Perfect_Competition.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "1593581e",
   "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": "d9ea6486",
   "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": "658978b1",
   "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": "54ec97c6",
   "metadata": {},
   "outputs": [],
   "source": [
    "a,b,c,d,tax,qd,qs,p,x,y,q = symbols('a b c d tax q_d q_s p x y q')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "20102a6c",
   "metadata": {},
   "source": [
    "###### Demand function (linear)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "ac121f11",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle q_{d}{\\left(p \\right)} = a - b p$"
      ],
      "text/plain": [
       "q_d(p) = a - b⋅p"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "demand = Function('q_d')(p)\n",
    "Eq(demand,a - b*p)\n",
    "# Where qd = quantity demanded, a = demand parameter, b = demand parameter, p = price"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9bba8fb9",
   "metadata": {},
   "source": [
    "###### Inverse demand function (linear)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "e8f4fec7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAioAAAAYCAYAAADUHdY8AAAM+ElEQVR4nO2dfawdRRmHn/JRiqC9pQT50HJQKR8hKoiASsulfIggChhBEaSAX1WBGwNRaJAjCPqHsYBFEBJTBAxia62iBVE5VBDQCgWUIiAcxFIpQmnFUCnl+sdvNme7nd2dmd29d+3ZJzmZdndn5t33fWd29p2ZvWPa7TYNDQ0NDQ0NDXVkk5LLOxG4B1gFrAPe6ZG3BQwDc0qS5UzgYeBlU+6QR95rgRXAViXJEkIRXQJ0zS9OG1gL/BP4KTA5XLxgWpRn5zLLAniXKe9TGde0GX0dlkGR9jFSFG0DNtoUt1+eXC3C/LIM2aqkX32mCHXpx0PyJMm6lxYV+vxmnoVmsSdwPfAf4MfAMlN5xFLgv4yM43wMuAy4H7jU1HsPUuaTaCAyPSXvu4GTgbPRvYwGeboMpQOMQzb4MLAjsJ9nGSNpx7JpkW3/P6HGchFwI/CS5ZoOxXVYJS72SWsfdaKubaAqucqQLZTGZ/6/5Ong7ycheeKM6r2UOVA5GBgDzAQut5yfD5wL7IIeFlXywVj6TOx4yyHvxcBq4MqSZfIhT5ehdMwP9FDeF9ga+wM5jaJ2XAbsgUbldeQbwL3o7fESy/kOxXVYJS72SWsfdaKubaAqucqQLZTGZ6qhTj4ckifOqN5LmVM/25h0acr5+SY9tsQ609jRpL4NajJwKHATCm+OFnm6LINHkONN8MxX1I5rTd3LA/NXzR+QfJ8lv32E6rBKXOwT2j5Gkrq2gZGQC0bWtxqfqYa6+nBd/T5VrnhH3KI3x7Q7CoG/gEI9dwKH51SyqUnXppxfDPwDOM5J5PXZH5iLQk2vAE8D36PXeCLa6B4ONv8fjv3a9N4WTkmcm26On4YU9aMUOcYAXwT+AqxB0YHZwHjsc4mh5OnSRZ48orI3zbxqQ/Ls2KLnR5ORLlcArwGDZM9ljgHOQvPgvvptoemaf5m8i+m9BYKb/SNuBCYBh2XUB+E6rJIs+7RJbx+QbzuQruYBT6DB/GrgLuCkDJn2M2UtQ1MGy4FfAcdn5HFtAyHyRITYz1WuiJC+NFS2UPrNZ/q9H6/a70v3edvUzy7A3cBDaDCwA3ACsBAtpkl7iOcxjEbuXwDeCDzrmO804GrkrD9Dg5Rd0YLHo4EDgL+bazsmnQ7sDHwtVk4HGEAPwgeQIiOWmPRQtEgobe71UjQlsNzItBbNq+0PjEWDqJFkNORxteNb0RTKo8ANwJaog8riCmAGemu7Gsn/IdRpbU56I9kZRUKeAK5Do/8TgAXIprfjZv+Iu0x6GHBrjsx1I8s+HZNOZ8P2ESfLdleiDnUR8ruJwJFI77sB5yfK+rTJsw6138eA7VCI9/MoelkEX3lGkqr60rLpN5+5lKYfr4pKfN42UJkKfAs4J3Zstqn8KlOh7YEzYNKsKZP5wBnICFc7yDfZ1NkFDkIjzYhD0Aj7Mnohy475DaJG1U6U10UPqiWWc1uhBT1LsS+ifS9ypr+hB+cL5vhM9CDcAXjK4Z5cGDBpli6LyrPGpC6j9iQudjwQrfc4L3G8lXL9FDRIeRQ10BfN8fOAX6PoWdr9DCJ7xjvRHwK3ID+OBipd0u0f548mnZpxDRTTIWjXxIDH9UtYf4CVRpp9OmS3j4g02wHshXwuzljUL3wFtdeone4JfBf1F1PQwyrOmzLuYcCkeVOwPvIkCbGfq1wQ3peGylaEfvGZph+v1u8r8XnbHPwq4MLEscVolDyAfR5zDHKqYbKVugh4PqUMGzPQm/RZbNjZ/AaNto8GXu9YXhY7oZBT