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A toy economic model of asset hording
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{ | |
"cells": [ | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"### 100% Horders\n", | |
"\n", | |
"Our aim here is to investigate the dynamics of hording by investors of a fictitious asset that is in finite supply and the value of which is determined entirely by its scarcity. We imagine that the faster this asset appreciates in value, the more people are inclined to horde it in the hopes of realising gains from further appreciation. Effective supply thereby decreases and the asset appreciates further due to increased scarcity. This induces further hording, and so on. This is contrary to the usual Law of Supply which says that supply follows price: as the price increases holders of the asset will want to cash out and enjoy the proceeds of their hording in the past. But let's imagine a market of investors who only care about what they think _future_ returns will be, irrespective of the asset price today.\n", | |
"\n", | |
"We set up a toy model with the following characteristics (which are not claimed to be realistic)\n", | |
"\n", | |
"- The _price_ of the asset is a function of time denoted by $p(t)$ and its rate of change by $\\dot{p}$.\n", | |
"- The _effective supply_ $s$ of the asset is the supply available after hording and ranges from $0$ (no supply) to $1$ (the total supply). The horded supply is $1-s$.\n", | |
"- The propensity to horde the asset increases with its price _rate of change_, this being taken by our imaginary investors as the predictor of future returns. To make this mathematically easy we'll say that the _log odds_ of hording is equal to the price rate of change $\\dot{p}$. After converting the log odds to a hording probability it follows that the horded quantity of the asset is given by the logisitic function\n", | |
"\n", | |
"$$\n", | |
"1-s = \\frac{e^\\dot{p}}{1+e^\\dot{p}}\n", | |
"$$\n", | |
"\n", | |
"and hence the effective supply by\n", | |
"\n", | |
"$$\n", | |
"s = 1-\\frac{e^\\dot{p}}{1+e^\\dot{p}} = \\frac{1}{1+e^\\dot{p}}\n", | |
"$$\n", | |
"\n", | |
"Let's pause to take a look at how the effective supply varies with price rate of change." | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 2, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"data": { | |
"text/plain": [ | |
"<matplotlib.text.Text at 0x7fac35850588>" | |
] | |
}, | |
"execution_count": 2, | |
"metadata": {}, | |
"output_type": "execute_result" | |
}, | |
{ | |
"data": { | |
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TZNo9Cfcd+Fr8JpIWTinOp7QojxfffZ/PThgWdhyRTqV3NIu0kZlxyegS3ly7h/2HasOO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\nY3In/OzHkxYHms3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| |
"text/plain": [ | |
"<matplotlib.figure.Figure at 0x7fac37b19cf8>" | |
] | |
}, | |
"metadata": {}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"%matplotlib inline\n", | |
"import numpy as np\n", | |
"import matplotlib.pyplot as plt\n", | |
"\n", | |
"dp = np.linspace(-10, 10, 200)\n", | |
"plt.plot(dp, 1/(1+np.exp(dp)))\n", | |
"plt.grid()\n", | |
"plt.xlabel(\"p'\")\n", | |
"plt.ylabel(\"s\")" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"As the price rate of change becomes very negative we see that $s \\rightarrow 1$ (no hoarding) while as the price rate of change becomes very positive we see that $s \\rightarrow 0$ (only hoarding). When the price is going sideways then half of the total supply is horded.\n", | |
"\n", | |
"Moving on, we now state the final assumption of this model.\n", | |
"\n", | |
"- The price $p$ is _inversely_ proportional to the _effective_ supply $s$, being driven higher by scarcity and lower by abundance. Note this means that the asset has a baseline worth of $1$ - it is not worthless in the absence of any hording. At the other extreme its price has no upper limit.\n", | |
"\n", | |
"Combining what we've defined so far,\n", | |
"\n", | |
"$$\n", | |
"\\begin{align}\n", | |
"p &= s^{-1} \\\\\n", | |
"&= 1 + e^\\dot{p} \\\\\n", | |
"\\dot{p} &= \\ln (p-1)\n", | |
"\\end{align}\n", | |
"$$\n", | |
"\n", | |
"Let's graph $\\dot{p}$ against $p$ to get an idea of the behaviour of this ODE." | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 5, | |
"metadata": { | |
