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    "# FUNCTION FOR CALCULATING AND GRAPHING THE LEVELS OF \n",
    "# SOLOW GROWTH MODEL VARIABLES IN SIMULATIONS\n",
    "#\n",
    "# might as well put \"check that common libraries are active\" as a default header\n",
    "# in every long python code cell...\n",
    "\n",
    "import matplotlib as mpl\n",
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd\n",
    "import scipy as sp\n",
    "import numpy as np\n",
    "%matplotlib inline\n",
    "\n",
    "# we are going to want to see what happens for lots of\n",
    "# different model parameter values and base conditions,\n",
    "# so stuff our small simulation program inside a function, so \n",
    "# we can then invoke it with a single line...\n",
    "#\n",
    "# we are going to assume the economy starts on its base\n",
    "# balanced growth path...\n",
    "#\n",
    "# we are going to want to keep track not just of what the\n",
    "# economy's variables are at each point in time, but also \n",
    "# what the base and alternative balanced-growth path \n",
    "# values of variables are. Given the parameters, the new BGP \n",
    "# is attracting the economy to it at the speed (1-α)(n+g+δ), \n",
    "# closing that fraction of the gap between its current state \n",
    "# and the balanced growth path attractor every period...\n",
    "\n",
    "def sgm_3_bgp_100yr_run(L0, E0, n=0.01, g=0.015, s=0.20, \n",
    "    alpha=0.5, delta=0.025, Delta_s=0, Delta_g=0, Delta_n=0, \n",
    "    T = 100, graphs=\"LEVELS\"):\n",
    "\n",
    "    sg_df = pd.DataFrame(index=range(T),columns=['Labor', \n",
    "        'Efficiency',\n",
    "        'Capital',\n",
    "        'Output',\n",
    "        'Output_per_Worker',\n",
    "        'Capital_Output_Ratio',\n",
    "        'BGP_base_Labor',\n",
    "        'BGP_base_Efficiency',\n",
    "        'BGP_base_Output',\n",
    "        'BGP_base_Output_per_Worker',\n",
    "        'BGP_base_Capital_Output_Ratio',\n",
    "        'BGP_base_Capital',\n",
    "        'BGP_alt_Labor',\n",
    "        'BGP_alt_Efficiency',\n",
    "        'BGP_alt_Output',\n",
    "        'BGP_alt_Output_per_Worker',\n",
    "        'BGP_alt_Capital_Output_Ratio',\n",
    "        'BGP_alt_Capital'],\n",
    "        dtype='float')\n",
    "\n",
    "    sg_df.Labor[0] = L0\n",
    "    sg_df.BGP_base_Labor[0] = L0\n",
    "    sg_df.BGP_alt_Labor[0] = L0\n",
    "    sg_df.Efficiency[0] = E0\n",
    "    sg_df.BGP_base_Efficiency[0] = E0\n",
    "    sg_df.BGP_alt_Efficiency[0] = E0\n",
    "\n",
    "    KoverY_base_steady_state = s/(n+g+delta)\n",
    "    YoverL_base_steady_state = ((s/(n+g+delta))**(alpha/(1-alpha)) \n",
    "        * E0)\n",
    "    KoverL_base_steady_state = (YoverL_base_steady_state *\n",
    "        KoverY_base_steady_state)\n",
    "    \n",
    "    sg_df.Capital[0] = KoverL_base_steady_state * L0\n",
    "    sg_df.Output[0] = (sg_df.Capital[0]**alpha * (sg_df.Labor[0] * \n",
    "        sg_df.Efficiency[0])**(1-alpha))\n",
    "    sg_df.Output_per_Worker[0] = sg_df.Output[0]/sg_df.Labor[0]\n",
    "    sg_df.Capital_Output_Ratio[0] = sg_df.Capital[0]/sg_df.Output[0]\n",
    "    \n",
    "    sg_df.BGP_base_Capital_Output_Ratio[0] = (s / (n + g + delta))\n",
