demand and supply - 3. market equilibrium.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notebook created by: Leshui He; Department of Economics, Bates College"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Import necessary packages."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "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."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "p, pb, pk, y, ph = symbols('p pb pk y ph')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 3.1 Define demand and supply functions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Define demand and supply functions:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle - 20 p + 20 pb + 3 pk + 2 y + 171$"
      ],
      "text/plain": [
       "-20⋅p + 20⋅pb + 3⋅pk + 2⋅y + 171"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# define linear demand function as in class notes\n",
    "Qd = 171 - 20*p + 20*pb + 3*pk + 2*y\n",
    "# show the defined function\n",
    "Qd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle 40 p - 60 ph + 178$"
      ],
      "text/plain": [
       "40⋅p - 60⋅ph + 178"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# define linear supply function as in class notes\n",
    "Qs = 178 + 40*p - 60*ph\n",
    "# show the defined function\n",
    "Qs"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 3.2 Plot the demand curves"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Step 1: inverse the demand and supply. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAIgAAAArCAYAAACjMsASAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAH+ElEQVR4Ae2c7XHUSBCGZZcD8PkiOJMB2BFgMoC7CGwygOKX/Y+CDIAI+MgALoIzzgAuAowz8L1P77RqNCvtzmrXqxGnrpJnpuerP96ZaWkl79ze3lbQxcXFoZKnVqiqfaWUX4n/JfBWStSPMT7qOtJ1rfK9lQaYGve2QLD9Cw3wQ9fvuswXbb4U70000YHyp+LdOG8HgIjBAIDBAQLvTDw6P1H+k3dYNVXfr+pzqbQee9UxpvarWUC2fpPaW2UW63ul5kul+Bzf0PY1Myi9r+RvXQ+U/w5vlz8iwHAm5mMrzf58CHmQuA4x6ed1Bpj65ltAPsSXOD6lUzFiX75T+UDtDRw0Vv5KyaWu55QhBwgVbCv11qLGdZ6GfUhjnIR+vY6pPnNOfSqO8icZdmAzsF0iaQsWAJnRHn/lSBz4m3HCH/F8N4nPqLhJTv6RGn3XWGuDLWeyqY1ZgN36mWxOSnjgtn+lsvlSvH1rqdgwpHFC3FKpzX1dVwaQuDZUsvIZ8KkavfV65eHjdI4NYgomggcd62oEOCpT90X9ABsBEO3pz7ht6FVVWSQ5CdbZct3QL5VnhaEXq60okkzIRZyBzX8qj+zsKp8Dv1J6o0ss8wlpTAS1EP6qjxjydAQ1z5TF+SjPeRTTI9W7sUDoocqvuZTH4QRCRuIBBoB0pOtK5behHYYGfMWT5AXgnOcE8M+5lOfsplwcOCSXkWTjiPHYAlubD2a19V9ABPhTwmeQ1XkMYhyU1oXDmeC9rq/Kg8RKKR3+IS8iT1smcfqmjO8m8DzPrpLuFoCnaJLMyAjgX7bIXyw4MKrkNZ8py85B+IDTv4nvPlGxImilbc1TnnYsYOiaPw2AwHBSY5xP44/KYyyeZTggGAgAxWTPOUJb+BwlgCg1JgKx+5ROrLx9ye8r0eVF/mKDbsnL8Wc7vfLEf/jBg1b3ZSU+vv2DOuWJWdA33gRsUe+JSWPbVpSmzrxUNQY5UZ2BQyllKDWSoU/1jkDaOaCsg+oQALClfa2+sD9/pnJG8pcMcByN42uS3J90sYB9l3df4qvG8ym185sSA8iuGDiMc5bjhPwyApGNO5PQD0B8oHMoA4bUkAhD3xSIdCuGgvzYIpXfFofqiwS4y60UxzdIPBwOMA4aFfMF4hUCXRsDgJDhAmXpwDSGYoNgpLhMPdsafQniIFZfpfHa2jl6z1S/T7uCKY2d2KqLBXfwH3coLM42wt7mE7V5rIu7nNoHoR8ngfuxjkFgNFYLA4hHZ25Jb5RWSikzQC2AeJR5QvfQ2ynPLpOCQywbz2OXe1F76oqhIBfyx3qyCNoWRzFyB0EAcR1ruHDSCfm51XXQo9u114eU4wV/14vAfouhUkyU92AGFgNwO1c7WnlAQ2QPAAAGxNlGO5+4Uh6wIWT9DIWGKnM+Qj+UT4O/WU0hfyUfi+GdLr9zQz/TXXW1TQoRtyGG5PNFGwMAfzTkVtn9QX/0nWtTA6QxQ0dBA4KwE6V2x9LR7JdkS2dWID9s7fySCnYotdvB72KPYYvtkn1dPrtmvfWuO9hY+mcDRCuHLYhjpxGrDKmoZGI3Y2Vvg/6XiyMLIHICsQfvCUAvtuiU2YzdfwEt152RdCW+4jEA8xD5x+f2nc1bysArxSClCO1yyFkA134Pct6UbtYCWTvIZqecRhuTBSaAjMlbA8g6AWQAo49pylHEIIo17PlLi2EPAi9+IOTN+CU5fvDn/EFTyUSwS8C/SnDNL66D3GLvnJ+fz757GNBsUr7Xwyf1WztI1Rgb17+vPuu64C50GcUO0mW4TQCka+yJP7PAFINMSFhogQkgC80zVU4AmTCw0AITQBaaZ6rc62sCBYiH6utvHh0pz60mnwZs83bsRnNybZykB+9U8PJM451NJhLPf4/hI6O592FoMyRJvmzfLNOl111MEIAfsernDGEivqnhjerGiylDGqvv3NKBF3znnqWIzw93fArhr07yPAMeetcvTak8CEkGwJHlmxxd+h4xrKDT2AKajN2E1cxbV6Mm6QLQ50h8Xi3gUwgDBw2UR2fKPMwrgbJ8k6tLX4DwbkTjhddgGXYODAiKR0mSnaMFp3OlxI7ZdoTyWiLvpuynHQYo5/omS5e+AAEIjU8fEkOUYKhEpOziX3J0413aqCfGJ9ZKycFE/dCU65ssXfb6aCMD1rFH0p/VV6m+bZUlTcsrSm6OltajQnU5oPffhgZTTnIu9c0quvTdQeYMoEkBB0eL39nMtSmZIfmRnW9KugJNd77vFrE6vqvkgCjut5V8i2+yddkYQKQpwal/wb8VxTc8Cbe0XUdL7lT+rxNy22+rXR/fmC4bAYgMy7bM53pzzwy2ZYF15pHc9knDkjF8l2hr5iuS5yJFUYdvsnVZGyDBuJXSsYKDo4U7r66jxRyuej9a2o4R5y0cY9vIkcz2xn/qm1V06RWkuqKaiPcx+ISyBofyGLxSWpSxXOaWFHmPJW/6/MZiqsDnjo3YijsE0y8Zx3cQ6osgybvMN1m69AaIBMCAGDYNShFs3bN8a0aW/BhqzrHi/4SvNL4rAET+mD2W8YEKPHX1XSau23pecuT4JkuXdR618wFValhWEv/GavSfZkoH3jQDIHxRV5PKPILnN6f4Ufu/4vHx+uC395KBHS7LNzm69N1BQB+CtH3VNriRJFdvktEIuPnxEeLpKMbmq3j/2Jzdgo/H/Kg5VrkIcEgOaBXfLNXlPwJHQ1jK48YLAAAAAElFTkSuQmCC\n",
      "text/latex": [