2tqJU016MT1nAin33BLqj3DVZVF5uiYd9BMPcLPjs6S/fdk4xaQX0xukgN4m8u7nKeDriWO3okhbyK6JVUiPk3Ku65p0MKAO0EDlAo/fMY7l+razJFm2Sz5wQDa6Ar34HBI7PsMcu4gNHzig6QYbrm3AV54kXZMO5tQRIheE9aWhshWlX3ym6cer9ftKfN4WUbkP+LfleAc9TPZG2zsBjkDh8anAPijUk7VlaR3wcxQCGk/+zo/3mPQgtG04yXZocDEZrRguwkSTrkw5v49J77CcuxPdWxF8dVlUnuuAz6HR7/tQePUa3OZnXez4AJquc2Vvk95pOXcP8GpG3iXY7/dpej7kywsoDJ5FER2C2y60EHzbWZIs200CvoweLpNQiD/OTrF/H2DShY71+rYBX3mSuNovRC7w60tDZbPRthybk5O3X3ym6cer9ftKfN42UElbcxAJGA/LHIGiHQB/Br6TkjfOT9B851EoPJ9FNHg4J/MqbWcqShTSGpdyPrpvm35eRYs4i+Cry6LyLEOh2lnAR82x23B/yObZ0XePfdb9rENve2m8mHL8VcJ3tm1JfpizqA6rxKedJUmz3VvQWqAJwO/Q1OsqZJ8W6oi2iF0/YNK0qZckvm3AV54krvYL6efAry8Nlc3GBZZjHYe8/eAzTT9erd9X4vO2TjztLXJ7k8ZH2kOm4mOAt6Fwe95K4tvQGhCXEGNU13gUfkr72Uajvqww6cSU85EsNv1sBmxbsP4h/HRZVJ6j0JzhfWgOeSy9hXMu5NlxOOV4GtG8pe1+NiXdLlWwCeowV+RcV1SHQ+jt1/V3jEfZPu0sSZrtvoTscDoKz56JFkK2sS86ftGkWVGNOEP4tQFfeZK42s9XrgifvjRUNhu2PtIlbz/4TNOPV+v3lfi8baCyD/Y1H4MmvT9xfDXaXTEPOdceGYKA5t4WotFaWvQiItp9MyXnOleiMJpN2cuB59AqdBv3mfQgy7kDU8r0xUeXReWZZtI2mgt23W4Z4WNHFyK/OtBy7gDK+Thhlv3j7IY69yU51xXV4RDVrFGB8u0D6qxA/pnE5odR+/2ARx0+bcBXniQ+9vPt58C/Lw2VrSz6wWeafrxav6/E520DlfHAVxPH9gU+gUZD81MqiRbZbJNyPs58NF2Tt7d6NhJ2Fva/ATAWv0HMSjTyty2SHEYLyral17jizDHpTNa/x3EoXFUmLrosKs8Ek3Z9BEvgakcXfmDSmawfHhyL/QuxIWTZP040T357znVFddgiO1KY/E33LL9M+0D6Yrf3Y//7SFei8PX5aDdHkqwdHC5twFeeJCH28+nnQvvSUNnKYGP3mTkm7ed+vEq/r8TnbW+pi5AD7Y++JxHtg94Efa0zbWtRNPpxWRNwM1r1fSzauZPGI+g7Kt9HI6xb0PbVzdHDZgqKguzuUCfos7z3mnw3mLKivfoPolHjR1AjejyR9y40R3cGmq+bS2+/+0rK/dKqiy6LyhOVnbVINQ9XO7pwB9oW+Rlk63nofo5GDv4M+ohUEfLsH3G4Ob4gp7wydFglZdoHtG30VPS3PuYim+yF3sBvQv1EnIfRdy+uQm9SC9ACuYlocfxqeh8SS+LSBnzlSRJiP59+LrQvDZWtDDZ2n2n68Wr9vhKft1X6JNrbvRKtwD0ehaeOJPtjLT5rElYDv0UPobzQ1vXor9reALwdfcHvJBT1mIuc2oeTgV+ghnIB2gYXrbyeh9YlfDIl71nIoVYhpX8czdsdSrkf5XHVZRny+K4lieNjRxdmoDntl5DvnYi+oXIY8AbyPxjnQpb9oTcnezPaNeRCER1WSdn2eRA9JH6P5pNnILschx4sNq5BIeyb0Vv1Oegjfs+h7alpuOg0RJ7QukKuDe1LQ+srg43dZ6Dpx0PyuF5bic+nzfsvRSM6H6KtaRMyr+oxHz0spqIQexeFt208hF/YezDj3OOoEdp4BX0l8BK0jSo5nzaMpqNme8gSgqsus+Rp5eSNyl6TeVU+PnYk5/xraJpvVuL4rigcnfw7E3l1DVqOZdkfNEgdh7bI5VGWDqskaR9Ibx9dsvUJeuBMSzmXlvduFKn0wbUNhMgTEWI/F7m6ibp9+9J4+aPhWxu7z/R7P16F33ep0OdDt27aeMykpwNvdih7AXowHVeiDGUwC30o7MJRlMFXlz5sgT6CNojenp4rWF6ZdtyeDe/1dWjwCNnzm2WwJfrI0jzs33OJKFuHVVLXdpZHXdtAlXJBPXyr8ZlyqJsP19Xvc+Uqs7Jfojm2o9CDfh36JH0az6LQ4hklylAGa9D0wGL0Wf3RwFeXrrTR/d2Lwq/fpvi6jzLtOIRCh9cC30QLzf6KwoYL0Tx3lbTQOpmzM65pU74Oq6Su7SyPuraBquQqQ7ayaHym3vK08feTkDxxRvVeytjyGfEyWt07DW1h2hr/j37VhUXmF8oAeui6MIcNVzlXpcsOWqj0PAqtLimhzDK5DXgHWsy6DZL1UeByFFWper5+Kdl/Awjqr8ONhbq2gSr7uaKy9Ttl22aAjacfD8kTZ1TvZUy73S6hroYELRQZcOFg/D4S1tDQ0NBQPS2afrwWlBlRaejRJX+BWUNDQ0NDfenS9OO1YLQXGzU0NDQ0NDQ0pNIMVBoaGhoaGhpqy/8AwS7gALD2XSoAAAAASUVORK5CYII=\n",
      "text/latex": [
       "$\\displaystyle p{\\left(q_{d} \\right)} = \\frac{a}{b} - \\frac{q_{d}}{b}$"
      ],
      "text/plain": [
       "         a   q_d\n",
       "p(q_d) = ─ - ───\n",
       "         b    b "
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "inverse_demand = Function('p')(qd)\n",
    "Eq(inverse_demand,a/b - qd/b)\n",
