Producer_Theory.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "945e0291",
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "from sympy import *\n",
    "from sympy.plotting import plot\n",
    "from sympy.printing.latex import LatexPrinter\n",
    "from sympy.core.function import _coeff_isneg, AppliedUndef, Derivative\n",
    "from sympy.printing.precedence import precedence, PRECEDENCE\n",
    "from spb import *\n",
    "from scipy.integrate import quad\n",
    "import numpy as np\n",
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "277d110f",
   "metadata": {},
   "outputs": [],
   "source": [
    "class CustomPrint(LatexPrinter):\n",
    "    def _print_Derivative(self, expr):\n",
    "        diff_symbol = r'\\partial'\n",
    "\n",
    "        \n",
    "        tex = \"\" \n",
    "        dim = 0\n",
    "        for x, num in reversed(expr.variable_count):\n",
    "            dim += num\n",
    "            if num == 1:\n",
    "                tex += r\"%s %s\" % (diff_symbol, self._print(x))\n",
    "            else:\n",
    "                tex += r\"%s %s^{%s}\" % (diff_symbol,\n",
    "                                        self.parenthesize_super(self._print(x)),\n",
    "                                        self._print(num))\n",
    "\n",
    "        if dim == 1:\n",
    "            tex = r\"\\frac{%s}{%s}\" % (diff_symbol, tex) \n",
    "        else:\n",
    "            tex = r\"\\frac{%s^{%s}}{%s}\" % (diff_symbol, self._print(dim), tex) \n",
    "\n",
    "        if any(_coeff_isneg(i) for i in expr.args):\n",
    "            return r\"%s %s\" % (tex, self.parenthesize(expr.expr,\n",
    "                                                  PRECEDENCE[\"Mul\"],\n",
    "                                                  is_neg=True,\n",
    "                                                  strict=True))\n",
    "\n",
    "        return r\"%s %s\" % (tex, self.parenthesize(expr.expr,\n",
    "                                                  PRECEDENCE[\"Mul\"],\n",
    "                                                  is_neg=False,\n",
    "                                                  strict=True))\n",
    "        \n",
    "def custom_print_func(expr, **settings):\n",
    "    return CustomPrint().doprint(expr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "47d55395",
   "metadata": {},
   "outputs": [],
   "source": [
    "init_printing(use_latex=True,latex_mode=\"plain\",latex_printer=custom_print_func)\n",
    "plt.rcParams['figure.figsize'] = 10, 8"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "ab6ee208",
   "metadata": {},
   "outputs": [],
   "source": [
    "q,L,k,khat,c,vc,ac,mc,avc,afc,fc,mpl,mpk,λ,l,mrt,pk,pl,qp = symbols('q L k \\overline{k} c vc ac mc avc afc fc mpl mpk λ l mrt pk pl qp')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "48d4c5de",
   "metadata": {},
   "source": [
    "###### Production function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "943026a0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle q{\\left(L,k \\right)} = \\sqrt{L k}$"
      ],
      "text/plain": [
       "            _____\n",
       "q(L, k) = ╲╱ L⋅k "
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "q = Function('q')(L,k)\n",
    "Eq(q,sqrt(L*k))\n",
    "# Where L = labor, k = capital and q = quantity produced"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b8ebd37b",
   "metadata": {},
   "source": [
    "###### Short run production"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "2fed137a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle q{\\left(L,k \\right)} = \\sqrt{L \\overline{k}}$"
      ],
      "text/plain": [
       "            ________________\n",
       "q(L, k) = ╲╱ L⋅\\overline{k} "
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Eq(q,sqrt(L*khat))\n",
    "# Where L = labor, 𝑘 = capital (fixed, so it becomes a constant) and q = quantity produced (production level)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "1053cb51",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "khat_ex = 10\n",
    "p1 = plot(sqrt(L*khat_ex), ylabel=q, xlabel='L',label = f'k = {khat_ex}',legend=True ,show=False)\n",
    "p1.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "966a388e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\frac{\\partial}{\\partial L} q{\\left(L,k \\right)} \\geq 0$"
      ],
      "text/plain": [
       "∂              \n",
       "──(q(L, k)) ≥ 0\n",
       "∂L             "
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# When labor increases, production also does, shown by\n",
    "Derivative(q,L)>=0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "fdf7a70e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAmsAAAAXCAYAAABUMwh3AAAPv0lEQVR4nO2deZAdRR3HPyEhgEAREgq5hEUgARQFREAkYRMgBDAcsRBFQyKIcoYoUBwp9HEJWijhvkQjoKAQYuQGkQW55QigBMP1kCMcciSihCOsf3y7ebOzMz3TM/02b5/zqXrVuzPdM318e7qnf909A2q1GhUVFRUVFRUVFa3JUh5+pwBPAO8C3cDUZkQoAPsA9wELgMXApks0NmHpQHk/o4+vcyBQA3YpcK9mlUcN+AB4BfgDMLxJYaK0s7ZgyekrBJVGw1MmXzoIq4Gy7c+vgdeA5QPFx9JB32u9WXEIdR3LF8z1vuPwU6P5eu9gyZdRaQYZdy7wHumV8evAmcAjwHTj974mx60IGwOXA/8BrgJeQiKA7DS2Ah3Ac+jBMnmJxqTBT4GjzN8fAnsD1+QM6yoPyzBgT2BXYBNgTeB94HHgV+b3UcK1u4BlUXnuDqwBbJkRnyJh8qal0ldxuo07oGD4SqPhaSW9p7U/HeTT8xeBicCRKD2WsroLRX94dqTRQXoZPIQ6YCcBVwLvJITvorze+3P+rQWcCIxDz5n5KM9OAN6KerSdtVnAscC6KOPjfCXivhw8uuEYjSreNOCs2LmsNPYHXgI2Qm+6fcEJqBF8HFW4i4ErUMN1Q47wrvKw7AWcj0R6O/BP4JPABOAXwM7GT3csXJf5gR4KWwArkPxAKBMmb1oqfS0ZKo02h1bSe1r705