"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"# fitting the Kremer model to historical population\n",
"# for years -8000 and -3000:\n",
"\n",
"import numpy as np\n",
"import pandas as pd\n",
"import matplotlib.pyplot as plt\n",
"%matplotlib inline\n",
"\n",
"Year = [-8000]\n",
"P = [2.5]\n",
"α = 0.5\n",
"π = 0.00003333\n",
"\n",
"for t in range(-7999, -2080):\n",
" Year = Year + [t]\n",
" P = P + [P[t+7999] + π*P[t+7999]**2/(1-α)]\n",
"\n",
"List = [Year, P]\n",
"P_df = pd.DataFrame(List).transpose()\n",
"P_df['Log Population'] = np.log(P)\n",
"nlabel = ['Year', 'Population', 'Log_Population']\n",
"P_df.columns=nlabel\n",
"P_df.set_index('Year', inplace = True)\n",
"\n",
"P_df.Population.plot()\n",
"\n",
"plt.ylabel('Population')\n",
"plt.xlabel('Years')\n",
"plt.title(' Human Population')\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"If we want to fit our three pre-1 benchmarks, we cannot have two heads being fully as good as one. So, instead, let us assume not that a 1% increase in the STEM workforce raises the rate of technological progress by 1% but rather by λ% for some parameter λ. So the dynamics for population then become:\n",
"\n",
"> $ \\frac{dp}{dt} = \\frac{\\pi p^{1+\\lambda}}{1-\\alpha} $\n",
"\n",
"$ α = 0.5 $, $ π = 0.00003264 $, $ λ = 0.8529 $ fit the pre-1 benchmarks well. But those benchmarks predict that the human population would have exploded in the following two centuries, and crossed rthe world's current population of 7.6 billion in the year 221. \n",
"\n",
"Even if two heads are not quite as good as one—are only 1.85 times as good as one—there need to be other sources of drag in order to have kept the world from an Industrial Revolution-class breakthrough late in the Later Han, and under the late Antonine and Severian dynasties:"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"jupyter": {
"source_hidden": true
}
},
"outputs": [
{
"data": {
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jzmZmVqN6PVZ1Z3pfK+mDkt5B9izsWnwGeDY3fxVwTUTMAjYC56f4+cDGiDgKuCa1Q9IxwNlkXWBzga9J8kgsM7N6qlM31BfTTQT/ErgQ+AbwuaKVJE0HPpjao+w+IacCt6cmi4Ez0/S8NE9aPju1nwfcGhFdEfEC2WNXT6wxbzMzq0FvPe46GxHfS5ObgP48YvWrwF+za9jtgcCrEdGd5juAaWl6GrA67a9b0qbUfhrwYG6b+XXMzKwOBjUaStI/VdtGRPxFlXU/BKyPiEclvb8UrpJjpWXV1snvbwGwAODwww+vlJaZmZUx2BsJLh/Evt8DfFjSGWTDbSeSHWlMktSSji6mA2tS+w5gBtAhqQU4gOy5GaV4SX6dN0TEQmAhQFtbm29yaGbWD4O6RXlELK62vGDdi4GLAdKRxYURcY6k75Bd/X0rMB+4I62yNM3/V1r+o4gISUuBb0u6GjgMmAU8PNC8zMzszeryDG5J91Km62eAF+X9L+BWSV8EHgeuT/HrgW9Jaic7ojg77eNpSUuAZ4Bu4IKI6BnAfs3MrIJ6XcF9YW56PPAHZP9x15ZExH3AfWl6FWVGM0XEduCsCutfCVxZ6/7MzKx/6vIM7oh4tE/oAUn3DzQpMzNrLvXqhpqSmx0FvBM4ZMBZmZlZU6lXN9Sj7BrG2g28wK4rr83MbJirVzfUEXXJxszMmlJdjiwkjQf+HHhv2uaPgevSSWkzMxvGIqI+5yyAG4Et7Hru9keBb1Fh9JKZmQ0fRYUCai8WR0fEcbn5eyU9MZCkzMysufTUUC1qvevs45LeeH6FpJOABwaYl5mZNZGiO85C7UcWJwHnSnopzR8OPCvpKSAi4jcHlqKZmQ213t7iNrUWi7mDysTMzJpW3Y4sIuIXko4D3pdC/y8ifM7CzGwvUEuxqOmchaTPADcDU9PrJkmfHlR2ZmbWFOrZDXU+cFJEbAWQdBXZrcT/qepaZmbW9Op2ZEF2m4/8bcF7KP8EOzMzG2ZqGTpb65HFN4GHJH03zZ/JrudQmJnZMFbPE9xXS7qP7HYfAs6LiMcHlZ2ZmTWFWq7grtoNJWm8pM9K+mfgXcDXIuIfaykUad2HJT0h6WlJl6X4EZIekrRS0m2Sxqb4uDTfnpbPzG3r4hR/TtJpxR/LzMxq1dM7+HMWi4E24CngdOAr/dh/F3Bquk3I8cDcdBX4VcA1ETEL2MiuW52fD2yMiKOAa1I7JB1D9ojVY8mu9/iapNH9yMPMzKqoxwnuYyLiYxHxr8AfAr9V684j81qaHZNeAZwK3J7ii8nOfwDMS/Ok5bMlKcVvjYiuiHgBaKfMY1nNzGxgahk6W1QsdpYmIqLmZ26XSBotaQWwHlgGPA+8mttWBzAtTU8DVuf2tQk4MB8vs05+XwskLZe0vLOzs7+pmpmNWPU4sjhO0ub02gL8Zmla0uaijUdET0QcD0wnOxp4W7lm6b3cUNyoEu+7r4UR0RYRba2trUWpmZlZMujRUBFRl3MDEfFqGk11MjBJUks6epgOrEnNOoAZQIekFuAAYEMuXpJfx8zMBqmeF+X1m6RWSZPS9D7AB4BngXvJzn8AzAfuSNNL0zxp+Y8ieyjsUuDsNFrqCGAW8HCj8jYzG2lqGAxV80V5A3EosDiNXBoFLImI70l6BrhV0heBx9l1cd/1wLcktZMdUZwNEBFPS1oCPAN0AxdERA9mZlYXtQydbVixiIgngXeUia+izGim9Dzvso9pjYgrgSvrnaOZmQ1xN5SZmQ0P9Rg6a2ZmezkfWZiZWSEXCzMzK+RiYWZmhWoZOutiYWY2wnX3+MjCzMwKdNcwHMrFwsxshOuuw/MszMxsL9fjbigzMyvibigzMyvkbigzMyvk0VBmZlbIRxZmZlaox+cszMysyM6h7IaSNEPSvZKelfS0pM+k+BRJyyStTO+TU1ySrpXULulJSSfktjU/tV8paX6lfZqZWf/V8vCjRh5ZdAN/GRFvI3v29gWSjgEuAu6JiFnAPWke4HSyR6bOAhYA10FWXIBLgZPIHpp0aanAmJnZ4O3sGcJuqIhYGxGPpektZM/fngbMAxanZouBM9P0PODGyDwITJJ0KHAasCwiNkTERmAZMLdReZuZjTRDfWTxBkkzyR6x+hBwcESshaygAFNTs2nA6txqHSlWKd53HwskLZe0vLOzs94fwcxsr9UUo6EkTQD+DfhsRGyu1rRMLKrEdw9ELIyItohoa21tHViyZmYj0JBfZyFpDFmhuDki/j2F16XuJdL7+hTvAGbkVp8OrKkSNzOzOhjSobOSBFwPPBsRV+cWLQVKI5rmA3fk4uemUVEnA5tSN9VdwBxJk9OJ7TkpZmZmdbCjJxgzulwnzi4tDdz/e4A/Bp6StCLF/gb4ErBE0vnAS8BZadmdwBlAO7ANOA8gIjZIugJ4JLW7PCI2NDBvM7MRZUd3L+NbRldt07BiERE/pvz5BoDZZdoHcEGFbS0CFtUvOzMzK+nq7mFsS/WOJl/BbWY2wnV19zLOxcLMzKrp6u5l3Jjq3VAuFmZmI9yO7h4fWZiZWXVd3b0+Z2FmZtV17fQ5CzMzK9DV3cO4gqGzLhZmZiPcjh4fWZiZWYGunT5nYWZmBXydhZmZFdq+0+cszMyswNaubvYbV/3uTy4WZmYjWG9vsHVHDxPG+cjCzMwq2LazB4AJ431kYWZmFWzt6gZwN5SZmVX2WioWE4aqWEhaJGm9pJ/mYlMkLZO0Mr1PTnFJulZSu6QnJZ2QW2d+ar9S0vxy+zIzs4F548hi7NAdWdwAzO0Tuwi4JyJmAfekeYDTgVnptQC4DrLiAlwKnAScCFxaKjBmZjZ4r20f4m6oiPhPoO/jT+cBi9P0YuDMXPzGyDwITJJ0KHAasCwiNkTERmAZby5AZmY2QFvSkcX+TXaC++CIWAuQ3qem+DRgda5dR4pVipuZWR1s2LoDgCn7ja3arllOcJd7VndUib95A9ICScslLe/s7KxrcmZme6tmLRbrUvcS6X19incAM3LtpgNrqsTfJCIWRkRbRLS1trbWPXEzs73RK6/tYL+xoxnfZI9VXQqURjTNB+7Ixc9No6JOBjalbqq7gDmSJqcT23NSzMzM6mDD1i6mTKh+VAFQ/YzGIEi6BXg/cJCkDrJRTV8Clkg6H3gJOCs1vxM4A2gHtgHnAUTEBklXAI+kdpdHRN+T5mZmNkCvbN3BlP3GFbZrWLGIiI9WWDS7TNsALqiwnUXAojqmZmZmydpN2zmqdUJhu2Y5wW1mZntYRNCxcRvTJ+9T2NbFwsxshHpl6w627+x1sTAzs8pWb9gGwLTJ+xa2dbEwMxuhfr5uCwCzpvqchZmZVfDs2i3sO3Y0h0/xkYWZmVXw9JpNHH3I/owaVe5mGbtzsTAzG4G27ehmxepXOXHmlJrau1iYmY1AD7+wgZ09wSlHHVRTexcLM7MR6PtPrmXCuBYfWZiZWXmbt+/kzqfWcsZvHMI+Y6vfQLDExcLMbIRZ9OMX2Lqjh3PfPbPmdVwszMxGkPb1W7juvuc54zcO4e3TDqh5PRcLM7MRYt3m7Xz8huXsN66FL3z42H6t27C7zpqZWfP4SfvLfPa2FWzt6ubmPzuZqfuP79f6LhZmZnup3t7ggedfZvFPXuSHz65n5oH7csN5J3LMYRP7vS0XCzOzvcSO7l5WvfwaT/9yMz95/hV+3N7Jus1dTNp3DBfOeQt/+r4jCx+fWsmwKRaS5gL/CIwGvhERXxrilMzMGi4i6OruZfPrO9m8fSebXu9m8/addG7p4lebtvOrzdv51abtdGzcxqrOrXT3BgCT9x3DKUcdxJxjDua0Yw8ZcJEoGRbFQtJo4F+A3wU6gEckLY2IZ4Y2MzPrKyKIgChNQ5pP8fx03zYDWTf7v5HeCutC0Nt33dx05XWDnl7o7u2lN7339MauV+ya7u4NetN7tTY9vb3s6O6lq7uXrp29dHX3ZNPdvWzfWZruSct62bajm82vd7Ojp7fiz3vKfmM5ZOJ4Dp+yL7PfdjBvPWR/3nrIRGZNnVDTPZ9qNSyKBXAi0B4RqwAk3QrMA8oWi5+v28IHrr5/t1iUvhX5WKW9lVlQqW1/tlumKVGmdbl21eJ7Kq/KbWtrV6l1xc9bdrsV8qoxh/6sX+kH1oi8sra1/Wz6970d3O8xazu475LtMkowrmU048eMYlzLaMaNGcW4ljTdMorxY0ZxwD5jUmwU+4xt4YB9xjBxnxYmjh/DxH3GMHF8C/uPH0PrhHFMnThu0EcMtRouxWIasDo33wGclG8gaQGwAGDiYUdy9MH7v3krZYpspborvXlJ5bYN2G6FDajMgnL7r7SJym37sd0aE97jeZXdbu1/WZX/PZZfv3+/89rzqvW70LC86rJdIWXbyt6z9SvGS/NSLpZvX31dBKPy6+baQVpWZl3SfLl1S9tsGaXsfbQYPUqMVnoflZaN6tNGpWWjGDWK3d/Vv+9jsxkuxaLcT3i3v2EiYiGwEKCtrS3+5ZwT9kReZmYjwnC5KK8DmJGbnw6sGaJczMxGnOFSLB4BZkk6QtJY4Gxg6RDnZGY2YgyLbqiI6Jb0KeAusqGziyLi6SFOy8xsxBgWxQIgIu4E7hzqPMzMRqLh0g1lZmZDyMXCzMwKuViYmVkhFwszMyukSrcpGM4kbQGeG+o8ChwEvDzUSRRwjoPX7PmBc6yHZs8Pasvx1yKitdyCYTMaqp+ei4i2oU6iGknLnePgNXuOzZ4fOMd6aPb8YPA5uhvKzMwKuViYmVmhvbVYLBzqBGrgHOuj2XNs9vzAOdZDs+cHg8xxrzzBbWZm9bW3HlmYmVkduViYmVmhYVksJB0v6UFJKyQtl3RiikvStZLaJT0p6YTcOvMlrUyv+bn4OyU9lda5VnV4lJWk21JuKyS9KGlFbtnFaV/PSTotF5+bYu2SLsrFj5D0UMr7tnSL9rqQ9Om0z6cl/X2z5SjpC5J+mftZntFsOea2f6GkkHRQmm+W7+IVaf8rJN0t6bBmyi9t98uSfpby+K6kSbllTfF7lnRW+nfSK6mtz7KmyLEg/7K59Ev2wPPh9QLuBk5P02cA9+Wm/4PsyXonAw+l+BRgVXqfnKYnp2UPA+9O6/xHabt1zPUfgM+n6WOAJ4BxwBHA82S3XB+dpo8ExqY2x6R1lgBnp+mvA5+sU16/A/wQGJfmpzZhjl8ALiwTb5oc0/ZmkN0+/xfAQc30XQQm5qb/Avh6M+WXtjsHaEnTVwFXNdvvGXgbcDRwH9DWrN/FCrlXzKU/r2F5ZEH2SNWJafoAdj01bx5wY2QeBCZJOhQ4DVgWERsiYiOwDJiblk2MiP+K7Kd6I3BmvZJMf3l9BLgll9+tEdEVES8A7cCJ6dUeEasiYgdwKzAvrX8qcHtaf3Ed8/sk8KWI6AKIiPVNmGMlzZbjNcBfs/ujfpviuxgRm3Oz++VybIr8Uo53R0R3mn2Q7EmYpRyb4vccEc9GRLm7QjRNjlWUzaW/GxmuxeKzwJclrQa+Alyc4tOA1bl2HSlWLd5RJl4v7wPWRcTKAeZ3IPBq7h9SPfN7C/C+dDh8v6R3NWGOAJ9K3ROLJE1uthwlfRj4ZUQ80WdR03wXJV2Z/q2cA3y+2fLr4+NkRy0DybHR38VyhnOO/dK0t/uQ9EPgkDKLLgFmA5+LiH+T9BHgeuADZIfHfcUA4oPKLyLuSNMfZddRBVX2V65oDyq/ohzJfveTybog3gUskXRkk+V4HXBF2t4VZF16H2+yHP+GrBvlTav1M5eGfRcj4hLgEkkXA58CLt2T+dWSY2pzCdAN3FxarcI+9/jvOfdv+k2rVdhnQ3IcoLrss2mLRUR8oNIySTcCn0mz3wG+kaY7yPqPS6aTdVF1AO/vE78vxaeXaT+o/FKOLcDvA+/MhSvlR4X4y2TdAy3pL5Ga8yvKUdIngX9PXQoPS+olu9FY0+TYJ9//DXwvzTZFjpJ+g6yf+ol0rnc68JiyARdN813M+TbwfbJiscfyqyXHdCL9Q8Ds9J2kSo5UiO+R72IfezTHAaqWY+0aeWKlUS/gWeD9aXo28Gia/iC7n7R7OMWnAC+Q/SU9OU1PScseSW1LJ+3OqFOOc4H7+8SOZcBARLMAAALjSURBVPeTYavITj61pOkj2HUC6ti0znfY/WTYn9cpv08Al6fpt5AdpqrJcjw0N/05sr7hpvo59sn3RXad4G6K7yIwKzf9aeD2Zsov92/lGaC1Wf+95HK6j91PcDddjmVyrphLv7bTyCQb+OHfCzyaPvRDwDtTXMC/kJ35f6rPL/XjZCef2oHzcvE24KdpnX8mXdVehxxvAD5RJn5J2tdz5EaTkI1O+XladkkufiTZKJT29CUbV6f8xgI3pc/+GHBqE+b4rfR7fBJYyu7Foyly7JPvi+wqFk3xXQT+LW3zSeD/AtOaKb+03XayP1ZWpNfXm+33DPwe2V/oXcA64K5my7Eg/7K59Ofl232YmVmh4ToayszM9iAXCzMzK+RiYWZmhVwszMyskIuFmZkVcrEwG6B059YfSzo9F/uIpB8MZV5mjeChs2aDIOntZGPl30F2MdYKYG5EPD+IbZau7jVrGi4WZoOk7FkgW8nu6rolIq5It6+4gOzix58An4qIXkkLgROAfYDbIuLytI0O4F/Jrmb+KtktGf4M2Ak8FREf28Mfy2w3TXtvKLNh5DKyq+B3AG3paOP3gFMiojsViLPJ7s10UURsSPcOu1fS7RHxTNrO1oh4D4CktcCvRcSO/MOAzIaKi4XZIEXEVkm3Aa9FRJekD5DdyXd5usHgPuy6RfRHJZ1P9m/vMLKH55SKxW25zT4N3CTpDuD/7IGPYVaVi4VZffSmF2T3XVoUEX+XbyBpFtndkk+MiFcl3QSMzzXZmps+DfhtsofU/K2kt0dET8OyNyvg0VBm9fdD4CPa9TzuAyUdTvZ0xy3A5txT6d5E0mhgekT8CPgroBXYd49kblaBjyzM6iwinpJ0GfBDSaPITlJ/AlhO1uX0U7JbRj9QYRMtwLcl7U/2B91VEbGl8ZmbVebRUGZmVsjdUGZmVsjFwszMCrlYmJlZIRcLMzMr5GJhZmaFXCzMzKyQi4WZmRX6/1NxYnQptjZsAAAAAElFTkSuQmCC\n",
"text/plain": [
"