    "    sg_df.BGP_base_Output_per_Worker[0] = sg_df.Efficiency[0] * (\n",
    "        sg_df.BGP_base_Capital_Output_Ratio[0]*(alpha/(1 - alpha)))\n",
    "    sg_df.BGP_base_Output[0] = sg_df.BGP_base_Output_per_Worker[0] * sg_df.Labor[0]\n",
    "    sg_df.BGP_base_Capital[0] = sg_df.BGP_base_Output[0] * (\n",
    "        sg_df.BGP_base_Capital_Output_Ratio[0])\n",
    "    \n",
    "    sg_df.BGP_alt_Capital_Output_Ratio[0] = ((s + Delta_s) / \n",
    "        (n + Delta_n + g + Delta_g + delta))\n",
    "    sg_df.BGP_alt_Output_per_Worker[0] = sg_df.Efficiency[0] * (\n",
    "        sg_df.BGP_alt_Capital_Output_Ratio[0]*(alpha/(1 - alpha)))\n",
    "    sg_df.BGP_alt_Output[0] = sg_df.BGP_alt_Output_per_Worker[0] * sg_df.Labor[0]\n",
    "    sg_df.BGP_alt_Capital[0] = sg_df.BGP_alt_Output[0] * (\n",
    "        sg_df.BGP_alt_Capital_Output_Ratio[0])\n",
    "    \n",
    "    for i in range(T):\n",
    "        sg_df.Labor[i+1] = (sg_df.Labor[i] * np.exp(n + Delta_n))\n",
    "        sg_df.Efficiency[i+1] = (sg_df.Efficiency[i] * np.exp(g + Delta_g))\n",
    "        KoverY_current = sg_df.Capital[i]/sg_df.Output[i]\n",
    "        sg_df.Capital[i+1] = (sg_df.Capital[i] * np.exp((s+Delta_s)/ \n",
    "            KoverY_current - delta))\n",
    "        sg_df.Output[i+1] = (sg_df.Capital[i+1]**alpha * \n",
    "            (sg_df.Labor[i+1] * sg_df.Efficiency[i+1])**(1-alpha))\n",
    "        sg_df.Output_per_Worker[i+1] = sg_df.Output[i+1]/sg_df.Labor[i+1]\n",
    "        sg_df.Capital_Output_Ratio[i+1] = (sg_df.Capital[i+1]/\n",
    "            sg_df.Output[i+1])\n",
    "\n",
    "    for i in range(T):\n",
    "        sg_df.BGP_base_Labor[i+1] = (sg_df.BGP_base_Labor[i] * np.exp(n))\n",
    "        sg_df.BGP_base_Efficiency[i+1] = (sg_df.BGP_base_Efficiency[i] * np.exp(g))\n",
    "        sg_df.BGP_base_Capital_Output_Ratio[i+1] = (s / (n + g + delta))\n",
    "        sg_df.BGP_base_Output_per_Worker[i+1] = sg_df.BGP_base_Efficiency[i+1] * (\n",
    "            sg_df.BGP_base_Capital_Output_Ratio[i+1]**(alpha/(1 - alpha)))\n",
    "        sg_df.BGP_base_Output[i+1] = (sg_df.BGP_base_Output_per_Worker[i+1] * \n",
    "            sg_df.BGP_base_Labor[i+1])\n",
    "        sg_df.BGP_base_Capital[i+1] = (s / (n + g + delta))**(1/(1-alpha)) * (\n",
    "            sg_df.Efficiency[i+1] * sg_df.Labor[i+1])\n",
    "\n",
    "    for i in range(T):\n",
    "        sg_df.BGP_alt_Labor[i+1] = (sg_df.BGP_alt_Labor[i] * np.exp(n + Delta_n))\n",
    "        sg_df.BGP_alt_Efficiency[i+1] = (sg_df.BGP_alt_Efficiency[i] * np.exp(g+Delta_g))\n",
    "        sg_df.BGP_alt_Capital_Output_Ratio[i+1] = ((s+ Delta_s) / \n",
    "            (n + Delta_n + g + Delta_g + delta))\n",
    "        sg_df.BGP_alt_Output_per_Worker[i+1] = sg_df.BGP_alt_Efficiency[i+1] * (\n",
    "            sg_df.BGP_alt_Capital_Output_Ratio[i+1]**(alpha/(1 - alpha)))\n",
    "        sg_df.BGP_alt_Output[i+1] = (sg_df.BGP_alt_Output_per_Worker[i+1] * \n",
    "            sg_df.BGP_alt_Labor[i+1])\n",
    "        sg_df.BGP_alt_Capital[i+1] = ((s + Delta_s) / (n + Delta_n + g + Delta_g + delta))**(1/(1-alpha)) * (\n",
    "            sg_df.BGP_alt_Efficiency[i+1] * sg_df.BGP_alt_Labor[i+1])  \n",
    "    \n",
    "    if (graphs == \"LEVELS\"):\n",
    "        fig = plt.figure(figsize=(12, 12))\n",