Ez/CnAQlSGrUjZvGzlensqcD8aGf1xwvkuyuu9vz571wPuAVYFZgNPoo7q4ajz9mXgDevZmkFnGXfPlIuuYdxW7qgBDDXu3IRzWWnsD3yACnR+H9zraOCHwF3AKPR2PQqJZyawfY5ruMrDMg/YDb1hfBNVuv2ADYEXgK+iRtHFk6hhWTlHnIqGyUpLpa++p9Jo82glvZdpf4YDOwC/RybUVqRsXrZyvX0Axe17ZE+7Kqr3/vrsPQ911KYAewDHAGOAM4AR6CXjY2zmPQi8SO8HTg29LY42/3dHftDTFjwc+B2aF/AR0Bm5zmT08HwWVZiFwN3AtxwJ2dJc7yU0xDkfuAX4miPMQON+kHAuLY2WaFo2REORb6Jh87uAsSnhJpM/bdF7xPOri8ZbwSR65vXkhPBl4pHFFOA04I8o3W+b448B26AGajawbcZ1XOVh+TNwLb3NSK8AF5i/OzPuY68/0OmrXJistDRDX5PxK9PoPULqyzcefUGl0WwGAIcCfwcWoWfpOcBKQN380iirdxdbAVej/HsfldWFNDpllhrp7U+NbD2DOtUDUF3oS5ZCpttuZJJfzuHX59mR1M5Gz0cZgEZpnsC//DuQ6fJfJuyDNEY4LTXylcGVwNrAjo77QXG9l9Ei5NcjlKtTUdZDz606cG7s3I9QuzCRyBxLawbtRr3TQ9Dw/qvmeJdxJwPrIJND2o3vR2+gv0HCXBg5fz5K3J2o0zUMTQS+DPUgj49d7wATZjF6GD+FeqBbAAejtyRf0tIYZ13gXmRWuRBYHc2BuRFNuI1Xet+0QXJ+zQPmoMr1KGrMLXNypK9IPJI4AD1kLkFvQ4tj5+toePYG4HpUAR/IeW1fbOX9sEnXD0kz9FW0TEPrK5S2QlFpNB/TUad2PnARiuvuqHEajBqmouTVe5z9TFzeQ8/2F4AN0CT08cDWyMwM7vanCxhCtp53QProyznWy6J6NwE1xFNIntNoyZuXWe1snHOBg9CI5EWovHdDAyFLk94RXwfVl2dRHR+KnlGzUX7ebvx1ka8M7jbujsDNjvgWpagWwU+PEK5O2ReQW+itjX+jPBtr7n8bNDproMQeZm58kTnWZX6dqABrKTfeFtmmj0s5/1ngmdixwaiBOga9nb5kjm+MhgcXAiNRIxFlrZR7gIQD6cPdSWmMMwo4ncaEZVDP+V4TzxvpWUF80mZJy68OJPw5pOd1GkXikcTF5ufidTRpN4shxi1ifhgE7Gv+vinD7yLjruRxfd8wQ4zrSktofRUt09D6CqWtUFQazWYb1Kg8gxrnN83xaaixXR143hF+iHHL6j3KcKSVOrAdPTWzPWq4zqRhzurC3f7Ucet5eTTpfC49FxY0k6Go0d8G1Y2f5AyXJy9d9TrOSNRRm4c6Em+b48cBf0KjRmnl34nyM9o5/i3S+FH07KzVyX6m/NW4o1LOW8ro3VeL4K/HsnUqygjjzks5/xTqrA3HdNaiNuQ70VyPInbfV0kfdYPeD3pQD/Rc9MCLzi05yBw7id4dNdBwZxIDkEC7Sc+wPGlcgFZnRHkQvckMSQjrkzZLVn4VoUg8mkme8nBxGuok3ED221jduJ0e1/cJkzctofVVtExD66vVtBWKdtJonG8b9xQajQqoQTw2I2xIvUc5CI3oHE7vzv1tqJMzHlgx5/WyWBOZ1PpqLtc6aERkS2TCyttRg3x56VOvJxn3FBodNVC9zSr/54GTY8duRiNMRVYmL0C6WzvDX924nQXuUaT/4qvHMnUqju2Qpi0KsceH2APRkbXFaF7GPuZCPitLHkXDiGmsjSYDb2/+jtvv14z8vbVxb8x573FoeHUUsDkyLcWX3lvypPFhNAwZpwtVgM3QMmWLT9osWflVhCLxaAY+5ZHGFOAINOF0Yg7/l6F9tk5H5q+n0MhLvWQY37SE1lfRMg2tr1bRVijaSaNpbG7cOxLO3UVv0zE0R+9RvmTc7Uge9VwVda6Go5WBZRlm3LcCXCuLEWh0fHm0Ovg2z/B58tKnXm9m3LsSzt2H22w/h2R9vECjDH15E5koXZTRe5H+i68ei9SpYAyK/X8Nmh+wKxr2zIurQn8a2b9XBv6ChhYXoIR1oAZqmYj/IcbNa1YZh3rGAH8Dzs7wn5XGNHu3TWN0iNY3bfFrhaJoPJqBb3nEORQNPT+BOgdvur0D0sqpaBXNXubYrbgreZ4wRdISSl9lyjSkvlpJW6FoJ42mYXWUpLcP0cTxOM3QexTbeTrK6UtbN4TAmnCXDXQ9F8ORCXQOeiErQlZe+tRrV/kvJrIlRAJvpxz/EL+N9KMsR/ZUgzJ6B//+i68ei9SpNGxnMs3ka4+/bQ/EM/5WZNv3NYV2O879AGXK/mh4cwqakFwj2XRgI5f3bX0qStgewPrmmq7VJFlpTOv9r2bcaI/dN20WV34VoWg8msFU/MojHvZs1FCMJv/DaVc09+BhZJYaTGNycpkwU/FPSyh9lSnTkPpqJW2FYirto9E0rI6S9DYIWCXh+FTC6z0pTishU2vaL2nkogivGXeY01cYrkXzwTZFo2pF7pmVlz712s57TSr/gfRNnliWQoMwr2X4K6N38O+/+OqxSJ1K4x/GTftiwwbG/XhOW7yztgiZH8cR7m1kfePOTDi3XcIxu2pnZ497LEQrVWaiTt5GDr9Zadyc5DkTncZ9JHLMN21Z2GFU36XLoeNRFp/ysByN3qjmoEYwq2JHGWPcGprn6NqGwTeMb1pC6asZZVpEX62mrVC0k0aTsKM7SWW0LekaCK33KPbZPjLDX16y9DwfLTQZkXI+NKcC30cmyC6yzX5xQra/9jmStHXN1vS2qhUlzzNlBOr0zMm4Vhm9g3/++eqxaJ1Kwi7SGEvvftiKyAz830gcE4c0Z6Fhv7R9xXypG7czdnwnkr8Zdj4aUjwerQyN41oNaifDDnX4AXcaV0IbbUbZAm2GuYDGBnzgn7Ys3kJvT1kTMeOEjkco8pbH8Wiy9kPIrOQznAyNTRTrTQyTNy0QRl82Xp0xv2XKtIi+mhGPVqKdNBplhnGn0TNty6JORRah9B7lHNQAn0HyiMJg/DpyWXruRhPPV6Hx0lGUGfTePyyJ6Wji+mfQiEzSXl0uQrW/lxp3Gj1NbYNJ/pJAUfI8U+w89NsdfqCc3i0++eerxxnGLVqnojyDppR0oC1HopyA5j5eRmQVc1Lv+jq0YmRPtBqiLOehVRRXoY3nXkZDnOPQfml7x/w/gfZSuwC9HcxGEw2HoUmAC2nsURLH9sSz7OquNN6JGqGt0Moeuw/WUmhPp+i2Hb5py+IdtI/OSLQ6cB6NveYec4QLHY9Q5CmPSWh15GI0J2pKgp867o/w2uv77HXlGyavtiCMvppRpkX01ZfamuE4dzB60wxNO2k0yt3IXHsYMtleTWNPqLfIXiEZSu9RnkT7Wv0SjZzchDS4NGrsR6KRsA1z3BPy6Xkm+sLETsDTKdeZ4biH1Z1PWVyARnkuQfV9DD336nIRqv29A21h8V2U1zNRmY5HL4Uv4977LS95ymCsOTY741pl9G7xyT9fPZatU3EORp+bOgu9AM5F7cJoE49pUc9JnbWFaMfu8WhYr+wKh8fMzU9GNulBaFXLBDQ/LelhfzHKjCPRG/0e6E32MfQtvjTy2vRdaXwOrUg5zbjLoOHPE+k9R6dI2rKYiHr644BvoOHjF3F31poRjxDkKY91jTsQzZlJ4g7cD1Sf+xUN4ztfpKy+mlWmvvrqS21NcpybSnM6a+2k0TiHo4f+IehF4A008nAcKsNQ9/RpMy439z4C6WosGj14GTV+vl8ayNLzTGSu3pfeO8Vb8uhuE7SK+/qc8ZqBVm5eSqPD9myOcCHb34NofOrpQHqW/4skb8lTBFcZ2DmQ16HVpHkoM+fWN/989VimTsV5BllVTkR5twvq8J2J40PucWaZwKPQ0GVnir86Kpgs7qFhj46TFv5e9Ebkg13WvLLTl4inMcpc1FvOg0/a6gnH4jyNhJaEK3zoeIQgT3nU8N8AOI69/iKnr3JhfLQFYfTlW2/qKcejFNFXM+KRdY2+op00GqcbmXrOKRC2rN7rpJfr42SbE6N0Os659AwaZZmOTH+b0XPOcV7dDQE+B/yM3tuA1B3XucL8fPHJS1ccPkKdqDNixzdApsK5Oa9j6Uw57iqDfZGZ8HTHdS1l9W7xzT8fPZapU0m8QGP/NidpQ9yzUUFPCBShvuIp4+4PfAr3EH5/TWN/wqc8irAM2qSxE71Rvd6kMOCflkpf/YN20mhI2knvZyAz5IkFw49E5q6fB4uRm1B5uRq9y+0TqPMKPedfN4Pl0GaxM0ne780SWu+trMXCpI2svUrxjwcvSW5A5tNdacwR2IzkVSj9NY39CZ/y8KWGPngb/T9rDkaRMBbftFT66h+0k0ZD0k56X4RMdaPRxG3fT09dS9/s1WYJlZdTkVmyC5nXVkNzo9ZCqyavCnAPFx1o3twMh58a4fXeylosTKjlu63Cu8gGPAYtOV+B8BvQVuSnmeXRhSaivoFM5nOaFMZSaas9aSeNhqTd9H6n+f0/cSvweTQPayjS1Tw0oX064ff7jDOX7OkDXbSG3lueAbVabUnHoaKioqKioqKiIoXQ8zMqKioqKioqKioCUnXWKioqKioqKipamP8BidiI0uwHezAAAAAASUVORK5CYII=\n",
      "text/latex": [
       "$\\displaystyle \\frac{\\partial^{2}}{\\partial L^{2}} q{\\left(L,k \\right)} \\leq 0$"
      ],
      "text/plain": [
       "  2             \n",
       " ∂              \n",
       "───(q(L, k)) ≤ 0\n",
       "  2             \n",
       "∂L              "
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# The slope decreases as labor increases, shown by\n",
    "Derivative(Derivative(q,L),L)<=0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "5a737a34",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "khat_ex = 10\n",
    "p1 = plot(diff(sqrt(L*khat_ex),L),ylabel=Derivative(q,L),xlabel='L',label = f'k = {khat_ex}',legend=True,show=False)\n",