"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"# fitting the Kremer model to historical population\n",
"# for years -8000, -3000, and 1:\n",
"\n",
"import numpy as np\n",
"import pandas as pd\n",
"import matplotlib.pyplot as plt\n",
"%matplotlib inline\n",
"\n",
"Year = [-8000]\n",
"P = [2.5]\n",
"α = 0.5\n",
"π = 0.00003264\n",
"λ = 0.8529\n",
"\n",
"\n",
"for t in range(-7999, 221):\n",
" Year = Year + [t]\n",
" P = P + [P[t+7999] + π*P[t+7999]**(1+λ)/(1-α)]\n",
"\n",
"List = [Year, P]\n",
"P_df = pd.DataFrame(List).transpose()\n",
"P_df['Log Population'] = np.log(P)\n",
"nlabel = ['Year', 'Population', 'Log_Population']\n",
"P_df.columns=nlabel\n",
"P_df.set_index('Year', inplace = True)\n",
"\n",
"\n",
"P_df.Population.plot()\n",
"\n",
"plt.ylabel('Population')\n",
"plt.xlabel('Years')\n",
"plt.title(' Human Population')\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**How Well Does This Fit Human History?**: Still, all in all, Michael Kremer says: it does not fit badly badly. And, indeed, up to 1900 the rate of change of the human population is indeed roughly proportional to the square of the population—as long as we start not with the invention of agriculture but with the invention of writing, and with a hiccup as the Roman and Han empires collapsed in the second third of the first millennium. After 1900 things fall apart: increasing populations and the increasing ability of people to use technology and wealth to help their investigations do not pay dividends, either in further accelerating population growth or in increasing the rate of growth of global incomes.\n",
"\n",
"\n",
"\n",
" \n",
"\n",
"Nevertheless, two heads are better than one. Or maybe not: surely the effective STEM labor force depends on means of knowledge recording and communication. And it is not foolish to expect _ex ante_ that there would be some diminishing returns from exhaustion of low-hanging fruit at some point. We do seem to see a jump up in growth with the invention of writing, and cities. Shouldn't we also see a jump up with the alphabet? Shouldn't we also see a jump up with the invention of printing? Perhaps the effects of the picking of the low-hanging fruit in exhausting opportunities and slowing growth civilization-wide are visible in the slowdown after the year one. Perhaps the effective STEM labor force gets big bumps up with the alphabet and with printing that together, in the large, offset this exhaustion.\n",
"\n",
"Clearly, however, two heads are better than one will not suffice to understand the relative constancy of global economic growth rates since the coming of modern economic growth around 1870, or even the failure of Roman and Han civilization to usher in an industrial revolution.\n",
"\n",
" "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### 6.2.3. Chad Jones on R & D-Based Models of Economic Growth \n",
"\n",
"Can we preserve the insights that ideas are non-rival and that technology is the ballgame and still understand why growth did not accelerate faster and bring us an Industrial Revolution early in the first millennium, and, in fact, has not further accelerated since the late 1800s? Chad Jones believes we can, and he lays out his case in **Charles I. Jones** (1995): _R&D-Based Models of Economic Growth_ :\n",
"\n",
">The prediction of permanent scale effects on growth from the R&D equation means that the models of Romer/Grossman-Helpman/Aghion-Howitt and others are all easily rejected.... However, the R&D-based models [remain] intuitively very appealing.... [Is there] a way to maintain the basic structure of these models while eliminating the prediction of [permanent] scale effects [on the rate of growth?]...\n",
"\n",
"Jones's answer is \"yes\". Jones accomplishes this by building a basic model that has both (a) an \"as the low-hanging technological fruit is picked, maintaining the same proportional growth rate for the ideas stock $ H $ becomes harder\" effect (the parameter $ \\phi < 1 $); and (b) an \"as the STEM workforce increases, researchers tend to step on each others' toes and get in each others' way\" effect (the parameter $ \\lambda < 1 $):"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
">$ \\frac{dH}{dt} = \\pi L_{stem}^{\\lambda} H^{\\phi} $\n",
"\n",
">$ \\frac{dH/dt}{H} = \\pi L_{stem}^{\\lambda} H^{\\phi - 1} $"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"To gain some intuition, let's consider six different economies in which the rate of growth $ n $ of the STEM labor force varies from 0 to 6% per year, in which the initial levels of both the ideas stock $ H_0 $ and the STEM labor force $ L_0 $ are set at 1, and let us set the R&D crowding parameter $ \\lambda = 0.5 $ and, just to get striking results, the exhaustion of low hanging fruit parameter at the very low level of $ \\phi = 0.1 $. Looking out at the evolution of the log of the ideas stock for 400 years:"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"jupyter": {
"source_hidden": true
}
},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"

"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"# watching how H evolves for different values\n",
"# of STEM labor force growth, from 0 to 5%\n",
"# per year\n",
"\n",
"import numpy as np\n",
"import pandas as pd\n",
"import matplotlib.pyplot as plt\n",
"%matplotlib inline\n",
"\n",
"T = 400\n",
"δ = 0.1\n",
"H_0 = 1\n",
"n = [0, 0.01, 0.02, 0.03, 0.04, 0.05]\n",
"nlabel = ['0%', '1%', '2%', '3%', '4%', '5%']\n",
"φ = 0.1\n",
"λ = 0.5\n",
"L_0 = 1\n",
"J = []\n",
"\n",
"\n",
"for i in range(6):\n",
" H = [H_0]\n",
" for t in range(T):\n",
" H = H + [H[t]+(δ*H[t]**φ)*(L_0**λ)*np.exp(λ*n[i]*t)]\n",
" J = J + [H]\n",
"\n",
"J_df = pd.DataFrame(J)\n",
"\n",
"Jones_df = J_df.transpose()\n",
"\n",
"Jones_df.columns=nlabel\n",
"\n",
"np.log(Jones_df).plot()\n",
"\n",
"plt.ylabel('Log Ideas Stock')\n",
"plt.xlabel('Years')\n",
"plt.title('Log of Ideas Stock for n Between 0 and 6% per Year')\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"What is going on here? We can see from the constancy of the slopes on the right hand side of this log grapch that the ideas stock $ H $ is heading for some steady-state growth rate that is higher the higher is the rate of growth of the STEM labor force. And for that convergence to a constant growth rate to happen, in the long run the increase in the effective STEM labor force $ L_{STEM}^{\\lambda} $ has to be exactly offset by diminishing returns to innovative effort $ \\delta H^{\\phi - 1} $. Thus along the ideas-stock steady-state balanced-growth path:\n",
"\n",
">$ \\lambda \\frac{1}{L_{stem}} \\frac{dL_{stem}}{dt} = (1 - \\phi) \\frac{dH/dt}{H} $\n",
"\n",
">$ \\lambda n_{stem} = (1 - \\phi) h^* $\n",
"\n",
"The level of ideas $ H^* $ at which that growth rate $ h^* $ would be attained is characterized by:\n",
"\n",
">$ \\frac{\\lambda n_{stem}}{1 - \\phi} = \\pi L_{stem}^{\\lambda} (H^*)^{\\phi-1} $"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"So $ H $ grows more rapidly than $ h^* $ until it closes in on the value of $ H^* $ that is on the steady-state balanced-growth path:\n",
"\n",
">$ H^* = $\n",
"$ \\left( \\frac{\\pi (1 - \\phi)}{\\lambda} \\right)^{1/(1-\\phi)} $\n",
"$ \\left( \\frac{1}{n_{stem}} \\right)^{1/(1-\\phi)} $\n",
"$ L_{stem}^{\\lambda/(1-\\phi)} $\n",
"\n",
"And then the growth rate in the steady-state is characterized by:\n",
"\n",
">$ h^* = \\left( \\frac{\\lambda}{1 - \\phi} \\right) n_{stem} $\n",
"\n",
"Thus the rate of growth of the ideas stock along the steady-state balanced-growth growth path will be proportional to the rate of growth of the STEM labor force with constant of proportionality $ \\lambda / (1 - \\phi) $ (the degree to which more researchers step on one anothers' toes divided by how important it is that the low-hanging innovation fruit has already been picked), and the level of the ideas stock along the steady-state growth path will vary inversely with the rate of growth $ n$ of the STEM labor force raised to the power $ {1/(1-\\phi)} $, and directly with the level $ L_{stem} $ of the STEM labor force raised to the power $ {\\lambda/(1-\\phi)} $.\n",
"\n",
"If $ H < H^* $, then $ H $ is growing faster than $ h^* $, and the scale variable $ H L_{stem}^{-\\lambda/(1-\\phi)} $ is rising. When $ H = H^* $, then $ h = h^* $, and the scale variable is then constant:\n",
"\n",
">$ H L_{stem}^{-\\lambda/(1-\\phi)} = \\left( \\pi (1 - \\phi)/\\lambda \\right)^{1/(1-\\phi)} n_{stem}^{-1/(1-\\phi)} $ "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"And, indeed, looking at the levels of the ideas stock over 150 years reveals, first, initial superexponential growth; that growth rate then declines until the growth rate asymptotes (for $ n > 0 $) to merely exponential growth at the rate $ h^* = \\lambda n_{stem} / (1 - \\phi ) $ :"
]
},
{
"cell_type": "code",
"execution_count": 51,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"