"scrolled": true | |
}, | |
"outputs": [ | |
{ | |
"data": { | |
"text/plain": [ | |
"<matplotlib.text.Text at 0x7eff9050ce80>" | |
] | |
}, | |
"execution_count": 5, | |
"metadata": {}, | |
"output_type": "execute_result" | |
}, | |
{ | |
"data": { | |
"image/png": 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CL9SB8PhrJxgYifEf3rUy6FJERAIX6kD40a4TtNSWc/MVjUGXIiISuEACwcz+3Mz2mtmr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\nQmCC\n", | |
"text/plain": [ | |
"<matplotlib.figure.Figure at 0x7effc06c62e8>" | |
] | |
}, | |
"metadata": {}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"p = np.linspace(1.0001, 10, 200)\n", | |
"plt.plot(p, np.log(p-1))\n", | |
"plt.grid()\n", | |
"plt.xlabel(\"p\")\n", | |
"plt.ylabel(\"p'\")" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"We can see that $p=2$ separates solutions of ever-increasing value from those of ever-decreasing value. This is also clear just from reading the D.E. Let's use a numerical solver to plot some solution curves around the initial value $p=2$." | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 9, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"data": { | |
"image/png": 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bCs5e8jGV587hvXQp9dspP7+tM+qYe3QupbpSNg7ciLOdGaVQjQbY8TyUZsFz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\n", | |
"text/plain": [ | |
"<matplotlib.figure.Figure at 0x7fac2deca7f0>" | |
] | |
}, | |
"metadata": {}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"import scipy.integrate as integrate\n", | |
"import matplotlib.pyplot as plt\n", | |
"import numpy as np\n", | |
"\n", | |
"def deriv_p(p, t):\n", | |
" return np.log(p-1) if p > 1 else None\n", | |
"\n", | |
"fig, ax = plt.subplots(figsize=(8,6))\n", | |
"ax.grid()\n", | |
"plt.xlabel(\"t\")\n", | |
"plt.ylabel(\"p\")\n", | |
"plt.ylim((1,4))\n", | |
"\n", | |
"for p in np.linspace(1.01, 2.5, 25):\n", | |
" t = np.linspace(0, 5, 5000)\n", | |
" \n", | |
" sol = integrate.odeint(deriv_p, p, t)\n", | |
" ax.plot(t, sol[:, 0])" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"Our market of horders sends the price of their asset one of two ways then. Either \n", | |
"\n", | |
"- $p > 2$ and $s < 0.5$: the asset price experiences slow (faster than linear, slower than any higher order polynomial) growth forever or\n", | |
"- $p < 2$ and $s > 0.5$: the asset price crashes very rapidly indeed.\n", | |
"\n", | |
"Vested horders must ensure that collectively they always horde a certain critical fraction of the total supply (the values of $p=2$ and $s=0.5$ themselves being unimportant and merely a consequence of us having ignored constants throughout). We can tell the same story more directly by graphing solutions for the horded supply $1-s$ against $t$." | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 4, | |
"metadata": { | |
"scrolled": true | |
}, | |
"outputs": [ | |
{ | |
"data": { | |
"image/png": 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p27cozM0DIBmNmHftwrx/H5b9+zHv2cOFW7cq17BQKjAcHubOmhqF312/W0ml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HsDfPlLcHPUrVPreHjawzwz/xny6vK49tNrWZe37rQ+g9Bo8L/vR4S/9irOlhZyrr+B2k8/Pa02\n3X62EEw4P5wrHpoECnz4p53sXZc/YqarVSo106+4husf+xOKovCfRx7iwIY1w90tSZKkXo3qoH7M\nnDh/Vt0/h/GhNn7y3738YVUanc4+ApNPFNz+FUz9IWx5Ft66CprdT4JbELGA9y57j3BrOPevv58X\n97142oHQNG0aUR9+gNf48RQ99FNKn/wjSodnisYERdmIuUgQnuzLt+9lsv6tQ3R2OD3ybE9wxCVw\n4x+eISQhiS//9QxrXvonnR0DXz6RJEkaKjKoHxVoNfDWHdO5aUYE//4mizvf2EFDax9BUaOHS56G\nJf+E3M3w4gKoyHT7eaGWUF676DUWRS3i77v/zs82/oyWjtMrqqfx9SX8lZex33gjVa+9Rt4Pf0hn\nbe1ptekutU6waPk4piyKJG1TMR8/s5vmevcSCs8GRquNq37xGFMXX8Xe1atY8fivaG7oY7lGkiRp\nGMigfhKtWsXjlyfz+JKxbMgo56p/bqag+hTbtiYug5s/hZYaeGkBZG1w+3kGjYEn5zzJ/ZPuZ1X2\nKm794lYqmytP6zMIrZagX/0Sx+9/T/OOneQsWzbk9eOPP1slmL44mgtuT6Ist54Vf9hBVfHQJ+95\nikqtZu6yW7nkvocoOZzOf379EDWlJcPdLUmSpONkUHfhppmRvH7rNIpqm1n6ry1klp5iRBYxE364\nHqwh8NbSrsI1bhJCcMe4O/jbuX/jcM1hbv7iZgobTn/vufeVVxD20kt0lJaRc931tKSnn3ab7oqf\nGsQV/28SHR1OPnx6JyXZnpkt8JQx58xj6a9+R3NtDf/59YMUH/bcdytJktSXUR3UnYpCpqJ2+d7s\nOD/eu2smnYrC1f/ewq68U6yZ2yPg1s8hdAqsuBW2v9yvvpwXfh4vXvgi1S3V3LTqJjKqT//oVdP0\naUS89RYIQe6yG2n8znMH4QVGWrnqoUnojVo+/utu8lJPbwbiTBOamMz1v3sarV7Pe4/9gtx9e4a7\nS5IkSaM7qL9YUM4jmPmw1HXATnRY+WD5LGxeWpa9uJWNmeV9N+jlDTd+CHEXwmcPwDdP96s/EwIm\n8PpFryOE4JYvbmFP2ekHCkNCPJHv/gdNUCD5d91Fw7ebTrtNd9n8jVz54CS8A4189tw+MneUeuzZ\nnuATHMr1jz+Nd