    "\n",
    "        ax1 = plt.subplot(2,3,1)\n",
    "        sg_df.BGP_base_Labor.plot(ax = ax1, title = \"BGP (base) Labor\")\n",
    "        sg_df.BGP_alt_Labor.plot(ax = ax1, title = \"BGP (alt) Labor\")\n",
    "        sg_df.Labor.plot(ax = ax1, title = \"Labor Force\")\n",
    "        plt.ylabel(\"Values\")\n",
    "        plt.ylim(0, )\n",
    "\n",
    "        ax2 = plt.subplot(2,3,2)\n",
    "        sg_df.BGP_base_Efficiency.plot(ax = ax2, title = \"BGP (base) Efficiency\")\n",
    "        sg_df.BGP_alt_Efficiency.plot(ax = ax2, title = \"BGP (alt) Efficiency\")\n",
    "        sg_df.Efficiency.plot(ax = ax2, title = \"Efficiency of Labor\")\n",
    "        plt.ylim(0, )\n",
    "    \n",
    "        ax3 = plt.subplot(2,3,3)\n",
    "        sg_df.BGP_base_Capital.plot(ax = ax3, title = \"BGP (base) Capital Stock\")\n",
    "        sg_df.BGP_alt_Capital.plot(ax = ax3, title = \"BGP (alt) Capital Stock\")\n",
    "        sg_df.Capital.plot(ax = ax3, title = \"Capital Stock\")\n",
    "        plt.ylim(0, )\n",
    "\n",
    "        ax4 = plt.subplot(2,3,4)\n",
    "        sg_df.BGP_base_Output.plot(ax = ax4, title = \"BGP (base) Output\")\n",
    "        sg_df.BGP_alt_Output.plot(ax = ax4, title = \"BGP (alt) Output\")\n",
    "        sg_df.Output.plot(ax = ax4, title = \"Output\")\n",
    "        plt.ylabel(\"Values\")\n",
    "        plt.xlabel(\"Years\")\n",
    "        plt.ylim(0, )\n",
    "\n",
    "        ax5 = plt.subplot(2,3,5)\n",
    "        sg_df.BGP_base_Output_per_Worker.plot(ax = ax5, title = \"BGP (base) Output per Worker\")\n",
    "        sg_df.BGP_alt_Output_per_Worker.plot(ax = ax5, title = \"BGP (alt) Output per Worker\")\n",
    "        sg_df.Output_per_Worker.plot(ax = ax5, title = \"Output per Worker\")\n",
    "        plt.xlabel(\"Years\")\n",
    "        plt.ylim(0, )\n",
    "\n",
    "        ax6 = plt.subplot(2,3,6)\n",
    "        sg_df.BGP_base_Capital_Output_Ratio.plot(ax = ax6, \n",
    "            title = \"BGP (base) Capital-Output Ratio\")\n",
    "        sg_df.BGP_alt_Capital_Output_Ratio.plot(ax = ax6, \n",
    "            title = \"BGP (alt) Capital-Output Ratio\")\n",
    "        sg_df.Capital_Output_Ratio.plot(ax = ax6, \n",
    "            title = \"Capital-Output Ratio\")\n",
    "        plt.xlabel(\"Years\")\n",
    "        plt.ylim(0, )\n",
    "\n",
    "        plt.suptitle('Solow Growth Model: Levels: Simulation Run', size = 20)\n",
    "\n",
    "        plt.show()\n",
    "        \n",
    "    if (graphs == \"LOGS\"):\n",
    "        fig = plt.figure(figsize=(12, 12))\n",
    "\n",
    "        ax1 = plt.subplot(2,3,1)\n",
    "        np.log(sg_df.BGP_base_Labor).plot(ax = ax1, title = \"BGP (base) Labor\")\n",
    "        np.log(sg_df.BGP_alt_Labor).plot(ax = ax1, title = \"BGP (alt) Labor\")\n",
    "        np.log(sg_df.Labor).plot(ax = ax1, title = \"Log Labor Force\")\n",
    "        plt.ylabel(\"Values\")\n",
    "        plt.ylim(0, )\n",
    "\n",
    "        ax2 = plt.subplot(2,3,2)\n",
    "        np.log(sg_df.BGP_base_Efficiency).plot(ax = ax2, title = \"BGP (base) Efficiency\")\n",
    "        np.log(sg_df.BGP_alt_Efficiency).plot(ax = ax2, title = \"BGP (alt) Efficiency\")\n",
    "        np.log(sg_df.Efficiency).plot(ax = ax2, title = \"Log Efficiency of Labor\")\n",
    "        plt.ylim(0, )\n",
    "    \n",
    "        ax3 = plt.subplot(2,3,3)\n",
    "        np.log(sg_df.BGP_base_Capital).plot(ax = ax3, title = \"BGP (base) Capital Stock\")\n",
    "        np.log(sg_df.BGP_alt_Capital).plot(ax = ax3, title = \"BGP (alt) Capital Stock\")\n",
    "        np.log(sg_df.Capital).plot(ax = ax3, title = \"Log Capital Stock\")\n",
    "        plt.ylim(0, )\n",
    "\n",
    "        ax4 = plt.subplot(2,3,4)\n",
    "        np.log(sg_df.BGP_base_Output).plot(ax = ax4, title = \"BGP (base) Output\")\n",
    "        np.log(sg_df.BGP_alt_Output).plot(ax = ax4, title = \"BGP (alt) Output\")\n",
    "        np.log(sg_df.Output).plot(ax = ax4, title = \"Log Output\")\n",
    "        plt.ylabel(\"Values\")\n",
    "        plt.xlabel(\"Years\")\n",
    "        plt.ylim(0, )\n",
    "\n",
    "        ax5 = plt.subplot(2,3,5)\n",
    "        np.log(sg_df.BGP_base_Output_per_Worker).plot(ax = ax5, title = \"BGP (base) Output per Worker\")\n",
    "        np.log(sg_df.BGP_alt_Output_per_Worker).plot(ax = ax5, title = \"BGP (alt) Output per Worker\")\n",
    "        np.log(sg_df.Output_per_Worker).plot(ax = ax5, title = \"Log Output per Worker\")\n",
    "        plt.xlabel(\"Years\")\n",
    "        plt.ylim(0, )\n",
    "\n",
    "        ax6 = plt.subplot(2,3,6)\n",
    "        sg_df.BGP_base_Capital_Output_Ratio.plot(ax = ax6, \n",
    "            title = \"BGP (base) Capital-Output Ratio\")\n",
    "        sg_df.BGP_alt_Capital_Output_Ratio.plot(ax = ax6, \n",
    "            title = \"BGP (alt) Capital-Output Ratio\")\n",
    "        sg_df.Capital_Output_Ratio.plot(ax = ax6, \n",
    "            title = \"Capital-Output Ratio\")\n",
    "        plt.xlabel(\"Years\")\n",
    "        plt.ylim(0, )\n",
    "\n",
    "        plt.suptitle('Solow Growth Model: Logs: Simulation Run', size = 20)\n",
    "\n",
    "        plt.show()\n",
    "    \n",
    "    if ((graphs != \"LEVELS\") and (graphs != \"LOGS\")):\n",
    "        fig = \"NONE\"\n",
    "        \n",
    "    print(\"The blue line is the initial balanced-growth path;\")\n",
    "    print(\"the orange line is the alternative balanced growth path;\")\n",
    "    print(\"the green line is the track of the economy as it transitions\")\n",
    "    print(\"from the baseline to the alternative BGP.\")\n",
    "    print(\" \")\n",
    "    \n",
    "    print(n + Delta_n, \"is the baseline labor-force growth rate\")\n",
    "    print(g + Delta_g, \"is the baseline efficiency-of-labor growth rate\")\n",
    "    print(s + Delta_s, \"is the baseline savings rate\")\n",
    "    print(\" \")\n",
    "          \n",
    "    print(n + Delta_n, \"is the alternative labor-force growth rate\")\n",
    "    print(g + Delta_g, \"is the alternative efficiency-of-labor growth rate\")\n",
    "    print(s + Delta_s, \"is the alternative savings-investment rate\")\n",
    "    print(\" \")\n",
    "    \n",
    "    print(delta, \"is the depreciation rate\")\n",
    "    print(alpha, \"is the orientation-of-growth-toward-capital parameter\")\n",
    "    \n",
    "    SGM_dict = {}\n",
    "    SGM_dict[\"df\"] = sg_df\n",
    "    SGM_dict[\"plots\"] = fig\n",
    "    \n",
    "    return SGM_dict"
   ]
  }
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