"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"# watching how H evolves for different values\n",
"# of STEM labor force growth, from 0 to 5%\n",
"# per year\n",
"\n",
"import numpy as np\n",
"import pandas as pd\n",
"import matplotlib.pyplot as plt\n",
"%matplotlib inline\n",
"\n",
"T = 250\n",
"π = 0.01\n",
"H_0 = 10\n",
"n_stem = [0, 0.01, 0.02, 0.03, 0.04, 0.05]\n",
"nlabel = ['0%', '1%', '2%', '3%', '4%', '5%']\n",
"φ = 0.1\n",
"λ = 0.5\n",
"L_0 = 1\n",
"J = []\n",
"\n",
"\n",
"for i in range(6):\n",
" H = [H_0]\n",
" for t in range(T):\n",
" H = H + [H[t]+(π*H[t]**φ)*(L_0**λ)*np.exp(λ*n_{stem}[i]*t)]\n",
" J = J + [H]\n",
"\n",
"J_df = pd.DataFrame(J)\n",
"\n",
"Jones_df = J_df.transpose()\n",
"\n",
"Jones_df.columns=nlabel\n",
"\n",
"Jones_df.plot()\n",
"\n",
"plt.ylabel('Ideas Stock')\n",
"plt.xlabel('Years')\n",
"plt.title('Ideas Stock for n Between 0 and 6% per Year')\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" \n",
"\n",
"How fast does this Jones model converge to its steady-state balanced-growth path with its constant rate of increase $ h^* $ in the ideas stock? To understand this, we need to look at our scale variable $ H L_{stem}^{-\\lambda/(1-\\phi)} $: \n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": 53,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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vRduMC3bn6Ut7NlgmLS0NX19fHBxUdmFfX18ANm3axJ/+9CcKCwtxcHBg6dKluLm51dlGamoqF110EYcOHWLq1Kn861//AuC+++5j06ZNFBcXc9VVVzFz5swz6j3zzDOsWbOGI0eOcNlll/Hvf/+7uV0+J605zfUzVH7nHkKIFCHEHSjFMEEIcQCYYGzbgOSAKQiWv4C/qz3PT41nyV9GMTbGn9eWHWTUv5Yze9VhSsorz92URqPRNJGJEyeSnJxM9+7d+eMf/8jKlSspKytj2rRpvPrqq2zfvp0lS5bg5ORUbxvbtm1j3rx57Nixg3nz5pGcnAyooavNmzfz+++/s3LlSn7//fcz6j311FMMGDCATz/9tE2UA7SiBSGlvK6eXeMa31oVJ2QXyFgGe76DnlOJ8nXh9ev7c++oXF5auJfnf9rDrNWHuX90V64dFI6jnblZ8ms0mo7Lud70WwtXV1e2bNnC6tWrWb58OdOmTePJJ58kKCiIgQMHAuDu7t5gG+PGjcPDwwOAuLg4kpKSCAsLY/78+cyaNYuKigrS0tLYvXs3vXv3bvU+NUSnWUldklEF3XrAihch9jIwKQXQK8SDj+9IZMPhbP6zeD8zvt/N2ysPc/+YrlwzMAwHi1YUGo2m5TCbzYwePZrRo0cTHx/PG2+80ah1CNXDU9VtVVRUcOTIEV5++WU2bdqEl5cXt956a4cIKdJhZzHVxumUmcxh90PmXtj1zVn7E7v4MO+eIcy9K5FQLyf+8d0uxvx7BXM3HKOsoqodJNZoNOcb+/bt48CBAzXb27ZtIzY2ltTUVDZt2gRAfn4+FRUVjWo3Ly8PFxcXPDw8OHHiBD///HOLyt1UOo0F4VLiwk7vMMb4xykroufUGivCmqFdfRlyrw9rDmbxyqL9PPHNDt5ccZAHx0ZzRf8QLOZOoxM1Gk0Ho6CggOnTp5OTk4PFYqFbt27MmjWL2267jenTp1NcXIyTkxNLlizB1dXV5nb79OlDv3796NmzJ126dGHYsGGt2AvbEVLK9pbhnIR5e8qZY66m4Ml4HnSMhPk3wZQ3od8NDdaTUrJifyb/Xbyf31NyifBx5sGx0UzpG6wVhUbTydizZw+xsbHtLUaHpa7zI4TYUr2WrCl0mqekucqeXVk7IfZSCO4Py/8J5Q2P0QkhGNPDn+/uH8a7Nw/Axd7CX7/YzthXVjJ3wzFKK/SsJ41Go6mPTqMgKswWjqbsRAJMmAl5KbBptk11hRCMjwvgh+nDmX3zALyc7Xjimx2M+tcK5qw9QnGZVhQajabl+OWXX+jbt+8Zf1OnTm1vsRpNp/FBlJlNOJ3IIyU/hbCokdB1HKx6GfrdBE6eNrVhMgkmxAUwPtafNQezeG3ZQWZ+v5vXlx3kzhFduHFwOG56wZ1Go2kmkyZNYtKkSe0tRrPpHBaEMFFhlvjnSH7PMhaPjJ8BJTmw9tXGNycEI6L9mH/PEObfM4SeIR68tHAvw19azn8X7yenqO2Wzms0Gk1HpVMoCJPJRKWoIjTXwraMberLoN4Qfw38+hbkpTa57UFR3nx0+yAWPDCMxChvXl16gGEvLuOFn/eQkdf+85A1Go2mvegUCkKYzFRRSnSpP9szt5/eMfZJqKpQ016bSe9QT2bdPICFfx7BuNgAZq86zPCXlvPol9s5mJHf7PY1Go2ms9EpFITJZIaqEvwKvdh/aj9F5UVqh1ckDLwDfvsYMve3yLFiAt3533X9WPHwGK4dFMaC7amM/88q7vxwE5uOnqQzTAvWaDSalqBzKAizGSmLcSywp1JWsit71+mdIx8BOxdYOrP+BppAuI8zz0zpxbrHxvHn8dFsSTrF1W+v54q31rFwZzqVVVpRaDQXIs3JB5Gdnc2YMWNwdXVtdF6I9qBTzGIyWcwgiykvtMdcKdmeuZ2BgSowFi6+MOxPsPw5OLoWIlt2BaK3iz1/Ht+de0Z25YstycxefZh7P9lClK8Ld43owhX9Q3RgQI3mAqG5+SAcHR159tln2blzJzt37mxFSVuGTqEgzBYzICm2d6VvZQjbM7afWWDI/bBlDix8DO5eUWcIjubiZG/m5iGRXD8onIW70nln5WGe+GYH/1m8jxsSI7hhcLhOXqTRtBU/PwbpO1q2zcB4mNywP7O5+SBcXFwYPnw4Bw8ebFnZW4lOMsSk9FixvTMDKsPYnrn9TF+AvTOMnwnpv8P2z1pVFovZxB96B7PggWHMvSuR+BCPmplPf5m/jZ3Hdd5sjeZ8pSXyQXQmOoUFYTIri6DEwZHYIsEpp1Mk5ycT7h5+ulD8VbDxHVj6DMRNAYe6szm1FEIIhnb1ZWhXXw5nFvDhuqN8sSWFr7ceZ1CkN7cPj2RCXCBmk+1hgDUajY2c402/tWiJfBCdiU5iQSgxSxycCDmpHrhnTHcFEAImvQAFJ2DNf9tUvi5+rsyc0ov1j4/j75fEcjynmHs/2cpII9NdbnF5m8qj0Whaj+p8EDNnzuT111/n66+/blQ+iM5E51AQhk+h3N4ep7RTuNi5nF4wZ03YQLV4bt3rcCqpjaUEDyc77hzRhZWPjObtG/sT4uXE8z/tYcgLS3nqu50cyixoc5k0Gk3L0Vr5IDoqnWqIqUxIyo4mEe8bf7YFUc34p2HP97Dkabj6g7YT0gqL2cRFvYK4qFcQO4/nMmftUT7fmMxH65MY3s2XGweHMz42QIcc12g6GS2RDyIyMpK8vDzKysr49ttvWbRoEXFxcW3cE9voFApCmExqNXVVKUUZuSR4xvPW3vfIL8vHzb6Wr8EjVE17XfkiDLobIoa2j9AGvUI8eOWaPjw2OYZ5m44xd8Mx7v1kK4Hujlw3KJzrBoXh765nP2k0nYGEhATWrVt31ve+vr78+uuvNrVx9OjRFpaq9eg0r7AOzq4giyi196B/RQhVsqruYSaAYQ+CWzD8/ChUdgxTz8/NgQfGRrPq0THMuimB7oFu/HfJfoa+uIz7P93K+kPZepW2RqPpUHQKCwLAyc2TsqwiSh08ic1zwCIsbM3YyojQEWcXtneBSc/Dl7fB5vcg8Z62F7geLGYTE3sGMrFnIEeyCpm7IYn5m1P4cUca3fxduTExnCsSQnHXYcc1mk7LL7/8wt/+9rczvouKiuKbb75pJ4maRqdIOTpgwAD5yKUXcXxfGr3TTPS9fhB/Cl6B2WTmo8kf1V1JSvj4cji+FaZvAVf/thW6EZSUV/L99lQ+2XCM7ck5ONubuaxPMNMGhtE3zPO8nSGh0TQGnXK0YS7olKNuPt4giyjzDqbs6FESAhLYmbWTkop6QnILARe/DOXFsOgfbStsI3G0M3P1gDC+u38YCx4Yxh96B/HdtlSmvrmOi/5vNXPWHtE5KjQaTZvTaRSEi6cnUhZR5hFE2dEk+gf0p7yqnB1ZDSy3941W/ojfP1dxmjoBvUM9+ddVfdj45DheuCIeRzsTM7/fzaB/LuXBz35j3cEsqnSgQI1G0wZ0HgXh4QmyklInd8qOHqWffz8Egi0ntjRcccTD4BEGPz0MlZ1nwZqbox3XDQrnuweG89ODI7h+UDgr9mVw/bsbGPPKCt5YflAnNNJoNK1Kp1EQzp5eABQJQWV2Nq6lgm5e3dh6YmvDFe2d4aIXIWM3bHinDSRteeKC3ZlxWU82Pjme/5vWlyAPR/79yz6GvLiMOz/czOLdJyivrGpvMTUazXlG51EQ7h4AFJcpK6Ds6FES/BPYlrmNiqpzTGWNuQSiJ8KKF5qVnrS9cbQzc3m/ED6/ewjLHx7NXSO6sC05h7s+2szgfy5l5ve72Hk8V0+X1Whakebkg1i8eDEJCQnEx8eTkJDAsmXLWlHS5tNpprk6e3gCUFFRRIXZUSmI3gl8vu9z9p7cSy/fXvVXFgImvwRvDoGfHoFrP20jqVuPKF8XHpscw18ndmflvky+2prCp78eY87ao8QEunFl/1Cm9AvWIcg1mhakufkgfH19+f777wkODmbnzp1MmjSJ48ePt6LEzaPTKAgXY4hJVhVR6uStFMT46wDYcmJLwwoCwLsLjH5cheDYvQDiLmttkdsEO7OJ8XEBjI8LIKeojO+3p/Ll1uM8/9MeXly4l5HRvlzRP5QJcQE6sZHmvOGljS+x9+TeFm0zxjuGvw36W4NlmpsPol+/fjWfe/bsSUlJCaWlpTXtdTQ6zRCTk5s7CIGUhVSEdKPs6FH8nP0IdwtnU/om2xoZ8gAE9lYO6+Kc1hW4HfB0tuemIZF8d/8wlvxlFHeP7MKetHymf/YbA59fwuNf72BLks6rrdE0lZbMB/HVV1/Rr1+/DqscoJ0sCCHEQ8CdgAR2ALdJKRuckmMym3F0caO8rIiKgEhKjyqlMChoEAuPLKSiqgKL6RzdMVvgstdg9lhY/BRc9r8W6U9HpJu/K3+7KIaHJ/Zg/aFsvtqawje/pfDZxmOEeTtxWZ9gLusTQo/A1s2bodG0Bud6028tWiofxK5du/jb3/7GokWLWlvkZtHmFoQQIgR4EBggpewFmIFrbanr4umFlEWUewVTduQosqqKxMBECsoL2J292zYBgvuqFKVbP4Qjq5vajU6D2SQYHu3Lf6f1ZfPfJ/Dvq3oT6ePCWysOMen/VnHR/63izRUHST5Z1N6iajSdgubmg0hJSWHq1Kl89NFHdO3atRUlbT7tNcRkAZyEEBbAGbBpapGLpydCFFPq7IcsLqY8NY2BgUprb0zfaPvRRz8OXpHw/Z/USusLBFcHC1cPCOPjOxLZ8MR4Zl7WE2d7M/9auI8R/1rOlW+t46P1R8kqKG1vUTWaDklz80Hk5ORwySWX8MILLzBs2LA2kbk5tLmCkFIeB14GjgFpQK6U8iw7SwhxtxBisxBic2ZmJqBmMgmKKTarOOulBw/g4+RDtFc0G9Jsn2qGvTNc+iqcPAQr/9X8TnVC/NwcuGVoJF//cRirHx3DI5N6UFBSwVPf7SLxn0u5+f2NfLklhfySzrO4UKNpbQoKCrjllluIi4ujd+/e7N69m2eeeYZ58+Yxffp0+vTpw4QJEygpqXvE/PXXX+fgwYM8++yz9O3bl759+5KRkdHGvbCdNg/WJ4TwAr4CpgE5wBfAl1LKT+qrM2DAALl582ZWfDSb3xb+jH/Xv9L/izvxf+RhfO64g5c2vsQX+79g3XXrsDfb2y7Mt/fD9s/gziUQ0r+ZPTs/2Juex4JtqSzYnkrKqWLsLSZGd/fj4vggxsX646ajzGraCR2sr2HOl2B944EjUspMKWU58DVgU1YfZw8vqirLyDtViNnPj9IDBwEYFDiI0srS+rPM1cek58A1AL69D8p12AqAmEB3Hr0ohtWPjuGr+4Zy/aBwtqfk8Od520h4dgl3friJr7emkKctC43mvKc9ZjEdAwYLIZyBYmAcsNmWijWL5UoLENG9KD2oFERCYAImYWJj+sYan4RNOHnBlNfgkyth+fMw8dnG9eQ8RghBQoQXCRFePPWHOLYeO8VPO9L5eWcaS/ZkYGcWjIhWlsWE2AA8nLVlodFUc77kg2hzBSGl3CCE+BLYClQAvwGzbKnr7OFhNFJEeVgPKr/fgKyqwt3enTjvODambeT+vvc3TqBu4yHhVlj3mgrJET64cfUvAEwmwYBIbwZEevP3S2LZlpLDT7+n8fPOdJbtVcpiWDdfLu4VxMSeAXg6N2KYT6M5D5k0aRKTJk1qbzGaTbusg5BSPg083dh6Lh6nV1OX+0ZgX1REeWoa9qEhJAYl8uGuDykqL8LZzrlxDU98Dg4tg2/uhfvWqox0mjoxmQT9w73oH+7Fk5fEsj0ll592pPHTjjQe/ep3nvhGkNjFm4lxgUyICyDY89wLhjQaTcek06ykhtNDTFIWUWJkiCs9qKacDQoaRIWsOHf477pwcIPL34JTR2DJjJYS97xHCEHfME+euDiW1Y+OYcEDw7hzRBfSc0t4esEuhr64jEtfW8P/lh5gb3qeXsGt0XQyOk0sJjg9xGQ2l1BscsMdKDt0CEaPpr9/fxzMDqxLXVd3nupzETkcEu+DDW+poaYuo1tS9PMeIQS9Qz3pHerJY5NjOJhRwOLdJ1i8O53/LN7PfxbvJ9zbmQlxAUyMC2BApDdmk06lqtF0ZC53MU8AACAASURBVDqVgjBb7HB0ccVsV0JhQRUWq5lMjhZHEgISWJvajMxx456Cg4vh2z/CvWvA2buFJL/w6ObvSjd/V+4b3ZWMvBKW7Mlg0e50Pl6fxHtrjuDtYs/YGH8mxgUwItoPJ3sdSFCj6Wh0qiEmABcvb4SpiPyTJThEd6uZyQQwLHgYR3KPkFaQ1rTG7Z3hynehIAO+fxD0kEiL4O/uyPWJ4Xxw2yC2PjWBN67vz4hoX37Zlc7dH2+h37OLuP2DTXz8axLHcy6cle2azklz8kFs3LixZoFcnz59Ovyspk5lQQC4evtQkpxNfnYJdl26UfT1V8iqKoTJxLCQYfx7879Zm7qWq7pf1bQDBPeDcf9Qwfy2fgQJt7RsBy5wXB0sXNI7iEt6B1FWUcXGIydZsucEy/ZmsGxvBv8AegS4MSbGn7Ex/vQP98Ri7nTvMZrzlObmg+jVqxebN2/GYrGQlpZGnz59uPTSS7FYOuajuGNK1QCuXj6kHzpCJZWYIqORVjOZunh0IcA5gLXHm6EgAIZMh4NLYeFjED4E/Lq3XAc0NdhbTAyP9mV4tC9PXxrHocxClhuK4t3Vh3l75SE8nOwY2d2PsTF+jOruj7eLnkKrgfR//pPSPS2bD8IhNobAJ55osExz80E4O5+eYVlSUtKoIH/tQedTEN7elBXlYW8nKfOPANRMJvvQEIQQDA8ZzqKji2wL/10fJhNMfQfeGgpf3aFCcVg6bsz28wEhRI3f4q6RXcgrKWfNgSyW7c1gxb4Mvt+eiklA3zBPxsb4M7qHP3FB7pi0o1vThkycOJFnnnmG7t27M378eKZNm8aQIUOYNm0a8+bNY+DAgeTl5TWYD2LDhg3cfvvtJCUl8fHHH3dY6wE6oYJw8fJGyiqQRZS6dgNOz2QCGBo8lK8OfMWOrB308+/XQEvnwD0IprwBn18HS5+BSc+3gPQaW3F3tOPi+CAujg+iqkqy43guy/ZmsHxfBi8v2s/Li/bj6+rAiGhf488PPzetxC8UzvWm31q0RD6IxMREdu3axZ49e7jllluYPHkyjo4dMzVwp1MQrt4+AMiqAgpLTDj7+1O6/3T43cSgREzCxNrja5unIABiLoaBd8L616HLGIge37z2NE3CZBL0CfOkT5gnD03oTkZ+Cav3Z7HqQCar9mfyzW8qp29ckDsjuvsyKtqPhEgvHCx6ZpSm5anOBzF69Gji4+N54403mjRUFBsbi4uLCzt37mTAgCbH02tVOp33z9VLTT01mYvIzy7BIaYHJfv21ez3cPAg3jeetcebMd3VmonPgX9P+PouyE1pmTY1zcLfzZErE0J59dp+bHpyPD9MH84jk3rg7mTh/TVHuP7dDfSduZjb5mzk/TVHOJhRoBfpaVqE5uaDOHLkSM2+pKQk9u3bR2RkZKvL3VQ6rQXh4FRKXlYxjj1iyF7/K7KsDGGvHJjDQ4bz5rY3yS7OxsfJp3kHtHOCaz6EWaPhy9vh1h/BrAPTdRRMJkGvEA96hXhw/5huFJRWsOFwNqv2Z7L6QBbL96lMgyGeToyI9mVoN1+GdPHRw1GaJlFQUMD06dPJycnBYrHQrVs3Zs2axW233cb06dMpLi7GycmJJUuW4Orqelb9NWvW8OKLL2JnZ4fJZOLNN9+scXR3RDqdgnDx8EIIExa7YqUgEmKgvJzSQ4dwNGKhjwodxRvb3mD18dVc3u3y5h/UN1rlr/7ydhWKQ/sjOiyuDhbGxQYwLjYAgOSTRaw6kMnq/Vn8uCONzzclA9A9wJWhXX0Z2tWHxC4+eDhppa85NwkJCaxbt+6s7319ffn111/PWf+mm27ipptuag3RWoVOpyBMZjPOnp6YTEXkZpVg3yMGgJK9+2oURIx3DP7O/qxMXtkyCgKg15WQtF75I8IHQ+ylLdOuplUJ83bmhsQIbkiMoKKyil2peaw7lM26Q1l8vukYH6w7iklArxAPhnT1YWhXXwZGeuFs3+luDY2mxemUd4GrlzcV5QVUlFZS6RWEcHKidO8eQCkDIQSjQkfx4+EfKassa1yWuYaY9Dwc36JCcQT0BO8uLdOupk2wmE01zu77RneltKKS7cm5rD2YxfpD2by/5gjvrDyMnVkFIRxiWBj9wj21w1vTKHQ+iHbExcub7GQVTiPvZCkO3aMpqbVoZlToKL7Y/wWb0zczNMSmhHXnxuIAV38A74yE+bfAHYuUj0LTKXGwmBkU5c2gKG8emgBFZRVsPnqKdYeyWX8oi9eXHeB/Sw/gaGeiX5gXg6K8SeziTb8wLx07StMgOh9EO+Lm7UPq3j1gD7lZxXjExJL3889IKWummyUGJeJodmRFyoqWUxAAXhFqEd1n0+D7P6nPHXw1pMY2nO0tjOzux8jufgDkFpez4XA26w5ls+noSf637AByKdiZVeTagZHeJEZ5kxDphbvO1a05D+mUCsLFy5uSwnwc7SvIzSwmIDaGnHnzqEhNxS4kBFDRXQcHDWZVyioeH/R4yy5p73ERjHlSpSkN6gtD/thybWs6DB5OdkzsGcjEnoGAUhhbk06x4chJNh7JrgkHYhIQG+SuLIwobwZGeuPjqmdJaTo/nVJBVE91dXarIC+zGMf+hqN6374aBQEwMmwkK1JWcDDnINFe0S0rxIiHIW07LPo7BMTp/BEXAB5OdoyJ8WdMjEpWVVxWyW/HqhXGSeZuOMactUcBFe58UJQ3A4y83uHezh0+7o5GU5vOqSC8lIJwdCsjN7MYh+5xIAQle/bgNnZsTbmRISMBWJmysuUVhMkEU9+Gd8fDF7fB3cvBK7Jlj6Hp0DjZmxnaTa2tACirqGLH8ZwahfH9tlTmbjgGgK+rAwkRniQYCqNnsAeOdtqPoenYdE4FUb1YzrGUnMxiTM7O2EdEULr3TEd1gEsAcT5xLD+2nDvj72x5QRzc4Nq5MHsMfH4j3PGLzmd9AWNvMZEQ4U1ChDd/HA2VVZIDGflsSTrFlqRTbE06xS+7TqiyZhO9QtxrFEb/cC/83TtmPB7NmTz//PPMnTsXs9mMyWTinXfeITExsVFtHDt2jLi4OGbMmMHDDz/cSpI2n3MqCCFEAPBPIFhKOVkIEQcMkVK+1+rS1UN1uA2zpYji/HLKSipwiI2hZMfOs8qODx/P/377H+mF6QS6BLa8MD5d4ar34dOr1fTXq+Yo60JzwWM2CWIC3YkJdOeGRBV5OKuglK1Jp9hyTCmMD9cnMXv1EQDCvJ1ICFcKo1+4Fz0C3bDTuTDqZPX8/WQlF7Rom75hroy4puHQ/s3NB1HNQw89xOTJk5sqapthiwXxATAHeNLY3g/MA9pNQTi6umG2swNZCEBuZjGOMbHk/7yQyvx8zFZx2MdHKAWx9NhSboi9oXUE6jYexs+Exf+AFdEw9u+tcxxNp8fX1eEMx3dZRRW7UnOVhXFMTbH9dlsqAI52JnoFe9Ss3egX5kmol5P2ZbQjzc0HAfDtt9/SpUsXXFw6/miDLQrCV0o5XwjxOICUskIIUdnKcjWIEAJXbx8qynIByDNmMgGU7t2LsxF2FyDKI4quHl1bV0EADJ0O2Qdh1b/VArq+17fesTTnDfYWE/3ClcUAIKXkeE4xW5JO8XtKLtuSc/jkV5XHG8DbxZ4+oaeVRp9QzwsyidK53vRbi+bmgygsLOSll15i8eLFvPzyy20sfeOxRUEUCiF8AAkghBgM5LaqVDbg7utPacEpQFkQEQlxABTv3HWGggBlRczeMZuTJSfxdvRuHYGEgEtegVNHYcGD4BkOkcNb51ia8xYhBKFezoR6OTOlr5qRV15Zxb70fLan5LA9OYftybms2H+gJmV6hI8zfUKVwugb5qEd4K1Ic/NBPP300zz00EN1BvLriNiiIP4CLAC6CiHWAn5AM/J5tgzuvn4k7diGo6sduZnFWHwjsAQHUbJjx1llx0eM553f32FF8gquiL6i9YQy28E1H8F7E+DzG+DOpeDbrfWOp7kgsDObaiLWVvsyCkor2JGSW6M0Nh89yYLtamjKYhJEB7jRK9id+FClMOKC3PXq7xaiOfkgNmzYwJdffsmjjz5KTk4OJpMJR0dHHnjggVaWummcU0FIKbcKIUYBPQAB7JNSlre6ZOfAzdefglMniYh0IOdEEQBOveIp3nm2o7qHVw9CXENYnLS4dRUEgJMnXD8f3h0Hc69WSsK5lawWzQWLq4OFIV19GNL1dDj7jLwStqfksi35FDuO57F0bwZfbFE5TExCrc3oFeJBr2AP4kOV0nBx6JQTGduNffv2YTKZiI5W0+ar80EsXLiQTZs2MXDgQPLz83Fycqozlejq1atrPs+YMQNXV9cOqxygAQUhhKjvSdpdCIGU8utWkskm3H39QEpcPMpJO6xmETjG9yJ/0SIqTp3C4uVVU1YIwYSICXyy5xPyy/Jxs6/bedRieEfBtZ/Bh5fC3Glw83dg73zuehpNM/B3d2RCnCMT4lSocykl6Xkl7EjJZWdqHjuP57LmQBZfb1UZ+ISAKF8X4g2l0SvEg54h7jpsSAM0Nx9EZ6Oh14eG4llLoJ0VhFrNau9YTHGeidLiCpziewNQsnMXriPOHP8fFz6OD3Z9wIrkFVzatQ1CdYcnwpWzVVC/L2+DaZ+CWb+tadoOIQRBHk4EeTjVzJoCZWnsTM1l5/E8dhzPZdORk3xnzJwC5dPoGaym58YGuRMb5EaIp549Bc3PB2HNjBkzWkiq1qPeJ5aU8ra2FKSxuPmqgGpmcwHgTk56Eb69eoIQFO/4/SwF0duvN0EuQSw8urBtFARA3BTluP7xLyqw35TXdWA/Tbvj7+7IWHdHxsYE1HyXVVDKLsPK2JGSy67UPH7akV6z393RQkyQO3GGwogNcqd7gJt2hp/n2LJQzgd4GhiOshzWAM9IKbNbWbYGcTPmH8uqPMCdnBOFBEQFYd+lS50L5kzCxEWRF/Hx7o/JKcnB09GzbQQdeAcUnICVL4GrP4x/um2Oq9E0Al9XB0Z192OUEckWlCN8X3o+e9Lyav7mb06mqEzNcjcZQ1TKyqhWHu4EuDtc8NbGhZQP4nNgFXClsX0DaqHc+KYeVAjhCbwL9EIpndullOsb04advQPOHp6UFedgMoVxKr3aUd2LgrVrzwj9Xc3kqMnM2TWHJceWcFX3NpyINfpxpSTW/AdcA2DwvW13bI2mibg6WGpCgVRTVSU5drLotNJIz2dbcg4//J5WU8bL2Y6YQHd6BLrRPcCN7gGuRAe4XVBpXS+kfBDeUspnrbafE0I0N4/nq8BCKeVVQgh7oEkeXHdfP/KzM3H3c6qZyeQYH0/ud99RkZ6OXVDQGeVjvGOIdI/k5yM/t62CEAIu+Q8UZsHCx8DFF+LbfaawRtNoTCZBpK8Lkb4uTI4/fX/llZSzNy3/DMVhbW0ABLo70j3Qje7+rkpxBLoR7e+qZ1J1YGz5ZZYLIa4F5hvbVwE/NvWAQgh3YCRwK4CUsgxofDATlKM6MzmJgGhnTlVPde0dD0Dxjh1nKQghBJOjJvP29rfJLMrEz9nvrDZbDZMZrnwPPrkCvrlHBfXr0fFjsWg0tuDuaFeTna+aqiq1KvxARj770gs4cCKffSfy+fhwNqUVVTXlQjyd6BHoRnSAKz0ClNXRzd9V+zc6AA1Nc81HDf8I1GK5T4xdJqAA5ZdoCl2ATGCOEKIPsAX4k5RGYKVG4Obrx+HfNtN9mBPJu09SVSVxiIkBOztKduzAfeLEs+pcFHURb21/i1+O/sKNcTc2sQtNxM4RrvscPpoC829Wn7uNa1sZNJo2wmQShHk7E+btfIZDvLJKknyyiH0n8g2loZTH6gOZlFeq5eFCQIS3M9383ejq70JXP1d6OFRRUVmFRQcwbDMamsXUWosFLEB/YLqUcoMQ4lXgMeAf1oWEEHcDdwOEh4fX2ZC7nz8VZaW4eFRRWVFFfnYJHn5OOPboQXEdjmqALh5diPGO4eejP7e9ggBwdIcbv4IPL1OrrW/8Uofk0FxQmK2GqSZZTb8tr6wiKbuQ/ScK2Jeez4GMfA5mFLBqfyZllVXMviwIkZaHxWTCwc6Eg8WEg8WMo/HZzmy64J3jLY1Ng39CCC8gGqgJWC+lXNXEY6YAKVLKDcb2lygFcQZSylnALIABAwbIuhqqnupqsVPGR86JIqUg4nuRt+B7ZGUlwny2mTo5ajL/3fJfkvKSiHCPaGI3moGzN9z8LXxwCXx6jfocNqjt5dBoOhB2ZhPd/N3o5u/GxVb+jYrKKlJOFXMq9QhBHo6UlldRUlFFbnE5lVWnR6dNQtQoDWsF4mAxYTK1nOJoTj6Io0ePEhsbS48ePQAYPHgwb7/9dovJ1tLYMs31TuBPQCiwDRgMrAfGNlSvPqSU6UKIZCFEDynlPmAcsLspbVUvlhOouPA5J4qI6OWDc79+5Hz2OaUHD+Jo/BDWXBJ1Ca9ufZUFhxYwvd/0phy6+bj4qhXWcybDJ1fCLQsguF/7yKLRdGAsZhORvi4UZ5rxc1PvqMs/mEXG0cNIoEpKqqRaOV4l1baUZ75TCgQmofyQJmH9GTWIDvhHdGHMrXc3KEtL5IPo2rUr27Zta1Sd9sKWwbw/AQOBJCnlGKAfyofQHKYDnwohfgf6ohISNRp3w4IoKcjGwcXCqXRlSTj1TwCgaMuWOusFuAQwJHgICw4toEpW1VmmTXALhFu+V/GbPp6qclxrNBrbEMpXYTYJ7MwCe4sJRzsTzvZmXOwtONlZcLCYsTObMJsEEqiokpRVVlJSUUlxeQWFZZUUlVVSUl5FQWkFWQWl5JeUU1pReZaSgbrzQQQHB7Np0yaGDh1Knz59GDRoEPn5+W18MloHW4aYSqSUJUIIhBAOUsq9QoizX8sbgZRyGzCgOW2AShxk5+BIflYm3kHhnExTCsIuJBiLvz/FW7bC9XXnZbi86+U8suoRNqZvZHDQ4OaK0nQ8QpWS+OAPKnbTTd9ASEL7yaPRdALO9aZfH1JKKqskpRVVlFVUGf8ra7ZTc4prygohsDeroSp7i/o/ZOQYZs5sej4IgCNHjtCvXz/c3d157rnnGDFiRJP60hbYoiBSjIVt3wKLhRCngNRz1GkThBB4+AeQm3kC7xBXDm4+UbNAzimhP0Vbt9Zbd0z4GNzs3Pju4HftqyAAvCLhtp+UgvjocrjhSxXLSaPRtChCCCxmgcVswsXhzH1SSmVhGIqjtKKy5nNBaQVVUk3q/GDBUn7buJ4tv67hqquv4cG/PoqvfwDRPftQVFaBs4trvTOtgoKCOHbsGD4+PmzZsoXLL7+cXbt2NZhDoj2xJdz3VOPjDCHEcsADWNiqUjUCj4AgctJT6TrQhV1FFRTlluHi6YBz/wTyf15IeWoqdsHBZ9VzMDswOWoyCw4t4MnEJ3G1b+fIi57hcOtP8NFlarjphvl6dpNG04YIoYaq7OpTHpWG5VFZRdDE8YwfO5aYuF58/N4syo0V5tWYTcr6sDesj9OfLXh5q7UiCQkJdO3alf379zNgQLMHVFqFen0QxoI2hBDe1X/ADlQspg4Tx9YzIJDcjBN4BSqTLjtVOaydE/oDULT1t3rrTuk2hZLKEhYnLW59QW3BIwRu/RE8w+CTq+DQ8vaWSKPRYCgPi4njSYfITk0i0MORcB9nThzZy4C+vcjNyiD32F4ifFxwM1XgamfCYjZRUl5FVkEZx3OKOZJVyPpdR/j92Cn2puexYtMO9u7fj6tvMKcKyygsraCsoqpO30d70ZAFMRf4A2ohW/WCOev/XVpdOhvwDAiioqwUBxc1k+BkaiHhcT44dO+OydmZ4q1b8PjDJXXWjfeNJ8ojim8PfsvU6Kl1lmlz3ALhlh/UYrq502Dax9C988d00WjOBxqXD8IFUNZHeaWkrLKKrSt/4YXnZmI2mxEmM//4538psziTfOq09SEwLBnD8rCrtj4M68bOYsLURus9Gloo9wehVp2MklIeaxNpmoBnoJovXZqfjbO7PdmpylEtLBac+valaEv9fgghBJd1vYxXt77KsbxjhLvXvSCvzXH1g1t/UENNn10Hl78Jfa5tb6k0mguepuSDEEJgb1GzrG69YRq33jDtjP1VVUp5lFcqR3l5ZRVllZJyw/dRUVlFbZvCrlpxmE3YWdRwVkl5JQdO5BPi5YSzfcvEt2qwFSmlFEJ8A3TYaTWeAUpB5JxIwzvYl5PHC2r2OSX0J+v1N6jMy8NcjxPo0i6X8vpvr/PVga94KOGhNpHZJpy9lZL4/AYVu6koG4bc395SaTSaFsZkEjiazPXGnqqSkorKKsoqzlYkReUVlJeodR9ZBWVMnavWL3s62xHsUf9MKluxRc38KoQYKKXc1OyjtQJuvn4Ik4mcE+n4BEeya81xZJVEmATOCQkgJcXbt+Naz1SyAJcARoWO4psD33B/3/uxN9u3cQ8awMENbvgCvr4LfnkCCjNh3NM66ZBG08FpyXwQJiGwt5ipzyiodqDLUw68em1fjucUk5pTTGpOSVNEPwNbFMQY4B4hRBJQiOGDkFL2bvbRWwCzxYKHXwA56al0GehCRVkVeUZMJqfevcFspmjzlnoVBMC0HtNYlryMxUmLuaRL3f6KdsPiAFfNgZ8ehjX/VUriD6/q9KWaC5K68rx0RNoyH4Saugv2FhNT4kPO2DenmXlBbXnKdPiY1B4BgeScSMc7WDmFTqYW4OHnhMnZGceePSna1LDxMzh4MGFuYczfN7/jKQhQocIv+Q+4+MPKF6HoJFz5rgoZrtFcIDg6OpKdnY2Pj0+nUBJthZSS7OxsHB0dz124kdiyDiIJQAjhj1Wwvo6EZ0AQ+w6twjtIPTCzUwuJ6qPCcLgkJpI9Zw5VhYWYXOp+oJqEiWu6X8MrW17hwKkDRHtFt5nsNiMEjHlcxXD6+VGYczFcP0/NetJoLgBCQ0NJSUkhM7O5kX7OPxwdHQkNDW3xdm0J1ncZ8AoQDGQAEcAeoGeLS9NEPAODKCksoLKiGDcfR7KtHNUuQwaTPXs2RZs34zpqVL1tTOk2hdd+e435++bz5OAn20LspjHoLvAIgy9vh9nj1IK6gA7zU2g0rYadnR1RUVHtLcYFhS3B+p5FRXDdL6WMQkVfXduqUjWS6plMuelp+Ia6kpVsNZOpXz+EnR2Fv26orzoAXo5eTIycyPeHv6eovKjBsu1Oj4vg9p9BVsJ7k+DgkvaWSKPRnIfYoiDKpZTZgEkIYZJSLkdFYO0weAaoYZacE2n4hbuRk1FEWUkFACYnJ5z69aOwnjnK1kzrMY3C8kJ+PNLkjKptR1AfuHOpiuP06TWw6b32lkij0Zxn2KIgcoQQrsAqVIjuV4GK1hWrcXjUKIh0/MLcQEJWypnDTKV79lBx6lSD7fTx60MPrx7M3TO3Qy13rxePEGVJdBsHP/4FfnoEKsvbWyqNRnOeYIuCmAIUAw+hgvQdAi5tTaEai52DI65e3uSkp+IbpjKlZiWfjsfuPFhFay3asLHBdoQQ3Bh3IwdzDrI+dX3rCdySOLjBtZ/BkAdg4ywVDbYwq72l0mg05wENBet7XQgxVEpZKKWslFJWSCk/lFL+zxhy6lB4h4RyMjUFF097nNzsyLT2Q8THY3JxofDXcz/0L466GF8nXz7a/VFrituymC0w6XmYOguOb4ZZoyG1c2Ss0mg0HZeGLIgDwCtCiKNCiJeEEB3K71Abr+AwTh5PAcA3zO0MC0JYLDgPGEDR+nP7IezN9lwfcz1rU9dy4NSBVpO3VegzDW5fCFLC+5Pg9y/aWyKNRtOJqVdBSClflVIOAUYBJ4E5Qog9QoinhBDd20xCG/EJCaW0qJDCnFP4hblxMrWQyvLT6USdhwymLCmJ8rS0c7Z1dfercTQ7di4roprgfnD3CgjuD1/fCQsfh4rG5czVaDQasMEHIaVMklK+JKXsB1wPTEWtg+hQeIeEAXDyeDK+Ya5UVcqaFKQALkOGAlBYRyTG2ng6ejKl2xR+PPwjWcWdcDzf1Q9u/g4G3Q2/vgkfXAK5Ke0tlUaj6WScU0EIIeyEEJcKIT4Ffgb2A1e2umSNxDtErSI8eTxFzWQCMq2GmRy6R2MJDKRg5Sqb2rs57mYqqir4bO9nLS9sW2Cxh4v/reI4ZeyBt0fAgQ6SGEmj0XQKGnJSTxBCvA+kAHcDPwFdpZTTpJTftpWAtuLq5YO9kxPZx5Px8HPCztFM5jErP4QQuI4cSeHatciycw+5hLuHMyZsDPP2zev4C+caotcVasjJPRg+vQqWPgOVHWqWskaj6aA0ZEE8AawHYqWUl0opP5VSFjZQvl0RQuAdHMrJ48kIk8AvzI2Mo3lnlHEdNZKqwsIG05Bac1uv28gtzeWL/Z3c2evbDe5cAv1ugtWvqGx1eshJo9Gcg4ac1GOklLOllCfbUqDm4B0SxsnjyQAERLmTlVJARXllzX6XwYMRdnYUrFxpU3t9/fuSGJTInJ1zKKlofmz1dsXOCaa8Dpe/Dam/wVtDYefX7S2VRqPpwNiyUK7T4B0SRsGpk5QWFREY5UFVpTwjLpPJxQXngQNtVhAA9/S+h+ySbL468FVriNz29L0O7l0NPtHw5W3wzX1Qmn/uehqN5oLjPFMQhqM6NZmAKJVi9MSRWsNMo0dRdvgwZcnJNrU5MHAg/f378/7O9ymrPE+mi/p0VeslRj4Kv38Obw+H5IZXmWs0mgsPmxSEECJCCDHe+OwkhHBrXbGahk/NVNcUXDwdcPVy4ERtP8TIkQA2z2YCuLfPvWQUZfDtwQ7nm286ZjsY+yTc+hPIKnj/Ilj+go7lpNFoarBlmutdwJfAO8ZXoUCHfFJ6+AdiMlvIrvZDRLpz4kjuGWXsIyOxj4ho1DDT4KDB9PbrzXs73qO86jx7gEYMgXvXQPxVKlvd7LGQvqO9pdJoNB0AWyyI+4FhQB6AlPIA4N+aQjUVs8WCV1AwYYPiYAAAIABJREFU2clJAPhHuZOXVUJx/plDQ66jR1G0YQNVhbZNyhJCcE/ve0gtTOW7g9+1uNztjqMHXDELpn0C+ekqltOKF/UKbI3mAscWBVEqpax5UgghLECHjYXtFxFFZtJRAALr80OMG4csK6Ngle3DTCNCRtDbrzdvbX+r889oqo/YS+H+DdDzCljxgrIm0ra3t1QajaadsEVBrBRCPAE4CSEmAF8A37euWE3HLyKK/OxMigvy8Qt3R5jEWX4I54QEzD4+5C1aZHO7Qgj+3P/PZBRlMHfv3JYWu+Pg7A1XzoZr50JhhlISy56D8vNUKWo0mnqxRUE8BmQCO4B7UCuq/96aQjUH/wiVszYr6Qh2Dmb+v73zDo+qSv/450xPZtILCUmA0Lv0oiBixV5/2IW1oGJ3V1d3V111VSysZS0rqyKufRXFtquADRCQKi20hAAhlfSembnn98edJJNkElImjZzP89znnHvuuee+c5K53zntPRFxdjKS645DCKORoNNPp+Snn9Eqmv/imxgzkWlx03hj+xsUVhYe+4buzNBzYf46GHkZ/Pysvm4i+YfOtkqhUHQgzXHWp3kWzP2flPIyT7zNXUxCCKMQYosQ4qu2luVNVL/+AOQcPABA74GhZKUU4nZpdfIFnXkGsqyM0tWrW1T+3ePupqSqhMU7FvvH4K5MYDhc8jpc+xkg4d8Xwac3Qkl2Z1umUCg6gKZ8MW0XQmxr7PDDs++iHbzC2kPDCAwJJbtaIAaF4nJqdfwyAdgnTcIYEtKibiaAIeFDOKf/ObyX9B7ZZT3kRTngVLh1Lcz4I+xaBv+YoO+BrWnHvlehUHRbmmpBnIe+tWhjR6sRQsQD5wJvtKWcxtAHqnWBiB0YCkD6voK6NpjNOE47jZLvf0BrhvM+b24bcxsu6eLVra/6x+DugNkGM/8Et6yB2NH6HthvngFHNnW2ZQqFop1oyhfTwaaONj73BeB+oNGfoEKIeUKIjUKIjTk5OS0qPKpvIrlph9DcbgKDLYT2CiR9f0GDfMFnnYlWUkLZ2pbtP50QlMAVQ65g6b6l7M7b3aJ7uz1Rg2HOl3Dx61BwSB/E/nw+FGd1tmUKhcLPNGeh3BQhxAYhRIkQokoI4RZCFB3rvibKOw/IllI2+dNTSrlISjlBSjkhKiqqRc+I6puI2+kkL133WNp7UCgZ+wvRtLpDJ4FTp2JwOCj637ct+xDoq6tDraE8tf4p/DAk070QAk64Au7YBCfdBds+hn+Mg9UvgKuys61TKBR+ojmzmF4GrkTfozoAuBH4RxueeRJwgRAiFfgQOFUI8W4bymtAlGcmU47XOERVuYvcIyV18hksFoJOP53i5ctbNJsJIMQawh3j7mBz9mb+l/o//xje3bAFwxmP6WsnEk+GFY/AK5Nh99f6vtgKhaJb0yxfTFLK/YBRSumWUi4GZrb2gVLKB6WU8VLKfsAVwPdSymtaW54vwnvHYzSZvMYhQgDI8NHNFHLhBWglJZR8/32Ln3PJwEsYFj6MhRsXdu9NhdpKxAC48gO4ZikYLfDhVbD4HOUAUKHo5jRHIMqEEBZgqxDiGSHEPYC9ne1qE0aTiYiEvmQdSAYgOCIAR7iVI3sbCkTgpEmYevWicNkXLX+OwcgDkx4gqyyLt3a81Wa7uz0DT4Nb18C5f4fc/fog9odXQ87ezrZMoVC0guYIxLWefLcDpUACftqTWkr5o5TyPH+UVZ/YgYPJSt6H9EzFjB8azpE9+Q3GIYTRSMj551GyejWu3NwWP2dcr3GcnXg2i3cs5lDRIb/Y3q0xmmHiDXDnFpj5F0j5CV6dDF/cCUUZnW2dQqFoAc0RiKNAlZSySEr5KHAfkN6+ZrWdmAGDqSwrJT9TNzVhWBiVZS6yDzYcXw++4AJwuyn65r+tetYfJvwBi9HCY+se63kD1o1hdcCM++CurTBpHmx9H14aC8sfgdKWC7FCoeh4miMQK4FAr/MAYEX7mOM/YgYOBiBzv969ET8kHIC0pIY7qNoGD8Y6bBiFX7S8mwkgOjCae8bfw/qM9SxLPg69vbYFeySc/TTcvgGGnQdrXoQXRsGKvyqhUCi6OM0RCJuUsmb6jyce2ET+LkF4XDxmWwAZHoEIDLYQmeDgcFK+z/whF1xAxfbtVKaktOp5lw2+jLHRY3lu43PklqsXXwPCE+HSN3T/TkNm6VNiXxwNKx5VQqFQdFGaIxClQohx1SdCiPFAefuZ5B8MBiMxAwaRuX9PTVrCsHAyUwqpqnA1yB9y3rlgMlHwaev2njYIA49MfYRSZynPbHim1XYf90QPhcve0oVi8Fmw+nkvoTja2dYpFAovmiMQdwP/EUKsEkKsAj5CH7Du8sQMHEx26gFcTn0XuIRh4Whu2cDtBoApKoqgU0+l8NOlLXa9Uc2A0AHcNOomvjnwDT+nNX+viR5JjVCshUFn6kLx/Ej45j7Ib+tCfYVC4Q+a4811AzAUuBWYDww71irorkLsgMFobhc5B/Vuo9iBIRjNBg77GIcACL18Nu6CAoq/bZkDP29uHHUjA0MH8sgvj1BQ0VCIFPWIHgb/t1hfbDfyUti4WB/M/vRGyNzR2dYpFD2apry5ThRCxABIKZ3AOOBvwEIhRHgH2dcm6g9Um8xG4gaHcnB7rs/ZRvapUzH36UP+Rx+2+pkWo4Wnpj9FQWWBmtXUEqKGwEWvwF2/wZRbYc9/4Z8nwbuXQepqtTJboegEmmpBvA5UAQghTgYWAO8AhcCi9jet7TjCI7CHhZOxr3Ycot+oSApzyinIarjyWRgMhF0+m/KNm6jcv7/Vzx0aPpTbx9zO8oPL+SrFr9tdHP+ExMFZT8A9O+DUv0D6Fnj7XHj9ZNjyntrZTqHoQJoSCKOUsrov5nJgkZTyUynlQ8DA9jet7QghiBsynLTdO2vS+o2OBODANt8DoiEXX4wwm8n/6OM2PXvuiLmMix7Hk+ufJKNELRBrMQFhcPJ9ulCc/yK4nbBsPjw/HFY+rhbdKRQdQJMCIYQweeKnAd7Oikw+8ndJ4oeNoPhoDoXZujvqoHAbEfEOUhsRCFN4OEFnnknh55+jlZa2+rlGg5G/TfsbmtR4cPWDuLSGM6cUzcAcAOPn6oPZ130BCZNh1UJ4YSR8cj0c3qC6nxSKdqIpgfgA+EkIsQx9WusqACHEQPRupm5B/PBRAKQl1Q54Jo6OJDO5kIoSp897wq65Gq24mIKln7Xp2QlBCfx5yp/ZlLWpZ20u1B4IAf1n6E4B79wCk26GfcvhzdP17qcNb0JFq73QKxQKHzS1YdATwO+Bt4FpXvtQG4A72t80/xAZ3webI4i0pLrdTFLCwR2+WxGBY8cSMHYseUuWIN3uNj3/ggEXcMmgS/jX9n+x+kjL9r9WNEJ4Isx6Eu5NgnOeA6npO9wtHApf3KHvcqdaFQpFm2lymquUcp2U8jMpZalX2l4p5eb2N80/CIOBuKEjSEvaXpMW3SeIwBALB35rfGFW+O/m4kxLo3h5272KPDjpQQaFDeLBVQ+SWZrZ5vIUHqwOmHQT3LIabvweRl4C2z/Rd7l7fTpseAMquk1jV6HocjRrP4juTvywERRkZlCSp7t0EAZB/zFRHNyR63NVNUDQaadh7tOH3LfeavNUVZvJxsIZC6lyV3H/z/fj1Hx3bSlaiRAQPx4ufBl+v0d3Nw7w9e/hucHwyQ2wbwW41TiQQtESeoRAJPgYhxg0IRqXU+PgDt9+gITRSPjcOVRs20b55rY3mBJDEnn0xEfZkr2FBesXtLk8RSPYgnV34zevgpt+gLHXQPJKeO9SfQbUt39WC/AUimbSIwQiqm8iloCAOgIRMyCUwBAL+zdmN3pf6MUXYwwNJfdfb/jFjlmJs7h+5PV8vPdjPtzd+sV4imYgBMSNg3MX6q2Ky9+F+Imw/nV9Ad5r0+CXl6FYdfkpFI3RIwTCYDQSP3wUB7dtrU0zCAaMi26ym8kQEEDYdddS8uOPlO/Y6TNPS7lz7J3MiJ/Bgl8XsD5jvV/KVBwDkxWGnQ9XvKeLxTnP6RsbffdnfWD77fP0WVAlOZ1tqULRpegRAgGQeMJ4CrIyajYQAhg0Phq3S2t0TQRA+HXXYQgJ4ejLL/vFDqPByILpC0gMSeTeH+9Vu9B1NPYIfWB73g9w268w4369FfH1vbBwMLxzIWx6W7kgVyjoQQLRb8x4AFK31voZjOkfgiPMyt4NWY3eZ3Q4iPjdXL0VsX17o/lagsPi4KVTX8IgDNy64la1f0RnETUEZv5J38zoljUw7V4oOARf3gXPDYJ/XwKb31EtC0WPpccIRGivGMJie5P6W+2AszAIBk/qxaGdeZQWVjZ6b9g112AMCeHoy6/4zZ6EoAT+ceo/yC7L5raVt1HmbOgbStFBCAExI+G0h+COzfoA90l3Ql6yvq7iuUHw5ln6bnhHW++jS6HobvQYgQDoO3och3Zuw+W138PQqbFITbJ3fdOtiPDrr6fkp58o/+03v9kzJnoMz814jt15u7n3x3vV9NeugBAQOxpO/yvcuVUXi1MeAGcZLH8YXh4PL0/U99Y+/CtoWmdbrFC0Gz1KIBLHjMdVWcmR3btq0sJi7PRKDGb3uowm1zuEXX01xogIsp591q8uvGckzOChKQ+xJn0ND695GE2qF06XoVosTnkAblkFd++As5+F4N6w9mV48wxYOASW3QY7P4Nytf+H4viiRwlEwvBRGE0mDmzdWCd92Imx5KWXkn2wuNF7jQ47UXfcQfnGTRQvX+5Xuy4dfCl3jL2Dr1K+4rG1jymR6KqEJsDkeXDdMrgvGS59E/pNg6Qv4T9z4Zn+elfUz8/qbspV60LRzelRAmG22UgYMZrkjevrtAIGTuiF0Wwg6ZemXUiHXnYp1kEDyX5uIbKV25I2xrzR87hp1E18uu9Tnlz/pNpoqKsTEAqjLtN3w7svBa7/DqbfC+5K+P5vsOgUfVbU0pth23+gpPH1NgpFV6VHCQTAoMknUpCVQc7BAzVp1gATA8dFs3d9JlXljbtjECYT0fffj/PQIfLef9/vtt0x9g5+N+J3fLTnI57Z8IwSie6C0QR9JusbHM37Ef6wHy5eBP1nwv7lsPRGfaD7lSnwzf2Q9BWU53e21QrFMek2+zr4i4ETprDiX6+y79e1RPfrX5M+6pR49qzPZM/6TEadEt/o/Y7p07FPm8bRV18j5PzzMUVE