    "# Where qd = quantity demanded, a = demand parameter, b = demand parameter, p = price"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f951c041",
   "metadata": {},
   "source": [
    "###### Supply function with tax (linear)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "7fe707c3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle q_{s}{\\left(p \\right)} = c + d \\left(p - tax\\right)$"
      ],
      "text/plain": [
       "qₛ(p) = c + d⋅(p - tax)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "supply_w_tax = Function('q_s')(p)\n",
    "Eq(supply_w_tax,c + d*(p-tax))\n",
    "# Where qs = quantity supplied, c = supply parameter, d = supply parameter, p = price, tax = tax"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d40d598f",
   "metadata": {},
   "source": [
    "###### Inverse supply function with tax (linear)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "a009602e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle p{\\left(q_{s} \\right)} = - \\frac{c}{d} + tax + \\frac{q_{s}}{d}$"
      ],
      "text/plain": [
       "          c         qₛ\n",
       "p(qₛ) = - ─ + tax + ──\n",
       "          d         d "
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "inverse_supply_w_tax = Function('p')(qs)\n",
    "Eq(inverse_supply_w_tax,qs/d -c/d + tax)\n",
    "# Where qs = quantity supplied, c = supply parameter, d = supply parameter, p = price, tax = tax"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "84051bc0",
   "metadata": {},
   "source": [
    "###### Supply function without tax (linear)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "674a7185",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle q_{s}{\\left(p \\right)} = c + d p$"
      ],
      "text/plain": [
       "qₛ(p) = c + d⋅p"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "supply_wo_tax = Function('q_s')(p)\n",
    "Eq(supply_wo_tax,c + d*p)\n",
    "# Where qs = quantity supplied, c = supply parameter, d = supply parameter, p = price"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "22e2987e",
   "metadata": {},
   "source": [
    "###### Inverse supply function without tax (linear)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "b1cdcd5e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle p{\\left(q_{s} \\right)} = - \\frac{c}{d} + \\frac{q_{s}}{d}$"
      ],
      "text/plain": [
       "          c   qₛ\n",
       "p(qₛ) = - ─ + ──\n",
       "          d   d "
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "inverse_supply_wo_tax = Function('p')(qs)\n",
    "Eq(inverse_supply_wo_tax,qs/d - c/d)\n",
    "# Where qs = quantity supplied, c = supply parameter, d = supply parameter, p = price"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2312c4ab",
   "metadata": {},
   "source": [
    "### Competitive market without tax"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "58b39aef",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Lets assume the following parametres\n",
    "ex_a_1 = 5\n",
    "ex_b_1 = 0.2\n",