    "p1.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "b63868c1",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Marginal product of labor (decreasing) = \n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\frac{\\partial}{\\partial L} q{\\left(L,k \\right)}$"
      ],
      "text/plain": [
       "∂          \n",
       "──(q(L, k))\n",
       "∂L         "
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# This means that when labor increases, it does less good for the production level (Diminishing product of labor)\n",
    "print(\"Marginal product of labor (decreasing) = \")\n",
    "Derivative(q,L)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "27c1439b",
   "metadata": {},
   "outputs": [],
   "source": [
    "# For example, if the number of machines is fixed and all in use, if we keep adding labor, it wont do much to grow production"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0d742c22",
   "metadata": {},
   "source": [
    "###### Total, marginal and average product"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "1bd6a827",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Lets say we only have one unit of capital, and we can choose how much labor to use\n",
    "labor = np.sort(np.arange(0,10,1))\n",
    "capital = np.ones(len(labor),dtype=int)\n",
    "short_term_production = pd.DataFrame(data={'labor':labor,'capital':capital})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "a3478c7f",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
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       "\n",
       "    .dataframe tbody tr th {\n",
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       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>labor</th>\n",
       "      <th>capital</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
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       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
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       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>4</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>5</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>6</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>7</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>8</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>9</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   labor  capital\n",
       "0      0        1\n",
       "1      1        1\n",
       "2      2        1\n",
       "3      3        1\n",
       "4      4        1\n",
       "5      5        1\n",
       "6      6        1\n",
       "7      7        1\n",
       "8      8        1\n",
       "9      9        1"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# We have a table with each combination of labor and capital\n",
    "short_term_production"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "e5dc071d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>labor</th>\n",
       "      <th>capital</th>\n",
       "      <th>total product</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>4</td>\n",
       "      <td>1</td>\n",
       "      <td>6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>5</td>\n",
       "      <td>1</td>\n",
       "      <td>7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>6</td>\n",
       "      <td>1</td>\n",
       "      <td>8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>7</td>\n",
       "      <td>1</td>\n",
       "      <td>9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>8</td>\n",
       "      <td>1</td>\n",
       "      <td>8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>9</td>\n",
       "      <td>1</td>\n",
       "      <td>7</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   labor  capital  total product\n",
       "0      0        1              0\n",
       "1      1        1              1\n",
       "2      2        1              2\n",
       "3      3        1              4\n",
       "4      4        1              6\n",
       "5      5        1              7\n",
       "6      6        1              8\n",
       "7      7        1              9\n",
       "8      8        1              8\n",
       "9      9        1              7"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Lets assume we already know how much product we can get from each combination,and we dont have a production function\n",
    "total_products = [0,1,2,4,6,7,8,9,8,7]\n",
    "short_term_production['total product'] = total_products\n",
    "short_term_production"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "4d976352",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
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       "\n",
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       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>labor</th>\n",
       "      <th>capital</th>\n",
       "      <th>total product</th>\n",
       "      <th>marginal product</th>\n",
       "      <th>average product</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
       "      <td>4</td>\n",
       "      <td>2</td>\n",
       "      <td>1.333333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>4</td>\n",
       "      <td>1</td>\n",
       "      <td>6</td>\n",
       "      <td>2</td>\n",
       "      <td>1.500000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>5</td>\n",
       "      <td>1</td>\n",
       "      <td>7</td>\n",
       "      <td>1</td>\n",
       "      <td>1.400000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>6</td>\n",
       "      <td>1</td>\n",
       "      <td>8</td>\n",
       "      <td>1</td>\n",
       "      <td>1.333333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>7</td>\n",
       "      <td>1</td>\n",
       "      <td>9</td>\n",
       "      <td>1</td>\n",
       "      <td>1.285714</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>8</td>\n",
       "      <td>1</td>\n",
       "      <td>8</td>\n",
       "      <td>-1</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>9</td>\n",
       "      <td>1</td>\n",
       "      <td>7</td>\n",
       "      <td>-1</td>\n",
       "      <td>0.777778</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   labor  capital  total product  marginal product  average product\n",
       "0      0        1              0                 0         0.000000\n",
       "1      1        1              1                 1         1.000000\n",
       "2      2        1              2                 1         1.000000\n",
       "3      3        1              4                 2         1.333333\n",
       "4      4        1              6                 2         1.500000\n",
       "5      5        1              7                 1         1.400000\n",
       "6      6        1              8                 1         1.333333\n",
       "7      7        1              9                 1         1.285714\n",
       "8      8        1              8                -1         1.000000\n",
       "9      9        1              7                -1         0.777778"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Now we can calculate the average product and marginal product\n",
    "average_products = []\n",
    "marginal_products = []\n",
    "for i in short_term_production.index:\n",
    "    if i == 0:\n",
    "        marginal_products.append(0)\n",
    "        average_products.append(0)\n",
    "    else:\n",
    "        marginal_products.append(short_term_production['total product'][i] - short_term_production['total product'][i-1])\n",
    "        average_products.append(short_term_production['total product'][i]/short_term_production['labor'][i])\n",
    "short_term_production['marginal product'] = marginal_products\n",
    "short_term_production['average product'] = average_products\n",
    "short_term_production"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "fb81b643",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x648 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig,ax = plt.subplots(figsize=(12,9))\n",
    "ax.plot(short_term_production['labor'],short_term_production['total product'],label='Total product')\n",
    "ax.plot(short_term_production['labor'],short_term_production['marginal product'],label='Marginal product')\n",
    "ax.plot(short_term_production['labor'],short_term_production['average product'],label='Average product')\n",
    "ax.hlines(0,xmin=0,xmax=10,color='black')\n",
    "plt.xlim(0,10)\n",
    "plt.ylim(-5)\n",
    "plt.xlabel('Labor')\n",
    "plt.ylabel('Total product\\nMarginal product\\nAverage product')\n",
    "plt.legend()\n",
    "plt.grid(True)\n",
    "plt.show()\n",
    "# We can see that the maximum total product occurs when marginal product equals 0\n",
    "# Total product grows when marginal product > 0\n",
    "# Total product decreases when marginal product < 0\n",
    "# Average product grows when marginal product > average product\n",
    "# Average product decreases when marginal product < average product"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1091c242",
   "metadata": {},
   "source": [
    "###### Long run production"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "06538ac6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle q{\\left(L,k \\right)} = \\sqrt{L k}$"
      ],
      "text/plain": [
       "            _____\n",
       "q(L, k) = ╲╱ L⋅k "
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Eq(q,sqrt(L*k))\n",
    "# Where L = labor, 𝑘 = capital and q = quantity produced (production level)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "6be58069",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle k = \\frac{q^{2}{\\left(L,k \\right)}}{L}$"
      ],
      "text/plain": [
       "     2      \n",
       "    q (L, k)\n",
       "k = ────────\n",
       "       L    "
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# We can modify the equation and we get\n",
    "Eq(k,(q**2)/L)\n",
    "# This new equation gives us each combination of capital and labor, for a specific production level\n",
    "# This curves are called isoquants"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "35f298e9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "q_ex = 10 # Example production level\n",
    "p1 = plot((q_ex**2)/L, ylabel='k', xlabel='L',label = f'q = {q_ex}',legend=True,xlim=[0,10],ylim=[0,1000],show=False)\n",
    "q_ex = 20 # Example production level\n",
    "p2 = plot((q_ex**2)/L, ylabel='k', xlabel='L',label = f'q = {q_ex}',legend=True,show=False)\n",
    "q_ex = 30 # Example production level\n",
    "p3 = plot((q_ex**2)/L, ylabel='k', xlabel='L',label = f'q = {q_ex}',legend=True,show=False)\n",
    "q_ex = 40 # Example production level\n",
    "p4 = plot((q_ex**2)/L, ylabel='k', xlabel='L',label = f'q = {q_ex}',legend=True,show=False)\n",
    "p1.append(p2[0])\n",
    "p1.append(p3[0])\n",
    "p1.append(p4[0])\n",
    "p1.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "95441c55",