6CDj576LVm7tg93lyRJGuVGdVC/MdiXMXRy78FcPiipcnlNuK+RFctnEuln4vbX\nd/BtZkXfjeqMcN3bMP5aWPc4fP1Uv/oUa4/lzYvfxK63s3zNcvaW7+3X/a5oHQ4i3ngDXWQkBffc\nQ8PXX592m+4y2fRc/sAkAqOtrH7l4IgL7CZvO9c88nv8wiL4+OknyNy6ebi7JEnSKDaqg7pJreZh\nGpjhbeZHaXm830tgD7AYeOeO6UT7mbj99e1sPnyKwK7WwuXPQ8r1sP4J2PiXfvUr2BzMywtfxsfg\nw/LVy9lfvr9f97ui8fEh/LVX0cXGUHDvj6hfN/THuB6j99Jw6b0pBB0N7Id3lnns2Z7gZbGy9Fe/\nIzAmlk+feVIGdkmShs2oDuoABgFvjY9m5tHA/nGZ66l4u0nH23dMJ9LXxG2vb+e7rFOsEatUsOQ5\nGHc1rP0tbPp7v/oVZArilYWv4K335q7Vd5Fakdqv+13R2O1EvPoq+oQECu+/36Nr7DrD0cAeZeWr\nl1M5sntkBXaDyczSXzxGUGw8K//2FDl7dw13lyRJGoVGfVAHMKpVvDk+mmk2E/cezOObKtfZ7r5m\nPW//cDphdiO3v7adA4WnyOpWqbtG7GOvgNW/hp2v9atfxwK7VW/l7jV3k1uX26/7XVHbbIS/9CK6\nyAgK7rmH5v0HTrtNd+kMGi79UQqBkRa+ejmVwvSBn1p3JtJ5Gbny4UfxDQnl4z8/QWF62nB3SZKk\nUUYG9aOMahWvj4sixqjn1gPZ7KlzvT/dz6znzdunY/PScutr28mvOsU+drUGrnwRYs+HlQ9Axpf9\n6pfD7OD5858H4K7Vd1HRfIqpfzeovb0Je+kl1N7e5N95J61Z2afdprt0Bg2X/F8KNj8vVv1rHxUF\nI+ugFIPZzFW/fByz3YePnnyU8ryc4e6SJEmjiAzqJ/HWang3JQa7Vs2yfVnkNLe6vC7IZuD126bR\n2t7Jza9uo7rxFJXT1Fq4+nUIGgcrboHCnf3qV6QtkmcXPEtVSxX3rLmHxvbTL+iiDQwk/JWXQaUi\n/4476Kj03JYzg0nLZfdNQGvQsPIfe6ivOr1Kemcak7edq3/1BFq9no+e/C2NNSNrRkKSpDOXDOrf\nE6TX8t+UGJyKwk37sqjvcH0ka1yghZdunkpBdTM/fGMHbaeqda43w7IVYPKHt6+B6v5NpY/3H8/T\n854mozqDh75+iE5nH0fFukkXGUnY88/TUVlJwY/uw9nmubKuFh8Dl/0ohfY2Jyuf3Utbi2fq1HuK\n1T+Ay3/6CM0NdfzvT4/T3ub6F0RJkqTBNKqDekdHA05lQ4/DVGKMBl5MjiSruZW7D+bS2cthK9Oi\nfPjz1SnsyK3mN5+4kchmDujax+5sh3eXQdsppu6/Z27oXH4+7edsLNzIs3ue7de9vfEal0zwk3+g\nedcuSn79iEdPWPMNMXPRnclUFzey9rU0lL4O0TkLBUbHsuhHD1JyJJMvnvsrinPkHHIjSdKZaVQH\n9aLiFSjKmxQVvdvjvdl2C7+LC2VNZR2/zyrutY3LUoK5e34M/9mWx9tb3Rh9+8XCVa9A6QH45F7o\nZxC9JuEaroq7ipf2v8QX2V/0697eWC++GL9776X244+peuWVQWnTXWGJPpyzNI6sPeVsX5Xj0Wd7\nQtzUmcxddisZ333L1v+tGO7uSJI0wo3qoB4W+gNgLOkZj1FX13Mv+K0hfvwg2Jfn8sr4tKym13Ye\nvDCB+Qn+/ObjVLbnuN7r3k3c+bDg13DgA9jcv61uQgh+Of2XTAyYyK83/Zr0qsGpO+73f/dgWbiQ\nsr/8laYdOwalTXeNPy+UMTOC2L4ym6w9p6jadxaacukVjDlnHpvfe5vc/bKcrCRJQ2dUB3Uh1KjE\nD9HpfNl/4F7a23tuUftdXAgTLUYeOJRHbi+Jc2qV4G/XTSTU7sW97+yi6lSJcwCzH4CkJbDmUcjd\n0q9+a9Va/jL/L1h1Vh78+kGa2vs3je+KEALHE79DGxpC4QP/z6OJc0II5i1LICDCwro30qirbPbY\nsz1BCMEFd96LPTiEz/7+J+qrTn8HgyRJkiujOqgDCGFhXPKztLaWcjDtoR5ryjqViufHRiAE3JWa\nS1sv66I2Ly3P3jCJ6sZ2fvr+3lOvTQsBi58F7wj44A5o7l+GtJ+XH3+Y8wdy63L5/dbf9+ve3qjN\nZkKfeYbOmhqKfvqwR9eANVo1F94xFqdTYfXLB3F2jqz1Z53Bi8UP/IKO1lZWPvMUzs7TT3SUJEn6\nvlEf1AFstgnExj5MRcVal+vrEV56/jomnD31TfzuSO/r68khNh6+eAxr0sp4Y4sb6+sGKyx9GRpK\n4JP7+r2+Ps0xjTvH38nHRz5mZdbKft3ba5cSEwn81S9p3LSJypf7d9Lc6bL5Gzl32RhKsmrZttJz\ne+c9xTc0jAvuvJei9INs/d97w90dSZJGIBnUjwoLvRkf+2wyMp+gqalnQLnE35tbQ/x4oaCcb6t7\nP1/9tnMiOW9MAE+sSuNQSd2pHxwyGRY8AmmfwK7X+93v5SnLmRQwice3PE5BfUG/73fF++qrsVx4\nIRV//wct6ad/BGx/xE0NJHGWg51f5FKYMfL2dyfOns+Yc+bx3QfvUnIkc7i7I0nSCCOD+lFCqEhM\n+iMqlY7Ugw/idPbcN/3rmGCivHT85FA+Db3sXxdC8Kel47EaNDy4Yi8d7kwjz/wRRM2DL38JNXn9\n6rdGpeHJOU8ihODRLY8OypY0IQRBj/4GldVK0cMPo3hw/zrAnGvjsfoaWPfmIdrbRt409YLb7sZo\n8+bzZ/8s969LkjSoZFA/iUEfxJiEx6ir20Ne3os93jeqVfxtTDgFLW08dqSo13Z8zXoeW5LMgcI6\nXtiYdeoHq1Sw5Oi+80/v7/c0vMPs4IHJD7C1eCvvZ77fr3t7o/HxwfH4Y7QeOkT5v/41KG26S6tX\nc95NidSVN7P1f258f2cZg9nMwrt/TFVRAd/+543h7o4kSSPIqA/q3x/ZBgZeir//RWTn/IOmppwe\n10/zNrM8zJ83iir5upeDXwAWjXNwcXIQz6zJ5HBZ79cd5x0O5z8KR9bBnrf79yGAq+OvZnrQdP68\n488UN/S+7t8flvPOw3bFFVS+8CIthw4NSpvuCkmwM25eCHvX51N8uPfthGeryPETSbngYnZ//qmc\nhpckadCM6qCelpbGtm3baG7uvoUqIf4RhNCSnu66wtpPoxxEe+n5WUY+LX1Mr/92yViMOjU/fX8f\nTneqpU25HSLOgS9+AfUl/fosQgh+e85vcSpOHv/u8UGrDBf48E9R22yU/OZRj1dEm3FFDBafrmn4\nzlOV4T0Lzb7+Zow2G6tffFZmw0uSNChGdVD39vamubmZDRs2dHtdrw8kNuYhqqo3UVL6cY/7vNQq\n/hAfSnZzG//M7/1c8ACLgV9dksSuvBre3+lGEptKBYv/AR3NsPo3/f04hJhDuHfCvWws3MiG/A39\nvt8Vtbc3AT99iOa9e6lZMThT++7SGTTMuz6BmtIm9q7N9+izPcFgMnPuLXdRln2E3V8Mzu4FSZJG\nt1Ed1B0OB8HBwWzbto2Sku4j45CQG7BaJ5KZ+QTt7T2z2Of5WFgc4M3fc0t7LUoDcOXEECZH2Pnj\nF4eobW4/dad8Y2DmvbDvXcj7rt+f6frE64n1juWP2/9IS8fgnH5mW7IE49SplP3lLx4tSgMQkexL\nVIof21fl0FA9sk5zA4ifcQ5RE6ew6b9v0tbgxjKNJElSH0Z1UAeIiorCYDDw+eefd5uyFkLFmITH\naG+vJif3OZf3/jY2GLUQ/CqzsNf2VSrBbxePpaqpjWfWuLk9bO6DYA2BVQ9CP09j06q0/GL6Lyhs\nKOTVA6/2697eHMuGdzY1UfbXvw5Km/0x++o4FKfCpg8Oe/zZQ00IwYLbluN0dlK4deNwd0eSpLPc\nqA/qWq2WBQsWkJuby4EDB7q9Z7Ek4XAsJT//dZqaehaTceh1PBAZxOrKOjb2kTSXHGLjhmnhvLEl\nl/QSN0ZjOhNc+DiU7Iedr/X3IzE1aCoXR17Mywdepqih9yz9/tDHxOBzww3UfviRx/euW/28mHxR\nBId3lI3Iveu2gCAmLVpCVcZBmTQnSdJpGfVBHWDSpEkEBQWxdu1aOjq670+PiX4AlUrL4SN/dHnv\n7SF+hBq0PH6kCGcfyWkPXpiASafmqS/czCIfe2VX0tyGP0Brg9uf5ZgHpjyAoig8t8f1LMNA+N29\nHJXZTNnTTw9am+6aeEE4ZruezR8e8ejxsJ4y/fKr0Ri8+PrNl0fk55MkyTNkUAdUKhULFiygpqaG\nXbt2dXtPrw8gIvwuysu/pLpme497DWoVP4tysK+hmf/1cZKb3aRj+fwY1h4qc+8kNyHg/N9CYzl8\n1/994kGmIG5IvIFPj3xKZvXgjP7U3t74LV9O48aNNGzaNChtukujUzP10ijKcupG5ElueqOJ4Gnn\nUJB2gMPb+3fAjyRJ0jEyqB8VGxtLREQEX3/9Na2t3RPfwsPvQKcLICvrLy5HUVcG2kk2e/H7rCJa\n+9j2deusKAIsev74+SH3RmNhU2HMpV3Hszb2P0HtjnF3YNaa+fuu/h3v2hf7jcvQhoRQ9qenPb7F\nbcyMIOwOE9/9L2vEHfgC4Jc4Hp/gUDb99y2c/cylkCRJAhnUjxNCcP7559PY2Mh333XPOlerDURG\n3k1NzTaqqzf3uFclBL+OCaagpZ23i3oPvl46NfefH8eO3GrWHep9K1w35/0K2hrg27/06/MA2PQ2\nbht3GxsKNrCrdNepb3CDSqfD//77aD10iPq1awelTbefrVYxY0k0NaVNpG0enPaziwAAACAASURB\nVAI7ZxKhUjFz6fVUFuSRseXb4e6OJElnIRnUTxIWFkZCQgKbN2+mpaX79qlgx7Xo9UFkZT/jcpQ9\n125mus3Es3llfY7Wr5kSRqSvkae/ynBvtB6QCCnXw7YX+12QBmBZ4jJ8Db78c+8/+31vb6yLFqGL\niKDin//y+PpvVIofgVFWdn6eS+cIHK3Hz5yNb2g4W97/jxytS5LUb6M6qHfWtuKdLboFpvnz59Pa\n2sr27d3Xz9VqPZGR/0dt7S6qqnpuPRJC8JPIQIpa23mvpPc1c61axf+dG0tacR0b0t1cG577IDjb\nYUv/k968NF7cMvYWthZvZV/5vn7f74rQaPC9ezmtaWk0eHi0LoRgyqJI6qtayNha6tFne4JKpWbW\n1TdQVVRA+qZvhrs7kiSdZUZ1UG9Or8IvXUXrkdrjrzkcDmJjY9myZQtt3zudLNixFIM+mOycZ122\nN89uYaLFyN9zy2jvoyzs5RNDCPH24tn1h90b6fpEQ/JVsOMVaHIjye57rkm4Bpvexov7eh5SM1C2\nSy9FGxFO+XP/9PhoPSLZF78wM7u+zHWv/O5ZJm7aLPzDI/nuw/96PG9BkqSz26gO6qaJgXToFOq/\n6V7Cdc6cOTQ1NfXIhFepdISF30Zt7U5qa3f3aO/YaD2/pY0PSvserd85N5qdudVsy3YzSM/+Sdfa\n+rb+B2aj1siyxGVsKNhAelV6v+93RWg0+N3VNVpv3OjZoilCCCZfFElNaRNHdrmZm3AWESoVUy+/\nmqqiArJ27xju7kiSdBYZ1UFdaFXURii0ZlTTXtJ4/PWIiAjCw8PZvHlzj33rwY5r0Ghs5Lo4mhXg\nAl8rY80Gns8v73MEe+3UMPzMOp7bcMS9zgaOhfiLYeu/BrRv/YYxN2DSmnj5wMv9vrc3tksvQePv\nT9Vrrw9am+6KmeiPPcjIri9zR+S+7vjp52Dx82fHpx8Od1ckSTqLjOqgDlAbpiC0qh6j9dmzZ1NX\nV0daWlq31zUaE6EhN1Be/hVNTdk92hNC8MNQfw41tvBtde/B16BVc+s5UXyTUU5mqZs1v2f/BJqr\nu+rC95NNb+OquKtYnbOa0sbBWYsWOh32G2+kcfNmNIW9l8odCkIlmHB+OBX5DSPyaFa1RsPkRUso\nSDtA8eHBmV2RJGnkG/VB3akD45RAmvaW01l7Yn96bGwsPj4+bN26tcc9oaE/QAgtefmvuGzz8gA7\nfloN/y7oOxHu+mnh6DQqXt+S415nw6ZB8ETY+gIMYHR63Zjr6FQ6eS/jvX7f2xv7tdcgvLwwejhh\nDiBuWiB6k4a969w4Ae8sNO68C9EbTez49KPh7ookSWeJUR/UASyzQ8Cp0LDtxJYxlUrFtGnTKCgo\noPB7o1C9PoCgoMUUF39ER0fPUbZBreLmEF/WVNZxpKn3k8V8TDoWpwTzwc5C905wEwKm3QUV6ZC1\nwe3Pd0yYJYz5YfN5P+N9Wjt7P1muP9Te3nhfcTmGbdvpKPdspTetTs3Y2cFk7ymnrrLZo8/2BJ2X\nkXELFpK5dTN1FSOvip4kSYNPBnVA4+uFId5O47YSlJP2Pk+YMAGdTse2bdt63BMasgyns5nikv+5\nbPOWED90QvBSQUWfz75lViTN7Z2s2OHmeeHJV4LJH7a94N7137MscRlVLVV8nv35gO53xX7TTYiO\nDmo+8Pz6b/K8UBCCAxs8O/3vKSkXLEJB4cD6r4a7K5IknQVkUD/KNN2Bs76NlrQT2egGg4GUlBQO\nHDhAQ0P39XGrdTwWSzKFhe+4TNTy12m5LMCbD0qraOqjSEpyiI0pEXbe2OLm9iyNHibfAumfQ1XP\nNf1TmRY0jVjvWN5Je6ff9/ZGHxVFW0I8Ne+/7/EtWBYfA9ET/Di4qYiO9pFXrMU7MIjIlEnsX/sl\nzs6R9/kkSRpcMqgfZRjjg9qmp2Fr9/KjU6dOpbOzk337ehZuCQ1ZRmNjBrW1O122uczhS12Hk8/K\n+07kumlmBHlVTWzJcrO++5Tbuqbid7/l3vUnEUKwNH4paVVpHKpy88Q4NzTNnk17QQGNWzx/GMnY\nOSG0NnWQvafvWZGzVcr5F9NQXUXWrp4HCkmSJJ1MBvWjhEpgmhZEa2YN7RUn1mcDAgIIDQ1l9+7d\nPUbkgYGXotFYKCx0Peqd6W0iykvXZz14gIVjg7AYNO5PwVuDIWYB7P0PDKCU6KXRl6JVafnfYddL\nBwPROmECam9vat5bMWhtuis0wY7Fx0Da5sE5O/5MEz1pKmYfX/auGbwlE0mSRqZRH9Q7mpuO/900\nNRAENO3svuVrwoQJlJeX90iYU6uNBAYuoaz8C5cJc0IIbnD48l1tY58JcwatmiUTgvn8QIl7CXMA\nE5dBXeGAEuZsehsLwhewMmslbZ1tp77BHVottiuuoH7tWjoqPDtiFirBmFkO8g9Vj8iEOZVazbjz\nLiRn7y6ZMCdJUp9GdVDft+YL9r7xPI011QCorXr0sd407S5DOWl9Ozk5GY1Gw549e3q04Qi6Aqez\nlbKyL1w+49ogH9QC3i7qu3Lc1ZPDaO1wsnKfm6PNhEXgZYc9b7t3/fdcEXsFta21rM9fP6D7XfG+\neil0dFC7cuWgtemuMTODADi0pf+H3pwNkuacB4rCoU1fD3dXJEk6g43qoB6ckAhOJ+knHXNpnBRI\nZ00rbTl1x18zGAwkJSWxf/9+2tu7j6St1hS8vCIpLnG9lzhAr2WBj5WPyqpx9rG3fHyojfhAMyt2\nuLnnWqOHcVdD2squgjT9NN0xnSBTEB9lDt4eaH10NIaxY6n71PNB3errRWiCnUObi7v9QjZSeAc5\nCI5PJG3j+hFZQU+SpMExqoO6X1gEXr7+HNq04fhrXmN9EToVTXu61xSfMGECra2tpKd3r+4lhMAR\ndDk1NVtpaXE9yr4i0E5xaztbaxtdvn+snasnh7Env4ascjfLwE5YBp2tkNr/tXG1Ss1l0ZfxXfF3\nVDa7maDnButll9KSmkprVv8z80/XmBlB1Fe1UJJdd+qLz0KJc86lIj+X8lzPf7eSJJ0dRnVQB/CJ\nHUNxZjq1ZV3TtiqdGq+xfjTtK0dpP7E9KzIyEpPJRGpqao82goKWAFBS8onLZ1zoZ8VLpeKj0r5H\n1JemOABYtb+4z+uOc6SATwykDmy0vTByIZ1KJ2ty1wzoflesFy8CIagbhin4qBR/1BoVh3eMvCNZ\nARJmzkal1pD27Ybh7ookSWeoUR/U7bFjADh00tnVxokBKC2dtKSfWAdXqVQkJSWRmZlJa2v3amxe\nXuHYbJMpLXUd1E1qNQv9rKwsr+nzSFaHzYspEXZW7nMzqAvRVYwmZyM09D+BKt4eT5Qtii9yXOcD\nDIQ2MADj9OnUrlzp8WlinZeGiHG+HN5VNiKPZPWyWImaOIVD326QR7JKkuTSqA/qequN4PjEbglI\n+hgbKqOG5tTu09LJycl0dHSQkZHRo52AgItpaEx3ecgLdE3BV7V38k1134e3XDLewaGSeg6XuXnI\ny9grQHFC2sfuXX8SIQQXR17MztKdlDUN3hGmtssupT0vj5b9+wetTXfFTg6gqbaN4syRd8gLQMKs\nOTRUV8lDXiRJcmnUB3WAMefMpSI/l8rCrn3iQq3CkOhLc1olSseJEVFYWBgWi8XlFHyA/0IAyspd\nl/