+M02IQT3jL8Hp+bk3aR3cWpO/jT5TxhEj9Px7o0jCk64XD80DTK2woGf9WPLv+HX1wEBsSdA4smQOAP6TNGdDyoUXQjRHX6lTpgwQW7cuPHYGZvJR48+QHlREXMX1t2j4T9PbcBZ6ebKRyYjhGj0/srkZFIuupiQc86m99NP+82uaqSUPL/5eRbvWMx5/c/j8ZMex2TocVp+fOKq0t2RVwtG2q/grgKDCXqP1YWiz1RImKIv6lMo2oAQYpOUckJr7++Rb51Bk07ih7dfJy89jfDeta2FUTPjWfl2Eml78kkYGt7o/dYBA4i48QZyX/snIRddhH3qVL/aJ4TgnnH3EGQO4qUtL1HqLOXZGc9iNVr9+hxFJ2CyQN+p+nHKH6GqDA6vhwM/wcG1uq+oX/6h540crAtGwhQ9DO+vz6xSKDqIHtmCKM49yqL5c5l2xXVMvnh2TbrL6WbJg78Q0z+Ec+ePbrIMraKClAsvBKD/F19gsLbPy/u9pPdY8OsCxvcaz4szXyTEGtIuz1F0EZwV+gyoQ2t14Ti0Dio802ft0R7BmAxx4/UuKktg59qr6NKoFkQrCIqIJHbwUHav+YlJF/1fTXeSyWxk5Iw4Nn6dSl56KeG97Y2WYbDZiH3kEQ5dfwNH//lPou+6q11svXrY1YRZw/jLmr9wzTfX8Mppr9AnuE+7PEvRBTDbalsYoI9hHN2jC8ahdXqY9IV+TRgherjutTZ+gi4aUUPBYOw8+xXHFT2yBQHw2/JvWPHGq1zz1Av06j+wJr28pIp3/vQLA8ZFc/rc4ccsJ/2PD1D41Vf0+/ADAkaN8quN3mzO2sxdP+gi9NKpLzE2emy7PUvRxSnOgvTN+lhG9VG9c57ZDr3H6KLReyzEnKB3TRnURIeeSFtbEB0uEEKIBOAdIAbQgEVSyhebuqc9BKKipIR/3nIto0+fxalzb65zbdXHe9nx4xGufnwKwREBTZbjLioi5YILMdhsJH62FENA0/nbwqGiQ8xfOZ/0knQePfFRzh9wfrs9S9GNkBLyUuoKRsY2fU0GgMUBvUbqq8JjRuth1FDdDbriuKY7CkQsECul3CyECAI2ARdJKXc1dk97CATAl88v4NDObdzyzyUYTeaa9OK8Ct79y1pGnBzHyVcMPmY5pevWcWju7wi76ipiHn7I73Z6U1hZyD0/3sOGzA1cPuRy7p94PxajpV2fqeiGuKogJ0kXisxtepi1A6pK9OsGsy4S1aLRa4TeXaVmTh1XdLsxCCllBpDhiRcLIZKAOKBRgWgvRsw4jb3rVpOyZSODJtbORAoKtzFkagw7Vx9h7Jl9CAq3NVmOfcoUwufMIW/JEhwzTsYxY0a72RxiDWHRGYt4afNLLN65mKTcJBaespAYe0y7PVPRDTFZ9EHs2BNq0zQN8g9Axm+1orHvO9j6Xm0eezRED9PFojqMGqJv5arocXTqGIQQoh/wMzBSSllU79o8YB5Anz59xh88eNDvz9fcbl6/dQ4xAwZx8R8fqXOtOK+Cdx9ey5DJMZx67bBjl1VZSersy3FlZpK49FPMcXF+t7c+yw8u56E1D2ExWHhq+lOcFHdSuz9TcZwhpb5hUvYuyE7yHLsgZ7fuwbaakD4QPVQXjahhEDkIIgbqLkcUXZZu18VU82AhHMBPwBNSyqVN5W2vLiaA1R/+m/Wff8wNL/6L0F51f4Wv/ngf235M48qHJxEW0/iMpmqqDh7kwKWXYenXj77vvdtuU1+9OVB4gHt/vJf9Bfu5Ztg13D3+brVeQtF2NA0KDuqCkZNUKx45e8DbLb09ulYsIgfXxkP76i5IFJ1KtxQIIYQZ+Ar4Vkr592Plb0+BKM47yr9uu55x51zIKdfeUOdaWVEV/35oLX2HhzPr5ubNUCpeuZK0224ndPZsYh97tD1MbkCFq4LnNz3P+7vfZ2DoQBZMX8CQ8CEd8mxFD8PthPxUOLoPju6F3H36Jkq5+6DMa2dEo0WfPRUxUD/CEyEsUQ+D49RU3A6i2wmE0BcdLAHypJR3N+ee9hQIgC9feJqD2zZz86tLMNvqjjds+PoAv355gAvvGUv8kLBmlZe9cCG5/3qDXg8/RPhVV7WHyT5ZfWQ1D615iMLKQuaPmc+cEXMwG8zHvlGh8Adlebpw5HrEo1o48g7UbXUYzBDWF8L61YpGTdgPzO03E7Cn0R0FYhqwCtiOPs0V4E9Sym8au6e9BeLI7l18+Mj9nH7jbZxwxtl1rrmq3Lz/1/VYAozM/tNEDMZjzyeXbjdpt99ByU8/kfDaq+06aF2fvIo8Hl/7OCsOrWBo+FD+euJfGRExosOer1A0QHNDYZre8sg/oAtGTZgKlUV18ztidLEI7QMh8RCSoO/FEZKgn1uO3d2r0Ol2AtEa2lsgpJS896d7qCovY+7fX8NQr/mbvCWb/72+g+mXD2b0zMY9vXqjlZaSeu21OFMP0vf997ANHdoepjfKioMreHL9k+RW5HLtsGuZP2Y+gWbllkHRxZBSb3n4Eo/CNCg6AtJd956AcC/BqBaPaiHpA4ERymeVByUQfmLf+l/44u9Pcs4df2DYtFPqXJNS8sWLW8lKLeKqRybjCGt62ms1zqwsUmfrLp/7vvculj4d6yKjqKqIFza9wH/2/odegb34/YTfM6vfrCY91SoUXQq3C0oyoeAwFHqOmniaHneW1r3HaIGgGAjqDcGxXqHnqI73gK4sJRB+Qmoa79x/B5qmMfe5VxD1XBMU5pTz4ePriRsSxrnzRzf7JVu5bx8Hr70OQ2Agfd97F3NsbHuY3ySbszaz4NcFJOUlMS56HA9MeoBhEceeuqtQdHmk1Ddf8haOonR96m5xhieeUXfKbjUBYbp4BMXUCklQL3D00mdnOaL0sBvv06EEwo/s/uVnvn7xGc67+wGGTJ3W4PpvKw+z+j/7OP13wxkyufkL08p37OTQ3LmYIiPp++93MEVF+dPsZuHW3Hy+/3Ne2vIS+RX5XDDgAuaPmU9vR+8Ot0Wh6FCk1H1VFWdCcToUZXiFXmml2eBrP3hzINijwBHtEQ9PvCaM9lyL1t2adKEWuhIIP6Jpbpb84XaklMx59mWMJlO965LPnttEfmYZs/888Zh+mrwp27yZQzfciLlXL/osfqtTWhKgdzst+m0RH+z+AA2N2YNnc9Pom4gMiOwUexSKLoPbBaU5ulCUVIeeozpemqOHZbmAj3enKQDskRAYro+FVB8B4Q3TAiP0tHb0iaUEws/s37ieZc8+zqnX38LYs85rcL0wp5yPnviVyDgHF907tlmzmqop27SJwzffgiE4iL5vvYWlXz8/Wt4yMkszeX3b63y27zMsRgtXDb2KOSPmEGZr3lRehaJH43ZB2VEv8fASlLJcfeC9LLc2XlnYeFkWh2/xCAgDW6i+Wt1XaDq2DzYlEH5GSsknf/sz2QdTueHFRdjsDfsf927IZPmbuxh/dl+mXDigReWX79zJ4RtvAqORhNdeI2DUSH+Z3ioOFR3ila2v8N8D/8VqtHLJoEuYM2KO6npSKPyJq0ofKynLhXJv8fAWk3rp1Y4VG8Nsb1w8AkIhIAwxeZ4SCH+TnZrCvx+4i/HnXMAp193kM8/37ySR9EsGs+aNZMC46BaVX5mczOF5N+PKzaX3ggUEzzrLH2a3iZSCFBbvXMxXyV8hkZyTeA5zR85lcNixvdkqFIp2wO3Ux07K86G8QN9ZsLmhR1zEo0VKINqD5YteZvv333HVEwuJGTCowXWX083nf99C7pESLrlvPFEJQS0q35WbS9rtd1C+ZQtRd99FxM03d4npp5mlmSzZuYRP931KuauciTETuXLolcxMmInJoHzrKBTdAo+4CEeUEoj2oKK0hCW/n09AUDBXP/VCgwFrgNLCSj5ZoNv1fw9OJDC4ZfsyaJWVZPzlIYq+/JKgs84i9vHHMAZ3DbfKBRUFfLLvEz7e8zEZpRlEB0Yze/BsLh18qRrQVii6CWoMoh3Zv2Edy577GyfOvpqpl17pM0/OoWKWPruJkF6BXHTPWGz2lvk+klKS9+abZD//AubYWOKe/3u7bl3aUtyam5/SfuLD3R+yNmMtRmHkxN4ncuHACzkl4RTlOVah6MIogWhnvnrxGfauW83lf32auCG+F5cd2pnL169tIyohiAvuGoPF1vKumLLNWzjyh9/jys4h+p67CZ87F2HsWh4vUwtTWZa8jC+SvyC7LJsgSxDnJJ7D+QPOZ3Rk8xcPKhSKjkEJRDtTWVbKv/94J5qmce3TLxHg8D3WkLIlh//9awe9B4Vw7vwTMFtb/nJ3FxSQ8dBDFC9fge2E0fR+4gmsAwe29SP4HbfmZn3GepYlL2PloZVUuiuJtcdyRt8zOKPvGYyOGo1BNH/6r0KhaB+UQHQAmfv38sHD99N39Bguuv+hBs78qtmzPpOVb+8iul8w5912AjZHy11tSykp+uprsp54Aq20lMj5txJ+ww0YLF1z3+niqmJWHlrJ8oPL+SX9F1yai16BvTij7xnMTJjJ2OixmI3K5bhC0Rkogeggtn73DSvffJVx51zIzDm+p76C3pL47s2dBEfaOP/OMcfcz7oxXLm5ZD3xBEXf/Bdznz70+uP9OE49tUt34xRVFfHT4Z/47uB3rDmyBqfmxG62c2LvE5keN51pcdOICux4NyMKRU9FCUQH8sPbi9j83y847fpbGXPWuY3mO7Inn69f24bZauTsm0cR0z+k1c8sWbWarAULqEpOxn7iVKLvv7/DXYe3hjJnGWsz1rIqbRWrjqwiuywbgGHhw5jSewqTYiYxLnqcckGuULQjSiA6EE1zs+y5J0jZvIFZt97NiBmnNZr3aFoJ//3nNkryKzn5isGMmB7X6udKp5P8Dz8i5+WX0QoLCTrrLKJuvw3roIbrM7oiUkr25u/l57SfWX1kNdtytuGSLozCyIjIEUyKmcTEXhMZEz1GCYZC4UeUQHQwrqoqPnvmMQ7v2MbZt9/bYO8IbypKnSx/cyeHduUxeHIvTr58MNbA1vfHuwsLyVuyhLwl76CVlRF01llEXP87AkaPbnWZnUGZs4ytOVvZkLmBDZkb2Hl0Jy7pwiRMDAobxOio0ZwQdQKjo0bTJ6hPl+5WUyi6MkogOgFnZQVLF/yVtKSdzJwzj3Fnn99oXk2TbPpvKhu+TsUeYuG0OcOIHxrepue78vPJe2sx+R98gFZSQsC4cYTPnUPQaad1uamxzaHMWcaW7C1sytrEtpxtbD+6nTKX7r8/1BrKqMhRjIwcydDwoQwNH0qsPVaJhkLRDJRAdBLOqkq+fvFZkjeuY8L5lzD9yjkYmng5Z6UWsWLxLgqyyhg6NYapFw9s8crr+rhLSilc+il5S97BeeQI5t69CbnkEkIvvghzXOu7tDobt+YmuTCZbTnbao6UwhSkx71ykCWIoeFDGRI2RA/Dh9AvuB82U+smBCgUxytKIDoRze3m+7cX8dt3X5MwYjTn3nkf9tDG3WU7q9xs/DqVrSsOYbYamXheIiOnx2E0t23NgHS7KV6xkoKPPqJ07VoA7FOnEnLxxThmzsTo6P6bvJc5y9hXsI89eXvYnbebPXl72Ju/lwp3BQACQZwjjv6h/ekfoh+JIYn0D+1PsKVruC9RKDoaJRBdgB0/rmDlG69icziYddu99B01psn8eRmlrPpoL2m783GEW5l4biJDp8S0aG+JxnAeOULBZ59TuHQpzvR0hMWCfdo0gs9YDJU1AAARqklEQVQ6UxeLLuLryR+4NTeHig+xJ38PBwoOkFKYQkphCqmFqVRpVTX5ImwRJAQlkBCUQHxQPPFB8XrcEU9kQKTqrlIctyiB6CJkp6bw1QtPk59xhJEzz2TGtdf73EuiGiklh5PyWL8sheyDxYREBTDm9ASGTIlt1SrsBuVrGuVbt1L87bcUffsdrsxMMJuxT5yIfdo0HNOnYRk48Lh8Obo1N+kl6TWCcaDwAGklaRwuPkxWaVZNVxWAzWgjPiie3o7exATG0Mveixh7DL0Ca0PVdaXoriiB6EI4qypZ+8kHbPxyKYHBIZw4+2pGnnJGk2MTUkoO/HaUjd+kknOoGGugiRHT4xgxvTfBkc3f0rQppKZRsW0bRd9+R8nPP1OVnAyAKSYG+0knYp80iYDx4zHHxR2XguFNlbuKIyVHSCtOqxGNtOI00kvSySrLoqCyoME9odbQGsGIDowmIiCCCFtEg9Buth/39afoXiiB6IJkpexn5eJ/krF3N+FxCUy7/FoGTpyCMDTehSSlJCO5kG0rD5OyNQcpofegUIZOjWHAuOhWOQBsDGd6OiVr1lC6ajWl69ahFRUBYIqOJmD8OALHjSfghNFYBw/GYOtZv57LXeVkl2WTWZpJVlkWWaVZNfHM0kyyy7IpqCyo0wqpxmq0NhCOUGsoIdYQQq2hBFuDCbGE1KSFWEOwGLumCxXF8YESiC6KlJL9G9ay6v0l5GccISw2jgnnX8yw6TMxW5p2kV2cV8GedZnsXpdBYXY5RpOB+KFhJJ4QSb/RkdhD/OdiW2oalfv2U755E2WbNlO2eROu9Az9otGItX9/bMOHYxs+DNvw4VgHD8YY0vqV4ccDLs1FfkU+uRW55Jbn1obecU9YWFmIS7oaLSvAFKCLhaVWRBxmB3azHYfFgcOsH3aLvSbuMDtwWPQ8drNdOUZUNIoSiC6O5nazd/0aNn65lKyU/VgD7Qw5cTojTzmDmIGDm+ySkFKSmVJE8uZsDvyWQ9HRChAQ3TeY+CFhxA8JI2ZgCGaLf9c+ONPTKd+5k4pdu6jclUTFrl24cnJqrhsjIrAmJmLp3x9L/0Ss/ftj6d8fc0wMwsfGSj0ZKSVlrjIKKwspqCygsLKQwqpCCiv0sDqtqLJIj1cVUuosrTmaQ7VQ2M12bEYbAaYAAswBBBgD9LjnsJlsdc59pduMNixGCxajBavRisVoUTsJdmOUQHQTpJSkJe1gxw/L2btuDa6qSsJiezNgwhQGTJhM78FDG/USW31/XnopKVtzOLwrj6wDRWiaxGAURPcNple/YKL7BRHdL5iQqAC/94W7cnKoSEqict9+Kg+kUJVygKrkZNyFhbWZjEbMMTGY4+LqHb0xx8ZiiorqcV1WbUGTWo1QlFSVUOIsodRZSrGzmNKq0prz6rDUWUq5q5xyVzkVroqauPfRGozCWCsYhrriUR3WT7MarZgNZsxGM2aDGZPBpJ974iZhwmysFxcmPZ+PeJ17PWVVx40GI0ZhVC0pHyiB6IZUlpWxZ+0q9q5bzeGd29HcLgKCgokfPpL4YaNIGD6SyIS+TY5ZVFW4yEwuJG1PPpnJheQcKsbl1ACwBpqIjHcQFmsnvProbScgyP/93a68PKpSUqhMScF5JB3nkSM1hys7u0F+Q1AQpshITFFRdY/oKIyhYRhDQzGGhWIMCcHgcKhBXz8ipaTCXdGkgFS5q6h0V1LprqyJV7mrauOajzSve5yasyatwlWBS3Ph1Jw+x2z8jUBgFEaMBl0sTMKEwWDQ0zzp1UJSP80ojBgMnnuqr3uXIwx17jcZavMBGIQBgzAgELVxITDgFW/B9ZrQk27AK96Mcqrzn9b3NCUQ3ZnKslIObN3EgS0bSUvaQVGO/lK12R1EJ/Ynqt8AevXrT1S//oT3jm90RpTm1sjLKCU7tZis1CLy0kvISy+lqsJdk8dqNxEcEUBwpK0mDIoMICjchj3EgiXA5NcXslZVhSs9naojR3BlZuHKycF19Kgeeh2yosJ3ASYTxpAQXTSqw9BQjEEODHY7BrsDg8MTd9gx2u1e53ooLBYlMl0At+bGJV043U5cmqtO3Cmdely69PNG4tViUz90a240qeGSLjSp4dbcuKUnTfOkST3N+5r3eXW8Tjn107SG5Ugp0dCQUiKRaFJDk1pNek1cajX5NKl1iGAC7Ji7QwnE8URhdhZpSTs4smcX2QdSOHo4FbfTCYDBaCIkuhdhsb0J7RVLqCcMCo/AER6J1V53mqWUktKCKvIySsjPKCM/q4zio+UU5VZQlFuO5qr7tzeaDQQGW7CHWAgMthIYYiEw2ILNbsZmN2O1m7AGmrF5QmuACWFo28tXSolWUoIrJwd3QYF+5BfgLiysPfeOFxSglZSglZVBc/53zWYMAQEYrFaEzYbBZtNDqxUREIDBZkXYPKHVhiHApoeec2GxIMzm2sNirnde77qPA5N/hVfR/fEWlPpiciyhaYkQDY8crgTieMbtcpGfnkZ2agq5aYfIz0ynIDODgswMnJV1f3mbLFYcYeHYw8JxhIUTEByMzRFEgCMImyMIW1AQNnsQAUFBWGyBVFUZKStyU5pfSWlhFWVFVZQV1o1XljU+AwcB1gAT1kATZqsJs9WI2WbUw0YOk8WI0WTAZDZgNBswmmpDk9mAwSQwmY0YTaIm3dfLVWoaWlk5WmkJWmmpLhqlpbhLqs+r00rQyiuQlRW1YUUlsrwcrbISWVGBVlGhh5V6uvQIsl8xGnVHiiYTwmDQ49VpNdeMCIMRYTKCoQXXjEa9O9JgACF00RbV5+jXhAEMwtNtKfRrBoEQLbhPCJ/l1L8Pz99LCFET1wsUNVFPhtq/rRC1F0TDvHXKapDXK0/9+5vz3Dp5a/Mc87n1qZfk80dBc9MaFnbMLL6eaZ80qU0C0SnTE4QQs4AXASPwhpRyQWfY0R0wmkxE9ulHZJ9+ddL11kE+BVkZlOTlUpqfR7EnLMnLJevAfipKSqgoLWn6l7YQmK02LDYbZpsNsy0Ai82G1RaAI96KwWhG/zMZAQNSGtE0A9JtwO0WaC6B221AcxkorzRQmgduF7hc4HZK3C79XAjPCwWD5/C8VDxpAs8LqPpa9SEEBqPAaDRiMAoMRgPCYKgXN+h9zSYTwhCG0RiOMOj3GcwCYRMYqs8N+otQCOF5nPC8I2pDkAjNjdTcCClBaqBpCE0D6dbjnlA/3AjNXS/uBrceSpdL/xtoWk1ZaBIp3aBJT9l6d0V1mVLTEFIPvZ+DS9am1bFBAp7yqm2W1DxPIj2fxfMMvK550oXnmkR6PqsEJC3rDWl+ZtGe3Szt9MO33Wxukb0d96O+wwVCCGEEXgHOANKADUKIL6SUuzralu6MEAKHp6XQFJrmprKsjIriIl0wSoopLymmqqyMqopynJUVOCvKqaqowFlRoadVVFBRXETx0UrcTiculxO303N44l2banGpjusDmHV//Xmde99zjHKb9z1uqpz6vwwbv9bUWQ3Vetva5ze4Vl1Y93Mbr/DBurbd3hktiEnAfillCoAQ4kPgQkAJRDtgMBgJ8HQz+QspJZrbhauqVjBqxMPl0rt/NLceut1obq1hmle8sTT9Zaz/YtajUu+j9fzi9Q5r0vGRVi+ul6n39UrNc179a9vrM9b90N5RWSdNL1dPr45XX/cup36ZTV3zfGAf+aoLrm+al0010fr5vM+l9yMaKbMd6cSe7e7Qrd4oLTDdHwPhnSEQccBhr/M0YHL9TEKIecA8gD59+nSMZYpmIYTAaDJjNLV+dzyFQtH+XP7wI226vzNWlvhq4zaQOinlIinlBCnlhKioqA4wS6FQKBTedIZApAEJXufxQHon2KFQKBSKJugMgdgADBJCJAohLMAVwBedYIdCoVAomqDDxyCklC4hxO3At+hTJd6SUu7saDsUCoVC0TSdsg5CSvkN8E1nPFuhUCgUzUO5P1QoFAqFT5RAKBQKhcInSiAUCoVC4ZNu4axPCFEM7OlsO7oIkcDRzjaii6DqohZVF7WouqhliJSy1W4Uustegnva4pHweEIIsVHVhY6qi1pUXdSi6qIWIUSb3GCrLiaFQqFQ+EQJhEKhUCh80l0EYlFnG9CFUHVRi6qLWlRd1KLqopY21UW3GKRWKBQKRcfTXVoQCoVCoehglEAoFAqFwiddWiCEELOEEHuEEPuFEA90tj3tjRDiLSFEthBih1dauBBiuRBinycM86QLIcRLnrrZJoQY13mW+x8hRIIQ4gchRJIQYqcQ4i5Peo+rDyGETQjxqxDiN09dPOpJTxRCrPfUxUce78gIIaye8/2e6/060/72QAhhFEJsEUJ85TnvkXUhhEgVQmwXQmytntLqz+9IlxUIr72rzwaGA1cKIYZ3rlXtztvArHppDwArpZSDgJWec9DrZZDnmAe81kE2dhQu4PdSymHAFOA2z9+/J9ZHJXCqlPIEYAwwSwgxBXgaeN5TF/nADZ78NwD5UsqBwPOefMcbdwFJXuc9uS5mSinHeK398N93RNbbv7erHMBU4Fuv8weBBzvbrg743P2AHV7ne4BYTzwWfdEgwOvAlb7yHY8HsAw4o6fXBxAIbEbfpvcoYPKk13xf0F3pT/XETZ58orNt92MdxHtefKcCX6HvUtlT6yIViKyX5rfvSJdtQeB77+q4TrKlM+klpcwA8ITRnvQeUz+eboGxwHp6aH14ulS2AtnAciAZKJBSujxZvD9vTV14rhcCER1rcbvyAnA/oHnOI+i5dSGB74QQm4QQ8zxpfvuOdGVXG83au7oH0yPqRwjhAD4F7pZSFgnh62PrWX2kHTf1IaV0A2OEEKHAZ8AwX9k84XFbF0KI84BsKeUmIcQp1ck+sh73deHhJClluhAiGlguhNjdRN4W10VXbkGovat1soQQsQCeMNuTftzXjxDCjC4O70kpl3qSe2x9AEgpC4Af0cdlQoUQ1T/yvD9vTV14rocAeR1rabtxEnCBECIV+BC9m+kFemZdIKVM94TZ6D8cJuHH70hXFgi1d7XOF8AcT3wOel98dfp1npkJU4DC6mbl8YDQmwpvAklSyr97Xepx9SGEiPK0HBBCBACnow/Q/gBc5slWvy6q6+gy4Hvp6XTu7kgpH5RSxksp+6G/E76XUl5ND6wLIYRdCBFUHQfOBHbgz+9IZw+yHGMA5hxgL3p/6587254O+LwfABmAE13tb0DvL10J7POE4Z68An2WVzKwHZjQ2fb7uS6moTd/twFbPcc5PbE+gNHAFk9d7AAe9qT3B34F9gP/AayedJvnfL/nev/O/gztVC+nAF/11LrwfObfPMfO6nekP78jytWGQqFQKHzSlbuYFAqFQtGJKIFQKBQKhU+UQCgUCoXCJ0ogFAqFQuETJRAKhUKh8IkSCIWCGk+Xq4UQZ3ulzRZC/K8z7VIoOhM1zVWh8CCEGIk+Z34sYERfezFLSpnchjJNstZHkELRrVACoVB4IYR4BigF7ECxlPJxIcQc4DbAAvwC3C6l1IQQi4BxQADwkZTyMU8ZaeieM2ehu4GIB25CXwC5XUp5TQd/LIWiVXRlZ30KRWfwKLo77SpggqdVcTFwopTS5RGFK4D3gQeklHkeHz8/CCE+kVLu8pRTKqU8CUAIkQH0lVJWVbvMUCi6A0ogFAovpJSlQoiPgBIpZaUQ4nRgIrDR40k2gFqXyVcKIW5A/x71Rt/YqlogPvIqdifwrhBiGfB5B3wMhcIvKIFQKBqiUbvXgADeklI+5J1BCDEIfVezSVLKAiHEu+h+f6op9YqfBcwALgT+IoQYKXX33QpFl0bNYlIommYFMFsIEQkghIgQQvQBgoFioMjjUvksXzd7ts6Nl1J+D9wHRKHvCqdQdHlUC0KhaAIp5XYhxKPACiGEAX2g+RZgI3p30g4gBVjTSBEm4H2PW2YD8LSUsrj9LVco2o6axaRQKBQKn6guJoVCoVD4RAmEQqFQKHyiBEKhUCgUPlECoVAoFAqfKIFQKBQKhU+UQCgUCoXCJ0ogFAqFQuGT/weEuzK3fKjgbQAAAABJRU5ErkJggg==\n",
"text/plain": [
"