   "metadata": {},
   "outputs": [],
   "source": [
    "# In this case, we have a Cobb-Douglas production function, where the exponents for each factor are 0.5\n",
    "# Lets see other types of production functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "dd60edbc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle q{\\left(L,k \\right)} = L + k$"
      ],
      "text/plain": [
       "q(L, k) = L + k"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Perfect substitutes\n",
    "Eq(q,L+k)\n",
    "# Where L = labor, 𝑘 = capital and q = quantity produced (production level)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "9d83be12",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle k = - L + q{\\left(L,k \\right)}$"
      ],
      "text/plain": [
       "k = -L + q(L, k)"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# We modify the equation and we get\n",
    "Eq(k,q-L)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "553c73f8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "q_ex = 4 # Example production level\n",
    "p1 = plot(q_ex-L, ylabel='k', xlabel='L',label = f'q = {q_ex}',legend=True,xlim=[0,12],ylim=[0,12],show=False)\n",
    "q_ex = 6 # Example production level\n",
    "p2 = plot(q_ex-L, ylabel='k', xlabel='L',label = f'q = {q_ex}',legend=True,show=False)\n",
    "q_ex = 8 # Example production level\n",
    "p3 = plot(q_ex-L, ylabel='k', xlabel='L',label = f'q = {q_ex}',legend=True,show=False)\n",
    "q_ex = 10 # Example production level\n",
    "p4 = plot(q_ex-L, ylabel='k', xlabel='L',label = f'q = {q_ex}',legend=True,show=False)\n",
    "p1.append(p2[0])\n",
    "p1.append(p3[0])\n",
    "p1.append(p4[0])\n",
    "p1.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "129bbd2d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle q{\\left(L,k \\right)} = \\min\\left(L, k\\right)$"
      ],
      "text/plain": [
       "q(L, k) = Min(L, k)"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Perfect complementaries\n",
    "Eq(q,Min(L,k))\n",
    "# Where L = labor, 𝑘 = capital and q = quantity produced (production level)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "67ecc29b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 720x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "q_ex = 2 # Example production level\n",
    "p1 = plot_implicit(Eq(q_ex,Min(L,k)), ylabel='k', xlabel='L',label = f'q = {q_ex}',legend=True,xlim=[0,10],ylim=[0,10],show=False)\n",
    "q_ex = 4 # Example production level\n",
    "p2 = plot_implicit(Eq(q_ex,Min(L,k)), ylabel='k', xlabel='L',label = f'q = {q_ex}',legend=True,show=False)\n",
    "q_ex = 6 # Example production level\n",
    "p3 = plot_implicit(Eq(q_ex,Min(L,k)), ylabel='k', xlabel='L',label = f'q = {q_ex}',legend=True,show=False)\n",
    "q_ex = 8 # Example production level\n",
    "p4 = plot_implicit(Eq(q_ex,Min(L,k)), ylabel='k', xlabel='L',label = f'q = {q_ex}',legend=True,show=False)\n",
    "p1.append(p2[0])\n",
    "p1.append(p3[0])\n",
    "p1.append(p4[0])\n",
    "p1.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0fb44615",
   "metadata": {},
   "source": [
    "###### Short term costs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "e883d446",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle c = 2 L + 3 k$"
      ],
      "text/plain": [
       "c = 2⋅L + 3⋅k"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Lets say the producer has the following costs function\n",
    "Eq(c,2*L+3*k)\n",
    "# Where L = labor, 𝑘 = capital and c = cost"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "a1616157",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle c = 2 L + 3$"
      ],
      "text/plain": [
       "c = 2⋅L + 3"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Given we are in the short term, we know one factor is fixed\n",
    "# In this case capital is fixed in one unit\n",
    "Eq(c,2*L+3*1)\n",
    "# Our variable cost is 2 times labor used\n",
    "# Our fixed cost is 3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "d5f95802",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "p1 = plot(2*L+3,ylabel='Cost', xlabel='L',label='Total cost',legend=True,xlim=[0,10],ylim=[0,20],show=False)\n",
    "p2 = plot(2*L,ylabel='Cost', xlabel='L',label='Variable cost',legend=True,show=False)\n",
    "p3 = plot(3,ylabel='Cost', xlabel='L',label='Fixed cost',legend=True,show=False)\n",
    "p1.append(p2[0])\n",
    "p1.append(p3[0])\n",
    "p1.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e18ea831",
   "metadata": {},
   "source": [
    "###### Long term costs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "c2466582",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle c = 2 L + 3 k$"
      ],
      "text/plain": [
       "c = 2⋅L + 3⋅k"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Lets continue using the same function, but this time, capital is not fixed\n",
    "Eq(c,2*L+3*k)\n",
    "# Where L = labor, 𝑘 = capital and c = cost\n",
    "# For each cost level, the producer can choose any combination\n",
    "# These combinations are represented by curves called isocosts"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "295638d7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "c_ex = 5 # Example production level\n",
    "p1 = plot_implicit(Eq(c_ex,2*L+3*k), ylabel='k', xlabel='L',label = f'c = {c_ex}',legend=True,xlim=[0,10],ylim=[0,10],show=False)\n",
    "c_ex = 10 # Example production level\n",