    "ex_c_1 = 2\n",
    "ex_d_1 = 0.3\n",
    "ex_tax_1 = 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "ddfa2d9a",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle q_{d}{\\left(p \\right)} = 5 - 0.2 p$"
      ],
      "text/plain": [
       "q_d(p) = 5 - 0.2⋅p"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Our inverse demand function looks like this\n",
    "demand = Function('q_d')(p)\n",
    "Eq(demand,ex_a_1 - ex_b_1*p)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "0d786533",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle q_{s}{\\left(p \\right)} = 0.3 p + 2$"
      ],
      "text/plain": [
       "qₛ(p) = 0.3⋅p + 2"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Our supply function looks like this\n",
    "supply_w_tax = Function('q_s')(p)\n",
    "Eq(supply_w_tax,ex_c_1 + ex_d_1*(p-ex_tax_1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "8477cc3f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle q_{s} = q_{d}$"
      ],
      "text/plain": [
       "qₛ = q_d"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# As tax = 0, in equilibrium this condition is met\n",
    "Eq(qs,qd)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "a397beaa",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle 5 - 0.2 p = 0.3 p + 2$"
      ],
      "text/plain": [
       "5 - 0.2⋅p = 0.3⋅p + 2"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# To find the equilibrium price we just have to solve the following equation\n",
    "Eq(ex_a_1 - ex_b_1*p,ex_c_1 + ex_d_1*(p-ex_tax_1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "5a1cee77",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle 6.0$"
      ],
      "text/plain": [
       "6.00000000000000"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eq_price_1 = solve(Eq(ex_a_1 - ex_b_1*p,ex_c_1 + ex_d_1*(p-ex_tax_1)),p)[0]\n",
    "eq_price_1\n",
    "# This is our equilibrium price"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "28062a3e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle 3.8$"
      ],
      "text/plain": [
       "3.80000000000000"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Now we just introduce this value in any of the supply or demand functions to get the equilibrium quantity\n",
    "eq_quantity_1 = ex_c_1 + ex_d_1*(eq_price_1-ex_tax_1)\n",
    "eq_quantity_1\n",
    "# This is our equilibrium quantity"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "5f3d6e7b",
   "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": [
    "# We can see the graphic solution\n",
    "p1 = plot_implicit(Eq(p,ex_a_1/ex_b_1-q/ex_b_1),(q, 0, 10),(p, 0, 10),label = 'Demand',legend=True,show=False)\n",
    "p2 = plot_implicit(Eq(p,q/ex_d_1 -ex_c_1/ex_d_1 + ex_tax_1),(q, 0, 30),(p, 0, 10),label = 'Supply',legend=True,show=False)\n",
    "p1.append(p2[0])\n",
    "p1.show()\n",
    "# Remember we are plotting the inverse functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "957ab73d",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Consumer surplus: 36.1000000000000\n",
      "Producer surplus: 24.0666666666667\n"
     ]
    }
   ],
   "source": [
    "# Now we can calculate consumer and producer surplus\n",
    "producer_surplus_1 = ((eq_price_1 - (-ex_c_1/ex_d_1 + ex_tax_1)) * eq_quantity_1) / 2\n",
    "consumer_surplus_1 = ((ex_a_1/ex_b_1 - eq_price_1) * eq_quantity_1) / 2\n",
    "print(f'Consumer surplus: {consumer_surplus_1}\\nProducer surplus: {producer_surplus_1}')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dfc10563",
   "metadata": {},
   "source": [
    "### Competitve market with tax"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "f615ba73",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Note: the tax we are assumming will be placed on producers"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "93732501",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Lets keep using the same parametres, but this time with a tax value different than 0\n",
    "ex_a_2 = 5\n",
    "ex_b_2 = 0.2\n",
    "ex_c_2 = 2\n",
    "ex_d_2 = 0.3\n",
    "ex_tax_2 = 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "8414e4a4",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAUcAAAAYCAYAAABp5j/9AAALWElEQVR4nO2df5BVZRnHP8svJXUgcBTL5BKxQDWTlCkmPxZEpAiNnIayEMTGIBV2xnEKmPJqgf5Rs2CYSI0tYY2VtEmGmJkLQVIhrmlAq+Q1fgkmsPxIFHD74/ueuWfPnh/vOffcu7vT+czceZdzz4/nvud5n/d5nvc5h6p8Pk9GRkZGRlu6ddB1rwc2Ay3AaeDimMcXzMdLHjgJvA78BqiuoFw5oBWoj3nNIOYC24C3zHlrYx6/EjgAnJWSPGmRI71+SvNcAJ8w5/tqyD55StOxjC5CRxjHDwMPAx8BVgOLkaKlQSPwfaAJuNZcJy25tpvzVoIvAkuBE8AS4C5ktHPYGYNPAtOBe4HjKctWyX5Imxzh/fccMnjfAc4O2KeR5DpWSQrot/p90hpvNlwIPATsBd42ci0B3mt5fH80WTUAryBnoQXYCNxEGW1Yj3KdOIRxQBWwELgv5XM3mg9I0S9BSn4sBbkagPnAIODVEuWM4rOudq9re87y+EXAEeCBFGVyKLUf9gDDkYJ3Ru4B/oI898U+3zeSXMcqTQsyRF4qJetg4M/AecBjwA7gUmAeMAm4Angz4hxfQHq8D3gG+DdwPvB54MfAp80+rWkL3xGeYz/Tbi/zdXYgY2c7Q0XJ1WDaqaUIZcn7TLs3dC9/qoEJwC/RLJs2pfbDSXRv9qUjTur8Fcn3NaLHR1wdqzSHURrA+/leha7/Q2QY5wKfA74JjAfqgKFoEo+iGbgGeaBfRhPzLGAYsAu4DhnK1PHe/CrgVuAfKKTbAywD+hCc54tLd9OejNgvTBYbnPN3D93LXq4twG6S3YjLgEdROPMOuqkPUjSCDnk0A44z/3aHQnmKntoMz3czXeeYhfruF55z5yiGlMNQ+HgQhd0bgYmWvyWqH9zXqTZyHADeBWoID22rkFexjfj6lwMeAf5jjt1C0QMH+/7DnOci4KqQ60F8Hft/YjDSqQJwv+e7O5HeTSc6J/5H4LdIf9y8Diw3f9dYypQjxhjwhtVLkJXfB6xAN/9aNLh7oYFdKTqTLKBObQBuQW79fsvjZiH53wbWIMM4BOVRpgAjUagAxXBtJjAQ5RpxfdcXGY8X0I11aHL9PQEtJm0OkGcQ8CzwIjLQFwDTgCfQgpTXqHqx7YfBKDxtBn4G9Eahfhj3A3OQx7wC3eNrUCjWk+CJayDy+P4FrEJRwDQUyk1A4Vgjdv0HsMm0VwFPRsjcmTkD+Aoy9MeBvwMbkH6UG2eC/z3tDdtR1McTkf4/nfAajj6cinmc1RhwG8dPIWO0EynjQbN9IVKuC4DXYovfnr6mDQv50pDlhGltPU0buRqA25CRXmFxzmo0uxWAscgTcrgSKc5SiiFqo/nUoAGf95yvgAZ3k893oFn4YpQaCFqIGYPCqjtc25YhZVmOFCTKiNn0wyiUv1vg2Z4L2H80MozNaAI8bLYvAP6AvOyge16D+sM9mfwcWId+p2McC4T3n8PfTDsmZB+Ir2NeainqnQ1NtDXqUQxAk4WbV4EbgfUxzpOEoaZtDvj+ZWQcq0lmHHsAN5i/18U81moMuI3jjaZdRNEYgRRgPlKwUqlCg6CVcOOWhiwF09YgTyENuTagBPJU7IzjHOTxzKOtYQQpxBrkPZ6DZtNSeT8K8cLyeS3A3Z5tW5B3NwP9tpUR17Hph/20NVZRzDDtIoqGEeQ9zkdhTxCvAd/1bHsSeeSXxpDBoQXp2kUR+xVMW0O0jvlRiyZBW1Zibxx/AvwJpaWOAh9Eaaqb0eC/nGQy2+JMGEELb872vgnPfy/wUWAt8b17qzHgNo4fN63fjLKR0lzxSShEGWOu8yDh5QRpyLIKmI1miCvQTPUj2uat4sp1GuU/rkc3P2rF9XLTjkXlNV7OQ8asGq18lkp/0x4K2Wcr/oa4ESnGCKKNo00/vIBSCbaMMK2fEdxMeOjUhL9O7KJ4D+JyEKUNwrDRsTByCWWzwTsxvYRkPQbcjjxnm0W1vM+2etJZf0jKXPQbdqC8ZVysxoDbODqW3i+HdAolupMyCXlPoJv0g4j905BlDwrr6tBSP8BTtDeOceQC+DXKCU5GoVsYjrG6I3Sv4Jq6uDgpgTND9gnKETqTgm2IGNUPcWvpwu75acJLPg4HbD9F8oqM3kSv9tvoWGdjOTIsUSkDhzt9tjUS/RudCTNIn5zthy3lcLgVpaK2odTUwfDdfbEaA27j6PyY81Fi200P4Fy0SpmEWuDbKEn7CHKDBxLsAaYhy2SkCJtQWUYz7RP6ceUCKf9xNOtGGUe3gkTl8dLggGn7h+wT5A0NMK1t/WFUP8StO3P6x++ed0e/yZuaKBfdULgXVcdpo2Nh1FLenKMfb5jW9smpqoTX+adpg54gGmLaoJykH7VoInoJGcYDoXsHYzUG3MZxKwotx9JeOUdRernCEbR6uBrVKw1HP9KPNGQZb9o8yrukIRcoF/UE8jrPpJiU92MzeiRtNPA7C5mjcIx20O/fh5R/aMD3oH71y3HWmPZ5S1ni9IMNz6NwZhTt7/lI0nlgIar/HIYio9AUsZ+tjgVRS/lyjkGMNK23j9PGWReYiCYb94r1OSgN8V+Cqyq8fAPlGZtQKqyUSNZqDLhDjnrTLqRYEA1S/HtKEMSLs+DRL2SfNGRxCnMLKcrl0IBC4ajawGXIk6jDfwbthQynLYeQRxa0UNCKFkvOBT4UsE8f5C27uQRNDC0Ui7xtsO0HG35q2oW0DcV64f+kShKi+s/BMSBRC39xdcxLDhlh289My/MOx98zzCGdhPI/9rgTVWPkUNmXm7uQfKtoX1UxGNUg9nRt+xYyjM8hj7EUwwiWY8A9G29CObfbkOf0KMXawkOk90SDE3aE5YLSkMU5v20NlI1cDo+jVdSpaMU5iB2ozvEh5FmsQ2FETzRARyNPb5iljMdQ7eBotLLWjLyhNaiGDeQBXwdcjZ5F9bIB1VhehvrZqfHqhkLDOOG/bT/YsB6tfN+M+mo1uidTkMLupX29XFxs+g9k7E+jiCKMuDpWKaahvOIGNOkfRUZnMnIw1lKZp2S+jh4fvA8Zte1I78ahvl/oc8zTyJsehCadGWhl+TRafZ/rc0yBeC8fsRoD3lBlnhH6FrPTm8iKLiC9ZX/bXFRastheL06O7Aiq3J+CQrSwHOXDSN7bkVJMRLPlXmT0o4quvUxHnugk4EvIo9hNW+N4ANWAeZ9MAOXRZqOZeDYqFN6KFDBuSUScfrBhDsVH92bT9p7vRt5IqUT1Xx/0qNvjaLXbhtSf6y2RZ1BqYAQKX89CCx8bkbe2isrIvBN5ZHej/v4McmyWIu8xrKrCYZBpuxP8Zqr1xDOOVmPAaxxbkdu9jPLhlHdEPY8aJkvO4jrO+W1zYbZyOTSgGz4GKWOB4OT1i9iHRBD+ONQryBgF8Q56umgxGhx+OcTtyAtPgzj9QMT37yLDVefZPgSF797n3qOuVeOzLar/bkDelY1nFVfHKsV6yl/kbcsuinXLNuQ8/84TXrCflMgx0BEvnnjZtDcBHyiDDGegwt8a5Nm8Ebp3crkeQ4O5LA+9l0gdKoD2FrqWgzT7YQDt+/09FN8sEycfmoTeqOB8NeFF50l1LKML0RGvLFuL8oiTKT5TPIJ03hGYp21dVh77PFVcufbTeV84cAKFj+NQSJX2Ox3dpNkPtSjUbUTh1wCUq7oQrYz/KqXrBJFDec/6kH3yJNexjC5EEuPYF/u3UtfTfiXvLZSHGI9W1c4m3ZfdnkK5qmeJZ3DLKVdHsMF8uhJPAR9Dedl+6F42o4T+EsqfJ9tOdAjXSHIdy+hCVCX4P2Ry2L/kdBzFN81kZGRkdBmSeI4FklfNZ2RkZHQJOmJBJiMjI6PTkxnHjIyMDB/+B2E+Uz9H9kqVAAAAAElFTkSuQmCC\n",
      "text/latex": [
       "$\\displaystyle q_{d}{\\left(p \\right)} = 5 - 0.2 p$"
      ],
      "text/plain": [
       "q_d(p) = 5 - 0.2⋅p"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Our inverse demand function looks like this\n",
    "demand = Function('q_d')(p)\n",
    "Eq(demand,ex_a_2 - ex_b_2*p)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "b691da86",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle q_{s}{\\left(p \\right)} = 0.3 p + 1.4$"
      ],
      "text/plain": [
       "qₛ(p) = 0.3⋅p + 1.4"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Our supply function looks like this\n",
    "supply_w_tax = Function('q_s')(p)\n",
    "Eq(supply_w_tax,ex_c_2 + ex_d_2*(p-ex_tax_2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "1dae35b7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAJUAAAAYCAYAAADzjL9JAAAEIklEQVR4nO3bS4gcVRTG8V8n8YEEHYMGFMQBQdSFivgA8TEJLgIBowsX6kKjoBA0Dm58zKY3ko3GoEE0q4gK4oMoSkBQMgGDUYko+AiK2orxGTURNRMzOi7ubabodFVXdVfb1bH/UByYufecM1/duo9TNbV6vW7EiDJZMKC4N2An9uNvnN+DrzoO4Xu8hDN7S+2IoFd9G/FqpS6H1osKBiuDc/A0/sDz2CMk2S3TOFYQbhVOxcU9ZTjclK1vkmk5tB7EoFqGGqbwSAn+puMFu3AhFuP3EnwPI2Xrm2RaDq0HsfwtifaTPvjeLQh6Yh98Dwv91DdJqtatg6qGO/ARZoSpcyNOkL7OFmVhtIc6tLsab+A7HMS32I41GX2aPhdmtBkkVdI3K5c8pGrduvxtwFrhRm6KHVfhEhyNv3IG7JXb8ISwF3gFe7EU52I1HvuP8iibDaqhb19zSQ6qS2OQz4XN1y/x51PYhlPwVbeBEoxFeyCjze3CH3Uefmz53UkZ/Waizfu0tTJpPr88vC+cgvJQJX3LyCVV6+SgWh3tA4kgzc73xWC9UsPlmNM56Vntp/C9GX0a0U7gg4K5EQbV6QXaPyn/oKqSvmXk0oh2QovWyT3VBdFub+PgTaHe0S0r8BDeiXE2yT7mPoPj8DEexjU4OUecpwQxH8RzgmjjBfIcF25M3uvmAr6rpG8ZuaRqnRxUzWnshzYOZmXPEJ1YgbuFI+iHeLRD+/W4SUh6LbbEvLZFH2nswTphhrsO9ys2qPpJlfQtI5dUrWuJ1zS7hBF8Br5ocbBImBq/0f1NOl6ooTyLn4VlJs8TMSbsAa7FLdiHs/BTm7Yr8Sp2CPuyT3U+BSWZ1L89VZX0LSOXVK2Te6r3YqAr2wS6TO/H9N/wMl7EjThbeKo6sQ9b47VAGFhXRD+tLI+2LhyVizKpf3uqKulbRi6pWieXv83RTpkvoBHK8utyBMlLcwO5JKNNsyrcytJo/0zp1yzENYqnhf7uqTZHWwV9y8glVevkTLVDWIvvFEb4C+ZrF78K9YwyaC5HWdX8LULpf6eQdPNUc5Ewdb+e0q/pc7bnLMunSvqWkUuq1q2B74qB9gvr5PV4DVcprzA3l6PNvXhXmKLXCEfgo3CPMIt12ifliTEIqqJvmbkcFq+1oj4nlOo3FnBalIPRZr2fezxeRWn6nMlsNTiqom+nXMZzxEnVehAvlD+L9lacVlIOxwiV4Qlhw9ruZPh/oR/6Jumo9SAG1VZhHV+Jr5Xzkd4M3haO1evxT08ZDjdl65ukLofW3XxPNSYcvfOw2eGngwNCkW65cOxdrPeP9GaF2sxbQu1omBlTLX2TTMuhda2Lb9TH8WXOtsvMf9Q1Ih/jhlzfbmaqhvY1pBHl0DDk+g7qHx9GHMGMBtWI0vkXdl5mYobieygAAAAASUVORK5CYII=\n",
      "text/latex": [
       "$\\displaystyle q_{s} = q_{d}$"
      ],
      "text/plain": [
       "qₛ = q_d"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# As tax = 0, in equilibrium this condition is met\n",
    "Eq(qs,qd)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "9b48d615",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle 5 - 0.2 p = 0.3 p + 1.4$"
      ],
      "text/plain": [
       "5 - 0.2⋅p = 0.3⋅p + 1.4"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# To find the equilibrium price we just have to solve the following equation\n",
    "Eq(ex_a_2 - ex_b_2*p,ex_c_2 + ex_d_2*(p-ex_tax_2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "fe60118e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAB8AAAASCAYAAACjMAXnAAABh0lEQVR4nMXUv0uXURTH8Zf6DWxLHBxLWpJsD0nImlwcDJvSgqQpInAQguBrU1uIQyUK/gPiIFoNFaIQCIFDqIiD9ANFRGhqyF/Dc7/w8PB9fuSX8AOXc57z3Hvel3MPp65cLjsr1cf8BzjOWYc5+ZoxiBls4g9+YwkPEzylmL+CkZSknbiFdznwPrzGNj7jO1rQiwl0hz3H1eArKUm/BDueA99AD+ZwFIs/wzLuhItMkyhDiq7hOn6FpFn6hNkEGHbwJvg3K8Ei8EfBTsp/8yz9DfagKPw87gXoRA3gEgaC/74o/C4uhAM/aoC/RDvm8aEovFLytzWAn2AI6+iP/8iCX0UHfopufBo9xihW0YX9ovBaG+0pxvAtgHeSG9LgjaISHQb4v2oYr0Rzowu71TalwfvQJJpoWY12GVdwLhZ7Lmqwr7iNvbTDpZR4peR5E+0jLqIVW7iPF6KKLYqaLaktTKXB23DD6RqtNdgG0ZtX00IWfA11BWGXEt/lsAqpyHj9bzpT+Amr+ldFffXpUwAAAABJRU5ErkJggg==\n",
      "text/latex": [
       "$\\displaystyle 7.2$"
      ],
      "text/plain": [
       "7.20000000000000"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eq_price_2 = solve(Eq(ex_a_2 - ex_b_2*p,ex_c_2 + ex_d_2*(p-ex_tax_2)),p)[0]\n",
    "eq_price_2\n",
    "# This is our equilibrium price"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "36810ebf",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle 3.56$"
      ],
      "text/plain": [
       "3.56000000000000"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Now we just introduce this value in any of the supply or demand functions to get the equilibrium quantity\n",
    "eq_quantity_2 = ex_c_2 + ex_d_2*(eq_price_2-ex_tax_2)\n",
    "eq_quantity_2\n",
    "# This is our equilibrium quantity"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "914e4154",
   "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": [
    "# We can see the graphic solution\n",
    "p1 = plot_implicit(Eq(p,ex_a_2/ex_b_2-q/ex_b_2),(q, 0, 10),(p, 0, 10),label = 'Demand',legend=True,show=False)\n",
    "p2 = plot_implicit(Eq(p,q/ex_d_2 -ex_c_2/ex_d_2 + ex_tax_2),(q, 0, 30),(p, 0, 10),label = 'Supply',legend=True,show=False)\n",
    "p1.append(p2[0])\n",
    "p1.show()\n",
    "# Remember we are plotting the inverse functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "413e2073",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Consumer surplus: 31.6840000000000\n",
      "Producer surplus: 21.1226666666667\n"
     ]
    }
   ],
   "source": [
    "# Now we can calculate consumer and producer surplus\n",
    "producer_surplus_2 = ((eq_price_2 - (-ex_c_2/ex_d_2 + ex_tax_2)) * eq_quantity_2) / 2\n",
    "consumer_surplus_2 = ((ex_a_2/ex_b_2 - eq_price_2) * eq_quantity_2) / 2\n",
    "print(f'Consumer surplus: {consumer_surplus_2}\\nProducer surplus: {producer_surplus_2}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "fd6594fa",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Deadweight loss: 0.720000000000000\n"
     ]
    }
   ],
   "source": [
    "# As we used the same parametres as the market without tax, we can calculate the deadweight loss that the tax caused\n",
    "deadweight_loss = (eq_price_2-eq_price_1)*(eq_price_2-eq_price_1)/2\n",
    "print(f'Deadweight loss: {deadweight_loss}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "698b2744",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Tax revenue: 7.12000000000000\n"
     ]
    }
   ],
   "source": [
    "# We can also calculate tax revenue\n",
    "tax_rev = ex_tax_2 * eq_quantity_2\n",
    "print(f'Tax revenue: {tax_rev}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "e989971c",
   "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": [
    "# Lets plot both situations together as the parametres are the same\n",
    "p1 = plot_implicit(Eq(p,ex_a_1/ex_b_1-q/ex_b_1),(q, 0, 10),(p, 0, 10),label = 'Demand',legend=True,show=False)\n",
    "p2 = plot_implicit(Eq(p,q/ex_d_1 -ex_c_1/ex_d_1 + ex_tax_1),(q, 0, 30),(p, 0, 10),label = 'Supply without tax',legend=True,show=False)\n",
    "p3 = plot_implicit(Eq(p,q/ex_d_2 -ex_c_2/ex_d_2 + ex_tax_2),(q, 0, 30),(p, 0, 10),label = 'Supply with tax',legend=True,show=False)\n",
    "p1.append(p2[0])\n",
    "p1.append(p3[0])\n",
    "p1.show()\n",
    "# Remember we are plotting the inverse functions"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.10.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}