"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"# watching how the scale variable evolves for different values\n",
"# of STEM labor force growth, from 0 to 5% per year\n",
"\n",
"import numpy as np\n",
"import pandas as pd\n",
"import matplotlib.pyplot as plt\n",
"%matplotlib inline\n",
"\n",
"T = 500\n",
"π = 0.01\n",
"H_0 = 10\n",
"n_{stem} = [0.005, 0.01, 0.02, 0.03, 0.04, 0.05]\n",
"nlabel = ['H_half', 'L_half', 'H_1', 'L_1', 'H_2', 'L_2', 'H_3', 'L_3', 'H_4', 'L_4', 'H_5', 'L_5']\n",
"φ = 0.5\n",
"λ = 0.5\n",
"L_0 = 1\n",
"J = []\n",
"\n",
"\n",
"for i in range(6):\n",
" H = [H_0]\n",
" L = [L_0]\n",
" for t in range(T):\n",
" H = H + [H[t]+(π*H[t]**φ*(L_0**λ)*(np.exp(λ*n_{stem}[i]*t)))]\n",
" L = L +[L[t]*np.exp(n[i])]\n",
" J = J + [H]\n",
" J = J + [L]\n",
"\n",
"J_df = pd.DataFrame(J)\n",
"\n",
"Jones_df = J_df.transpose()\n",
"\n",
"Jones_df.columns=nlabel\n",
"\n",
"Jones_df['Sc_half'] = Jones_df.H_half*(Jones_df.L_half**(-λ/(1-φ)))\n",
"Jones_df['Sc_1'] = Jones_df.H_1*(Jones_df.L_1**(-λ/(1-φ)))\n",
"Jones_df['Sc_2'] = Jones_df.H_2*(Jones_df.L_2**(-λ/(1-φ)))\n",
"Jones_df['Sc_3'] = Jones_df.H_3*(Jones_df.L_3**(-λ/(1-φ)))\n",
"Jones_df['Sc_4'] = Jones_df.H_4*(Jones_df.L_4**(-λ/(1-φ)))\n",
"Jones_df['Sc_5'] = Jones_df.H_5*(Jones_df.L_5**(-λ/(1-φ)))\n",
"\n",
"sclabel = ['Sc_half', 'Sc_1', 'Sc_2', 'Sc_3', 'Sc_4', 'Sc_5']\n",
"\n",
"Jones_df[sclabel].plot()\n",
"\n",
"plt.ylabel('Scale Variable')\n",
"plt.xlabel('Years')\n",
"plt.title('Scale Variable for n Between 0.5% and 5% per Year')\n",
"plt.show()\n",
"\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 55,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/Users/delong1/opt/anaconda3/lib/python3.7/site-packages/ipykernel_launcher.py:10: RuntimeWarning: invalid value encountered in log\n",
" # Remove the CWD from sys.path while we load stuff.\n"
]
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"