    "p2 = plot_implicit(Eq(c_ex,2*L+3*k), ylabel='k', xlabel='L',label = f'c = {c_ex}',legend=True,show=False)\n",
    "c_ex = 15 # Example production level\n",
    "p3 = plot_implicit(Eq(c_ex,2*L+3*k), ylabel='k', xlabel='L',label = f'c = {c_ex}',legend=True,show=False)\n",
    "c_ex = 20 # Example production level\n",
    "p4 = plot_implicit(Eq(c_ex,2*L+3*k), ylabel='k', xlabel='L',label = f'c = {c_ex}',legend=True,show=False)\n",
    "p1.append(p2[0])\n",
    "p1.append(p3[0])\n",
    "p1.append(p4[0])\n",
    "p1.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1233f035",
   "metadata": {},
   "source": [
    "###### Optimum production level"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "bc8355eb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle q{\\left(L,k \\right)} = 2 L^{0.5} k^{0.5}$"
      ],
      "text/plain": [
       "             0.5  0.5\n",
       "q(L, k) = 2⋅L   ⋅k   "
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Lets say we have the following Cobb-Douglas production function\n",
    "q = Function('q')(L,k)\n",
    "Eq(q,2*L**0.5*k**0.5)\n",
    "# Where L = labor, k = capital and q = quantity produced"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "d377c0ec",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle mpl = \\frac{1.0 k^{0.5}}{L^{0.5}}$"
      ],
      "text/plain": [
       "           -0.5  0.5\n",
       "mpl = 1.0⋅L    ⋅k   "
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# With this function, we can calculate the marginal productivity for each of the factors\n",
    "Eq(mpl,diff(2*L**0.5*k**0.5,L))\n",
    "# Marginal productivity of labor"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "f99fbce0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXoAAAAXCAYAAAAFvYSgAAAKZklEQVR4nO2df7QVVRXHP6gFpeYDV6loeuEl/si1UjMLM3iQGUquwCz6udJVllHS02hlmXWfSlqLCKyUIAsktTIgsqRomUioUKZI5kMJeWZPI7J4oGgB0R/fM+tO82bOPWfmzv3xnO9asw5vZu+Zc/Y+Z5+z99nnMqhcLlOgQIECBQYu9ml0BUIoAXuBBY2tRiZMAx4Bnkdt6WxobZLxfmAN0AfsAU5saG3qi4uAMnB2Sv5ml10Z2AX8DfgpMConnjCqyaREbcZ2Ft01u97AXw/O9PvVoHIvFnQD/ya5g7wXmAM8CMw2tGvqUTFPHA/8AHgOuA3oRR0livOAsai9rwMOBG4GPpjyu0cAVwITgIOBp1Hn7AL+5fGevaYclKIOXwM+a/69G5gCLPHgd5Ud1K69PcBRCc+2AIdG7q0EhiC9vRMYDpxa5RtpeAL4yCQLsuiuFfQG/npwpi8MvTuWAp8HRgCbY56/I1Q+Va9KpcA4ZCQvB66z0H0RGfhngb8Cx2b4ZjtwL/AqYBmwAXXIT6MB9WbgmQzvd0EXMhR/BK4C5gO3ApOBOxzf4Sq7Wre3Dy0eong25t5KcwH8ATgFOCCBNgtPAFeZZEFW3bWC3sBfD870haF3R2DoJwOzYp4PN2UzG3mAYabsrkJ3CTLwf0Yr+7syfPN6NHimAd8M3Z9lvjMDueV54XPAl4DVwDnANuBR4JfAYjQ53+nwHlfZ1bq925Cb7osNwMnAUNyMdhoeV5mkRS1012p6A389WOnDMfoSlThaO/ATNHvtAFYAJxi6VwLzkEvzAvB7NGOGEX7Xscj1+SdynVYDZzpUPFzHOeZ9S4CXefDWEvcjw3du5H4Z1S2Qwd7QFaBERR6jgB8Bfwf+C3QYmvNRx30cxfi3A/dgD5Wcat7Vi0JFTyNdvcfCs68pd1loQIZ9Y6QdadCO9N0DfDvy7MuoT3wI2D/jd5IwDbgW+JmpxzZzfz1wGvAkWr2d7vAuF9k1ur1hBPXc10qVjce1P8Wh2tiule5aTW/grwcrfdxmbAlYCxyCDNMK4AzkIhyN4s5vQAbmx8i9Xw4cGfOuEcB9aEb9DoqPvd7QT3Go/BDDMw0J/zxkBBuBvWhVPxrJJsBK5Fo+Yf7uCl1RtCPZllC8ex4y6AA3oJjeKuTu/dD8vQi5q1FciNzMSab8OvALtCKZ6tm2PBFMgCvQxBbGDjSZvRx4Uw7fvhAZkhvRBB3tOz3IHe9GsnONS9uQR3sHown/CyiMMA4/492MqDa26627Aa23uNDNWBSfnRG6dwXaoFiLjPtUKsL4NXATcm0uibxrDDCTyiYKwLeQ8Z+LDP524jEMzeSnAZcBX3VpkEEn0OZBvw55HdWwFLgYbXzMM/dWmqsDGeayhf904Bqk+ChOADZF7r0UyegyJK9ec/945GZuB94C/CnCd4SlDm2mrNeEeYwpH0t4vhGtpEbhFj7xwXxz2bAVLVxc0GZKm+zyaO+haMIPYzNwAXC3he8FUx7k+J00PG2m9OlPLmO7lrprM2Wr6A389WCljzP0PchdCmMhMvSDkdEOz3i3AN8jPhulz/CFcT9azX4YxbsXxvAdhWJw7chdujmu8hZ0krzjHYeFuBn6VSicNZmKoffBFuJX+tDfyAP8B612xgNvRRMqwCeQ7q6iv5EHhZjiMAhNDHupeCB5I+h4fQnPg/tt+VclE1xlV+v2fh/4LdLzDmAk8CngY2gRMBp4KIG3x5QdFposPGn6U9ax7YtW1Bv4685KHxe6WYfyTMMINhgfQ5UOYw8yYHGryAdi6KGyU3xSzLNj0Ip/OHAW6TpCCSnY9Trf8b17gNuR4fVZJQV4CMXS43AkMuobgJ1U4vyLzfPDQ7SB+7jc8bsTUGjnd2jDZh75pMANRDRadl3Ab9AY2wk8jDYEZ6GYdtnCuwgZt5nIE5+BxoYNLjxpZVKLse2KVtYb+OvOSh9n6ONmtN2WZ8Hzl8Tc35JAHwg8zliOAg5Dm5IPJPA3EktQSGViCt6kjjYStfUiQ/Nd4GrUWQKPZ3CIvs2UvbhhAnApSr96mP/PKMgbQZ9JmhiD+9vyr0oq+MquXu2da8oxFppeFCrcBbwbhQxLVd7rwpO2P9VzbLey3sBfd1b6vNMrD0m4HxwWiJs4bkfpU19BsbC34Z9j3Uk+MXrQnsRzKHxzi8c3IDmD5VJ0OOMC+p8efB8Kc4WxzZSHIw+gGjpRito4tMn7K+RCRz23PPCoKZNO7R1tyqTYaKPRiZ/s6tXeraa0ZYFMRIblHuDj5pvVsmNceDpJ159qMbZd4VvHZtIb+OvOSp+3oT8ZnaiMhm86TPlgAt81aOPkGyjMcwbJ3kEcOsknRg/a9FiOVgxDqGyCZMFrTLk45tnYmHtr0ErlLNwMPWjjdpn5xgeA49BKJ28E+fdnIg8yvL9zIMqc2ElzniIO4CO7erU3CN89bqEZb8oy8Xs5WXjS9qesY9sHrao38NedlT7v37o5CM2qYZyChN6HsliSMBttOr4W7VAPt9BGUSKfGH2ApegEms95ABt6TNkRuf924KMx9DegcNkVKAMnClvWTbAhNcxCkwbt6MxENIS3CaWslYBPRp51oZXNIuQlNTtcZJemvUmyO474lV8JZa+BjvYnYagpeyw0WXnS9KfZpB/baZCX3iBed1n1Bv56sNLnvaJfhQzVG5FLcRjKn98HuRdJqZUB5qIV843mXeOBv+RVWQ/8HGXETEZpYllxPQrb3IYOqj2F0i0noI2V6JmDR1CK61zkFS1D6V8Ho3Sz7fQ/xBYgcOeqTfKTzAWVUNtoKqGlfwDTQ/R3Ii9qBP0721SU638dyh7qRn1iHHIxL69SlzgssDybilZftYar7HzbmyS7KcBnUN9/AnnG7chNH4KO/8+01COo524LTVYeV5lEUc+xnZfeIF53WfUWrqurHqz0eRv6zWiD8VpTDkabMFeimJkLFqBMlZuodIhqbk/e2I521M9BByCyxrrXo850NeoM+6EMnXNRPD7ucNl85IZOR57AJGR816PN3CS4nnQ9kf57AyPNBerA03HDJuTJBT8WdTY6xTsH/x+LChCtWxid5GPoXWVXq/behTJVTkKhg/1Rf1iNVpeLHOuU5nSzK0+Wk9MLqM/YblW94UFnpQ8b+h7svwhoe1ayPOtGB4yqwfb9W83VTFiKOsMYpNgOC20P1X9t8V4qcbYoknjvA95V5b1RBOmdQ61UivWVPd5bqvL8SeS1ZEU1OeYJV9mBX3tLCffvpvrBGhuCevrsI/nyuMikh8aO7bz0BvG6y6o38NeDlT7vGP1AxjK0YRP97Ztmx0ZTfgR4NUUf8EGryG4w+kmADuR9brVSp+eB1pBJK9QxgK8enOibucHNji0obHNxoyviiTtQyGciiok263/C0IxoBdmV0apuLfAKdEAn+tstteAJ0AoyaYU6gr8enOmLnyl+8eF5FIccj7IDDqA4JeuKVpDdSrQh9wwK7a3LiSdAK8ikFeoI/npwph9U/J+xBQoUKDCwUYRuChQoUGCAozD0BQoUKDDA8T88/6QVRl7FUwAAAABJRU5ErkJggg==\n",
      "text/latex": [
       "$\\displaystyle mpk = \\frac{1.0 L^{0.5}}{k^{0.5}}$"
      ],
      "text/plain": [
       "           0.5  -0.5\n",
       "mpk = 1.0⋅L   ⋅k    "
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# With this function, we can calculate the marginal productivity for each of the factors\n",
    "Eq(mpk,diff(2*L**0.5*k**0.5,k))\n",
    "# Marginal productivity of capital"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "c812b1be",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle c = 2 L + 3 k$"
      ],
      "text/plain": [
       "c = 2⋅L + 3⋅k"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Lets say we have the following costs function\n",
    "Eq(c,2*L + 3*k)\n",
    "# Where L = labor, k = capital and c = total cost"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "9a6b6b08",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle l{\\left(L,k,λ \\right)} = 2 L + 3 k - λ \\left(2 L^{0.5} k^{0.5} - qp\\right)$"
      ],
      "text/plain": [
       "                           ⎛   0.5  0.5     ⎞\n",
       "l(L, k, λ) = 2⋅L + 3⋅k - λ⋅⎝2⋅L   ⋅k    - qp⎠"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Now we can minimize the cost, given the production function\n",
    "# We get the following function\n",
    "l = Function('l')(L,k,λ)\n",
    "Eq(l,2*L + 3*k-λ*(2*L**0.5*k**0.5-qp))\n",
    "# Where L = labor, k = capital and qp = quantity produced"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "0c10c064",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle - \\frac{1.0 k^{0.5} λ}{L^{0.5}} + 2$"
      ],
      "text/plain": [
       "   -0.5  0.5      \n",
       "- L    ⋅k   ⋅λ + 2"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Now we get the partial derivatives\n",
    "# First we get the derivative for labor\n",
    "diff_1 = diff(2*L + 3*k-λ*(2*L**0.5*k**0.5-qp),L)\n",
    "diff_1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "a13bb902",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle - \\frac{1.0 L^{0.5} λ}{k^{0.5}} + 3$"
      ],
      "text/plain": [
       "   0.5  -0.5      \n",
       "- L   ⋅k    ⋅λ + 3"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Now we get the derivative for capital\n",
    "diff_2 = diff(2*L + 3*k-λ*(2*L**0.5*k**0.5-qp),k)\n",
    "diff_2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "c83afe15",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle - 2 L^{0.5} k^{0.5} + qp$"
      ],
      "text/plain": [
       "     0.5  0.5     \n",
       "- 2⋅L   ⋅k    + qp"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Now we get the derivative for λ\n",
    "diff_3 = diff(2*L + 3*k-λ*(2*L**0.5*k**0.5-qp),λ)\n",
    "diff_3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "de826e77",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\frac{2.0 \\sqrt{L}}{\\sqrt{k}}$"
      ],
      "text/plain": [
       "2.0⋅√L\n",
       "──────\n",
       "  √k  "
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# We solve the first equation to λ\n",
    "sol_1 = solve(diff_1,λ)[0]\n",
    "sol_1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "734961ed",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\frac{3.0 \\sqrt{k}}{\\sqrt{L}}$"
      ],
      "text/plain": [
       "3.0⋅√k\n",
       "──────\n",
       "  √L  "
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# We solve the second equation to λ\n",
    "sol_2 = solve(diff_2,λ)[0]\n",
    "sol_2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "f2b2a340",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle L = 1.5 k$"
      ],
      "text/plain": [
       "L = 1.5⋅k"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Now we can equal these two solutions and solve again for one of the variables, in this case L\n",
    "sol_3 = solve(sol_1 - sol_2,L)[0]\n",
    "Eq(L,sol_3)\n",
    "# This means that one unit of labor equals the solution\n",
    "# This is our expansion path\n",
    "# Now we know that all combination that respect this condition, are optimal"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "id": "eef376d2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle q{\\left(L,k \\right)} = 3.0 k^{1.0}$"
      ],
      "text/plain": [
       "               1.0\n",
       "q(L, k) = 3.0⋅k   "
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Our production function now looks like this\n",
    "Eq(q,2*(1.5*k**0.5)*(k**0.5))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "id": "f51dae68",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAF0AAAATCAYAAADyIwHfAAADe0lEQVR4nO3YW4hWVRQH8N9IUSrhVCRYkjMNjWG9RGVX6ep0EaIgekroIaMUckKGAolGoqKw0soSohiJHkKyzC4qDJXQ5SmFyNKwi6gZFo1GltntYZ2TxzPfGc+Zbz6HifnDsPjO2mftddbs9d//vZu6u7uN4uhizHAn8D9AC/5BT9kXRmrRr8br2I0D2IV1uKFinMl4KXn/AL7FEpw4RHnWxDGNDN4gPI4u7MCb+BGn4DxcgXdKxmnDR5iI1fgS0zEf1+FS/DSEef+HkVb0OaLgK3An/sj5j60Q6zlR8HvwTOb5k7gXD+OuQWc6AGrRy3S8ip2i5b7HetzaiAQq4DhRiO1qFxwOlozVhg5BJ8tyvgfxK2Zj/GASTTAGSwXfr8LYrCOLOaLlbkrsE3hbrIi5dSQwFJgpaGQV/sYs3Cfo4OKKsa5M7PokVha/4EOMw0WDzPV4rBRdtAy34LfUmaWXaaLl9mEGPs8Fmlxywk40V0hwE94oMe6CxP6OjTgn598gPm5PiVhTE7u1wP+V6IR29JaIl8VJYq+5BPfjsfyAbNHvTn4/pH/BiY2rDDoxpUKSK5Qr+sTEdmGzWBib0IrFokgrxWZ6JExI7N4Cf/q8uUSsLKZgraCv2Xil1qBs0dNWerfiRHm01Pl+EVIq/BM3Cj6Gz3AztuByQTUfNyiHgTA1mXc8rjdAh2Q5vTmxOxuWVn3oS+xGhwqeYr/Q6YQQOBLSlTyhwJ8+7yvw10I7JuFrfDrQwOxKTyc4TWjWwaJTYzh9S2L7Cvw/J3Zsgb9WrPYC/5mJLeL8WliTxH1ErPKZCnR+tuif4HzRGvUWvRGc3ivk1zTRoXnVkW6s35SI9V5iO2rEOkEcjPaLmlTBo0KlPIX3cQ1+yA/K0svzgi8fEB+WR1n10oKmCn+3l4z7nVhNpwuZmEUHrhVdsDbna8NZDj84bRNysQXzcuMXCV5+Wej1qlgiRMnZ+ACn5gdkV/pmocWXC95cLaTTyUKu7XNI3w4X5uFccWqcJfJsFeeKv3CH/oqkV3Req8P3grniLPK0uMv5AheKb9yKhXXkuVxI2xeFlL1KHOrQ/3D0Ai7DW0J6dQmlsEf/k9twYIe4Y3lW8O58kecaQQmvVYi1TdBpjyj2AtEVS4WSq/fepQe3iX/4BpyROppG79OPPkbq1e6IxmjRhwH/Aib7tUlPdk+9AAAAAElFTkSuQmCC\n",