Oc72PBplHzcVnfU/CLxjkQAj7b52YWd0AS+MUPaF0dYGHUQhQUVueuHtD9rlgWLAC1mvo1nj/k\nJXKcHxq9msydI++cdYDoiVNQqTVkbvN8kR9Jks58MqgDMVNmAHBkx4kT2bySfVFaOmk9cmLEd/IU\nfEtL933nBkMwVst4ysu/dPkMvUrFBb5W1lTW0dHH1HCg1cDUSB/3t7YJ0TVaz/kW6vu/lhxtiybe\nHs9XOYNXW1zt7Y1x6lTqh+HkNq1eTeQ4X7K+ty1xpNAbTUSMSyFz22aZBS9JUg8yqANWP38ComI4\nvOO7468ZYu0InbrHFHxiYiKdnZ1kZWX1aMfffyF1dXt7zYK/0M9GVXsn2+t6z4IHuDg5iMyyBnIq\n+r7uRKcWAwpkDGxt/Nywc9lTvoealsGbsrYsWEDbkSPDkgUfleJHc307pTkjMws+dtosaktLZBa8\nJEk9yKB+VOyUGRRnph8vRCO0Kgxj7DSnVnYb8YWFhWEwGHpsbQMICOiagi8vdz2VfZ6PBZ0QfFlR\n22dfFowJBGDdITenkAPHgi0MMlzPEpzK/LD5OBUnGws3Duh+VywLzgOgYZ3nR+vhSb4IlSB738is\nBR87ZTpCqOQUvCRJPcigflTs1BmgKBzZedIU/Fg/nI3ttOWdGPGp1Wri4uLIzMzE+b0MZKMxCpMp\njvIK11vEzBo159jNfFlR2+fUabivkbgAM2sPuTmdLgTEL4Ss9dDeezna3iT5JuHn5ceG/A39vrc3\n2uBgDElJw7KubjBpCY61kTNCg7rR5k3ImCQOb5dBXZKk7oY0qAshLhJCpAshDgshfubi/QeEEAeF\nEPuEEGuFEBFD2Z+++IVHYvUP7LaubojzBgEtGd2T2+Lj42lqaupRCx7A13ceNTU76OhwPXW+0M9G\ndnMbmU2tLt8/5rzEALZmVVHf4mYt+PiLoL2pa229n1RCxbzQeWwq2kR7p5vPc4P5/AU0793r8Vrw\nAJHj/agqaqSuYuTVgoeuQ14q8nKorxqZv7hIkjQwQxbUhRBq4DngYiAJuF4IkfS9y3YDUxRFGQ+8\nDzw1VP1xpTy/npI9TpxOBSEEMZOnkXdgHx1tXYecqIxadOFWWtK7B/XY2FiEEC63tvn6zENR2qiu\n+a7HewAL/awAfOXGFHyHU2Fjppv/aEfOAa1xwOvq88Pm09jeyPbSwTve0zx3HigKjZs3D1qb7ooc\n7wcwYqfgIydMBiBn765h7okkSWeSoRypTwMOK4qSpShKG/AusOTkCxRFWa8oyrFj0r4DQoewPz1U\nlzRSeQjK87r2hEeMn0hHWytFGWnHrzHE22kvbKCz4cRpZl5eXoSHh7sM6t7ek1GrjVRWuj54w6HX\nkWAynHK/+qRwb2xeWtakuTkFrzVA9LldQX0AWdHTHdPRq/VsLBi8dXVDUiJqu52Gb/s/e3C6vAOM\neAcayTsweCVwzyR+YRGY7T7k7JFBXZKkE4YyqIcAJx8QXnD0td7cDnj0wOjQBB8ACg51VY4LGzsO\nlVpDzr7dx68xJNiBnlPwsbGxlJaW0tDQvU67SqXHbp9JZeXXva6bz7Nb2FrbSHNn71XBNGoVc+L8\n+Dazwv2tS7ELoDYfKo+4d/1JvDReTAiYwNaSrae+2E1CpcI0axaNm7cMSwW0sEQfig7X0Nk+8qqv\nCSGInDCZ3P27cXZ2Dnd3JEk6Q2iGuwMAQogbgSnAvF7evxO4EyAwMJANGzYM2rO1Fif7t2RRb8gB\nwBgQxIFN3+AMjuy6QIFInYq8jYcorTsxgq+r60qe++yzzwgMDOzWplNxoChr2bDhvwgR1OOZdkVD\nK2Ze+GYzKaKj1775dbZTVt/Gfz5bT7D51L9/eTV5MR3I+PJFikIuPuX13xfQHMDWmq18svYTrGpr\nv+5taGhw+f/F4OuLraKCTe+8Q0eoRydiqOtQ6GhT+OKjrzEFCI8+eyB6+w5706Q10NrYyKoV72IO\n6uv35dGjv9+h1JP8Dk/fcH6HQxnUC4Gwk34OPfpaN0KI84FfAvMURXGZPaYoygvACwBTpkxR5s+f\nP2idLNm9jpojKmbPmoNGp8ZQVcqm/77JtEkTMVptAFSVpaPLqGbMvOkI0RUcnE4nBw8exGAw8P3+\nNDdHs3nLW8TGthIW1rOvUzs7+evGA9SERjE/tvd/jKMrm3gtdT3tPtHMnxV56g+jKHDoCeI1RcQP\n4Dvyr/Dn088+RR2lZn50/+7fsGFDj+8BoD0xicNvvEFiayu+g/j/zR2tzR28vOkb/AwRTJ8f7dFn\nD0Rv32FvWqZM4Z+rP8OuUjjHw9/tmaq/36HUk/wOT99wfodDOf2+HYgTQkQJIXTAdUC3E0+EEBOB\nfwOLFUUZlrqepkBBZ4eT4iNdiWuR4ycCkLt/z/Fr9NE2nI3tdJQ1HX9NpVIRGRlJdnbPAiBeXuEY\n9MFU12xz/Uy1mik20ynX1cN9jYTavdh8xM1kLyEgel7XAS8DmO4e4zMGq87K1uLBm4LXBgagj4sb\nlnV1vZeGgEgr+WlVp774LGQwmwmIiiE/1fM19iVJOjMNWVBXFKUDuBf4EkgD3lMUJVUI8ZgQYvHR\ny/4EmIEVQog9QgjXx5wNIaM/qNTi+Lp6QHQMBpOZvP17j1+jj+4asbdmdc9Yj4qKoqamhqqqnkHD\n2z6dmpptfa6rpza0UN7W9xayc2L82HKkkk53S55GzYPmaijZ5971J1Gr1Ex3TGdL8ZZBLUFqnDmD\n5t17UNraTn3xIAtL9KEsp47W5t6XOc5moUnJlBxOp72t7y2SkiSNDkO6T11RlFWKosQrihKjKMoT\nR197RFGUT47+/XxFUQIVRZlw9L/Ffbc4+NRaQVC0jYJDXYlwKpWa4DFJFB46cWiL2seA2qajNbt7\nUI+O7prSdTVat3vPoL29isbGTJfPPcduBmBbbd+lYGfF+lLX0kFqUd9b4I6Lmtv1Z7br7PtTmR40\nnZLGEvLq8wZ0vyvGyVNQWlpodnEQzlALHWNHUaAoo++DdM5WYUnJdHZ0UJIpT22TJElWlAMgOM6b\n8vwG2lq6RnMhCUlUFxeeKBkrBPpob1qzuleC8/Pzw2w2k5OT06NNu306ANU1rqeyx1u8MKgEW2v6\nDuozY3wB2HLEza1ZVgf4JUD2wLamTQmaAsCu0sHbKmWcPAmA5p07B61NdwVGWVFpBMWH3fyl6CwT\nMmYsCEH+wQPD3RVJks4AMqgDQTE2FKdy/ACQ0MSxABSmHzx+jT7ahrOhnY7yExXKhBCEh4eTn5/P\n9xkMoej1DmqqXQd1nUrFRKuRrbUNLt8/JsBiINLXyM7cfow0w2dAwbYBratH2aKw6qzsLtt96ovd\npPHzQxcVRdP2HYPWptvP1qoJCLccz5kYaQwmMwER0RSkyaAuSZIM6gAERdtAQMnRf/gDo2PR6PQU\nHjopqEe5XlcPCwujpqbm+Ba3Y4QQ2O3Tqa7Z2uv69HSbmQMNzTR29L3PeHKEDztzq91f5w6bDi21\nUNGzOM6pqISKCQETBjWoAxinTKZp9+5h2a8eFONNWV4dHe0jcz93aFIyxRmH6GgfvBK/kiSdnWRQ\npytL2jfYTPHhrqNH1Rotjtj47uvqvgZUZm23w12gK6gDLkfr3rYptLdX0dzsen16ms1EpwI765pc\nvn/M5Ag7lY1t5Fb2fd1x4V3nw5PvulTtqUwMmEhOXQ7VLYO3Dm2cMgVnXR2tma5zDIaSI8aGs0Oh\nLLfv3QZnq9DEsXS0t1GWfXi4uyJJ0jCTQf0oR4yNkqw6nEervIUkjqUsO4u25q5AKoRAF2ahLa97\nYAgKCkKj0bgM6lbrBADq6vb0eA9gqs2ECk45BT85oquqndtT8D7RYPSFfNdb6k5lgn9Xv/eUue73\nQHhN7lqrb9rh+Sl4R0zXLEvJCJ2Cd8QmAFCc2f+ZGUmSRhYZ1I8KirHR3tpJZWFX4lpIfCKK4qTk\nyImRpS7cSkdFM86mE9OcGo2GkJAQl0HdZIpDpfKitpegbtGoSTJ7nTIDPi7AjMWgYWeem0FdiK4p\n+PyB7TdP9ktGo9Kwu3zwpuC1IcGo/fxo2ef5PdVeFh3egcbjMzEjjdnHF7OvH8WHZQa8JI12ozqo\nN3y7Ce+//x1nS8uJ0dzRNfPAmLiun08O6mEWANoKuo+sw8LCKC4upu17+7BVKg1W6zjq6vbSm0lW\nI3vrm/pcL1epBJPC7ezM6cd0eNg0qDwMjf0/pcygMZDkk8Test773V9CCLzGjaN5//AUSgmKtlKS\nXTeo++/PJI7YeEqOyJG6JI12ozqoO5ub0B9MozU9HYuvAYNJe/zENi+LFVtgEKUnB/VQMwh6rKuH\nhobidDopKSnp8QybdQL19Wk4na6Lg6RYjNR1OMlp7rswy6RwOxll9TS0ullEJaxrSx0FA5vuHus3\nlrSqNDqdg5dcZhiXTFt2Np0NfS83DIWACCstDe3UV7V4/Nme4IhNoLa0hKa6kbnEIEmSe0Z1UPca\n27V1rTk1FSEE/hEWyk5aMw+MjqMk60RQVxk0aAKMtOV3X1d3OBwAFBcX93iG1ToBRWmjvv5gj/cA\nUixeAOyt7zsJblyoFUWBtOK6Pq87LmgcXSn9/a8sB5Dkm0RzRzO5dbkDut8Vr3HjQFFoOeD5IjT+\nEV2zLOV5IzNZLig2HoCSw3K0Lkmj2agO6hqHA6fJRMvRSmcB4RaqihrpaOsanQbFxFFXXtZt9KML\ns9CWX99tGtdqtWIymVwHdVsKQK/r6gkmL/Qqwe5TBPXk4K7lgf0Fbo7E9BbwjYWigSW7JfkmAZBa\nOXgB2JCcDEDz/oH9onE6/ELMqFSC8hGaAR8YHYsQKrmuLkmj3KgO6kII2iPCaTnYdaSqf4QFxalQ\nUdg1PRx0fF39xOhHF2bB2dRBZ01rt3YcDofLoG7QB6HTBVBf7zo4alWCsWYv9p5iW1uA1UCARc8B\nd8vFAjhSoHhg6+LRtmgMagMHK13PMAyExm5HGxZGy37PF0rR6NTYg03dZmJGEp3BC9+w8G45IJIk\njT6jOqgDdISH05qZibO1lYCIrjPEj43mAqNiQAhKj5zY/6t1mABoL+qese5wOCgrK6PdRQEQiyWR\nhoa0Hq8fk2Ixsr+hmc5TJHElh9g4UNiPoB48AeoKBpQsp1FpSPBJGNSgDuA1LpnmA8OTLBcQYaE8\nt37EJssFREZTntvzHAJJkkaPUR/U28PCoaOD1oxMzHY9BrP2+GhO52XExxFC6UlFPbRBJhDQXtw9\n2cvhcKAoCqWlpT2eYTYn0th4BKfTdTJcisWLxk4nR5r6PmkrOdjK4bIGmtvcTF5zdE39UzzwKfjB\nTpbTJybSUVRMZ52buQGDKCDcQktjO/WVIzNZzj8iisbqKpksJ0mjmAzqEeEAtBxNlgsIt3Rbd/WL\niKIiL+f4zyqdGo2vF23F3UfqwcHBgOtkOYs5EUVpp7HRdcWvZHNXstzBhmaX7x+/LsSGU4GDbifL\nje/6c4BT8EORLGdI6CqU0prh+YQu//CjMzH5I3MK3j8iCoDyHDlal6TRatQHdaevLyqrlZaDXdPM\nviFmqksb6TxaWc4/PJLastLjleUAtMEm2r8X1G02G15eXi6DutnclXTW2xR8nMmAWsChxr5HkMkh\nXclybh/D6uUN9qgBB/UxPmMAyKgZvACsj+/K0m5J93xCl09w1yxLVVHfxX7OVseCellu1jD3RJKk\n4TLqgzpCoI+Lo/Vw1yjaJ8SEs0Ohtqxr1OwXHglARf6J+u1ah4nOqhacLR0nNSMICAigrKysxyOM\nxghUKgP1vQR1vUpFtJeetMa+R+oOmwGLQUN6ST9GmoFjoaz39fy+RNmiUAkVh6sHr6a4JjAQlc1G\na7rnR+pavRqrn9fxqoEjjdFqw+zjK9fVJWkUk0Ed0MfF8v/bO7cYSdPzrv+e71jnY1f1YXpOuzN7\nCAgRWDmWgiKbkxywYhCJlEhEXAR8ASsFgYSSG6RwQxAScINAFgniJG8iApJlIpJI9golgcRe4xA7\nsXfHuzvHnpnu6VNVdXUdXy7e6kN1V3VVV9d0ub96ftJou3drqt/9ZvT96v88z/t+jXv3MMZQXEkB\nR2mudOMmQF8J3l+2rzmZ1svlMuvr66cGsURcUqk3hu5VB3gzFec71bOTuojw2mKaD56d4/CW0hvw\n4nvQPrtfP4jQDbmRvsH3tr937t87DBEh9tprMym/AxRXkmw+ufzDby6L0s3bKnVFmWNU6kB45y7d\n3V3az9fJLyV6JVp7488slAnicdaPST04mIA/IfVSqUSj0Tj1GFaAVOoNqtXvDp28fiMZ4/5+c+Rj\nWF9bTPH+83NMcJffBNOxR8ZOwJ3cHe5tT/fpX+Hrr9N4//2ZPIa1sJJk+3mdTuvyf/ZlULp5m83H\nD/UxrIoyp6jUgfCu3Y/e+OADvMAlW4ofJnVxHIrXb/YPy2UCJHRprffvLS+XywADS/DJ5B3a7W1a\nrc2Ba3gzGQPguyP66nfLabb3WqxXx0zeJdsXn7QEfyd/hweVBzQ650/6wwhff43u3h6tx4+n9p7j\nUlxJYbqGrWdjPsb2irFw4xbdToftp09mvRRFUWaASh1bfgdo3LMHdxRXUrw4NkxVun6LjQcfH6Zj\nEcErJ2g/7xdDqVQCYH19/dTPSCZeBaBWG1zKfrM3AT9qWO61RXvc6dgl+IW7IO7kUs/doWu6fLQz\nvZJurDcsN4sSfGHFVlmiWoIvrKwCsPnk0YxXoijKLFCpA16hgFsoHA3LrSTZeb5Hu2VL4cXrN9iv\nVdnbOXp0p1+K01rvH2xLJpMkk8khw3JW6nt7g6V+IxYQd5yRw3KvLdp+/vvPxhyW80L7fPX174z3\n+hPczdkqxgdb0zupLLhtp7SbH11+7ze3mMBxpO9DW5QoLF8DYPOxSl1R5pG5lvrDykN+t/K7tLot\nwrt3aX5wJHVjYOupTeIHN8qtJ0flYq+coLvb7JuAB4ZOwMdiyzhOnNoQqTsi3EmEIw+gKaVDsnGf\n988zLFd+c+Kkfj1zHd/xp9pXdzMZ3GKRxgyk7noOuaVEZLe1+bEY6WJJk7qizClzLfX3nr3HFze/\nyFp1jfDVV2h8+CHGGDssB4fb2vIrvfSzdiR1v2Rf0z6R1kulEhsbGwMm4B2SiVfYG1J+B3glEfJh\n/Wyp2wn4FPeen2NbW+kN2Ppoogl43/G5nr7Oxzsfn/v3nkVw+xbNj6b7nuOSKyfYeR7NnjpA4dqq\nJnVFmVPmWuo30vY0uQeVBwQ3b9KtVOhsb5PtCXu7d+NPL5RwfZ+tteNJUteaSAAAFzxJREFU3fbA\nWyfkUCgUaDab1Gqnk2Ai+erQpA7wSjzkQb1Jc8RU+K1iko9fnENKxTtgurD9YPRrB3Ajc4MHlcl+\n7zDC27dnUn4HyJbj7GzU6XajeQZ8YWWVzSePInvGvaIow5lvqWd6Ut99gH/Dft26fx8/dElmg8M0\n5zguucVlttaOJoq9Qgxcob1+WuoAm5unp9yTiVfY339MpzO4b/5KIqQL3K8PPiP+gFsLSdYrDWqN\n9pmvO1rUK/afm5OdNHYzfZOHlYd0zfS2gQW3btPZ2qKzvT36xVMmV07QbRuqm9E8A76wskprv051\n68Wsl6IoyiUz11IvxoqEEvKw8pDg5i0AmvftOefZcuKw/A6QX77G1rE+pbgOXjFG63m/oIvFIgAv\nXpy+oSaSB8NygxPqq/EQgI9GlOBvFe0E9/1x0/qB1F9MdojMjcwNGp0Gz/dOzwpMysGw3Cz66tle\nlWU7oiX4wrXeBLyW4BVl7phrqYsIJa/E/d37BKvXwHFo3rdl5lw53nfTL6xcY/vZU7qdo8NhvGKc\nzom0l8vlEJGBST0Rt6fT1esPB67ndsJKfdSw3M2ibQ/cfzHmsFeiAGF24qR+UNGY5oNdgtu3AGbS\nV8+Ve+2VZ2fvNLiqHMyAHK8sKYoyH8y11AEW/AUeVh4iQYC/stKX1OuVFs26LXHnl6/R7bTZXT9K\nq14hRntzv6936bouuVxuoNTjcSvH+v7g/nTe9yj47shhuVsLNql/NK7URaD4yoXK7zBlqa+uguse\nXu/LJJEN8EI3ssNyqVwB1/fZef501ktRFOWSmXupl7wSj6qPaHfbBDdu0HxwkNT7h+Vyy/bRqlvH\nTupy8zFMs0O31n8kZ6FQGCh1z0vjebmhSR3ssNyopJ4KPRZSIfc3ziGlwuRSX0wuErohD3anNywn\nvo+/tDSTU+VEhGwpzvbzaCZ1cRwypUV2nz+b9VIURblkVOpeiXa3zVptjeDWTZr372OMOey7HvTV\ns6VFgFNJHaB9ogRfLBbZ3NwcOH0cj1+nXh8ux1vxkAf7o7ee3Som+HjcpA5W6tsPoHP+M8Edcbie\nvs79ynRTtb+6SuvRbPq+uXI8skkdIFteZFuTuqLMHSp13x7t+mC3t61td5fO9jaZkpX67gsr9WQ+\nj+O67G4ck3rRSr2z1S/1QqFAo9EYuK3NSn14Ur8eC1hrtGiP2G51s5g8p9RftQ922ZpMzNfT13lU\nma6A/WvXZpLUAbKlOJXNfUxEt7Vly0ua1BVlDpl7qRc9O63+pPYE/5odMGqvreEHLrGUT+WFFbbj\nuKQXSn1J3c0PTuq5XA6AnZ2dUz8vHr/B/v5jjBn8NLbVWEDHwFrz7ER9o5Dg2W6Dxoinuh2St31x\ndiYroa+kVlirrU1177O/eo32+jrdxvQeFjMu6UKMbsewt3v29sGrSra8yH6tyn4tmmfcK4oymLmX\nesbN4IrLWnUNb3kZgNYT2zdPF2JUNo+Eky2V2Vk/Sj9O4OKkfNov+qWezWaBIVKPrWJMi0ZjcIpa\njQUAPByxV30lZz9QPN0Zc6911m5zYmeytL2cXKbWqlFpneMkuxEEvQ9RrceXP6Wd6rVOKhHdq54t\n23bRjqZ1RZkr5l7qrriUE2We1p7ir9hhuNaTNeBA6kc3/UxpsS+pg+2rn9zWdqbUDybgh/TVr/ek\n/qhxttSv5Wx74Mn2mFJKL4M4E0t9KbkEwFp1baLfPwh/1X7QmEUJPh15qds/Ly3BK8p8MfdSB5tC\n12pruLkcEovRWrPiShVCqse2rGUWytS2Nmk3j4TrFmK0t/vLx/F4HN/3B0o9FrMiq+8PlutK6APw\naP9sqS8fSn3MCW7Xt2K/QFIHeFqb3vCVf5jUZyj1F1GVuk3qOiynKPOFSh2bQtdqa4gI/vLyodTT\nhRitRofGnt2rnimVAai8OHpeupsN6ew0+nrNIkI2mx0o9TC0CWpY+T3mOpQDj4ejpJ61Uhpb6gCZ\na7AzfEjvLFZStorxpDa9UrlXLoPv05rByWdB3CNMeJE9KjaWTBHEE31/VxVFiT4qdWwKfbb3jK7p\n9qR+1FOHozR3sK1t5/iwXCaAjjm1V32Y1F03xPfzNBrDE9T1WDAyqcd8l4VUwJOdc0g9uwo7k6Xi\nQqyA7/is1aZXfhfHsdd7Bj11gFQ+FtnyO0CqUKS6qee/K8o8oVLHSr3dbfOi/gJvZZn2QU+92N93\nTS/Y7W99e9Wz9mjXzokp6mFSB5vWhyV1sMNyo6QOsJKL83jcnjr0pP4IJphgd8RhKbnE0+p0y7l+\nuUx7wPPnL4N0sX8QMmqo1BVl/phvqVeeUnjxDZbiCwCs1dbwl5ftNqtmk1S+X+rJvH0CW2376LQ4\n90DqO/1yyGaz1Go1Wq3TW9PCcJHG/nA5LgU+TxvtkdvHVrLx85Xfs6vQaUBtY/zfc4yD2YNp4pXL\ntNZnJPV8GOmkni4UqajUFWWumG+pf/Cb/Kk//AWWsMNpT2pP8JfsQFj72TPiaR/HFfZ6wvZ8n1g6\nQ23rmNQzdlp9UFIH2N3dPfVjw3CJ/cZwOS6GPvVul0rn7EedruSs1MfeO364rW2yvvpScomne9NN\n6l65TPv5+kye/Z3MhzTrbVrNMff6XzFShSK1rU263Wj+/ymKcpr5lnrK9siXeqeKre+t2+EtoL2+\njoiQyATUdo6EncoXqB6TupMOwDmd1NPpNACVyul93WG4RKu1Sbc7uPS71JuAf9Y4+wCapWzIXrND\nddznqmfssBuVydL2QnyBjfrGVAXslcuYep1u9fIPSUlkbJVlbyeaB9Ck8kVMt8vekDaQoijRY86l\nbgWe2a/iOZ7tqZdsKb69bkvUiWzYd+pYMpfvS+riCG4qoHNCDKlUCoDqAFnFDifgB5edy4EHwLMR\np8qV0lZK65Ux+8JJ+/9LdbJy90J8gXa3zW7zdPVhUg4/RM2gr57M2irL3k40++qpgj0tUfvqijI/\nzLnUbVKX2jOKsSIb9Q28hZ7UX/Skngn6klwqX+xL6tDb1rbbL4YDqQ86/z0M7c8dNiw3blJfSFmp\nb1THTJpJO+h3EakDbNQn68kPwivbNc1C6okDqUf0qFiVuqLMH/Mt9WOSK8aLbOxv4Obz4Dh0Ng6S\nesDeMWEn83lq21uY7lG/28mcTurxeBwRGZjUj6Q+uD+9GPSk3jy7rH7upO4FEM9DdbJTxl6G1P0Z\nJvWD8nstouX3dNH+eanUFWV+mG+puz5NPwPVZyzEF9isbyKui1soHJbfk5mAerVFpze0lsoXbJ9y\n96hP6ab8U/vUHcchlUoNlLof2ATVbJ1+5jpAynVIuM7YSX29co4J7tQi1C6W1Nfr0zvQxCvZD1at\nGUg9nvIRR/o+tEWJRCaLiNO3W0NRlGgz31IHmkEeqs8Ph8AAvIUF2htHPXUM1HetYFN5K+Ta9tbh\nezhJn+5e69RjPIdK3csBQqs5+GYrIiwG3sieej4R4DoyfvkdbHXiguX3F/XpJT8nmcRJpWg/u3yp\niyMk0n5kB+XEcYil030fQBVFiTYq9SAHVdtT39zfpGu6/VLPHPRdbZpL5PIA/dvakj4Y6O71S3iY\n1B3Hw/dzNFvD5bgY+COl7jpCMRmMX34Hm9QnlHrKTxFzY1MtvwN4xSKdzdmkyZODkFEjkclSH7Ct\nUlGUaKJSD2yPuRgv0jEdthvbJ5J6/zBVPJ0BoF492qrmpGwP/GQJPplMDpQ6gO8XaQ5J6gDFwGOz\nNXp/8UIqZKN6HqmXJ5a6iNjZgylL3c3n6RyrfFwmiWxALaLT7wDxTEaTuqLMESr1IGcH5WK2rL5R\n38ArWakbY0ikT0rd7j/frxylHyfZO4Cmejqp12o1ut3Th8gEQZFWc3hSz3seW63R+89L6ZD180q9\nVYPGZPvCj7cppoWbz9Pe2p7qe45LIh1Qr5xdEbnKJNJZ6ip1RZkb5l7qLT8L7X2KfhKw/WK3UIRW\ni26lQqyXwvd7KTxMJhFxqB+TujskqadSKbrdLvv7pwfZAr8wdFAOIO+7bLZGHxW7kArPV34/2Ks+\n4bBcPsyz05iuJNx8ns7WbJJ6LOnTqEVX6vFsTpO6oswRcy/1tmf3k+eNvRQ7jR3cjC2xd3Z38UMX\nxxEaNZuaHcclTKWoHzspzkkOlno8bp95Xq+fPp/dD4o0z0rqvkfbQHXEUbGFpM/23jmklLAVCfYm\nk2gmzExf6rkcna2tmRwVGyY92q0u7YgeFZvIZNivVuh2ovn/pyhKP3Mv9ZZvpZ7tnY+929zFzdlz\n2zvbO4gIYcpn/5g44+lMX1J3ElbqJ8vvZ0k98Au029t0u4NL7HnfBWBzRAk+G/eptzo02mPetON2\n0I/9yaSeDbPsNKed1HOYRgMz4Dq9bGLJg0rMmEftXjHiGft3+fjfV0VRosvcS/0gqWfa9qZ+PKl3\ne2XLWMKjUe2X+n716CYpruAkPLrV0wfQwBCp9/aqt1qD5Vr07VGxo4blsgnbz9+pj5nWD6Ren6yH\nnQ2y1Fo1Wt3play9vF1TZ/vy++pHUo9mCT5xIHUtwSvKXDD3Um/5dvAtbFSJuTF2m7s4vSesdXoP\nwoglTyb19KltQk7Cp1vvT3tnSd3z7c9otwffbPM9qY8alsvGrZR2xi3Bx3P2n/XJkzrAbmN6yc/N\n2TW1Z9BXD3tSj2pfPZbsDXbWLv+BOYqiXD5zL/WDpM7+NpnA9ovdQ6lbcYVJv688G09n+ra0AUjM\npbvfn6rPlLpnb7bt9umnuMFR+X2U1HM9qW+Pm9RjB1KfMKn3pD7NErx7kNRnMAEf9aQeJhIANPb2\nZrwSRVEuA5X6gdTrW2TCjO2pn0rqXl+Si6XSp3qUTszD7PcLOBaL2beeROremOX38yZ1LwA/OXlS\nD15eUp9N+d1e56hKPUjYXR3NvdMPFlIUJXrMvdQ7bgwc30q9l9SdWAwJAjq9PqRN6seknkzRabVo\nN4966BK6dBv9AnZdlzAMB0vdPVvquYOk3h6R1BPnTOpg++r7kwk0E9p5g2lOwDspey1m8Uz1UJO6\noigRYq6l3u50qbbAxHNQ3+6b7Haz2aOknvBoN7t0WnZ7WdC7UTbrRzfKQUkdbFqfJKm7IiRdh1r7\n7C1tB0l9e+8cR53G8xdO6tuN6aVqJ2nTZHcGfV8/cHE9h8ZeNKffw15Sb2hSV5S54KVKXUQ+IyLf\nFZF7IvJzA/57KCK/0vvvvycit17mek7yq19/xNtf2aMTZGF/m3SQpta0Nz8nm6Hb66kHcVuibTbs\njT+M99JPn9RP99QBwjCk0Th9OIzXK/u3O4OlDvZpbZUR+4vTMSv1auMcUoplYH+y8nkqsOuutqYn\nYCcRBxG6A549fxn4MZfWgD+7KOAFAa7n9f1dVRQlurw0qYuIC/xr4EeBHwB+SkR+4MTLfgbYMsbc\nAf4l8M9e1noGkQxtibvtJaBZI+El2Gvbm5+bTB0mRz+0Uj+48R/1KY9ulBLzMI3OqSe1hWFIs3k6\nRbtuEpChSR0g7bkjD59xHSHmO9TOI/UgBc3JpJzsnby315qeJMRxcJJJOjMovwMEMZfmgCpLVAgS\nSe2pK8qc8DKT+ieAe8aYD40xTeAd4HMnXvM54D/0vv6vwF8QEXmJa+ojGVhZt92e1P0EtVYvqadS\ndHrJMYhb+R/c+MPeVHvzRFIHMCdOJhuW1EUcPC91ptRTrktljENlUqFH7TwnogXJiaXuOz6eeIcf\nfqaFk0rRrc4qqXu0GtFM6mD76tpTV5T5wHuJ730NeHjs+0fADw17jTGmLSI7QBGY7hNDhvAjr5X4\nN38xQfJZFqpPSfpJWt0WrU6LlV/8p+BaUa/cyfHX/+EPklmwMl95/U3e/ve/QhCLH76XE7OXsrvf\nPvwa4JOf/CTtIcNunps+U+p/YzGP74z+jJMIvHMm9SQ0JxOoiJDwE+y3T59nfxGcVHJm5fef+Pm3\ncN3ojpcE8UTfB1BFUaKLvKzztkXkx4HPGGP+du/7nwZ+yBjz9rHXfKv3mke977/Xe83Giff6PPB5\ngMXFxT/7zjvvTG2d1WqVP7HxZcLGJt9+7e/g4OCKe+73cVr2VzvG2PUPY+pAiMjFhFJpGgIXQne8\nIkd87zFee49K5u5EP69jOqeuUbVaJZVKTfR+AN79+5gwpLO0NPF7XHUueg2H0W21EM/jEotgM+Nl\nXcN5Qq/hxZn2Nfz0pz/9njHmrXFe+zKT+mPg+rHvV3v/btBrHomIB2SBU085McZ8AfgCwFtvvWU+\n9alPTW2R7777Lrc/+28BWJnau84f7777LtP8c5lH9BpeHL2GF0ev4cWZ5TV8mTXHrwF3ReS2iATA\nTwJfOvGaLwF/q/f1jwNfMbN4VJeiKIqiRICXltR7PfK3gd8AXOCXjTHfFpF/AnzdGPMl4JeA/yQi\n94BNrPgVRVEURZmAl1l+xxjz68Cvn/h3//jY1/vAT7zMNSiKoijKvBDdkV9FURRFmTNU6oqiKIoS\nEVTqiqIoihIRVOqKoiiKEhFU6oqiKIoSEVTqiqIoihIRVOqKoiiKEhFU6oqiKIoSEVTqiqIoihIR\nVOqKoiiKEhFe2qNXXxYisg7cn+JbLnBJz2+POHodL45ew4uj1/Di6DW8ONO+hjeNMaVxXnjlpD5t\nROTr4z6nVhmOXseLo9fw4ug1vDh6DS/OLK+hlt8VRVEUJSKo1BVFURQlIqjU4QuzXkBE0Ot4cfQa\nXhy9hhdHr+HFmdk1nPueuqIoiqJEBU3qiqIoihIR5lrqIvIZEfmuiNwTkZ+b9XquGiLyyyLyXES+\nNeu1XFVE5LqIfFVE/khEvi0iPzvrNV01RCQmIr8vIn/Qu4a/MOs1XVVExBWR/ysiX571Wq4qIvKx\niPyhiHxTRL5+6T9/XsvvIuIC7wN/CXgEfA34KWPMH810YVcIEfkRoAr8R2PMn5z1eq4iIrIMLBtj\nviEiaeA94K/p38PxEREBksaYqoj4wG8DP2uM+T8zXtqVQ0T+AfAWkDHGfHbW67mKiMjHwFvGmJns\n9Z/npP4J4J4x5kNjTBN4B/jcjNd0pTDG/C9gc9bruMoYY9aMMd/ofV0B/hi4NttVXS2Mpdr71u/9\nms+0cgFEZBX4q8C/m/ValMmZZ6lfAx4e+/4RejNVZoiI3AJ+EPi92a7k6tErG38TeA78ljFGr+H5\n+VfAPwK6s17IFccAvyki74nI5y/7h8+z1BXl+wYRSQG/Bvx9Y8zurNdz1TDGdIwxfxpYBT4hItoO\nOgci8lnguTHmvVmvJQL8OWPMnwF+FPh7vTblpTHPUn8MXD/2/Wrv3ynKpdLrA/8a8F+MMf9t1uu5\nyhhjtoGvAp+Z9VquGD8M/FivH/wO8OdF5D/PdklXE2PM494/nwP/HdvqvTTmWepfA+6KyG0RCYCf\nBL404zUpc0ZvyOuXgD82xvyLWa/nKiIiJRHJ9b6OY4dfvzPbVV0tjDE/b4xZNcbcwt4Lv2KM+Zsz\nXtaVQ0SSvYFXRCQJ/GXgUncHza3UjTFt4G3gN7DDSb9qjPn2bFd1tRCRLwL/G3hdRB6JyM/Mek1X\nkB8GfhqbjL7Z+/VXZr2oK8Yy8FUR+X/YD+u/ZYzRLVnKLFgEfltE/gD4feB/GGP+52UuYG63tCmK\noihK1JjbpK4oiqIoUUOlriiKoigRQaWuKIqiKBFBpa4oiqIoEUGlriiKoigRQaWuKMpIRCQnIn93\n1utQFOVsVOqKooxDDlCpK8r3OSp1RVHG4ReBV3uH4/zzWS9GUZTB6OEziqKMpPcEuS8bY/RBKYry\nfYwmdUVRFEWJCCp1RVEURYkIKnVFUcahAqRnvQhFUc5Gpa4oykiMMS+A3xGRb+mgnKJ8/6KDcoqi\nKIoSETSpK4qiKEpEUKkriqIoSkRQqSuKoihKRFCpK4qiKEpEUKkriqIoSkRQqSuKoihKRFCpK4qi\nKEpEUKkriqIoSkT4//VXwxOB/rm+AAAAAElFTkSuQmCC\n", | |
"text/plain": [ | |
"<matplotlib.figure.Figure at 0x7fac357ae5f8>" | |
] | |
}, | |
"metadata": {}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"fig, ax = plt.subplots(figsize=(8,6))\n", | |
"ax.grid()\n", | |
"plt.xlabel(\"t\")\n", | |
"plt.ylabel(\"1-s\")\n", | |
"#plt.ylim((1,4))\n", | |
"\n", | |
"for p in np.linspace(1.01, 2.5, 25):\n", | |
" t = np.linspace(0, 5, 5000)\n", | |
" \n", | |
" sol = integrate.odeint(deriv_p, p, t)\n", | |
" ax.plot(t, 1-1/sol[:, 0])" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"Other points of interest.\n", | |
"\n", | |
"- My initial thoughts led me to expect this model to exhibit a finite-time blowup of the asset price due to runaway hording. But in fact its asset price can only approach $+\\infty$ very sedately. However this is probably due to how flat the arbitrarily-adopted logistic function is away from the origin. It would be interesting to see the behaviour of alternatives.\n", | |
"- Where instability can arise is if some disruption increases the effective supply e.g. an unexpected discovery suddenly increases the effective supply.\n", | |
"- The price collapse solutions don't end in a worthless asset, they end in $p=1$ and $s=1$ (no hording). Of course the road to get there has made some horders poorer than they were and reset the Gini coefficient for this market. This model doesn't describe a solution for $p=1$ but does show that small amounts of hording $s=1-\\epsilon$ revert to $p=1$ extremely quickly.\n", | |
"- There is a constant-price, constant-hording solution at $p=2$ and $s=0.5$ but it is unstable.\n", | |
"- This model doesn't describe any real world asset I know of but I found its dynamics unexpected and interesting nonetheless." | |
] | |
} | |
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