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]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"Jones_df['Div_Sc_half'] = Jones_df['Sc_half'] - 4\n",
"Jones_df['Div_Sc_1'] = Jones_df['Sc_1'] - 1\n",
"Jones_df['Div_Sc_2'] = Jones_df['Sc_2'] - 1/4\n",
"Jones_df['Div_Sc_3'] = Jones_df['Sc_3'] - 1/9\n",
"Jones_df['Div_Sc_4'] = Jones_df['Sc_4'] - 1/16\n",
"Jones_df['Div_Sc_5'] = Jones_df['Sc_5'] - 1/25\n",
"\n",
"asymplabel = ['Div_Sc_half', 'Div_Sc_1', 'Div_Sc_2', 'Div_Sc_3', 'Div_Sc_4', 'Div_Sc_5']\n",
"\n",
"np.log(Jones_df[asymplabel]).plot()\n",
"\n",
"plt.ylabel('Log Scale Variable Divergence')\n",
"plt.xlabel('Years')\n",
"plt.title('Log Scale Variable Divergence for n Between 0.5% and 5% per Year')\n",
"\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" \n",
"\n",
"#### MEMO: Start with the Jones Rather than the Kremer Equation\n",
"\n",
"We can also start with the Jones model dynamic equations:\n",
"\n",
">$ \\frac{dH_t}{dt} = \\pi H_t^{\\phi} L^{\\lambda} $"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"And consider how they would operate back in the Malthusian régime, in which the workforce is near subsistence and increases with ideas as:\n",
"\n",
">$ L = c_1 H^\\gamma $\n",
"\n",
">$ \\frac{dH}{dt} = \\pi_{mal} c_1 H^{\\phi + \\gamma \\lambda} $\n",
"\n",
"After the Malthusian régime ends, if the population were to then become constant, we would find a shift to:\n",
"\n",
">$ \\frac{dH}{dt} = \\pi_{post} c_2 H^{\\phi} $\n",
"\n",
" "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Notes and Musings: Growth of the STEM Labor Force**:\n",
"\n",
"25 bachelor's degrees per 1000 23 year olds in 1900...\n",
"\n",
"300 bachelor's degrees per 1000 23 year olds today...\n",
"\n",
"60-fold multiplication in college graduates in the U.S....\n",
"\n",
"20-fold multiplication in h since 1870\n",
"\n",
">$ \\frac{\\lambda}{1-\\phi} = \\frac{1}{3} $\n",
"\n",
"45,000,000\n",
"\n",
"Inflection points in the effective STEM workforce\n",
"\n",
"* writing\n",
"* printing\n",
"* formal education"
]
},
{
"cell_type": "code",
"execution_count": 63,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
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"\n",
" \n",
"\n",
"----"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Memo**:\n",
"\n",
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" \n",
""
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.7.4"
}
},
"nbformat": 4,
"nbformat_minor": 4
}