      "text/latex": [
       "$\\displaystyle c = 6.0 k$"
      ],
      "text/plain": [
       "c = 6.0⋅k"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Our costs function now looks like this\n",
    "Eq(c,2*1.5*k + 3*k)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "id": "6e3d1944",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAMYAAAASCAYAAAAANKFkAAAC7ElEQVR4nO3aTagURxQF4M+gGBdCXCgK8Q8RjCZxIQlE/EOJggFRUHFhwE3choDuJHmuAlkJrhRdCLoSERTUBETwiQE3TwwIgugTfwhEUETUhBizqB4d+3UPb2reNCXWgabornPqngtzmbpdPW5gYEBGRsbb+KB0vxn7MYgneIWjPcZYg5P4E3/jAX7F+jHiN6VJ1VfOZXT8HcLvudP1skUeXxLvwWI8xT0s6JDAaPALdhdrncJDTMUSrMKZHvlNaVL1lXMZPf8q9lbEhOVYjbOtB+XC+KEIchMrcaFmodHgu8L0EezEP6X5CT3ym9Kk6itGk6qvGE23/KvFVYXfi/Fg68G4Dj3GKqEwjmF7HakGE3EXzzHfSNO98pvSpOorRpOqrxhNTIw6fIZruI/Ziu1U+R9jrPC18Je2D//hG3yKF7jiTYXG8pvSpOor59J9jDrsLMbDOvQYY4UvivEFhgTT7bgoNPp/RfKb0qTqK+fSfYwqTBJ2Qy9xqH2i/FZqrDCtGHcL3f5yTMbn+A0rcLwHflOaVH3lXLqPUYWt+AjnhK3Za/SrMFrr/osNuCS86foDm4QGfyW+iuQ3pUnVV86l+xhVaG2jDpQn+lUYj4txCMOluWfCe2b4MpLflCZVXzGaVH3FaGJilLEIS4UiGvHquF+FcaMYH9fMPyrGSZH8pjSp+orRpOorRhMTo4zKpruFfhXGeWHvt7AmRqtZuh3Jb0qTqq8YTaq+YjQxMdrxIb4VCuJwFaHXwpgnnI6XD1Pu4DRm4fvS3FqsE6r9XCS/KU2qvnIu3cdoxxZMEU6671YRygd8G4sLphcBbgnfThGO3He18YeFQ5G5Ru71PsZlzBQqfKjgbRSqfRtO9MBvSpOqr5xL9zFaGMQyoXE/XUUoF8YAfqpZjFCpc9ruh9UXBuEQ5sfCwAzhw8RB/CwcxPTKb0qTqq+cS/cxPsF1oemeo6K/oPMnIRkZ7y361XxnZLzTyIWRkVGB/wGIbireYRSZagAAAABJRU5ErkJggg==\n",
      "text/latex": [
       "$\\displaystyle 1.66666666666667$"
      ],
      "text/plain": [
       "1.66666666666667"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Example\n",
    "# Lets say we want our costs to equal 10, we can use this to know how much capital and labor is needed\n",
    "c_ex = 10\n",
    "k_ex = solve(2*1.5*k + 3*k - c_ex,k)[0]\n",
    "k_ex\n",
    "# This is the capital needed"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "id": "1df893dd",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle 2.5$"
      ],
      "text/plain": [
       "2.50000000000000"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Now with our expansion path we can get the labor needed\n",
    "L_ex = 1.5 * k_ex\n",
    "L_ex"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "id": "ced9baa1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle 4.08248290463863$"
      ],
      "text/plain": [
       "4.08248290463863"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# This allows us to know how much we can produce with this combination\n",
    "q_ex = 2*L_ex**0.5*k_ex**0.5\n",
    "q_ex\n",
    "# Now we can plot this problem"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "id": "5dd9f15a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 720x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "p1 = plot(L/1.5,label = 'Expansion path',ylabel='k',legend=True,xlim=[0,10],ylim=[0,10],show=False)\n",
    "p2 = plot_implicit(Eq(c_ex,2*L + 3*k),label = f'c = {c_ex}',legend=True,show=False)\n",
    "p3 = plot_implicit(Eq(q_ex,2*(L**0.5)*(k**0.5)),label = f'q = {q_ex}',legend=True,show=False)\n",
    "p1.append(p2[0])\n",
    "p1.append(p3[0])\n",
    "p1.show()\n",
    "# As we can see, there is tangency between our isocuant and our isocost exactly where the expansion path curve is"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "id": "e4c45587",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\frac{pk}{pl} = \\frac{mpk}{mpl}$"
      ],
      "text/plain": [
       "pk   mpk\n",
       "── = ───\n",
       "pl   mpl"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# In this point there is another condition met, which is\n",
    "Eq(pk/pl,mpk/mpl)\n",
    "# pk = 3 and pl = 2\n",
    "# We can check this"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "id": "73e0d9ff",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\frac{1.0 L^{1.0}}{k^{1.0}}$"
      ],
      "text/plain": [
       "     1.0  -1.0\n",
       "1.0⋅L   ⋅k    "
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "diff(2*(L**0.5)*(k**0.5),k)/diff(2*(L**0.5)*(k**0.5),L)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "id": "8122f7f7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle 1.5$"
      ],
      "text/plain": [
       "1.50000000000000"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# If we change k and L for the values we got\n",
    "L_ex/k_ex"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "id": "aa70209b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle 1.5$"
      ],
      "text/plain": [
       "1.5"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# And if we do the same for our relative prices\n",
    "3/2\n",
    "# This is another way of knowing if we solved the problem correctly\n",
    "# We could try with using another cost level or production level as example and we would get the same result\n",
    "# This result would have different isocosts and isoquants"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
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  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
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   "file_extension": ".py",
   "mimetype": "text/x-python",
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   "pygments_lexer": "ipython3",
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