD+SOl1AOHk3Owajc+l49gLGjfYtT2duORwj+OxzNVoRCf2bmTv82aRZHO\nfEt7AtONKIJ7jJvijxXjHe/FO86Lt9SLZ5wHf7kfcWhPeLQZci04EckAHEqpziF3LnI60AU80McA\n3Q40K6XuEJFvAnlKqRtFZBbwF2AxUAb8F5iqlFIisgr4klJqtYg8A9yllHpORL4AnKSUukZEPgK8\nXyl1uWnk1gALAQHWAgt7DV0/GdUttyhuuulgW0N3A9N+MY3mG5pxOmyqxfbqq3DttbBunT3XT3OU\nUtxaVcXPqqv599y5LE7hXVE11pCIJWh+qplQZeid0FvHGx2E94WZ9ptplH5Ol9w5FqyoBXfUEJyI\n5IrItcDNwI9E5G4RuXsonSulXgX65zNfAvzJfP4n4FLz+fuAh5VSMaXUXmAXsERESoAspdRq87wH\n+rynb1+PAWeZz98L/Ecp1a6UagP+A5x3ODn7h+DWHVjHotJF9hkfgIwMaGuz7/ppjohwaUEBIoKn\n/xdAk5Y4XA4KLy2k7CtluAvcBHcGiXfFKb6qmPwL8u0W74RkKP95zwCTgE0YnkTvY7gUKaXqAZRS\ndUBvtc1xQHWf82rMtnHA/j7t+822Q96jlIoD7SKSf4S+BqV/CM7tcGN7lfDqaiMEl0hubUK6x6GT\n0W9zdzezAwFmpXCShx4/6wntC7HnW3vIPz+fU+tOZeb9M/GN91l+nXQfOysYyhyQTyn11RGUwcpf\n+mG5g488cjVdXZMAyM3NxTvOS2fEiDT2fol6UypH7fgf/4Drr2eFWZB0uP1t2LDBHvlH6TgZ/S4c\nM4YfPfEEnpdeYv2nP838rCzb9dHjNzrXn/PkHHZ+bicvrXwJ/yQ/Z194NtlLs1m5a6Wtn0cqH69Y\nsYL7778fgEmTJmEFR50DEpGvYMzjPAW8szBFKdUypAuITAT+1WcOaBuwXClVb4bXXlRKzRSRG41u\n1e3mec8C3wP29Z5jtl8OnKmU+kLvOUqpVSLiBA4opYrMc5YrpT5vvuc3Zh+PDCKfuvNOxXXXHWzb\n2riVyx65jO1f2j4UFUeGq682UrG/8x37ZEhT9oVC/Kelhf/X2soLra1ku1ysXrSIMXozuhOKfbft\nY89Ne945DswKMOeJOfgm+vS220NgVOaAgAjwY2AlB8Nva47hGsKhnsmTwNXm86uAJ/q0Xy4iHhGZ\nDFQAb5phunYRWSLGYqQr+73nKvP5h4AXzOfPAeeKSI6ZkHCu2TYojn6fQmVLJWXZZceg4ghw7rmw\ncaO9MqQh3fE4C9as4bM7d9ITj7Ph5JPZvXSpNj4nIPnn5ZP33jwKP1RI4YcLcee7eevdb7HlQ1vs\nFu2EYSgG6GtAhVJqklJqsvkoH0rnIvIQ8DowTUSqROSTwG0YxmEHcLZ5jFJqK/AosBVj3ukaddA9\n+yJwL7AT2KWUetZsvxcoEJFdwPXAjWZfrRhJE2uAVcAPzGSEQek/B7ShbgOLxi4aioojR0cHWJCZ\n1etCpyvHql+G00nNsmV8Y/x4MpxOynzWx/6tRI/fyJE1P4t5z85j9qOzmf3IbBa8soDp902n+Ylm\ntl25jYbHGpLqP93HzgqGMgf0NjCsfQGUUlcc5qVzDnP+rcCtg7SvBU4apD0MfPgwfd2PsXboqDQ1\nHXrsdDhRlk5NDYPWVr0GaIRwirCus5NLC5JfbKhJL/LOzmPxtsW0PN3C1g9tpfGDjQRmBHDluii9\nphSn38bM2DRkKAaoG9ggIi9y6BzQtSMm1SjT2Hjo8cyCmfx+3e/tEaYXvx8akrsDg/SvRzUc/d7s\n6ODl9nZ+O3269QJZjB6/0UVEyJiRQcaMDPLPz6fmFzXs+799AOSfn0/GrKEXKk013VKRoYTgHgd+\nhBFKsyINO+XoH4ILuAPEEjaXu4vFQNcoGxGWZmdzfVkZF27cyHMtLUSTTHXXpCcZszLIPTsXgKzF\nWfTsTH6DSM2hHNUAKaX+NNhjNIQbLVz9/MCWYAt5/jx7hOklFDIWoyZJusehh6Ofy+HgtvJyvjhu\nHN/avZtLNm+2XjCL0OM3Oqi4ItoWJVQVomtTF+2vtdP8TDMqpqi4uwIc0PyvY6vLmCq6pTKHDcGJ\nyKNKqQ+LyCYGrtVRSql5Iyva6NE/C6493E6uN9ceYXrJyLBkQzrN4DhE+HJZGSdlZPDut95iZXs7\ny3Jy7BZLM8o0/rORLZcZWW/ObCeuHJfxN9t18HmOi5zTcyi4WM8ZWs2R5oB6V8ZsA77Rp12AO0ZM\nIhuI9Yu2eZ1eemI2u9vZ2QMnp4ZBusehk9XvRbPc0faenpQ0QHr8RpZE0Ai/OvwOpv5yKiWfKLGs\nb7t1Ox44rAFSSvVuuVChlNrX9zURmTGiUo0y0eihx3n+PDrCHfYI08v558M3vgE1NTDusFWENMPk\n1bY2Hm5o4Fe1tfx8yhQ+OXas3SJpRpF4ME7bijYa/9FoGJ9fTaXgEu3hjDaHnQMSkS+Y4bfpIrKx\nz2MPkFYrJOPxQ4/HZo6ltrPWHmF6GTcOrrgCfv3rpLpJ9zj0cPRriUa5ePNmfl1by50VFVxbZvOi\n4yOgx29kqP5xNZVfrSRjTgYL31jI2E+OxZU9lKTgoZPuY2cFR/rEHwL+jbEu58Y+7Z1DLcNzvODt\nt/O20+EkoVIgM6qjw5JEBM2h5Lvd1C5bxuNNTVz39tts7e7mV1On4uo/GahJW5wZTtxFbko/V4p3\nrPfob9CMCEPeDyhdERH1ta8pfvKTg23/3f1fbn31Vp6/8nn7BNuxA844A3btsqQigmZwXmlr4/Kt\nWynxeFh78sl2i6MZJRKxBHu/s5fa39aSd24eYy4eQ+bcTPzT/Dh9erHpULCiFpy1PudxSv85oM5w\nJ9lem3/0Kyth1ixtfEaYnkSC2kiE8/L1fjAnEg6Xg/Jbyyn7ahlNjzex+8bdRGoi4AD/FD+zH5tN\n5txMu8VMe3TMgYEGqDXUSobb5tBXMAgWZGWlexw6Wf2WZWdT5HbTFovZvwfUIOjxG1lUVOEp8hjG\nByABwV1B1sxbQ6wrucXodut2PKA9IKB/SbCHNz/Mx+d+3B5hesnMhJa0mmpLORJKsbOnh2XZ2TzV\n3ExVOMzEFC9OqrGWNfPWEG2KDvrahndtILw/TLQpSvnt5Uy4YcIoS5f+aAPEQEcjGAtSkmndeoBh\nEY8PXKA0DNJ9LUIy+n1z925+V1vL/4wdy5bFi1PS+OjxG1mW7FpC8O0gwZ1But7qonNtJ11ru4i1\nxeja0AWAuAR34bFv12G3bscD2gAxMA0715dLZ7jTHmF68XoHlunWWErA4eBL48bxo/Ih7S6iSSNi\n7TFezX31YIMTSq4uofiKYiZ9bxL+Cj+eEg+i6zGOKHoOiIGORigWwu20eYMyvx8smJNI9zj0cPVb\n09HB1p4e1nTafKNxFPT4jQyuHBcnbzyZWY/MYuK3J5L/nnwaH2uk+sfV1P+5nrYX2oh3xI/e0RFI\n97GzAm2AGOgBLStbxpraY9n0dQSYMQOqqwcKp0ma5miUxevWMSsQ4BdTp9otjsYmMk/KpOjDRUy+\neTJzn5nL3H/PBQcc+N0B3r7+bVr/22q3iGmPXgckor77XcUPfnCw7aev/5TqjmruPO9O+wQDWLgQ\nfvYz0LFky6gOhbhw0yYuHDOGW3XoTWOilOIlx0vvHGcuyMRT6sFb6sU3yUfG7AwCswP4J/sRpw7L\ngV4HZBn9t4PxuXyEYiF7hOnLzJlGLTiNZVy0aRMfKy7mhvHj7RZFk0KICMvVchLRBJH6CJEDxiNc\nGya0O0Tt72rp3txNtClKYEaAjNkZZM7LZNyXxuHw6kDScNGfHNB/DWJFfgW7WnbZI0xfMjONrbmT\nIN3j0Mei39rOTqrCYb4+fvxxM7msx290cbgd+Mp8ZMzKIDAjYDymH3w4vA6CO4P07OihZ0cPiejh\nS3almm6piPaAMPZ+60uOL4fG7uS3QkiaceNg/367pUgLIokE52/cyGnZ2VSFQkz2++0WSZMi9Ozs\noeGRBjpXdxJ8O0i4NowKKyMEN86Lb7IRgss7O4+MORl4x3sRx/FxA5Pq6DkgEfXTnyq++tWDbTub\nd3Len89j93W77RMM4OST4eabja0ZNEnzbHMz52/axLtzc3lh/ny7xdGkCJvfv5mmx40lD77JPvLO\nzSN7WfY73o87z+aM2BRFzwFZhMdz6HHAHSAcD9sjTC/hMGzdqqthW8jjTU2UeDw8NHOm3aJoUog5\n/5yDSiiCu4N0v9VN97Zu2p5vo/ZXtfRs78ERcBCYHiDeE2fWX2YRmB6wW+S0Qc8BMXAdUDAaxO+y\nOUTj9cKnPw3PJ1eRO93j0EPVry4c5rcHDvDwrFmU9N9/I4XR4zc6iEMIVAQo/EAhk749iZkPzmTR\n6kWc3nE6J687GfEIXWu7jP2gh0iq6JbKaA+IQQxQLIjfnQJzBCtXwt132y1FWtBurqe6Zd8+8l0u\nTsrUlY41gxNrj9HybAvdW7vp2dZD9+ZuQvtCZC/Lxjcx9co1Hc/oOSARdcstiptuOti2o2kHFzx0\nAZXXVtonWCgEhYVGGrbeksESookEvztwgO/v3cvL8+czU4c3Nf2of6iet697m+yl2WTOzyQwM0Bg\nZoCMkzJwuHTAqC96Dsgi+ntAPdEe+7djqKqC4mJtfCzE7XDwmbFj+Xl1NTt6erQB0qCUIlIbIbw/\nTLgmzLaPbQMga0kWk74zyV7hTgC0SWfgfkAJlbC/Flxb28AFSsMg3ePQx6qfS4Qyr5fv793LU8dB\nsVc9fiNHqDrES46XWFm2ko3nbaTuvjpKryml6GNF5Jyq9+IaDbQHxEADFIqF8Dg9g588mjQ1Gdlw\nx9GkearjEOGuqVN51/r1tFqw3YXm+KLluZZ3Khr0brcAEGuL0fxUM0t2LCEwTWe5jRbaADHIltyR\nTgJum7+EixcbhUj37oXp04fdTbrvSTIc/RoiEbKdTn5ZU8Pm7m7OysvjPXl5KVkdQY+fNcS741T9\nuIrae2op/kQx7gI3BZcVMPYzY3EXuHEXuHHlu/CWWHezl+5jZwXaADFwDmh+yXzW1q5FKWXfj1JP\nj7EjalmZPddPY87Nz2fP0qVcvGkTd1RX82p7O+/OzcWTggZIYw0923uoubsGT7GHSG2EeEecSH0E\nZ6bTeGQ4Dz7ve5ztxDfep+u9jRDaAAGRyKHHPpePuIrbe0ecSIDLBQ0NMHnysLtZsWJFWt+JDVe/\njnic51pb+dOMGVxZYvPut0dAj581ZC3KYmnVUtpWGPv8xLvixLuNv7HWGOH9YaOtK06iO/HO81h7\njPBhXp8AACAASURBVHBtGE+RUZbHmeVkzpNzcPqcKaPb8Yw2QAwst9YZ7iTTY/M6kawsOPdceO21\npAyQZnACDgeZTic/2Ls3pQ2QxjpcmS4KLio46nmRhgibL9mMw+8gUBrAleOia0MX4eow/ql+HB7t\nDVmFXgckoi69VPHPfx5sS6gEebfnsfva3YwJjLFHsMZGY+7n5Zdhzhx7ZEhj2mMxTlm7ljumTOF9\nBUf/UdKcOIRrw6wsWwnmT6O4hNzlueSckcOYC8eQtTDLXgFTBL0OyCJ8/RY3O8RBvj+f1lCrfQao\npcVIw9bGZ0RojkbZHw6T79L/AppD8ZZ6WZ5YDhjeUM+2nne2X9h43kb8U/04M5w4Ag5jrsh8ODLM\n40Cf5+Yj65QsXJn6u9Yf/Ykw0ADFEjFqOmqYkDPBHoEA2tvBkbyrn+5x6OHqV+73c824cdy4ezfX\nlZXxvoICvBZ83lajx89ePEUePEUecs/MBWD818cTrAwa80Q9xjxSojthzCd1x43khgMR4t1xVu5Z\nyQIW0P5KOzMenEHx5cU2a5N6aAOEMdffl2A0iMvhsnct0BNPwNy59l3/BOCWyZP5wJYtfHjrVh6a\nOZOPFusfCM2R8Y714h17MFU7EU7QvbmbznWdhPaGjJ1U64xH5/5OOugg65QsCi8rtFHq1EUbIKB/\nstvetr1Myp1kiywAKAVPPw3XXJN0V6l8d2kFyejncjj41sSJrOns5C/19SlpgPT4pTYv+14etN0/\n3c/n934ed5E7JdeXpQraAA2CQxxE4pGjnzhStLTArl3wmc/YJ8MJQrnPx+KsLF0XTjMszoyfSbQl\nSvvL7Wz5wJZ32mNtMRwZDm18jkLqBb1toP93pCvSRZ4/zx5hAOrrjQSExOH3mx8q6V6PKhn9nmxq\nomzlSlpiMb41wcb5viOgxy/16N7aTd2f6qj8ZiWbL9nMmpPWsPOanRRfVcyZiTNZrpZzWt1pvLrm\nVbtFTXm0B8RAA9QZ6STLY2Oq5cyZkJkJ69YZJXk0I8IZOTm8r6CAF9vayNTZcJpBiLZG6dnWQ7Ay\nSLAySNeGLjrf7CT3rFwyZmZQ8qkSKu6uwDfJp72dYaD/6xhogFqCLfalX4MhUGmpsRYoSY73GPvR\nSEa/XLebb06YwN8aG3mmuZkLxtg45odBj589KKVYfdJqerb0AOCb5DPWAV00hpkPzsSVdfSfzlTV\nLZXQITgGGqC2UBu53lx7hOnlzDPhL3+xV4Y0pyce56pt2yj3+fR6IM0hRA5ECL4dfOc4tDdE/QP1\nVH6lEhU9sRfvW4n+r2OgAXKIA4XNX7LqaliwIOluUn2dxf9v78zD46iuRP87rV7UWixLshZLsiTb\nsmxsbIM3bDwsMQRMnBeSfJCx4YU1ECYQCHlkgISXkBfmS5iZJLzHkGTGLGYyiUkICUswDCHELF7A\ni2QZeZG8W7Z2WfvS3er7/qiSLattsNXVrlbp/r6vP1VdVd86R0fdp+65554bLdHot6enh5BS7F24\n0FqhLETbz3ra1rfRvbubUGuI0DHjFTwWNI7NtkBdgJwVOSRNS8JX4MOb78VX4MOX5yMh6dPrwIHz\nbWcF2gER6YC8CV76+vvsEWaACROM/YA0MSPJ5aKjv59gOIwnDhehamJD2eIyUhekMmbhGNzpbvwl\nflLTU3Gnu3Gnu/Gke0gsTiQh+cwcjWb4aAd0CtJ8abT1ttkrxMcfw7JlUXfj9CewaPSb7PdzcVoa\nf1dWxqszZ5LjjYNNCIeg7WctSimSzkuiZ08Pnds68eX78BX4SJ6ZTMkTJbjc1j2ION12VqAf+4gc\nAXUHu/F7/PYIM4DHA7299srgcESE30+fzoIxY7hj927Co7ww72hARJi3bR7zyucx641Z5N2ZhyfT\nQ90zdXR93GW3eKMO7YCIdECB/oD9W3J3dVmyFfdIXGdxNkSrn4jw4IQJbOvs5KkjR6wRykK0/aKj\nc3snh/75ELvv3E35knI2FG7g/eT32bpwK/se3Efbhja8471M/ulkUmZbuwWL021nBbaF4ETkANAG\nhIGgUmqBiKQDvwOKgAPAV5RSbeb1DwO3ASHgPqXUW2b7HGAVkAisUUp9y2z3Av8JzAWagL9XSh06\ntSwnn5dmlvKzjT+zTtnhsH493HOPvTKMEgoSE/leUREvNjbyTb0D7YhGhRVNf2qi9d1W2t5vI9AQ\nIOu6LFIuTCHr+iz8U/z4CnyWhto0w8dOK4SBy5VSFyqlFphtDwFvK6WmAu8ADwOIyHTgK8B5wDXA\nL+TEqq9fArcrpUqBUhG52my/HWhRSk0BngD++XSCDHVA41PHc6znWPQaRkNJCezcGXU3To9DW6Hf\niw0NPLxvH8syMqIXyGK0/c6OvsN9VF5XyZEnj6DCitybco8nFIT7wgSOBujd10uoI0Ss90Jzuu2s\nwM4kBCHSAV4LXGYePw+sxXBKXwBeUEqFgAMiUg0sEJGDQKpSapP5nv8Evgj8t9nXD8z2PwD/dqaC\ndQe7SXQnfvqFseSii6Cy8tOv0wwbpRRrWlr4RnU1f5k9mzmpeqOxkY6v0Mfsv84mUB8g1BIi2Byk\n92AvnWWdBJuDhFpCBBoDBGqNWo/e8V68uV584314sj14Mjy4M9yRPzM9eLPjL0llpGOnA1LAX0Sk\nH/h3pdTTQI5Sqh5AKVUnItnmtfnAhkHvPWK2hYDBG2rXmO0D7zls9tUvIq0ikqGUahkqyOHDJ5+n\n+dLoCto8Ibl8uSXVsJ2+FiEa/da2tvL57dtZM3Nm3Dofbb+zQ0RIX3LqOo5KKcK9YcI9xivQaIyG\nevf30rO3h77DfbRvbKevpo9gQzDi/XO3zD2r3VCdbjsrsNMBLVZK1YpIFvCWiOyGiNWfVo6RT1uo\nacOGW3j00WIAxo4dS+HUQoL9xj/gwETiwD/SOTufMgX272ftG2+A3z/s/srLy+2R/xydR6Pfx11d\nXLp/P36jIS700fazpv954+ax5749bOnaQu+BXma2zSTcF6bcXU6CN4G5Y+bi8rsoC5fh8rpYkLMA\nV6KLisQKZIaw6HOLcPldbGrahPiEa265htQ5qbb/vew8X7t2LatWrQKguLgYK5BYx0HPSAiRHwCd\nwNcw5oXqRSQX+JtS6jwReQhQSqnHzevfxAivHRy4xmxfDlymlPqHgWuUUh+KSAJQq5TKPsW91a23\nKp599kRbf7ifxH9KpOu7XfZlwzU2QmkpVFVBlt7MKhZcVlZGYzDI27Nnk2dBxqEmfmh8uZHKLxkh\n7NKVpeTcmIPL50JcumCoVYgISqmo/qC2JCGISJKIpJjHycBVwHbgVeAW87KbgVfM41eB5SLiFZGJ\nQAnwkVKqDmgTkQVmUsJNQ95zs3l8PUZSwykZGn3pCnbhS/DhcXmiUTM6du82qiFo5xMznp02jZ3d\n3axuaLBbFI3FZH0xi0uDl+JOd1N1RxVbF279hBiIxi7syoLLAT4QkTJgI/CamVb9OPBZMxx3BfAT\nAKXUDuD3wA5gDfANdWLodjfwDFAFVCul3jTbnwHGmQkL38JIZjglCUMqbhxsPUjR2CJ7y6s3NsK4\ncVF3MzCEdirR6Jfr9XJpWhpBC/ZdihXafsNHhRQz/jgD/xQ//sn+c/55drrtrMCWOSCl1H7gglO0\ntwBXnuY9PwZ+fIr2LcDMU7T3YaRufypDHdDGmo1MzZx6Jm+NHRYtRNWcnu/v38/Wzk5enDHDblE0\nMWDH9Tto/nMzqQtSKXmixG5xNKdA14Ij0gFtOrqJqyZfZY8wA6SkWFKKZ2Ay0alEo99jEyfyp6Ym\nqrq7yfbGZ4qttt/wmfGnGRx87CAHf3iQ7cu248504xnnwZNpvsZ58OZ5yfpyFi6v9cEgp9vOCrQD\nItIB5aXmUd1cbY8wAyxdCjfeCC0txvbcGstxi9AUDDLZb3PdP01McLldFP+gmLw78wg2BQk2B4//\nDDWH6Kvpo/n1ZvZ/dz+pc1NJnJRIYmEinmwPWddl6R1OzwHaARHpgGZkzWDVtlW2yHKc1ath0iQY\nG93GeGsdvhYhGv2OhUIooL2/n/GWSmUd2n7RISL48ox9fE6FUorOsk66q7rZueJE5ZEFVQtImpIU\n1b2dbjsr0AWRiHRAW2q3cFH+RfYIM0BvL0yZAi5toliR5fFQ6PPxO50FN2oREVLnpJKzPIc5H81h\n/J3jSb86nYprKuwWbVSgR0BEOqCwCtubgg3Q1gZjxkTdjdOfwKLRLwzUBgJ09/dbJo/VaPvFlvrf\n1tOxpYNAnVGeJ1AboK+2D//E6MOydus2EtCP18DQLNySjBI+bvzYHmEGePdd+NKX7JXB4YSVIqwU\nRwOBmBem1MQnwZYgodYQ/Z39hPvCKKXob+uns7yTtbKWtg02b0zpcLQDIjLZbPGExWys2WiPMAAd\nHVBWZlRCiBKnr0WIRr++cJgSv583W1r4ZnU1e7q7rRPMIrT9rKf3cC9Nf26i/jf1oCCxMJHE4kT8\nk4z1QgAF3y5g1luzGHPR8KMQTredFegQHJHLbWraaygeW2yLLAC8+SbMnAnnnWefDKOAFLebzfPm\n8XpzM5/fvh0R4ckpU+wWSxNjdt26i9a/tpL1lSw8WUYF7MSJiXjmGpWvix8tJnVeqs6COwdoBwS4\nh/wVAv0B/G4bU3MvvBA2b7akK6fHoa3Q7/m6Or5dUMBPS+JvsaK2n7Uopeir6QNg+urpMa0N53Tb\nWYEOwQFDw/+hcAhPgo1JCFu2wJw59t1/FNEXDvN+Wxs/q6nR80CjgIYXGujZ3YMrUX/1xQPaCsDe\nvSefh8Ih3C4bB4eVlXDxxZZ05fQ4dLT6BcJh6gIB/jp7dlyGXLT9rCV7eTalK0sJ94Y5+qujMb2X\n021nBdoBAYHAyefp/nTqO+vtEQbA44G+PvvuP4pIdbu5Nz+fR/bvt1sUzTlARBh/u7HsuPruanr2\n9xBoDNDf3a9HwDag54CAzMyTz7uD3fjcNhYC9Xqhvd2Srpweh7ZCv0SXi1nJydELEwO0/axHRMhY\nmkF3dTfll5fT39VPuCtMuC+MK8lFQlICCckJuJJdJCQnHH+5klyU/qIUT+aZheedbjsr0A6IyCSE\nI+1HmDR2kj3CgJGAsGyZffcfZZR1dvI5XW9vVDHrjVkRbapf0d/df9wh9Xf1H3+Fu8NU31PNunHr\ncCW5CPeGjZXMwPzK+SRPj88HmHhHh+CAoaH/tMQ0Wnpb7BGmqgr+8AeYPNmS7pweh45WvxcbGvhb\nayu3j4/PanDafucOSRDcqW58uT78k/2kzEohbVEa6Z9J59jbx0gsNgqVhrtPOB93phvxnHruMJ50\ni1f0CAhjymUwR9qPkJ+ab48wpaXw+ONw//2wdq2xLYMmJmxoa+OWXbt4acYMUocOgzUaExVWNL3c\nRN/hPgruL2DyTyfHZcLKSESPgIh0QAqFS2z80zzwAHR3w9tvR92V0+PQw9GvMRDg1l27uK6ykv+Y\nOpX/MXQSMI7Q9rMfl8fFokOLmP232dStqqN945nNz44E3exGOyAiHVBWUhaN3Y32CANGBey774bn\nn7dPBgfz24YGVtXV8fOSEpZnZ+unWc0nEuoI0bahjZ7qHnyFProqu+wWyTFoB0TkHND52eez4fAG\nwip86jecCxIToaYm6m6cHocejn735uezsrSUxw8d4tKysriuhq3tZz+bZmyiYmkF7evbyfmfOYy7\ndtwZvW8k6GY3OvBNZMZzwZgCjnYcJazC9oXi1q2D226z594OR0T4Wl4eHf39fHvvXp6oqeGhwkJc\neiSkMQm1h+g92EvvwV4SUhIQtzD12al6tGwx2gERWYz0oyMfcXnx5fZWQ8jNjSzRMAycHoeORr97\n8vMJAw/s3cuDhYWWyWQl2n7nln2P7OPoL44SOhY63pbz1RyKf1h81s4n3nSLR7QDAoZGYFK8KbT1\n2bwPiN8PBw/aK4PD8bhcFCcm4hMhpBQJ+ul21BJsDtL0WhMdH3Ycdz4JaQn4J/rJWJphyQZ1mkj0\nHBDQ1HTy+cKChew7to+PG2zclO7ee+G116A+upJATo9DD1e/YDjM2y0tXFdZyVdzc/HGqfPR9js3\nVN1VRf2v68m+IZu5W+ey+NhiLmm9hHll88i5IWdYfcaLbvGMHgERuSW33+Mn059JfWc952efb49Q\naWlQVASHDkHO8D4AmtPzjepq3mtt5Y7x4/luYaGO7Y9ywsEwWddnMf7W+FyQ7FRktBfgExF1112K\nX/7yRNv+Y/u55LlLOHz/YXu/mO6+20jJfvJJ+2RwKDfv3MnitDTuzMuzWxRNHND05yaqvl7F5H+Z\nPOwRz2hDRFBKRfUFqUNwwNAyYHta9jAlc4r9T8XBIEyYYK8MDiXf56N2aBl0zaglc1km2V/Jpvre\narZfu529/7iX/q74Tc93CtoBEZkFt/7wembnzLZHmMG8/josWRJVF06PQw9Xv4VjxvDogQMc7O21\nViCL0faznvaP2qlYVsHWRVv5cNqHrMtdx3uJ71HzRA2h5hDNrzZz+F8O01nRGdV9nG47K9BzQERm\nwSV5kmjuabZHmAHa2qCzE8aMsVcOh3K1OewNjfIQ9Gij92AvO/5+B7m355J+RTrusW7jle4mITHh\n0zvQWIqeAxJR992neOKJE20vVr7Ib7b/hpeXv2yfYI8+aiQgPPusfTI4nOsrK0lyufhVaSn+oZko\nmhGNUorOrZ00r2mmp7qHnr3GSwUUOTflMOknk7TDiRIr5oD0CIjIHVHzUvNo6GqwR5gB3G6jHI8m\nZjwzdSp37t7NBZs382hxMSt0tqFjqPp6FbUra8lYlkHG1RmMv308/hI/3vFexKUzHuMFPQcEJCWd\nfB4MB/EmeO0RZoDOzsid8oaB0+PQ0eg3xu1m9fTpXJ+VxQ07d8ZlTThtv+GRckEKaZem0fJ6C3vu\n3UP55eVsKNhAoOHcJZ443XZWoEdAGEUHBhPsD9pbhgeMOnDz58Njj+l5oBgiIjxXV8fXx48nSYfh\nHEPOjTm4x7ppe6+N9CvTSV2QStK0JLw5Nj9Yak5COyAis+AUyv4U7NJSWLzYyIRbsWLY3Ti9HpUV\n+mV7vXxx3JlVOD7XaPsNj1237aKzvJOpT08l97ZcWz7PTredFegQHDA0D0MphRAHceIdO/Q6oBjz\nSlMT5Z2dvNZsc9ajxlKyV2QTbApS93wdB75/gKZXmug50MNoT7qKN7QDAsJDtv3pCHTYH4KrqTH2\niSgqiqobp8ehh6vf/p4elldWcv+ePbw0YwZPlJRYK5hFaPsNj+zrsllUs4ii7xWhwoqjvzrKljlb\neNf1Lpsv3EygMfZzQU63nRXoEByRDqh4bDHVLdX2CDNAVZUxNEtOtlcOh7KhvZ0/NjWx/sILmafn\n2ByJO9WNN99L7dO1hFqNCtcuv4vO8k569/XizdLzQXajR0BEOqDNRzczP2++PcIMsGSJEX7bsyeq\nbpwehx6ufjfk5LA4LY3fNticbv8paPtFR9sHbQQbgqiAQvUr3GPdJM9OpnxJOfse2RfTezvddlag\nR0BEOqAJYyZwtOOoPcIMJjcX6urslsKRNAUCrG1tZfV559ktiiaG5N+VT/5d+QCEA2Fq/l8N+75j\nOJ6kKUmf9FbNOUCPgIh0QBcVXERFfYU9wgxm/nzYuDGqLpwehx6ufs/V1VHk85Hp8VgrkMVo+0WH\nUordd+1mXe46Phj7Afu+s4+UuSlcFrqM3JtzY3pvp9vOCrQDItIBhcJGvNj2jJm+vshCdRpLuDU3\nFwX88MABu0XRxID+rn4aX2qkdmUttf9eS7A+SLjH+KB3bunkXfe7bCyJ7uFOEz06BAd0d598npOc\ngzfBS017DRPSbEyDnjQJtm6Nqgunx6GHo98L9fWs2LmTZRkZ/EN+vvVCWYi239mjwoqG3zdw4PsH\nyFiawYTvTMCd7saT4cGdbhQelQTBXxrbbbadbjsr0A4IaGw8+VxEKEwr5EjHEXsdUFERvGxjQVQH\nopSiwxxV/nnWLJul0VhF7bO1NKxuoPdAL72HelEBRd438ih9qtRu0TSfgA7BAadKhCoaW8S+Y7HN\nkvlUUlKgoyOqLpwehz5b/TZ1dHBnVRXPT5sWG4EsRtvvzEiemUz61elkfC6DzM9nkjo/laO/OMru\nO3dz7G/H6KvtO+chdafbzgq0AwJaWiLb5o6fy+ajm8+9MIOZMwd27owcommGTUVnJ/NSU7kuK8tu\nUTQW0FfXR9MrTbSvbyfcHUbcgjvdTWKRUUm+dmUt25ZsY0PeBt51vWuztJqh6P2ARNQ11yjWrDm5\n/Z397/DIO4+w/vb19gg2wDXXGIVJr7/eXjkcQkMgwPmbNtEbDrN9/nyK9JYXI5JwKMx7nveOn3vG\neci4JoPkWcm409zHXwlpCSfOM/Smc1ai9wOyiFPNQy8qWERFfQVdgS6SvTZWI8jMhNpa++7vMMa6\n3aQmJNAYDFIXCGgHNEJxuV3M2TSHnqoeund101XZRcsbLXRs7iD31lxybswhIUk7m3jH8SE4EVkq\nIrtEpEpEHjzVNampkW1+j5/MpEwau20OfyUnw7Fjw3670+PQZ6vfsVCIkFIsz85m2tCNoOIQbb/T\nM2beGHJuyGHi/5nI+S+dz8X1FzPtuWnU/6aeQz8+ZJ2Qw8TptrMCRzsgEXEB/wZcDcwAVojIGc8+\n5yTnUNVcFSvxzoyFC6NKxS4vL7dQmPjjbPTb093Nldu28dWcHFZPn06aBRv+xRptv09G9St69vXQ\nvKaZmidqOPLUEbq2dXHwsYOofnunF5xuOyuI/09gdCwAqpVSBwFE5AXgWmDX4ItOV27tjjl38K/r\n/5UrJ12JS2zy1V/+Mtx1F3R1DaswaWtrawyEih/ORr9/OnSICT4fP5o4MYYSWYu23+npPdTLR+d9\nRLjbWGAqPmHiYxOZVz6PpBlJSIK9W6o43XZW4OgREJAPHB50XmO2ncTm0yS73TT7JrqCXdz9+t0x\nEe6MGHhKj/OSMSOBe/LzWdfWxipdX29EEw6F6T1krPcpfLiQ1PlGDF31KdKXpJMyOwWX2+lfbc7A\n6SOgM6KpCYLByO94n9vHmhvWsODpBdzx6h2s/MLKcy9ccjIsXQo/+pHxOksOOLzUzJnot2LHDt5r\nbaUnHGZJejrLMjNjL5hFaPsZ1K6qpXZlLX2H+gjUB/Bke0ickIi/xE/m5zMp+HYBKTNTSJ4RP9uX\nON12VuDoNGwRWQg8qpRaap4/BCil1OODrnHuH0Cj0WhiSLRp2E53QAnAbuAKoBb4CFihlNppq2Aa\njUajcXYITinVLyL3AG9hzHc9o52PRqPRxAeOHgFpNBqNJn4Z1akiZ7JINd4RkWdEpF5EKga1pYvI\nWyKyW0T+W0TSBv3uYRGpFpGdInKVPVKfGSJSICLviEiliGwXkXvNdqfo5xORD0WkzNTvB2a7I/Qb\nQERcIrJVRF41zx2jn4gcEJFtpg0/MtscoZ+IpInIi6aslSJykeW6KaVG5QvD+e4BigAPUA5Ms1uu\nYejxd8AFQMWgtseBfzSPHwR+Yh5PB8owQq/Fpv5itw6foFsucIF5nIIxnzfNKfqZMieZPxOAjRhr\n1xyjnyn3/cB/Aa866f/TlHkfkD6kzRH6AauAW81jN5BmtW6jeQR0fJGqUioIDCxSHVEopT4Ahtbq\nuRZ43jx+HviiefwF4AWlVEgpdQCoxvg7xCVKqTqlVLl53AnsBApwiH4ASqmB7RB9GB9ehYP0E5EC\n4HPA04OaHaMfIERGkka8fiIyBrhEKfUcgClzGxbrNpod0BktUh2hZCul6sH4EgeyzfahOh9hhOgs\nIsUYI72NQI5T9DPDU2VAHfAXpdQmHKQf8HPgOxiOdQAn6aeAv4jIJhH5mtnmBP0mAk0i8pwZPv0P\nEUnCYt1GswMaTYzoTBMRSQH+ANxnjoSG6jNi9VNKhZVSF2KM7BaIyAwcop+ILAPqzVHsJ60XGZH6\nmSxWSs3BGOXdLSKX4Az7uYE5wFOmfl3AQ1is22h2QEeAwkHnBWabE6gXkRwAEckFBvZ8PQIM3mM8\n7nUWETeG8/m1UuoVs9kx+g2glGoH1gJLcY5+i4EviMg+YDWwRER+DdQ5RD+UUrXmz0bgZYywkxPs\nVwMcVkoNFCp7CcMhWarbaHZAm4ASESkSES+wHHjVZpmGi3DyE+arwC3m8c3AK4Pal4uIV0QmAiUY\ni3PjmWeBHUqp/zuozRH6ici4gSwiEfEDn8WY53KEfkqp7yqlCpVSkzA+X+8opb4KvIYD9BORJHN0\njogkA1cB23GA/cww22ERKTWbrgAqsVo3uzMtbM7yWIqRWVUNPGS3PMPU4bfAUaAPOATcCqQDb5u6\nvQWMHXT9wxgZKjuBq+yW/1N0Wwz0Y2QolgFbTZtlOES/maZO5UAF8D2z3RH6DdH1Mk5kwTlCP4x5\nkoH/ze0D3yEO0m82xoN6OfBHjCw4S3XTC1E1Go1GYwujOQSn0Wg0GhvRDkij0Wg0tqAdkEaj0Whs\nQTsgjUaj0diCdkAajUajsQXtgDQajUZjC9oBaTQjCLM215fN4/tEJHHQ7zrsk0yjOXu0A9JoRi7f\nApIHnetFfZoRhXZAGk0MEZEHxNgWHhH5uYj81Tz+jIj8l4h8VkTWi8hmEfmdWXEYEfnf5mZ1FSLy\nq1P0+00gD3hnoE+jWR4TkXKzz6xzpKZGMyy0A9JoYsv7wCXm8VwgWUQSzLYK4BHgCqXUPGAL8L/M\na59USl2klJoFJJmVpY+jlHoSowTT5UqpK8zmZGC9UuoC8753xFAvjSZqtAPSaGLLFmCuiKRi1Ovb\nAMzHcEA9GDtJrjP3BLqJExXarxCRjWJstf4ZYMZp+h9chLZPKbVm0H2LrVREo7Eat90CaDRORikV\nEpEDGBWE12GMej4DTMbYzvktpdSNg98jIj7gKWCOUuqoiPwASOTTCQ467kd/vjVxjh4BaTSxnJJ0\nogAAALpJREFU533gAeA94APgLowKyh8Ci0VkMhwv7z8Fw9kooNks93/dafptB8YMOv+kTd80mrhD\nOyCNJva8D+QCG5RSDRiht/eUUk0YI6PVIrINWA9MVUq1AU9j7L/yBifvqzI4020l8OagJASdBacZ\nUejtGDQajUZjC3oEpNFoNBpb0A5Io9FoNLagHZBGo9FobEE7II1Go9HYgnZAGo1Go7EF7YA0Go1G\nYwvaAWk0Go3GFrQD0mg0Go0t/H+/3S1xURjd4gAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10b495240>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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dvTx8FANdc5hLRESakKjFZLWZXW5mLcPH5cDqXAbbkyTxuHJlii6JuZQpGmWK\nT9Ri8gPgEqAMWAlcBIzIUSYREWlioh4aPB4Y7u5rAcxsX+D/EhQZqWb16jWMGDGuarmsLE1hYVGN\nfXv3LmD8+JvjCZahtLQ0cZ+QkpgJkplLmaJRpvhELSaHVxYSAHdfY2ZHZrNhM+sE/BH4X0AFQWFa\nCDwF9CE4l+USd18f9r817FNOcCTZ9Gy2n0vl5VBUNC6jpZSiosE19k2nx9XYLiLSlEQd5mphZp0r\nF8I9k6iFqDb3Ai+4+wDgm8BHwGjgJXc/GJgB3BpubyDBMNsA4Czgt+E1wpqE2gpJPiXxk1ESM0Ey\ncylTNMoUn6gF4S7gDTP7S7h8MfDvu7tRM+sInOjuIwDcvRxYb2bnAieH3R4BSgkKzBDgybBf2swW\nAUcDb+1uBhERaTxR72fyKHABsCp8XODuj2Wx3b7Al2b2sJm9Z2Z/MLO2QHd3XxVuswzoFvbfD1ia\n8f7lYVuTkE6X5jvCLpJ4rHsSM0EycylTNMoUn8hDVe6+AFjQiNs9Crje3d8xs7sJ9kCqX9tlt671\n8lFJCW0KCoINtWlD+8JCCoqKAFiXTu/Ut3K5+uvZ9C/f8vU1MNPpUsrKUlVDXZWFpXK5rCy904Rc\n5Q9arpcrxbW9prycSqUSlSdTUvIkdTmVSiUqT5J+nkpLSykuLgagKPz7lY28XJvLzLoDb7h7v3D5\nBIJi0h8Y7O6rzKwQeNndB5jZaIKr308M+08Dxrr7LsNcubo21+sP/gcnXPPTSH3fnfwQP75qSaS+\n6fQ4iovHReorIpIr2V6bq8H3M2kM4VDWUjM7KGw6FZhPcMmWEWHbcOC58PnzwFAz28vM+gIHALPj\nSywiInXJSzEJ3Qg8bmYpgqO5fg1MBE43s48JCsydUDXE9jTBMNsLwHXehC53rDmTaJKYCZKZS5mi\nUab4ZHt4725z97nAd2p46bRa+k8AJuQ0VCPZum09JaUjqpY3rSsjlS6usa9v+RwYF0csEZGcyVsx\n2ZNVv1x9AUW19s3X5eorJ+SSJImZIJm5lCkaZYpPPoe5RERkD6FiEoPqhxcnQRLHbZOYCZKZS5mi\nUab4qJiIiEjWVExiUNAIJwQ1tiSO2yYxEyQzlzJFo0zxUTEREZGsqZjEQHMm0SQxEyQzlzJFo0zx\nUTEREZGsqZjEQHMm0SQxEyQzlzJFo0zxUTEREZGsqZjEQHMm0SQxEyQzlzJFo0zxUTEREZGsqZjE\nQHMm0SQ63JvWAAAQuklEQVQxEyQzlzJFo0zxUTEREZGsqZjEQHMm0SQxEyQzlzJFo0zxUTEREZGs\nqZjEQHMm0SQxEyQzlzJFo0zxUTEREZGsqZjEQHMm0SQxEyQzlzJFo0zxUTEREZGsqZjEQHMm0SQx\nEyQzlzJFo0zxUTEREZGsqZjEQHMm0SQxEyQzlzJFo0zxyWsxMbMWZvaemT0fLnc2s+lm9rGZvWhm\nnTL63mpmi8zsQzM7I3+pRUSkulZ53v5NwAKgY7g8GnjJ3SeZ2SjgVmC0mQ0ELgEGAL2Al8zsQHf3\nfIRuqLrmTFavXsOIEeMirad37wLGj7+5UTIlcdw2iZkgmbmUKRplik/eiomZ9QLOBv4duCVsPhc4\nOXz+CFBKUGCGAE+6ezmQNrNFwNHAW3FmzoXNX60nFXEYbM5HnzdaMRERaUz5HOa6G/gpkLl30d3d\nVwG4exnQLWzfD1ia0W952NYk1DVnUtGqnILBRZEem8vXN1qmJI7bJjETJDOXMkWjTPHJy56Jmf0L\nsMrdU2Y2uI6uuzWM9VFJCW0KCgBo1aYN7QsLq4aaqv9hr1yu/no2/X3rjp36byorq7W/b93BunS6\n3u1XLlf+IFbuKu/ucqXGWt+evJxKpRKVJ1NS8iR1OZVKJSpPkn6eSktLKS4uBqCoEU5fsHxMO5jZ\nr4HLgXJgH6AD8CzwbWCwu68ys0LgZXcfYGajAXf3ieH7pwFj3X2XYS4z85PHjq03w4qZM9i8YiUH\nXnxZpMyvP/gfnHDNT/Pad9nfSvjknVSkviIiDWFmuLvt7vvzMszl7re5e2937wcMBWa4+xXAFGBE\n2G048Fz4/HlgqJntZWZ9gQOA2THHFhGRWiTtPJM7gdPN7GPg1HAZd18APE1w5NcLwHVN5Ugu0Hkm\nUSUxEyQzlzJFo0zxyfehwbj7K8Ar4fM1wGm19JsATIgxmoiIRJS0PZM9kq7NFU0SM0EycylTNMoU\nHxUTERHJmopJDDRnEk0SM0EycylTNMoUHxUTERHJmopJDDRnEk0SM0EycylTNMoUHxUTERHJmopJ\nDDRnEk0SM0EycylTNMoUn7yfZyLR5ety9SIi9VExiUFjzZmUl0NR0bhIfdPpuvslcdw2iZkgmbmU\nKRplio+GuUREJGsqJjHQnEk0ScwEycylTNEoU3xUTEREJGsqJjHQeSbRJDETJDOXMkWjTPHRBHwT\nsnXbekpKR0Tq61s+B8blMo6ISBXtmcSgseZMGvN+8Ukct01iJkhmLmWKRpnio2IiIiJZUzGJgeZM\nokliJkhmLmWKRpnio2IiIiJZUzGJgc4ziSaJmSCZuZQpGmWKj4qJiIhkTcUkBpoziSaJmSCZuZQp\nGmWKj4qJiIhkTcUkBpoziSaJmSCZuZQpGmWKT17OgDezXsCjQHegAnjQ3e8zs87AU0AfIA1c4u7r\nw/fcCvwAKAducvfp+cjeVNR375OysjTFxaWA7n0iItnL1+VUyoFb3D1lZu2Bd81sOjASeMndJ5nZ\nKOBWYLSZDQQuAQYAvYCXzOxAd/c85W+QfMyZ1Hfvk8xI9d37JC5JHUtOYi5likaZ4pOXYS53L3P3\nVPh8E/AhQZE4F3gk7PYIcF74fAjwpLuXu3saWAQcHWtoERGpVd4v9GhmRcARwJtAd3dfBUHBMbNu\nYbf9gDcy3rY8bGsS1qXTse+d1HdRyE3rymhfUAgk56KQpaWlifzUlsRcyhSNMsUnr8UkHOL6K8Ec\nyCYzqz5stVvDWB+VlNCmoACAVm3a0L6wsOqPefXJ8Mrl6q9n09+37tip/6ayslr7+9YdOxWbqHnq\nW668KGRtr7cn+J6sS6f58o3lVXkrJwcrf9i1XEoqlUpUnkxJyZPU5VQqlag8Sfp5Ki0tpbi4GICi\nRviwa/madjCzVsDfgKnufm/Y9iEw2N1XmVkh8LK7DzCz0YC7+8Sw3zRgrLu/VcN6/eSxY+vd/oqZ\nM9i8YiUHXnxZpLyvP/gfnHDNT/fIvsv+VsIn76Qi9RWRPZOZ4e62u+/P56HBDwELKgtJ6HlgRPh8\nOPBcRvtQM9vLzPoCBwCz4woqIiJ1y9ehwYOAy4D3zWwOwXDWbcBE4Gkz+wGwmOAILtx9gZk9DSwA\ntgPXNZUjuSA/cyb1ycy0ek0ZI24eEel9vbv3Zvyt43OSKaljyUnMpUzRKFN88lJM3H0m0LKWl0+r\n5T0TgAk5C9WMlds2is4ritQ3XZLOaRYRaZp0BnwMkrZXAsnMlNRPa0nMpUzRKFN8VExERCRrKiYx\nSOK1uZKYqfphr0mRxFzKFI0yxSfvJy1K/m3dupWSktJIfX3OV7kNIyJNkopJDJI4P5GZqcKhoGBw\npPct21ySm0Akdyw5ibmUKRplio+GuUREJGsqJjFI4vxEEjMldSw5ibmUKRplio+KiYiIZE3FJAZJ\nnzNJiqSOJScxlzJFo0zx0QS8NMiy5Z9zwLePiNS3Z5fuvPriizlOJCJJoGISg6Rfm6shyluU0+tf\nz6u/I8HViBsiqdcsSmIuZYpGmeKjYiI509ALSJ5y3Cm5DSQiOaNiEoOk7ZVAPJkaegHJpH5aS2Iu\nZYpGmeKjCXgREcmaikkMknhORxIzJfX4+yTmUqZolCk+GuaSnGnoNb9GRJvXF5EEUjGJQXOdM2nI\nNb/mLv09xSXFFJcU19s3l3d7rEkSx7iVKRplio+KiSSC7vYo0rSpmMRgTzrPJJfSqTRFRxTV229O\nak6s96xP4nkByhSNMsVHxUSanM3bNmsvRiRhVExikLQ9AEhmpih7JQ01Z84CRowYF6nvZ599TL9+\nB9f4WnFx6S5tvXsXMH78zVmk231J/GSrTNEkMVNjUDGRRGjIkV/LlpVF7vvxwoWYDYzUd/En73HK\nKX+O1Bfg2WfPZ8mSdZH65rPwiMShSRUTM/secA/B+TGT3X1iniNFksT5iaRlqnBgXVGkTOU73o58\nlFh5i7cpGFz/OgE+/XRGje3pdClFRbtub/Nmp6hoXKR1p9PR+kWVxHF3ZYomiZkaQ5M5adHMWgC/\nAc4EDgW+b2aH5DdVNJvKyvIdYRfKFF1ZWSrfEXaRSilTFMoUn6a0Z3I0sMjdFwOY2ZPAucBHeU0V\nQfmWLfmOsAtl2tXWbespKR2xS3tZOkXZll3/AKz+6sPI654zZ27kuZsoQ2Lr1kUbXouTMkWTxEyN\noSkVk/2ApRnLywgKjEijqGhVXuOQ2LrSdI3tCz58tsbiU5OPV7yKde4Uqe+cjz6PPL8yZsIYlqxa\nEqlv3Cd7SvPSlIpJZCveLK23z45NXwGW8ywAWxL4SUSZoqstV23Fpybli7ZE7jv30Wn1nkfz+vTX\nSa9LM2feHM4fc36k9T477tmcFJ7KglaZqS6fLfqMfgf2i7TehvStLW86y2vQNaRYR837+vTXqdi7\nIieFvSF5oXE/YJi7N8qKcs3MjgXGufv3wuXRgFefhDezpvEFiYgkjLvv9ifsplRMWgIfA6cCK4HZ\nwPfdPfrAtYiI5ESTGeZy9x1m9n+A6Xx9aLAKiYhIAjSZPRMREUmuJnOeSX3M7Htm9pGZLTSzUTFu\nd7KZrTKzeRltnc1supl9bGYvmlmnjNduNbNFZvahmZ2Ro0y9zGyGmc03s/fN7MZ85zKzvc3sLTOb\nE2Yam+9MGdtpYWbvmdnzCcqUNrO54fdrdhJymVknM/tLuI35ZnZMnn+mDgq/P++F/643sxsT8H36\nkZl9YGbzzOxxM9sr35nC7dwU/u7l5m+Cuzf5B0FR/AToA7QGUsAhMW37BOAIYF5G20TgZ+HzUcCd\n4fOBwByC4cWiMLPlIFMhcET4vD3BXNMhCcjVNvy3JfAmwaHdec0UbutHwJ+A55Pw/xdu6zOgc7W2\nfP//FQMjw+etgE75zpSRrQWwAtg/n5mAnuH/3V7h8lPA8Hx/nwhO9J4H7B3+/k0H+jdmrpz8x8b9\nAI4FpmYsjwZGxbj9PuxcTD4CuofPC4GPasoFTAWOiSFfCXBaUnIBbYF3gO/kOxPQC/g7MJivi0ne\nv0/A50CXam15ywV0BD6toT3v36tw/WcAr+U7E0ExWQx0Dv8QP5+E3z3gIuDBjOVfAD8FPmysXHvK\nMFdNJzTul6csAN3cfRWAu5cB3cL26jmXk+OcZlZEsOf0JsEPTd5yhcNJc4Ay4O/u/na+MwF3E/xS\nZU4e5jsTYZ6/m9nbZnZ1AnL1Bb40s4fDYaU/mFnbPGfKdCnwRPg8b5ncfQVwF7AkXP96d38pn5lC\nHwAnhsNabYGzCfbiGi3XnlJMki4vRzmYWXvgr8BN7r6phhyx5nL3Cnc/kmBv4GgzOzSfmczsX4BV\n7p6i7jNY8/H/N8jdjyL4pb/ezE6sIUecuVoBRwEPhLk2E3x6zevPFICZtQaGAH+pJUOcP1MFBJd5\n6kOwl9LOzC7LZyYAd/+IYEjr78ALBENYO2rqurvb2FOKyXKgd8Zyr7AtX1aZWXcAMysE/hm2Lyf4\nNFApZznNrBVBIXnM3Z9LSi4Ad98AlALfy3OmQcAQM/sM+DNwipk9BpTl+/vk7ivDf78gGKY8mvx+\nr5YBS939nXD5vwiKSxJ+ps4C3nX3L8PlfGY6DfjM3de4+w7gWeD4PGcCwN0fdvdvu/tgYB3BXGqj\n5dpTisnbwAFm1sfM9gKGEoxVxsXY+ZPt88CI8Plw4LmM9qHh0R19gQMITr7MhYeABe5+bxJymdk3\nKo8UMbN9gNMJxmvzlsndb3P33u7ej+BnZoa7XwFMyVcmADNrG+5VYmbtCOYD3ie/36tVwFIzOyhs\nOhWYn89MGb5P8GGgUj4zLQGONbM2ZmYE36cFec4EgJl1Df/tDZxPMCzYeLlyMRmWjwfBp9yPgUXA\n6Bi3+wTBUSRbCX6QRhJMvr0U5pkOFGT0v5XgyIgPgTNylGkQwS5simB39r3w+7NvvnIBh4U5UgRH\nlfw8bM9bpmr5TubrCfi8ZiKYn6j8v3u/8uc5Abm+SfDBLQU8Q3A0V74ztQW+ADpktOU709hw/fOA\nRwiOMM37zznwKsHcyRxgcGN/r3TSooiIZG1PGeYSEZE8UjEREZGsqZiIiEjWVExERCRrKiYiIpI1\nFRMREcmaiolInoTXubogfH6TmbXJeG1j/pKJNJyKiUgy3Ay0y1jWCWDSpKiYiERkZj+x4NbRmNnd\nZvaP8Pl3zexPZna6mc0ys3fM7Knw6qyY2S8tuDHYPDP7fQ3rvYHgooAzKtcZNNsdZpYK19k1pi9T\nZLeomIhE9xpwYvj8WwRXhG0Zts0juEfEqe7+beBd4Mdh3/vd/Rh3PxxoG16tuIq7309wSZ7B7n5q\n2NwOmOXuR4TbvSaHX5dI1lRMRKJ7F/iWmXUguBbbGwQ3+DoR+B+Cu9PNDO/ZciVfX8n6VDN704Jb\nO3+X4K53Ncm8WOhWd38hY7tFjfmFiDS2VvkOINJUuHu5maUJrrI6k2Bv5LsEtz/9DJju7pdlvsfM\n9gYeAI5y9xVmNhZoQ/22ZzzfgX5XJeG0ZyLSMK8BPyG4AuvrwL8RXIX1LWCQmfWHqsvIH0hQOBxY\nHV5W/qJa1ruB4Na4leq6WZdI4qiYiDTMawT3yn7D3f9JMLz1qgc3ZhoB/NnM5gKzgIPdfT3wR4J7\nf0xl53tCZB6x9SAwLWMCXkdzSZOiS9CLiEjWtGciIiJZUzEREZGsqZiIiEjWVExERCRrKiYiIpI1\nFRMREcmaiomIiGRNxURERLL2/wETin5RovFi4QAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10a923588>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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UdNNTp5MU35Iy1a2QGGMKH+vmipCRS0cSt6YXt9/+68eC2EdqmcIXxFyWKTyW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\nWCbvFJr/zbfu30qZYmWoVqY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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1011bb908>"
      ]
     },
     "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": [
    "# Uri Wilensky Version\n",
    "\n",
    "[Another version](http://www.decisionsciencenews.com/2017/06/19/counterintuitive-problem-everyone-room-keeps-giving-dollars-random-others-youll-never-guess-happens-next/) of this simulation made the rounds in 2017. This version has these rules:\n",
    "\n",
    ">Imagine a room full of 100 people with 100 dollars each. With every tick of the clock, every person with money gives a dollar to one randomly chosen other person. After some time progresses, how will the money be distributed?\n",
    "\n",
    "To implement this all-at-once transactions rather than one-at-a-time transactions, I'll define a new `step` function:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "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",
      "  2,000 0.24  43.4   16   48   93  165  208\n",
      "  4,000 0.33  58.7    3   27   96  185  247\n",
      "  6,000 0.37  66.1    2   15   99  188  326\n",
      "  8,000 0.38  68.2    6   13   91  178  368\n",
      " 10,000 0.40  72.5    2   15   85  200  321\n",
      " 12,000 0.42  75.7    1   12   92  210  351\n",
      " 14,000 0.41  74.2    3   15   79  230  295\n",
      " 16,000 0.43  78.9    2   18   83  220  354\n",
      " 18,000 0.45  84.9    5   16   78  227  424\n",
      " 20,000 0.50  93.7    2    7   70  230  395\n"
     ]
    },
    {
     "data": {
      "image/png": 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JNBGbkZk1C556Cqqs5YS/6Hyn+Mn0T7gx+UbfC/QEiqJmZT58GO6807n+yBF1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\nyn19+ZsOb2LY8569cvKuls1hbrBj4qWEsjLYsQPG6tFzuaAHsf70E0y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      "text/plain": [
       "<matplotlib.figure.Figure at 0x10a92ea90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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0XFdXS3V1daZ5W1tuXJeXPG0tX3311VRVVeUmT8jj2TJr1nnaWq6pqeH888/P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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10a03bcf8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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sOaPHhYzgTs5IeT5wT1U35FuVE+UspgADpgygU+NOVC1T1e8oxpgk56mHISIf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\nAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10a9284e0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def give_dollar(population, transaction, interaction):\n",
    "    \"Everyone with at least a dollar gives a dollar to a random person.\"\n",
    "    N = len(population)\n",
    "    for i in range(N):\n",
    "        if population[i] >= 1:\n",
    "            population[i] -= 1\n",
    "            population[random.randrange(N)] += 1\n",
    "    return population\n",
    "\n",
    "show([100] * 100, k=200, step=give_dollar)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So we see that inequality rises from a Gini of 0 to about 1/2 over 20,000 time steps. Let's try again starting from the first 100 actors from our initial (Gaussian) population:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   t    Gini stdev   1%  10%  50%  90%  99%\n",
      "------- ---- ----- ---- ---- ---- ---- ----\n",
      "      0 0.12  19.4   58   71   95  119  151\n",
      "  2,000 0.29  48.1   10   35   91  169  205\n",
      "  4,000 0.39  66.5    3   13   88  187  329\n",
      "  6,000 0.40  67.7    5   11   97  194  283\n",
      "  8,000 0.39  65.8    3   13   87  179  274\n",
      " 10,000 0.38  64.5    3   21   84  187  294\n",
      " 12,000 0.40  71.8    5   27   78  187  376\n",
      " 14,000 0.44  80.8    2   13   70  201  460\n",
      " 16,000 0.47  84.3    2   11   80  193  443\n",
      " 18,000 0.45  81.7    5   13   79  202  421\n",
      " 20,000 0.45  80.6    0   10   79  204  400\n"
     ]
    },
    {
     "data": {
      "image/png": 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v/dfs2AFA/ZQpmDSTmEaAkFJNNWORSjZnq/N9yXcloIeMlzPYedNOpFWxZpQu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\nRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10aa73080>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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D4HP06vePFrONyWShI2Qlhu0ZQ0ZQztBiyZkrFQYREcmgwhBALP2OGmMIJ4aM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\nAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10b95b438>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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9Bb/+CjfeGB05CxIt7VkQy+keP2QE/+T06x4GwN3AByJSGtgIDAZKAp+IyBBg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\nAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10a82f3c8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "show(population[:100], k=200, step=give_dollar)"
   ]
  },
  {
   "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."
   ]
  }
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