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"text/plain": [
" H*\n",
"φ \n",
"0.1 1.921481e+00\n",
"0.2 1.799492e+00\n",
"0.3 1.617165e+00\n",
"0.4 1.355092e+00\n",
"0.5 1.000000e+00\n",
"0.6 5.724334e-01\n",
"0.7 1.821815e-01\n",
"0.8 1.024000e-02\n",
"0.9 1.024000e-07"
]
},
"execution_count": 63,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# MEMO: dependence of H* on φ\n",
"#\n",
"\n",
"φ = 0.0\n",
"λ = 0.5\n",
"n = 0.01\n",
"L_STEM = 1\n",
"π = 0.01\n",
"H_star_list = []\n",
"φ_list = []\n",
"\n",
"for i in range (9):\n",
" φ = φ + 0.1\n",
" H_star = (π*(1-φ)/(λ*n))**(1/(1-φ))\n",
" H_star_list = H_star_list + [H_star]\n",
" φ_list = φ_list + [φ]\n",
"\n",
"D = [φ_list,H_star_list]\n",
"Dep_df = pd.DataFrame(D).transpose()\n",
"deplabel = ['φ', 'H*']\n",
"\n",
"Dep_df.columns=deplabel\n",
"\n",
"Dep_df.set_index('φ', inplace = True)\n",
"\n",
"Dep_df"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" \n",
"\n",
"## Lecture Notes: What Economists Have to Say About the Rate of Ideas Growth \n",
"\n",
"\n",
"\n",
"* Ask me two questions…\n",
"* Make two comments…\n",
"* Further reading…\n",
"\n",
"H* | |
---|---|

φ | |

0.1 | 1.921481e+00 |

0.2 | 1.799492e+00 |

0.3 | 1.617165e+00 |

0.4 | 1.355092e+00 |

0.5 | 1.000000e+00 |

0.6 | 5.724334e-01 |

0.7 | 1.821815e-01 |

0.8 | 1.024000e-02 |

0.9 | 1.024000e-07 |

\n", "\n", "----\n", "\n", "weblog support: