consumer theory - 2. budget constraint.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Import necessary packages."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# import all functions from python labrary: sympy\n",
    "from sympy import *\n",
    "# import python library: matplotlib (for nice plots)\n",
    "import matplotlib\n",
    "# set sympy output to print pretty math expressions\n",
    "init_printing()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Declare variables we are going to use as 'symbols'. We will add more along the way, if necessary."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "q1, q2, p1, p2, y = symbols('q1 q2 p1 p2 y')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 2. Budget Constraint"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Define the budget constraint"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First, define an expression for expenditure."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "exp = p1*q1 + p2*q2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, the budget constraint is such that the expenditure is less than or equal to the budget."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle p_{2} q_{2} \\leq - p_{1} q_{1} + y$"
      ],
      "text/plain": [
       "p₂⋅q₂ ≤ -p₁⋅q₁ + y"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "solve(exp <= y, q2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We see that the inequality solution is not just in terms of $q_2$. This is because the inequality solver in sympy has limited functionality for now. \n",
    "\n",
    "Our ideal form is\n",
    "\n",
    "\\begin{align}\n",
    "    q_2 \\leq \\frac{-p_1 q_1 + y}{p_2} \\label{eq1}\\tag{1}\n",
    "\\end{align}\n",
    "\n",
    "But this is no big deal, let's treat it as an equality, and keep the sign in mind."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left[ \\frac{- p_{1} q_{1} + y}{p_{2}}\\right]$"
      ],
      "text/plain": [
       "⎡-p₁⋅q₁ + y⎤\n",
       "⎢──────────⎥\n",
       "⎣    p₂    ⎦"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "budget_sol = solve(Eq(exp, y), q2)\n",
    "budget_sol"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\frac{- p_{1} q_{1} + y}{p_{2}}$"
      ],
      "text/plain": [
       "-p₁⋅q₁ + y\n",
       "──────────\n",
       "    p₂    "
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Retreive the first and only element in the solution, which is our expression for the budget constraint.\n",
    "bc = budget_sol[0]\n",
    "bc"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The slope and intercept of the budget constraint is better seen after expanding the expression."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle - \\frac{p_{1} q_{1}}{p_{2}} + \\frac{y}{p_{2}}$"
      ],
      "text/plain": [
       "  p₁⋅q₁   y \n",
       "- ───── + ──\n",
       "    p₂    p₂"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bc.expand()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Plot the budget constraint"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Let's plot a budget constraint with $y=5, p_1 = 1, p_2 = 1$. \n",
    "\n",
    "Note the use of different brackets in the subs method."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# we substitute a list [(y,5), (p1,1), (p2,1)] into bc\n",
    "# the list has three elements, each as a pair: (y,5), (p1,1), (p2,1)\n",
    "bc_plot1 = plot(bc.subs([(y,5), (p1,1), (p2,1)]), xlim=[0,10], ylim=[0,10], xlabel=\"$q_1$\", ylabel=\"$q_2$\", show=False)\n",
    "bc_plot1.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Creat a few budget constraints with different $y$, while holding prices constant."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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iMcm9unrYKG9nAJqPNlG2tAR/hp+EvATyZheqyE+k+1A4fJYNBnG2bcHZ/gokpeCfdjtm8DDvayc++Qie+gWcOQ7X3wx3fR/SszwdwWlzqNpcQfUrlfjTw0V+V6vIT6QbUDh8EVt2ltDqZdizpzBXfAvftHn4MrxtWSXYDi8vg7WL3ftE3PV9NyiiUeS3tIS2s62kXZNO/twi4tJV5CfShSkcvox1QjjvbMU5+CEEyvDfOhMzfJT3q4gzx91jEccOwdBRcPcPICff0xFsyFL9aiVVGyswiT63yG+EivxEuiiFQ0c4lQGcNcuxJ45i+l/mVnBke9uyihOCLS+5RX5+P9zxPRg3xfMiv7ayVsqWlNByvJmUq1IpuLOY+GwV+Yl0MQqHjrLWwe7eQWjTGreCY8JUfKPGeV/kFyiBpx+FQ+/DFUPh3oegsIenI1jHUru9mop15WAMeTPyyRyTrSI/ka5D4XChbF2NW+R3+CCmZx/8sxZgCoou6nt89RAWtm2A5b+H3gPds5km3e6uKDzUXtVG+dJSmj5uJGVwKvmzC0koSPR0BhG5JBQOX4e1FrtvD6ENL0JLC77xk/CNnYDxe3yQtroClj/hdjX1u9yt4OjV39MRrLXU76ylbmctLcebyZmSR/bNuSryE4ltCodvwjY2ENrwInbfHigowj9rAb6efS7Z+33+EBZ2boXFv4GmBvfiuWkLIN7bKu5gbTvlK8to/LCexF7hIr+eKvITiVEKh4vB+Wg/oXUroaEO3+jx+G6ZgvH4y5n6Wlj6O3jnVejR111FDLjS2xmA+g/qCKwsJdQYIntiLjmT8/DFq4JDJMbEXjgYY/zALuCMtXbGlz3Xq3AAt8jP2bwWZ/c7mCuH4Bs1Dl+/yzx577+wdwc8+yuoqYRJc9wbC3le5Bci8FIZ9TtriS9IoHBhMcn9UzydQUS+kZgMh58AI4GMzhQO54Q+OYzz8osQKMV37Wh8k2dgkjxuOG1uhJVPwutr3SK/e38MV13j7QxA46EGypeVEKwJkjk2m7zpBSryE4kNsRUOxphewNPAvwI/6YzhAGDb28JFflshLcMt8rt8sOdz8PGH7sVzZWfcayLu/B543BXltISoWBeg9s1q4rLCRX5XqshPpJOLuXBYAfwbkA789PPCwRjzAPAAQJ8+fUacOHHC2yHP45w56Rb5lZdihgzHP2UOJtXjL8a2Vlj9J9i4EgYPh5tnwPAbvJ0BaD7mFvm1l7eRPSGH7Il5+FNU5CfSScVOOBhjZgDTrLUPGmNu5gvC4XzRWjmcz4aCONtfxdm6BZKS3IAYMtz72onjH8Oy37urietugrv+FjI8LvJrd4v86t6pAXCL/IZmeDqDiHRITIXDvwH3AEEgCcgAVllr7/6ibTpDOJxjy0vcIr8zJzGXD8Y/fR7G4y9ngkHYEC7yS0yChd+H0RM8L/JrPdNC2eKztJ5pJW1oOvnziojLUJGfSCcSO+HwF0PE0MrhfNZxcHZsw3n1ZfD78U+egbl2FMZ4fJD27Am3DvzYIbj6OrjnR9Ep8nstXOSXYMifXUj6dZkq8hPpHBQO0WCrKgitWY49fgTTb6Bb5JeT5+0QTgheXQOrngSfH+b9Fdw0zfsiv/Jwkd8nzaRckUrB/CLiczy+RkREPis2w6GjOms4QLiCY0+4yC8jE9811+EbfVMUivxK4ZlH4eAeuPxq97TXol6ejmAdS+1b1VSsDYC15E0vIHOsivxEokjhEG22rpbQGxuxu3dgevTGP3sBpqDY4yEsvLkZlj0O7W0w6x64dW4UivzaKV9eQtOhRpL6JVOwsJjEQhX5iUSBwqEzsNZi979P6OUXoaUZ37iJ+MZOxMR5fJC2phKe+zXsecs9o2naAug9wNMRrLXU76ojsLYMf6KfjOsyyZ6gIj8RjykcOhPb1EBo42rs3vcgvwj/rPn4evX1eAgL7213byoUKIGp82H6Xd4X+dUFCbxQSsP79ST2TKRgQTFJvT2+0lyk+1I4dEbOxwcIrVsBdXX4Ro9zi/wSPN690lDn7mZ6awsU9XaL/C7z/irvhg/rKV9e4hb53ZJLzq15+BJUwSFyiSkcOivb2oKzZR3OrrcgOxf/zDvx9R/k/SD7dsEzv4TqAEyYBbffBx53RYWaQlSsLqNuRy3x+eEivwEq8hO5hBQOnZ1z/CihNcugqgIzfBT+W2d6X+TX0gSrnoJXV0NugXtG07dGeDsD0PRRI2XLSghWtYeL/PLxJamCQ+QSUDjEAtvejvP6Rpx3t2MKi/GNnYjvyiHeD3J4n1vkV3oaxkyGBQ9AarqnIzitDpXrA9Rsq8Kf6adwQQ8V+YlcfAqHWOKUnCL04lIoL8F86xr8U+dgPP5ypr0N1jwHG5ZDeqZ7dfU1USjyO95EzWtVNOytJ31kJvlzCvCnqoJD5CJROMQaGwrivPkaztbNkJDoFvldfa33tRMnj8D6JbBrO4wYC99+EDJzPB3BCTpUb66kaksF/hQ/+fOKSBuWrgoOkW9O4RCrbKDULfI7fQIz6Cq3yC8z29shgkHYtAJWPwcJibDgb2DMpOgU+S0pofV0C6lXp1Ewr4i4zHhPZxDpYhQOscw6Ds67290iP2PwTZqBb+Ro74v8Sk7B07+AIwfgW9e6u5ryijwdwYYsNW9UUbkhgPEb8uYUknG9ivxEviaFQ1dgqysJrV2OPXYY02cA/lnzMbnetqziOO5tSVf+0X089364ZWZUivzKl5XSfLSJ5EEpFCwoJiFXRX4iF0jh0FVYa7Hvv0to42oIBfHdfBu+G27C+Dw+1bOyzL0uYv977kVzix6G4t6ejmAdS+3bNTTsraPleDO50wrIGqciP5ELoHDoamx9LaH1q7CH9sGAQcRNnoUp6uHxENa9snrp79zblM78Dtx2B3jcFdVeHS7yOxgu8ltQTGKRivxEOkDh0BVZa7EH9+Lseht74ii+GyfgGz/Z+yK/2ip4/jduV1PvgXD/w9DnMk9HsNZSv7uOwAtl2BaHnFvzyJ6oIj+Rr6Bw6MpsUyOhTauxH+yCvEK3yK93P+8HeW87PP9rSEqFa2+EWd/xvsivPkjghTIa9tSR0CORwoUq8hP5EgqH7sA5cojQ2hVQW4Nv1Fh8E6Z6X+TXWA/rFsOmVVDY0y3yG+T9Vd4NH9ZTvrKUUF2Q3Kn5ZN2UoyI/kUgKh+7CtrbgvLIeZ+ebkJWDf8Yd+AZe4f0g+3fDs49CRZl7NtO8+yHJ2xK9UHOIqs0V1LxW5Rb5LSgmeaCK/ETOo3DobpwTx9wiv8oA5prr3SK/ZI+/GFua3ftFvPISZOfDvT+CISO9nQFoOtxI+dIS2ivbybwxi9wZBfhV5CcCCofuyQbbcV7fhPPW65Caim/qXPyDh3o/yNED8NQjUHISbpjkFvmlZXg6gtPqULkhQM0bVcRlxlFwZzGpg1XkJ92ewqE7syWnCa5eCnEJmIxM/FNvx6RFochv3RJ4eSmkpMN3HoQR4zyv4Gg50UzZ4rO0lbWRPiKD/DmF+NNU5CfdlsKhu7OhEM47W3Fe2wDx8W6R39AR3tdOnDoGT/0CThyG4WPcIr/sPE9HcIIO1VsqqdrsFvnl3V5I+vAMVXBId6RwEJetKHOL/E4dxwy8Av+MOzBZ3rasEgrB5lWw9nko6OHeee7GW70v8jvrFvn5Enz4kn0U3KEiP+l2FA7yKWsdnJ1v4WxZ5xb5TZyG77ox3hf5lZ6BZx6Bjz+Eq4a7d57Lj0KR37YqKteHi/xmF5AxKkurCOkuFA4SydZUEVq7Anv0I0yf/vhnzsfkFXg7hOPA1pdhxR/ACblFfhNmgsddUW2BNsqXldB8pInky8JFfnkq8pMuT+Egn89ai/1gF6GNL0F7O+amyfhuuBmf1xUcVQG3yG/fThh4FSx6CHr09XQE61jqdtRQsbocG7LkTssna3yOivykK1M4yJezDXWEXn4BGuqxbW3EzZqPKe7l8RAWdrwGS37rXiMx4y6YMt/zIr9gTTvlK0pp3N9AYp8kChcWk1ic5OkMIh5ROEjHhA7uxVm/Chob8d14C76bJmPiPD5IW1cDi/8Ldr4BvfrDfT+BfoM8HcFaS8OeOgKrygi1hMiZlEfOpDxMnFYR0qUoHKTjbHOTW+T3/k7Izcc/awG+Pv29H2TP2/CnX0FRL+h/Bcy6271NqYdCDUECL5ZR/14dadekk31zLkl9VeQnXYbCQS6cc/Qjt8ivphrfdWPwTZyGSfR490pjPax8Eraud4v8Fj0El1/t7QxA48EGypeVEKwNknVTDrlT81XkJ12BwkG+HtvWivPKyzjvbofMLLfI77IrvR/k4PvwzKMQKIGbZ7hFfsmpno4QaglRuaac2rdqiM+Np2BBMSmDvJ1B5CJTOMg345z6hNDqZVBRjhk2Ev9ts70v8mttgRefgS0vQlYO3PMjGHq9tzMATUfCRX4V7WSMziJvVgH+ZBX5SUxSOMg3Z4PtOFu34Lz5KhQU4x83Ed/gYd4PcuwQPPVzOHsSRt0CC78P6ZmejuC0OVRtCFD9ehX+jDgK7igibYjHfVUi35zCQS4eW3qG0BubsYc+xFx1Nf6pczHp3ras0t4G65fC+iWQkgZ3PQjXjfe+yO9kM2VLSmgraSVteAb5cwuJU5GfxI7YCQdjTG/gGaAIcIDHrbWPftk2CgfvWSeE89YbOK9vdIv8bp2FueY672snTn/iFvkd/xiuvwnu/GvPi/xs0FL1agVVmytI6p1M5o3ZpF+rIj+JCTEVDsVAsbV2tzEmHXgPmGOtPfBF2ygcosdWBtwiv5PHMAMud4v8snO9HcIJucchPtgBJ4/Cnd+DcVO8L/IrbaF8SQktJ1pIGZxGwR1FxGeryE86tdgJh88yxrwEPGat3fxFz1E4RJe1Ds6ut90iP2vDRX43Ynwen+pZdtYt8vtoL1w5zC3yK+jh6QjWsdRsq6ZyfTnGGPJmFZAxOksVHNJZxWY4GGP6AVuBIdbaus/8tweABwD69Okz4sSJE57PJ3/J1la7RX5HDmF69cU/awEmv9DbIRwHtm2AFU+41eBz7oVJczwv8muvaKNsWQnNh5tIHhgu8stXkZ90OrEXDsaYNOAN4F+ttau+7LlaOXQe1lrsh7sJbXgR2lox42/Ff+MtGL/Hp3pWBeBPj8HeHe7V1fc9DD37eTqCtZa6d2upeLHMLfKbkk/WTTkYv1YR0mnEVjgYY+KBtcBGa+3Pv+r5CofOxzbWE3r5BWx9PbQ2EzdrAaZHb4+HsG4/0/P/Bc2NMPseuHUueNwVFawNF/ntayCxd7jIr4eK/KRTiJ1wMO4pHk8DVdbahzqyjcKh8wod+hBn3SporHerwG++DRPv8UHa+lq3yK/sNASDsOhhGHCFpyNYa2n4oJ7AylISihJIHpBK9uRcfHGq4JCoiqlwGAtsAz7EPZUV4H9Ya9d/0TYKh87NtjS7RX573oWcPPyz5uPrO9D7QT7Y4Rb51VTB5NvdlYTHXVGhxiAVa8qp21FLQmECBQt7kNxPRX4SNbETDl+HwiE2OMc+JrRmOdRU4Rs5Bt+k6d4X+TU1wso/wBvrIb/YLfK70vurvP+iyG9cDrnT8vElahUhnlM4SOdg21pxXtuA8842yMh0i/wGXeX9IIc+gKcfcYv8xk+FO74HKVEo8lsboPbNauJy4ilcUEzK5SryE08pHKRzcU6fILR6KQTKMENH4L9tFiYlzdshWltg9bOw6QXIzIa7fwjXjPZ2BqD5aBNlS0toD7SRMSqTvNmFKvITrygcpPOxwSDOti0421+BpBT8027HDB7mfe3EJx+5FRxnjsO4qTB3EaRneTqC0+ZQtamC6tcqSe6XTNbNuaRdrSI/ueQUDtJ52bKzbgVHdaVbwXHbLIzHLasE2+HlZbBvF5Sdgbv+Fq6/2fsiv9PNlC0uoe1sK2nD0smfV0Rcuor85JJROEjnZp0Qzu53cDauBn8c/ltnYoaP8n4Vcea4eyzi2CEYOgru/gHk5Hs6gg1Zql+tpGpjBSbRR/6cQtJHqshPLgmFg8QGW1XhriJOHMX0vwz/zPnRKfJ7ZTW88JRbu3Hnd93dTR53RbWVtVK2pISW482kXJlKwfxiFfnJxRj4u64AAAzQSURBVKZwkNhhrYPdvYPQpjXgOPgmTMU3apz3RX6BEvfWpAffd+9bvegh9z7WHrKOpXZ7NRXrysEY8mbkkzkmW0V+crEoHCT22Loat8jv8EFMzz5ukV9BkcdDWNi+EZb93j0uMedemHQ7eNwV1V7VRvnSUpo+biSpfzKFC4tJKEj0dAbpkhQOEpustdh9e9wiv5YWfOMn4Rs7AeP3+CBtTaVb5Pf+29BvkFvB0XuApyNYa6nfWUvgxTJsuyV3Wj5Z41XkJ9+IwkFim21sILThRey+PZjBw/CNuRlfzz4eD2Fh1zZ4/tfQ1AC33wcTZ0O8t1Xcwbog5StKCFYHAdwiv54q8pOvReEgXUPo8EGcNcuhoQ7f6PH4bpmC8fjLmYY6dzfTgd3uVdWLHoaB3l/lXf9BHYGVpYQaQ2RPyCXn1jx88argkAuicJCuw7Y042xZh/Pe25Cd6xb59bvM+0H2vgvP/tLd5TRxDty+KApFfiECq8uof7eW+IIEChcUkzwgxdMZJKYpHKTrcT45QmjNMqiuxHftaHyTZ2CSPG44bW6EVU/Ca2shrwgW/RiuGu7tDEDjoQbKl5USrGknc2w2edMLVOQnHaFwkK7JtrfhvLYR5503IC0D//R5+K74lveDfPyhe/Fc2RkYexvM/2vwuCvKaXWoWFdO7fZq4rLiKZhfROqVHvdVSaxROEjX5pw5SWj1MigvwYwaj3/cREyqx1+Mba2w+jnYtMLtZrr7BzB8jLczAM3HwkV+5W1kjMkib1oB/lQV+cnnUjhI12dDQZx3t+NsWQ+Jifin3o4ZMtz72onjh+HpX8CpYzByHNz1oNv66iGn3aFqcwXNR5por2gjf14R6cMyPJ1BYoLCQboPW15KaPVS7JmTmMsH458+D5PhbcsqwSBsXAFrnoNB34Ixk2D0RM+L/FrPtFC2+CytZ1pJGxou8stQkZ/8mcJBuhfrODg7tuG8+jL4fPgmz8Q3YhTGeHyQtuSUWwd+9AAMuQ7u+SHkFng6gg1Zql+vpGpDBSbBkD+7kPTrMlXkJ6BwkO7KVlcSWrMM+8kRTL+BbpFfTp63Qzgh92ymVU8CBu74K7hpuvdFfuXhIr9Pmkm5IpWC+UXE53h8jYh0NgoH6b6stdg94SK/UBDfLVPwjR6P8Xl8kLaiFJ75pXvx3KAhbpFfUS9PR7COpfatairWBsBa8qYXkDlWRX7dmMJBxNbVElq/EvvRfkyP3m6RX2Gxx0NYeGszLH3cPbtp9j1w67woFPm1U768hKZD4SK/BcUkFKrIrxtSOIhAeBWx/31CL7+IKSjE9BmAb9wkTFwUivye+zXseQv6XAb3/yQ6RX676twiv1aH3Ol5ZI3PVZFf96JwEDmf01iPs3kt9oNdkF+If9YCfL36ej/Ie9vdkGisgyl3woxve1/kVx+kfGUJ7eXtGB8ULCgmqbfHV5pLtCgcRD6P8/EBQutWQF0dvtHj3CK/BI93rzTUw7Lfwc6t0P9KmHsfXDbY2xmAhr11lK8IF/ndEi7yS1AFRxencBD5Ira1xS3y2/UWZOXgn3knvgGXez/Igd3w1CNQHYAJs9xKcI+7okJNISpWl1G3o5b4/AQKF6rIr4tTOIh8FefEUbeCo6oCM3wU/ltnel/k19IEq56C19ZATj7c+2P41ghvZwCaPmqkbFkJwapzRX75+JJUwdEFKRxEOsK2t+O8vhHn7dchNd2tAx/k/b0aOLzPLfIrPQ1jJsOCByA13dMRnFaHyvUBarZVEZcZR8H8YlKvUpFfF6NwELkQztlThDavhbOnMIOuwj91DsbjL2fa29z6jQ3LIT0Tvv13MGKstzMAzcebKF9SQltZG+kjM8mfU4A/VRUcXYTCQeRC2VAI581XcbZuhoRE/FPmYK6+1vvaiZNH3AqOk0fdcLjrQcjK8XQEJ+hQvbmSqi0V+FP85N9RSNrQDFVwxD6Fg8jXZQOlhFYvw54+4a4ips/DeNyySjAIm1a6ZX4Z2TDlDnd3UxSK/EoXn8UYQ1x2HAXziojLjPd0BrmoFA4i34R1HJydb+K8sh6MwTdpBr6Ro6NT5PfMI3B4P3zrWrjnR+4d6DzkBB1qt1ZTuSGA8Rvy5hSScb2K/GKUwkHkYrDVlYTWLsceO4zpO8At8svN93YIx4HX18LKJwELc++HW2Z6X+QXaKN8aQnNR5tIHpRC4fxi4vNU5BdjFA4iF4u1Fvv+TkKbVkOwHd/Nt+G74Sbvi/wqy+DZX8G+Xe5Fc4sehuLeno5gHUvt2zVUrinHWkvutAKyxqnIL4YoHEQuNltfR2j9KuyhDzHFvfDNmo+vqKfHQ1h45xVY8jtobYGZ34Hb7gCPu6Laq8NFfgcbSeqbRMGCHiQWq8gvBigcRC4Fay324F73tFfr4Bs6Et/4yd4X+dVWw+LfwK5t0Hsg3PcQ9B3k6QjWWup31xF4oQynJUTO5DyyJ+Tii1cFRycWW+FgjJkCPAr4gSestT/7sucrHCTanKZGnE2r3SK/vEL8s+7E17u/94PsfhOeewzqa90VxMzvgMddUcGGIIFVZbSVtgCGwoXFJPVRkV8nFTvhYIzxAx8Dk4HTwE7gLmvtgS/aRuEgnYVz5BChtSugtgbf9WPxTZzqfZFfYz0sfwK2b4TCnnDfT9z7WHusYX895ctLCdUFybo5h9wp+Sry63xiKhxuAP63tfa28ON/ArDW/tsXbaNwkM7EtrbgvLIeZ+dbkJnlFvkNvML7QQ7shrXPw7GPYNxtMO+vIMnbEr1Qc4iKNeXUvV1DfF48BQuKSbks1dMZ5EvFVDjcAUyx1n4v/PgeYJS19gefed4DwAPhh0OAfZ4O2nnlARXRHqKT0GfxKX0Wn9Jn8akka+2QC9kgmsUpn5dkEUllrX0ceBzAGLPLWjvyUg8WC/RZfEqfxaf0WXxKn8WnjDEXvMslmjsGTwPnn6zdCzgbpVlEROQ80QyHncAgY0x/Y0wCsBBYHcV5REQkLGq7lay1QWPMD4CNuKey/tFau/8rNnv80k8WM/RZfEqfxaf0WXxKn8WnLviziKmL4ERExBs6GVlERCIoHEREJEJMhIMxZoox5iNjzBFjzD9Ge55oMcb0Nsa8Zow5aIzZb4z5cbRnijZjjN8Ys8cYszbas0STMSbLGLPCGHMo/O/jhmjPFC3GmIfD/3/sM8YsNsYkRXsmrxhj/miMKTfG7DvvZznGmM3GmMPhPzt0B6tOHw7hmo1fA1OBwcBdxpjB0Z0qaoLAf7PWXgWMBv6uG38W5/wYOBjtITqBR4EN1torgWF008/EGNMT+BEwMnzRlx/3TMju4ilgymd+9o/AK9baQcAr4cdfqdOHA3A9cMRae8xa2wYsAWZHeaaosNaWWGt3h/9ej/sF4HF3dOdhjOkFTAeeiPYs0WSMyQDGA38AsNa2WWtrojtVVMUBycaYOCCFbnT9lLV2K1D1mR/PBp4O//1pYE5HXisWwqEncOq8x6fpxl+I5xhj+gHDgR3RnSSqHgH+HnCiPUiUDQACwJPhXWxPGGO6ZbGRtfYM8J/ASaAEqLXWboruVFFXaK0tAfcXTKCgIxvFQjh0qGajOzHGpAErgYestXXRnicajDEzgHJr7XvRnqUTiAOuBf7LWjscaKSDuw66mvD+9NlAf6AHkGqMuTu6U8WmWAgH1WycxxgTjxsMz1lrV0V7nii6EZhljDmOu6txgjHmT9EdKWpOA6ettedWkStww6I7mgR8Yq0NWGvbgVXAmCjPFG1lxphigPCf5R3ZKBbCQTUbYcYYg7tf+aC19ufRniearLX/ZK3tZa3th/tv4lVrbbf8DdFaWwqcMsac6wufCHzhfVG6uJPAaGNMSvj/l4l004Pz51kNLAr/fRHwUkc2imYra4d8zZqNrupG4B7gQ2PM++Gf/Q9r7fooziSdww+B58K/QB0D7o/yPFFhrd1hjFkB7MY9u28P3ahGwxizGLgZyDPGnAb+GfgZsMwY813c8LyzQ6+l+gwREfmsWNitJCIiHlM4iIhIBIWDiIhEUDiIiEgEhYOIiERQOIiISASFg4iIRFA4iIh0McaYQcaY140xu4wx/2GMOXKhr6FwEBHpQsL3wHkG+Im1diSQDFxwq4TCQUSka5kDHDh37xfcbqm9xpgBxpg/hOtFvpLCQUSkaxkOvH/e42HAB+Ebpn23oy+icBAR6VoqgSsBjDGjgHuBvRf6IgoHEZGu5VlgpDHmQ2AubljogLSISHdmra2w1o6y1l4NPAacsdY6xphcY8xvgeHGmH/6qtfp9PdzEBGRr20Y4V1K1tpK4Psd3VD3cxARkQjarSQiIhEUDiIiEkHhICIiERQOIiISQeEgIiIRFA4iIhJB4SAiIhH+Px7SxxemHiWAAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# create plots with different parameters\n",
    "bc_plot1 = plot(bc.subs([(y,5), (p1,1), (p2,1)]), xlim=[0,10], ylim=[0,10], xlabel=\"$q_1$\", ylabel=\"$q_2$\", show=False)\n",
    "bc_plot2 = plot(bc.subs([(y,6), (p1,1), (p2,1)]), xlim=[0,10], ylim=[0,10], xlabel=\"$q_1$\", ylabel=\"$q_2$\", show=False)\n",
    "bc_plot3 = plot(bc.subs([(y,7), (p1,1), (p2,1)]), xlim=[0,10], ylim=[0,10], xlabel=\"$q_1$\", ylabel=\"$q_2$\", show=False)\n",
    "\n",
    "# combine plots into one plot\n",
    "bc_plot_combo = bc_plot1\n",
    "bc_plot_combo.extend(bc_plot2)\n",
    "bc_plot_combo.extend(bc_plot3)\n",
    "\n",
    "# assign colors for each line\n",
    "bc_plot_combo[0].line_color='salmon'\n",
    "bc_plot_combo[1].line_color='tomato'\n",
    "bc_plot_combo[2].line_color='orchid'\n",
    "\n",
    "# show plot\n",
    "bc_plot_combo.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Creat a few budget constraints with different $p_1$, while holding $y$ and $p_2$ constant."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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za1gwbt76X9SiJVz9D9h6O7jzepg0sVFjme/jH9CLyEWDsMIigmcejc8iNtA+XERkS1A4bECLXVrRrnd7lk1aytJP1n8jIPJbwFXXQ9cd4a4b4IM3Gj2eFZXgn3cpXu8TsOrlRG8fTvDxezi3wVtdiIikjMJhI9od1p6sDtnMe7KSVZUbWJuQVwBX/A126AH3Dod3xzd6PPM8/L1/h3/86VinrYi9+DTBA3fgFjTuJkciIo2lcNgI843Sc8vwcrz4+YeaDTTSy82Dy/4XuvWE+0fCWy9u3rhtC/H7XIR/3Om4uZVE7xxB8O4bauQnIluMwmETIq3jDfrWVK1m7hOVGz5ZnJMLl/0FeuwJD90Cbzy/WeOaGV7PveKN/LbrRuy1F4jecwtuzsbbiIuIJIPCoR7ytyug8Ogiln++jCVvb+REcVY2DPx/sNu+8OjtMP7pzR7bWrbCP+1c/FPPgaWLid59E8EbL6mRn4iklMKhntoeUkjBzi2oem4uK2es2PALs7JhwJ+g/Hfw/hvw4hObPbaZ4XXfNT6L6LE7sbdfI3rXSGI/z9jsfYuIrI/CoZ7MjOKzOpLVNos5D8wium6DvroiEbjwGujcFcbeD88/DElYu2D5BUROOBP/7Avjjfzu+zfBW+PVyE9Ekk7h0AB+nk9Jv07xBn0PradB33+92Id+V8J+veLh8MzopAQEgLfdjvFbk+5/ELGJr8Ub+X3/TVL2LSICCocGy+2US9HJJaz8tpqFr2ziXtGeD/2uggOOjB9eeuqepAWE5eQSOewY/HMGgO8TPDyK6HNP4FZu5JCXiEg9RcIuIBO13qcNNT+uYOH4+eR2yaOgW4sNv9jzoO/lEMmKn6COroEzL47fYS4JvK27YgOuJvbWq8TenUB0+lT8o07G69YjKfsXkeZJM4dGKjq5hOyOtQ36Fq7e+IvN4oFw+MnxS1wfugViyVv5bJEs/EOPInLhFdCiJcGTo4k+9QBu+dKkjSEizYvCoZH+u0HfrPU36KvLDE69AI46HSa+BKNvgiQvarPSTkQuuBLvkKNw33wdb+T3xSQ18hORBlM4bIbsomyKz+rIqp9rmP/M3E1vYAYn9oPj+sB7r8K9IyBIckD4Pv7vDiUyYBBWVEzw7GMEj9yNW7wwqeOISNOmcNhMLXq0pO3B7Vjy3mKWTtpAg766zOLhcFI/+PBNePJuSMGCNmtfjH/eJXhHnoib+SPRO0YQfPSOGvmJSL3ohHQSFB7dgZqZNcx7spKcshxySnM3vdFRZ0B+S3j4Vlg4D/pfE19Al0RmHv5ev8X7TXeCcU8Re+kZ3JTP8Y49Da99h6SOJSJNi2YOSWC+UdK3I16ux4KX5hNsqEHfug46Gs4aGL9Z0O1/hTWbOLHd2PratMM/uz/+8WfggoBg1EiCt1/HJfmQlog0HQqHJIm0zqKkXyeqpyxj3uMbadC3rkOOi1/q+tXHcOtfYFVNSuozM7zd9sQ/vV+8kd8bLxK951+4yoqUjCcimU3hkET5XfMpPKoDy79YxuKJDbiT24FHxW87OvUzuOV/oGZlymr0WrYmctq5+KeeC8uWEr37XwSvv4iLrud+2SLSbCkckqztIe0o6NGC+c/PZeUPDVit/NvD4fwh8O1kuPlPsLI6dUUCXvddiFwyFNt1D2LvvE70zhuJzfwxpWOKSOZQOCSZmVF8Zkey2mVR+eAsossacCXSPofARdfAj9/ATX+CFctTVyhgeflEjj8Dv09/iEYJ7r+N4MWxuBQd2hKRzKFwSAE/z6e0XydiKwLmPDRr4w361lV+AAz4M/w0HW68FpYvS12htbxtdyAycAjeXr8l9vF78UZ+06elfFwRSV8KhxTJKatt0PfdCha83MB7QPfcFy75H5g1A0YMhWWLU1JjXZadg3/kCfi/vwSysggeuZvos4+pkZ9IM6VwSKHWe7eh1d6tWfTqApZPaeAMYJe94velnjcbhg+FJVtmhbPXeRsiFw3C+91huK8+JXrbP4l9/cUWGVtE0ofCIcWKTiohpyyHuY/MZs2CBq5j2Gl3uPz/YP5ceOQ2WLSJFuFJYpEs/EOOJHLhldCqDcFTDxJ98WncMjXyE2kuQgsHM+tsZhPMbKqZTTGzK8KqJZV+bdDniDfoW9PA9hU77gqD/gFffwbDhsCCeakpdD2spIzIBZdjhx2N+3Yq0duHEfvsIzXyE2kGwpw5RIGrnXPdgH2AS8yse4j1pExW+2yKz+7IqooaqurToG9d23WHQX+H5Uth+BCompP8IjfAPJ/I/ocQ6XsR1qGU4PknCB4epUZ+Ik1caOHgnKt0zn1a+/0yYCpQFlY9qdZi55a0PbSQpe8vZunHjTjB3HVHuPoGWLkChg2GubOSX+RGWGERfr+L8Y46GVfxE9HbhxN8+DYuifelEJH0YelwiMDMugATgZ2dc0vX+Vl/oD/AVltttcdPP/20xetLFhc4Zt05k5qfVtL5yi7kdKxHg751/fxD/BJX34+HRcetkl/oJrgliwjGjcFNn4Z12hr/uNOxouItXoeI1FuDbz0ZejiYWQvgLeB659zYjb22vLzcTZo0acsUliLRZVFmjvgRL8ej81Vd8PP8hu9k1ox4QDgHg2+Asi7JLnOTnHO4rz4lePlZWL0K74DD8fY/GPMb8X5EJNUaHA6hXq1kZlnA08AjmwqGpiLSMkLpOWWsWbCauQ1p0FdXWRcYOiw+exg+FGZ+n/Q6N8XM8HbZI96CY8ediU14iejdN+Fm/7zFaxGR5AvzaiUD7gWmOudGhlVHGPK2zaf9MR2o/nIZi99q5Indks4wZDhk58CIP8CMb5NbZD1ZQUsip5yDf3o/qK4mes8tBK+Nw61RIz+RTBbmzGF/oC9wiJl9XvvfUSHWs0W1OagdBbu0ZP5/5rGiIQ366iruCEOHQ34LuPEa+P7r5BbZAN6OPeKziN32JPbuBIKxjxD7acvPaEQkOUI/59AQTeGcQ13ByoC5j8+mZkYNWw3ehkjLRt6Yb2FVfPawZBFc+TfYfqfkFtpAwQ/fEnv5Oaiag1e+H95hR2M5jTj5LiLJklnnHJo7P8+n8IgiYisD5jw4Cxc0MqjbFcVnEDvvATf9EaZ+ntxCG8jv+hsiF1yOt88BxCa9T/T24cS+mxpqTSLSMAqHkOV0zKXDKSWsnN6IBn11tSmEsy6BotL4DYMmhzvDsuwc/COOxz//MsjJIXj0HqLPPIpLcRtyEUkOhUMaaLVXG1rt24ZFry1g+eTNaNHdui0M/mf8ZPW//xe++DB5RTaS12lrIv0H4R14OG7yZ0RvG05s8mdqwSGS5hQOaaLoxGJyOuXGG/TNb2CDvrpato4vjuvUBW7/K3z6btJqbCyLRPAPOoJI/0FYm7YETz9M8MT9uGVLwi5NRDZA4ZAmvCyP0n5l4EHl6IqGN+irq0VLGHQDbL0d3Hk9fDwxeYVuBisuxT//Mrxex+K+/4bobcMIPv9YswiRNKRwSCNZhdmUnNWRVbNWUTW2EQ366soviDfr27Y7jLoB3n89OUVuJvN8/P0OInLxEOjYidg7rxM8dCdu0YKwSxOROhQOaaZgp5a0PayQpR8sZulHm3kHuNz8+KWtO/SA+0bAO+OTU2QSWLv2RPpehL/vgbjZFfFGfu+/pUZ+ImlC4ZCGCo8sIm/7fOaNmcOqWTWbt7Oc3Pgd5br3hNEj4e2Xk1NkEph5eHvsS2TgEKzr9sTGP09w3624eVuuJbmIrJ/CIQ2ZZ5T0LcPL96kcXUGwMti8HebkwqV/gX0OhbGj4fXnklFm0lirNvhn/B7/pLNxixYQvWskwVvjcUE07NJEmi2FQ5r6tUHfwjXMfWz25p+0zcqGflfGbxz02B3wypjkFJokZobXY3ciA4diO+1C7M1XiI66mdismWGXJtIsKRzSWF7XfNof24Hqr5az+M0k3HktkgUX/RHKD4Cn7oFxj23+PpPMCloQOakP/hm/h5UrCO69hWD8f3BrNuPyXhFpsEY285Etpc2B7aiZsZL54+aRu1Ueedvmb94OIxG48A/xr88+AEEUjusD1uDWKynl7bATtnVXYq+9QOz9N4l9Mxn/2FPxumwXdmkizYJmDmnOzOhwRilZhdlUPlBBdEkSWmH7Pvz+atj/cPjPIzD2/viNg9KM5ebhH3MK/jkXg3MEzz1O9IUxuJqVYZcm0uQpHDKAn+tTel4ZsVUx5jw0u/EN+uryfDj3SjjwaHjpSXhyVFoGBIC3zXZELh6Mt9veuE8+iDfy+za89uQizYHCIUPklObS4dRSVn6/ggUvbkaDvro8D/pcCoceD68+A4/eDmm6zsCysvEP7IV//uWQl0fw2L1En34YV61GfiKpoHMOGaRVeWtqflzBojcWkNsljxY9Wm7+Ts3gjAHxcxCvPA3RNdD38nhwpCGvbCus/1XE3nmD2MTXiP7wLX7vE7Cde2Jpdt5EJJOl528A2aD2JxaT0zmXuY/OZlXVquTs1AxOuQCOPiO+SG70SIht5tqKFDI/gn/g4UQuGoS1LSQY+wjB4/fhlm7minIR+ZXCIcN4kXiDvpzOucx7tJLY6iQdBjKDE/vB8X3jfZievBuC9A0IAOtQgv/7y/AOPw73w3fxRn6T3se59Dw0JpJJFA4ZKKtdNm0PKqRmxkqqxia51cSxZ8OZA+G1Z2HUPyCa3quUzfPw9z0w3oKjrDOxF8YQPHgnbuH8sEsTyWgKhwxV0L0F7XoVsvTDJSz5MMmHUw45Fk7rD5+8A3f+DTJgAZq1LcTvOwD/2NNwlbOI3jGc4L0JuDQ+PCaSzhQOGaxd7yLyflNA1dNJaNC3rsNPgrMGwucfwG1/zYyAMMPbfW8ilwzFtt2B2KvjCO69ldicWWGXJpJxFA4ZLN6gryN+vk/l/Ulo0LeuQ46Dc66AKZPglutgVZIDKEWsZWv808/DP6UvbvEiYi8/SzDhZVyaHyITSScKhwwXaRGhpF8ZaxatYe6js3GxJC9kO+BI6DcIpn0Bt/wPZMjqZDPD22k3/IFDoHVbYhNfJTpqJLGKn8IuTSQjKByagLwu+bQ/rpjqyctZNCEFd1TbvxdcMAS+mww3/wlWVid/jBTxCloQOfEs/LMugFU1BPfeSvDKc7jVSboMWKSJUjg0EW0OaEuL3Vqy4IUqVkxPwS/vvQ+G/tfCj9/AyD/Cisxamext343IwKF45fsS+2Ai0TtGEPvh27DLEklbCocmwswoPr2UrKJs5jw4KzkN+tZV/jsY8GeY+T2MvgmWL03+GClkObn4R5+M328geB7BQ3cRff5JNfITWQ+FQxPi5fqU9utEbFWMygdnJadB37p67hu/q9w3X8KIP0AGrkr2tt6WyIDBePsdjPv8I6K3DSM2bXLYZYmkFYVDE5NTmkOH00qp+WEl81+Yl5pBepTDRdfCvNkwYigsTsF5jhSzrCz8XsfgX3AFFBQQPHE/0ZeewVUvC7s0kbSgcGiCWu3Rmtb7t2Hxu4tYPjlFh3667w5X/BUWzIPhQ2FRZq5I9jp2JnLhVdjBvXHTJsdnEV9+svm3ZRXJcAqHJqr9CcXkb1fA3EcqWV2VogVsO+wCV14PSxbBsCGwYG5qxkkx830iB/Qi0udCrLCI4JlHCR67F7dkUdiliYRG4dBEeRGPDieXgGdUjq5IXoO+dW2/Ewz6e/zk9D+HQFVlasbZAqyoBP+8S/F6n4Cb8T3R24cTfPyeGvlJs6RwaMKy2mVR0qcjqytXMe/pOak7VNJ1Rxh8A6xaGZ9BzKlIzThbgHke/t6/I3LxYKzTVsRefJpg9B24BUm6wZJIhlA4NHEF3VrQrld7ln20hKXJbtBX19bbw+B/xm8WNHwIzJ6ZurG2AGtbiN/nIvzjTsfNqyR65wiCd99QIz9pNhQOzUC7I9qT/5sCqp6eS83PKbymv3NXGDIs/v3wIVDxY+rG2gLMDK/nXkQGDsW260bstReI3nMLbs7ssEsTSTmFQzPwa4O+Fj6Vo2cRrEjhX78dt4YhwyGSFb8n9U/fpW6sLcRatiJyej/8U8+FpUuI3n0TwbsTcNEULDQUSROhhoOZ9Tazb8xsupldE2YtTZ3fIkLJuZ2ILklRg766SjrFZxBLFsGN12TZ6XAAAAUZSURBVMIP36RurC3I675LvB34Xr8l9to4oneNJPZzZs+ORDYktHAwMx+4DTgS6A6caWbdw6qnOcjrkkfRccVUT1nOojdSvHCtQ0cYdD3kt4CR18L0r1M73hZieflEjjge/+wLYc0agvtuI3jpWTXykyYnzJnDXsB059wPzrnVwOPA8SHW0yy0/l1bWvRsxYIXq1jxXYq7qxYWw9Dh0Lot3PTHeMuNJsLbbkciFw/G23M/Yh+9Q/T24cS+bxozJBEAC2slqJmdAvR2zl1Q+7gvsLdz7tJ1Xtcf6F/7cGdATXDi2gOZuSw5+fRZrKXPYi19FmvlOud2bsgGkVRVUg+2nucSkso5NwoYBWBmk5xz5akuLBPos1hLn8Va+izW0mexlplNaug2YR5WqgA613ncCdA1giIiaSDMcPgY2N7MtjGzbOAM4PkQ6xERkVqhHVZyzkXN7FLgFcAH7nPOTdnEZqNSX1nG0Gexlj6LtfRZrKXPYq0GfxahnZAWEZH0pRXSIiKSQOEgIiIJMiIc1GYjzsw6m9kEM5tqZlPM7Iqwawqbmflm9pmZjQu7ljCZWRszG2Nm02r//9g37JrCYmZX1f77mGxmj5lZbtg1bSlmdp+ZzTOzyXWea2dmr5rZd7Vf29ZnX2kfDmqz8V+iwNXOuW7APsAlzfiz+MUVwNSwi0gD/wJeds7tCOxKM/1MzKwMuBwor1305RO/ErK5GA30Xue5a4DXnXPbA6/XPt6ktA8H1GbjV865Sufcp7XfLyP+C6As3KrCY2adgKOBe8KuJUxm1go4ALgXwDm32jmXwpt3pL0IkGdmESCfZrR+yjk3EVi4ztPHAw/Ufv8AcEJ99pUJ4VAG/FzncQXN+BfiL8ysC9AT+DDcSkJ1MzAUaO738ewKVAH31x5iu8fMCsIuKgzOuVnACGAmUAkscc6ND7eq0BU75yoh/gcm0KE+G2VCONSrzUZzYmYtgKeBK51zS8OuJwxmdgwwzzn3Sdi1pIEIsDtwh3OuJ1BNPQ8dNDW1x9OPB7YBOgIFZtYn3KoyUyaEg9ps1GFmWcSD4RHn3Niw6wnR/sBxZjaD+KHGQ8zs4XBLCk0FUOGc+2UWOYZ4WDRHhwE/OueqnHNrgLHAfiHXFLa5ZlYKUPt1Xn02yoRwUJuNWmZmxI8rT3XOjQy7njA55651znVyznUh/v/EG865ZvkXonNuDvCzme1Q+9ShQNO4gUbDzQT2MbP82n8vh9JMT87X8Txwbu335wLP1WejMLuy1ksj22w0VfsDfYGvzOzz2uf+6Jx7McSaJD1cBjxS+wfUD8B5IdcTCufch2Y2BviU+NV9n9GM2miY2WPAQUB7M6sArgNuAJ40s/OJh+ep9dqX2meIiMi6MuGwkoiIbGEKBxERSaBwEBGRBAoHERFJoHAQEZEECgcREUmgcBARkQQKBxGRJsbMtjezN81skpkNM7PpDd2HwkFEpAmpvQfOg8Ag51w5kAc0uKuEwkFEpGk5Afj6l3u/EO8t9aWZdTWze2vbi2ySwkFEpGnpCXxe5/GuwBe1N0w7v747UTiIiDQtC4AdAcxsb+Ac4MuG7kThICLStDwElJvZV8BJxMNCJ6RFRJoz59x859zezrkewL+BWc65mJkVmtmdQE8zu3ZT+0n7+zmIiEij7UrtISXn3AJgQH031P0cREQkgQ4riYhIAoWDiIgkUDiIiEgChYOIiCRQOIiISAKFg4iIJFA4iIhIgv8Pl9ixrsze4tAAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# create plots with different parameters\n",
    "bc_plot1 = plot(bc.subs([(y,5), (p1,1), (p2,1)]), xlim=[0,10], ylim=[0,10], xlabel=\"$q_1$\", ylabel=\"$q_2$\", show=False)\n",
    "bc_plot2 = plot(bc.subs([(y,5), (p1,1.5), (p2,1)]), xlim=[0,10], ylim=[0,10], xlabel=\"$q_1$\", ylabel=\"$q_2$\", show=False)\n",
    "bc_plot3 = plot(bc.subs([(y,5), (p1,2), (p2,1)]), xlim=[0,10], ylim=[0,10], xlabel=\"$q_1$\", ylabel=\"$q_2$\", show=False)\n",
    "\n",
    "# combine plots into one plot\n",
    "bc_plot_combo = bc_plot1\n",
    "bc_plot_combo.extend(bc_plot2)\n",
    "bc_plot_combo.extend(bc_plot3)\n",
    "\n",
    "# assign colors for each line\n",
    "bc_plot_combo[0].line_color='salmon'\n",
    "bc_plot_combo[1].line_color='tomato'\n",
    "bc_plot_combo[2].line_color='orchid'\n",
    "\n",
    "# show plot\n",
    "bc_plot_combo.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can use polt_implicit to  plot the inequality budget constraint to show the feasible consumption choices, corresponding to inequality (1)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<sympy.plotting.plot.Plot at 0x7ff050524090>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot_implicit(q2 < bc.subs([(y,5), (p1,1), (p2,1)]), (q1,0,10), (q2,0,10), xlabel=\"$q_1$\", ylabel=\"$q_2$\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}