       "$\\displaystyle \\frac{3 ph}{2} + \\frac{q}{40} - \\frac{89}{20}$"
      ],
      "text/plain": [
       "3⋅ph   q    89\n",
       "──── + ── - ──\n",
       " 2     40   20"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# define a new symbol q\n",
    "q = symbols('q')\n",
    "# solve the equation Supply = q, which is equivalent to (Supply - q) = 0. \n",
    "#   Notice how we solve for the equation and retrieve the first element of the list in one step\n",
    "SInverse = solve(Qs - q, p)[0]\n",
    "SInverse"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle pb + \\frac{3 pk}{20} - \\frac{q}{20} + \\frac{y}{10} + \\frac{171}{20}$"
      ],
      "text/plain": [
       "     3⋅pk   q    y    171\n",
       "pb + ──── - ── + ── + ───\n",
       "      20    20   10    20"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# define a new symbol q\n",
    "q = symbols('q')\n",
    "# solve the equation Supply = q, which is equivalent to (Supply - q) = 0. \n",
    "#   Notice how we solve for the equation and retrieve the first element of the list in one step\n",
    "DInverse = solve(Qd - q, p)[0]\n",
    "DInverse"
   ]
  },
  {
   "cell_type": "raw",
   "metadata": {},
   "source": [
    "Step 2: create plots for both demand and supply"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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P5FP79noaPtRMfkU+/V/roe9rPUwdnfI6NBHxiBKUZJSS5hIaP9xM9e/XMRudoetzhxn4Zi/z45pGIZJrVOKTjGM+o+KKSvxbyol/N8rQTxKMvjBC1S0RKq7UNAqRXKEdlGSsvJI8InfX0vTRNRTVFxN9oJ/Ozx1m8tCE16GJyDJQgpKMV1RXzKo/aaL2PatITsxz9H920Psf3cwmZrwOTUSWkEp8khXMjPKLApRt8pN4cpCRXwzR9bkjVF4XSk2jyNdrLZGVRr/VklV8hT6qbonQ8IHVFK8pYfCxKJ1/1874S6NehyYii0wJSrJSQbiQ+vc1Uv9/NoLP6Pm3o3T/axfTA9NehyYii0QJSrJa2Xl+Vn+shfDt1UwemiD6jV5ijw2QnE56HZqILJDOQUnWs3wj+Noq/FsDDD46QOIHg4w+n5pG4b9Y0yhEspV2ULJiFFQUUPuOVTR8cDV55fn0/UcP3V/sZLpb0yhEspESlKw4JWtKafyzZqp/r5aZvmk6P3uY2MP9zI9rCK1INlGJT1Yk8xkVVwbxbwkw+HiUycMTDH/yEOFbIwSuqMR8KvuJZDrtoGRFyyvNo/ruWqrfWkdRbRED3+yj63OHmWzXNAqRTKcEJTmhqL6YVR9oovbdq5gfn+foFzro+1o3s0OaRiGSqTwt8ZnZnwF/CDhgJ/Be55zOaMuSMDPKL05No4g/GSPx9CAzAzP4twQIXhfC8lX2E8kknu2gzGwV8EGgzTl3AZAHvM2reCR3+Ip8hG+tZvVftJAfyGfw0QE6Pt3O+J4xr0MTkeN4XeLLB0rMLB8oBXo8jkdySGG4iPo/bKR+WyMAPfd20fOlLmZiKvuJZAJzznn35GYfAv4GmAS+75x7x0lusw3YBtDU1HRJR0fH8gYpOcHNORI/jBN/IgbzjtAtESqvDuIr8vo1nEhWW1Dd3LMEZWZB4AHg94Eh4JvAt5xzXzvVfdra2tyOHTuWKULJRXPDs0QfHWBy/wTmg/DtNfgvKtc0CpFzs6BfHC9fHt4IHHbORZ1zs8B24CoP4xEhv6KAunesou49q8gry6Pvq910/2Mn0z3q3RFZbl4mqE7gCjMrtdTL09cBezyMR+RlJS2lNH5kDZG31DLdk5pGMbC9j/kJTaMQWS6etZk7554zs28BvwLmgF8D93oVj8iJzGdUXh2k/KJyBr8bY/jZBDO905RvDRC4XNMoRJaap00SZ0vnoMRL091TDDzQx9ThSYoaiom8uYaS5lKvwxLJZFl7DkokqxStKqbhT1dT88565kbnOHpPB33/q4e5kTmvQxNZkTQsVuQsmBmBSyrwX1BO/IkYiWcGGd85SujWCJVXBTWNQmQRaQclcg58RT7Ct1Wz+i/WUtxSwtivR+j4TDvjezWNQmSxKEGJLEBhpJBV25oI3lgFSUfPv3TRc18Xs4OaRiGyUEpQIovAf345TX/RQtUbI0zsG6fjU+0kno6RnEl6HZpI1tI5KJFF4sv3EboxTHlbBbFH+hl6NsHQs4nUNIotmkYhcra0gxJZZAWVBdS9q4Had6zCV5JH31e66f6nTqZ7p70OTSSrKEGJLJGStaU0fWQNkTfXMN09RefftxPd3sf8hNrSRc6ESnwiS8jyjMrXhCi/OMDgd6KM7xtj9IURqm6tJnBZhaZRiJyGdlAiyyCvLJ/qt9ZR+65VFIQLGfh6L133HGGqY9Lr0EQylhKUyDIqbihJTaN4Rz1zQ3N0/cMR+u7vYXZk1uvQRDKOEpTIMjMzAm0VNH+iheANVcz0TdP5yXYSzwzi5rNnNqbIUlOCEvGIrziP8JuqqfmDeoqbS4g9NEDnZ9qZ2DfudWgiGUEJSsRjRTVF1G9rpO79Dbg5R/c/d9Lz70eZ0TQKyXHq4hPJAGaG/4JySjeUMfRMnMEnoswlZinb5Cd4QxW+Qr2WlNyjBCWSQXwFPkI3hSm/pILYowPEvxdj5BfDRO6spuxCTaOQ3KKXZSIZqCBUQN27V7HqA034in30/ns3/ff3MtOvaRSSO5SgRDJY6boymv58DZG7apjpmaLj0+1EH+pnfnLe69BElpxKfCIZzvKMymtD+LcGGHwsytAP44z+cpjwbdWUt2kahaxc2kGJZIl8fz41v19H44ebKQgV0n9/L31f62GqU9MoZGXyNEGZWaWZfcvM9prZHjO70st4RLJBcVMJDR9cTc0f1DE7ME3XPxyh/z97mBvVEFpZWbwu8d0DPO6ce4uZFQKlHscjkhXMZwQuraTswnLi348x9MM4Yy+OEro5QuVrglieyn6S/cw5b0armFkAeBFocWcYRFtbm9uxY8fSBiaShWb6p4k+2M/EvnHKNvupfE2I0tYyr8MSWdArJS8T1EXAvcBuYAvwS+BDzrnxE263DdgG0NTUdElHR8dyhyqSFZxzjO8aI/6DGNOdU/i3lBO+o4aCYIHXoUnuytoE1Qb8HLjaOfecmd0DjDjn/u9T3Uc7KJFXl5xJknhmkMQPBgEI3lhF8LVV+ArUEyXLbkEJysv/Y48CR51zz6V//haw1cN4RFYEX6GPqtdHWP2JtZRt8hP/boy+r3YztnMUr16QipwLzxKUc64P6DKzDemLXkeq3Ccii6AgWEDd/9FA/R83Mjc6R+99R+n5ly5No5Cs4VmJD14+D/VvQCHQDrzXOZc41e1V4hM5N27eMfyTBIPfjZKcSVJ5bYjQG8LkFed5HZqsbAsq8XnaZu6cewFo8zIGkVzw8jSKiwMMPjbA0A/jTBwcJ3hNSNMoJGPprKlIDskvz6fmbfU0friZwkgR/ff3cvQLHUx1aRqFZB4lKJEcVNxUQu0766l5ex2zsRm6Pn+E/q/3MjemaRSSObyeJCEiHjGfEbgsPY3iezGGno0z9uII4TuqCbRVahqFeE47KJEcl1eSR+TOGpo+1kLJulKiD/TT+dnDTBwcf/U7ixzHOYcb6GX+x08y9+//c8GPpx2UiABQVFtE3XsbGN85SvTbA3R/sRP/ReWEb9c0Cjk1NztL8vAB3KF9uH0vwXC6Ebu2fsGPrQQlIi8zM/ybA5Se5yfx1CCJpwYZ3z1G6MYwldeHNI1CAHDDCZIH9uAO7MG1H4C5WWhYjdXW47vmRqx1IxaoWPDzKEGJyO/wFfqoujlC4LIKYg8NMPidKKMvjFB1S4Sy8/2Y6fxULnHJJK67A7d/D66vG3dwb+qKyhC+rZdjrRthdQu+gsJFfV5P36h7tvRGXRFvTOwbZ/inCcZ+M0rpxjIid9ZQWF3kdViyhJKTE3Bo38s7JSYnwHzYlkuwSA2+1k0Qrn61FyvZ+0ZdEckOpRvKKFlXytCzceLfi9Hx6XaC11URuqkKn6ZRrAjOOYj2kzywO1W6Gx6CoTiUlmGtG/Gt34St3YAVlyxbTEpQInJGLM8IXl9F+SUVDD46QOKpQUZ2DBO5sxr/RQGV/bKQm5vFdR7G7d1F8sCeVEICqK3Hd+FWbP1GrL4J83lz7lElPhE5J1Mdkww82Mf88Bz5wQIid9dS3FDsdVjyKtzIEO7AHpL7d+MOH4RgCBJxrKUVX+vGdIND5WI9XXZ+HtS5UIISySwu6Rj5xTCDjw0wPz5PxZWVVN0aIa9MxZlMkWpw6MR1HCK56wXo70ldURnC17oRWjfiW7MOy1+StxLoHJSIeMN8RsUVlfi3lBN/PMrQjxMvd/tVXBXUEFqPuKlJ3MG9qQaHg3thYhxbvRYrLsZuvA3f+o0Qrsn4sqwSlIgsWF5JHpG7aglcUUl0ez/RB/qZ2D9O8LoqStaWeh3eiuecg1g/8/t2w+EDqdKdS0JJaarBoXVjqsGhJLuOhUp8IrKonHOM7xolur2fuaE5/FsDRN5UTX6lplEsJjc3iztyCLd/9281ONjGC7Gqamz9JmyVdw0OaSrxiUjmMDP8FwYo3eAn8WR6GsWuUUI3padR5GsaxblyI8OpBocDu2FmBnf4AOQXYC2t2NU34Gs9D6sIeh3molGCEpEl4Sv0UXVLhMClFUQf7mfwsSgTB8YJXhui7Pxyr8PLCsn5eeg9mt4l7Ya+dINDRRDbtJm8K6/DmtdhBStzd6oSn4gsi/H940Qf6GN2YIbSTf7UNIrI4o7GWQnc1CTu2ASHzsPp0p1hjc3Y+o2pCQ6RzG9wSFObuYhkBzfnGHo2zuD3YjDnqLw+ROimML6i3C37pRocBlITHAb6cDt/Bcl0g8O687ANF+Brac26Boe07E5QZpYH7AC6nXO3ne62SlAiK8Pc8CyxR6OM7hgmvyKf8O3V+C/OnWkUbm4O19mO2/dSqsEhMQiAbdyMVUVSb5ZtWO11g8NiyPoE9RGgDQgoQYnklsnDE0S392MFBgbVd9dStGplTqNwo8OvTHBoPwD1DdDdlWpwONYKvoIaHNKyt4vPzBqANwJ/A3zEy1hEZPmVrCml8c+aGXluiMHHonR+9jAVVwWpuiVCXll2D6F1Lonr7koNXo1HcbteSF1REcS3pQ3OuwBfU8uKbXBYDF538f0D8N+AU7b0mNk2YBtAU1PTMoUlIsvFfEbFlUH8WwIMPh5lOD2NInxrhMAVlVk1jcJNTZJs34/bvxt3YC9MjIEZdv5F+F53K771myBSmzOlzIXyrMRnZrcBtzrn/sTMrgc+qhKfiEz3TBHd3s903xSF1UWEb6umpCUzGwScczAYTZXtDuzBdbZDdR0MxbHW8/C1pj+iorTM61C9kp3noMzsk8C7gDmgGAgA251z7zzVfZSgRHKDc46xnaPEHkxNoyi/JED4TdXkV3hfDnNzc7iOQ7gjh0i+9MLLDQ5U16bOI60/H2townzZXaJcJNmZoH4rCO2gROQkktNJ4k/GGHoqDvmWmkZxXXDZp1G40ZH0BIc9uPb9MDMNa1qx/PxXGhwqQ8saU5bI3iYJEZHT8RX5CN9aTeCySmIP9TP46AAjvxwiclsNZZv8S/a8ziVxPekJDgf3wmAUpqcgUJn+IL9N2Jp1WIHeaLyUMmIHdaa0gxLJbeN7xhh+bojxF0cpO99P+M4aCsOLkyTc9FRqgkNPF+6F52E83eDQsDrV5NC8DqrV4HCWtIMSkdxQttFPaWsZicY48SdidH6qncrXhgjdeG7TKJKD0XTH3W5cx2FIzkNjM7Ym/emy687L5QYHzylBiUhWsXwj9LoqAm0BYo8MkPjBIKM7hgnfXoP/ovLT7nDc/Byuo/2Vj6gYHYH5eaiK4LvyWqx1E9a4Wg0OGUIlPhHJapPtE0S39zHdPU35pRUErw9RVP/KNAo3lm5w6O3Gvbgj1eCQl586h7R+U6rJQQ0OSyX7u/jOlBKUiJyMSzpGdgwTe3iA5OQ8FVvyqaw9jK9jN66nCyBVrqsIpubcrVmHFRZ5HHVO0DkoEclxs9OUl3dSfGUXiZ/NM/zrtYxamGBdI4HrLyBvwyaoqVODQ5ZRghKRrJSMR3H796SaHDraITmPzx8gfFELFVXTxF6sZLBjE2M7iok0VVKi5JR1lKBEJCu83OCQnghOcQn0dEGkBt8V16TOJzU2Y7488oGG6x1jvx4h+lA/0Qf6KKwrTk2jCOjPXrbQkRKRjOXGRlNz7g4fwO3f/dsNDq2b8L3lXViw6qT3NTPKt1ZQuslP4geDDD0TZ3znKKE3hKm8JoTla0eV6dQkISIZw7kkrrc7/d6kPa80OKxdj1WEsPUbsTWt59TgMBOdIfrtfiZ2j1FQXUjkrhrKzlu6aRQCqItPRLKZm57Cte8n2dGOe+kFGBsFLDVwtXUTvvUboaZ+0Rocxl8aJfrtfmZjs1RcEyR4bYiCRZpGIb9DXXwikl1cPJb+iIrduCOpBgda1mOrW1IfUbHuPKxsaXY3ZeeXU7KhjKEfxhl6Js7Iz4YI3lBF8HVV+Aqz/iPWVxQlKBFZcm5+Dtd5ONV1NzSI27srdUW4Bt/l16RKd41rsLzlmeDgy/cRel2YwCUVxB4ZIP79GCO/GCJ8Rw3+LaefRiHLRyU+EVkSbmwUd3APyf17cIf2pRsc8rDNl2A19fjWbzplg8Nymzw0wcD2PmZ6pilpLSV8Zw3Fx02jkHOmc1Ai4j3nktDbnfrMpAN7cMkk9B6F8kDqXFLrRqzl3BocloNLOoZ/NsTgd6IU1ubKt4EAAA9eSURBVBZS3FBM6OYIeSWay7cAOgclIt5wM9OpBof9u3EH9sLYCGDYqkZ8my/B96a3Qu2qrCiZmc+ovDqIf3M5g49HGXo2weivRqh6YzWByyowX+avYaXRDkpEzoqLx0ge2EPy0D7obIfpaSgqxtZuSO2SWs/Dysq9DnPBpo5OEd3ex9ThSYoai6l+cy3Fq0u8DivbqMQnIkvHzc+nGhwO7E5NcBiMpq4IV+O7YCu2es2yNjgsJ+cco78aIfbwAHllPooaSgjfpmkUZ0ElPhFZXG58lOSBvbiDqX9MT6UaHJrXYpdendophcJeh7nkzIzAJRX4z/eT+FGc+Pdjvz2NIk9lv6WkHZSI4JyDvu5Ux92B3bjuLsBhzWshWJXquGtZn7ENDstlZmCa6IP9TOwdp7CmkMhdtZRu0CfunoZKfCJy9tzMNMkjB3F7X8IdTH+6LGCrmlIf4te6EepWYaY3rx7POcf4S2PEvt3P7OAsZZvLCd9eTWGVplGcRHaW+MysEfgqUAskgXudc/d4FY9ILnCJwXTH3R7ckYOQTIK/HGtsTpXt1m3E/Nnf4LCUzAz/BeWUbihj6Jk4Qz9NcPSeI1RcFSR4g6ZRLCbPdlBmVgfUOed+ZWblwC+BO51zu091H+2gRM6Om5/HdXfi9u0iuX8PxPpTV1RFUiOF1m+EpmZ8eQXeBprFZhOzxB4ZYOzXI+QHCwjfUY1/s6ZRpGXnDso51wv0pr8fNbM9wCrglAlKRF6dGx/DHdxL8sBu3MF9EAzBQD/W3IJdckXqfFIONDgsl4JgAXXvXsXEVZVEt/fT9+VuSlpLidxdS1Ftbp+zW6iMOAdlZs3Aj4ALnHMjJ1y3DdgG0NTUdElHR8eyxyeSyZxzuL7uVNnuwB7c0U7ApUp36zZi6zfha2nFijS6Z6m5ecfwTxMMfjdKYV0RxQ0lhG4O5/I0iuxukjAzP/BD4G+cc9tPd1uV+ERS3Mw07vCBdNfdHghUQncHVt+ItaaSkqnBwTNzY3Mknogx9GyCvLI8qm6rJnBpTk6jyN4EZWYFwKPA95xzn3u12ytBSS5LJgZf2SUdPgjzc1BYlPowv42b8a1Zh/kDXocpx5nqmiS6vZ+pI5MUNRVTfXfOTaPIzgRlqTOIXwHizrkPn8l9lKAkl7jkPK7rCG7/bpIH9sDcHCQGIRROnUdq3YitbsHy9H77TOaSjtFfjhB7pJ/56SQVl1USen2Y/PKcOG7Z2SQBXA28C9hpZi+kL/tL59x3PIxJxFNuYgx3cN8rDQ5Tk+DLw1a3QOtGfOs34quq9jpMOQvmMwKXVlB2oZ/hZxMMPh5ldMcwoZsjVL4mqGkUp+H5OaizoR2UrDTOORjofeW9SaPDMJSAsnKs9bxXJjiowWHFmOmfJvrt9DSK2iIid9dQ2rpip1FkZ4nvXChByUrgZmdwhw+mS3e7YWQYINXgcMHFWNMarL5BDQ4rmHOO8V1jRL/dz1x8Fv+WcsK311AQWnHvR8vaEp9IznBDcZL7d5Ns3w+HD8DMzMsNDr7r0xMcytXgkCvMDP+F5ZSeV8bQ03HiP4gxPzFPydpSgq/VNIpjlKBElsArDQ57Ug0O0b7UFaEwviuuSzU3NLVg+foVzGW+Ah+h14fxtwUYfDRK/PEYI78YJnJnDWUX+HN+GoVKfCKLxE2MvzLBIRaDvqPg86WSUeum1PmkqojXYUoGmzgwTnR7PzN905RuKCNyVw2FNVk9jULnoES88HKDw6H9uL07cUc7wDko88O6VIODr2U9VpxT73uRBXLzjuGfpKZRJGeSVF4XInRTFXklWbnbVoISWS6/3eCwB0aGsMZmmJt7ZYKDGhxkEcyNzjH42AAz0RlmozOE31RN+SVZN41CCUpkKbmhOMkDe3C9R3E7f5V6w2xBIbZ2Q+ozk1o34Cuv9DpMWaEmOyeIPtDPdOcUxc0lRO6uobgxa3blSlAii8kl53FHO17ZJQ2kGhzsvAuwimB6gsNaNTjIsnFJx+iOYWKPDDA/Pk/g8kqq3hgh35/x/w+qzVxkodzkxCsNDok4HO1INTg0tWCvvz21U6qK5HxXlXjDfEbgskrKLiwn/r0YQ8/GGfvNCFW3Rqi4YuVOo9AOSnJSqsGhj2THIdxLL+C6jqQaHEr90HoevtaN+NZuUIODZKTpvmmGfhhn5OdDFNalp1Gsy8hpFCrxiZyJ5MwMdBx6pXQ3nIDGNTA7k/q48/WbUtMcfGpwkMznnGN85yjRbw8wl5jFf1F6GkUwo6ZRqMQncipuOJFqcDg25663O9Xg0NKK75obU+3gFWpwkOxjZvg3Byg9z0/iqUESTw0yvnuM0I1hKq8P4SvI/hda2kHJiuKSSZJHj+AO7sPtfwn6e1NXBKuw1k1Y6wZ8zeuw/Ix6lSmyYLPxGWIPDTD2m1EKqgoI31VD2SbPp1GoxCe57ZUGhz24g3thcgLqGrCiIqx1I771m6Cq2utfVJFlMbFvnIHtvViej/yK/NQ0imrPplEoQUlucc5BtD/1ERXR/tR7k1wSSstSCal1I7Ssx1dS6nWoIp5IziUZ/skQ8cejJGeTBK8NEXp9GF9x3nKHonNQsvK52VnckYMk2/fj9uxMNTgANK3B95ob1OAgchxfvo/gdSHKtwYYfHSAxNNxRnYME35TDeVtgaypJmgHJRnLjQyR3L8Hd2A3rv0AzM1iq9dCcTG+1vRHngcqvA5TJONNdUwysL2P6c4pSjeUUfXGyHJNo1CJT1YGl0ziujtSH1HRcSj1ZlnnoDL0Sht481o1OIicA5d0jDw/zNgLI0zsGydwRSXhWyPkLe00CpX4JHu5qUnc4YMk9+7EHdiTanAwH9bUjL3hdnwt6yFckzUlCZFMZT6j4vJK/JvLiT8eY+jHccZeHKHqlggVV2bmNAolKFlWzjlctA93YG/qvUmdhyFQATPTLzc42NoNmBocRJZEXkkekbtqCFxRSfTBPqIP9DP8syGq766lZG1m/d55WuIzs5uBe4A84N+cc5863e1V4stObm4Wd+S4CQ7FJdDXDTX16WngG7FVTfjylr3DSCSnOecYe3GU2MP9zCXmqLw+SOV1VRRULloZPTtLfGaWB3wRuAk4CjxvZg8753Z7FZMsHjcyjDuwm2RHO27vLpidgfwCrKUV27QFX/NarCLodZgiOc3MKL8oQNmm1DSK4R8nGP7pEKGb0tMo8r3tivWyxHcZcNA51w5gZv8J3AEoQWUhl0zierrSu6Td0NcDgK0/H99Fl6Y67prXYQVqcBDJNL5CH1U3RwhcWkH0oX4GH4sy8twQ4Ttr8J9f7llcXiaoVUDXcT8fBS4/8UZmtg3Ylv5x2sx2LUNsmSQMxLwOYplpzStfrq0XsnHN/9eCH2GXc+6Cc72zlwnqZLXJ3zkh5py7F7gXwMx2OOfaljqwTKI154ZcW3OurRdyd80Lub+XBcajQONxPzcAPR7FIiIiGcbLBPU80Gpma8ysEHgb8LCH8YiISAbxrMTnnJszs/8KfI9Um/l9zrmXXuVu9y59ZBlHa84NubbmXFsvaM1nLatGHYmISO7Q6GcREclISlAiIpKRsiJBmdnNZrbPzA6a2ce9jmepmNkRM9tpZi8ca880s5CZPWFmB9Jfs3r8gpndZ2YDx7+f7VRrtJT/kT7uvzGzrd5Ffu5Oseb/bmbd6WP9gpndetx1n0iveZ+ZvcGbqBfGzBrN7Gkz22NmL5nZh9KXr9hjfZo1r9hjbWbFZvYLM3sxveb/N335GjN7Ln2cv55uhMPMitI/H0xf33zaJ3DOZfQ/Ug0Uh4AWoBB4EdjkdVxLtNYjQPiEyz4NfDz9/ceBv/M6zgWu8VpgK6k38J12jcCtwHdJvWfuCuA5r+NfxDX/d+CjJ7ntpvT/40XAmvT/+3ler+Ec1lwHbE1/Xw7sT69txR7r06x5xR7r9PHyp78vAJ5LH79vAG9LX/7PwB+nv/8T4J/T378N+PrpHj8bdlAvj0Ryzs0Ax0Yi5Yo7gK+kv/8KcKeHsSyYc+5HQPyEi0+1xjuAr7qUnwOVZla3PJEunlOs+VTuAP7TOTftnDsMHCT1O5BVnHO9zrlfpb8fBfaQmh6zYo/1adZ8Kll/rNPHayz9Y0H6nwNuAL6VvvzE43zs+H8LeJ2d5rN0siFBnWwk0ukOejZzwPfN7JfpEU8ANc65Xkj9AgDVnkW3dE61xpV+7P9rupx133Gl2xW35nQZ52JSr65z4lifsGZYwcfazPLM7AVgAHiC1E5wyDk3l77J8et6ec3p64eBqlM9djYkqDMaibRCXO2c2wrcAnzAzK71OiCPreRj/0/AWuAioBf4bPryFbVmM/MDDwAfds6NnO6mJ7ksK9d9kjWv6GPtnJt3zl1EahrQZcDGk90s/fWs1pwNCSpnRiI553rSXweAB0kd7P5jpY701wHvIlwyp1rjij32zrn+9C92EvhXXintrJg1m1kBqT/U/8s5tz198Yo+1idbcy4cawDn3BDwDKlzUJVmdmwQxPHrennN6esrOE35OxsSVE6MRDKzMjMrP/Y98HpgF6m1vid9s/cAD3kT4ZI61RofBt6d7vC6Ahg+Vh7KdiecX7mL1LGG1Jrflu52WgO0Ar9Y7vgWKn1e4UvAHufc5467asUe61OteSUfazOLmFll+vsS4EZS596eBt6SvtmJx/nY8X8L8JRLd0yclNddIGfYKXIrqY6YQ8BfeR3PEq2xhVRHz4vAS8fWSao++yRwIP015HWsC1zn/aTKHLOkXk29/1RrJFUO+GL6uO8E2ryOfxHX/B/pNf0m/Utbd9zt/yq95n3ALV7Hf45rfg2p0s1vgBfS/25dycf6NGtescca2Az8Or22XcD/k768hVSyPQh8EyhKX16c/vlg+vqW0z2+Rh2JiEhGyoYSn4iI5CAlKBERyUhKUCIikpGUoEREJCMpQYmISEZSghIRkYykBCUiIhlJCUpERBaVmbWa2TNmtsPMPm1mB8/lcZSgRERk0ZhZHvBV4CPOuTaghNR0nLOW/+o3EREROWN3Artd+rOxSM3mGzqXB9IOSkREFtPFpOYQHrOF1IzRs6YEJSIii2kQOA/AzC4H3k1qmOxZ07BYERFZNGYWBh4DSoHvAO8Amlzq87DO7rGUoEREZCmYWSPwLefc5edyf5X4RERkqWzhHMt7oB2UiIhkKO2gREQkIylBiYhIRlKCEhGRjKQEJSIiGUkJSkREMpISlIiIZCQlKBERyUj/P6Ht0FF/UplIAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# use plot function\n",
    "Splot = plot(SInverse.subs([(ph,1.5)]), (q,0,300), ylim=[0,16], xlabel=\"$q$\", ylabel=\"$p$\", show=False)\n",
    "Dplot = plot(DInverse.subs([(pb,4),(pk,Rational(10,3)),(y,Rational(25,2))]), (q,0,300), xlabel=\"$q$\", ylabel=\"$p$\", show=False)\n",
    "\n",
    "# combine curves into one plot\n",
    "Eqplot_combo = Splot\n",
    "Eqplot_combo.extend(Dplot)\n",
    "\n",
    "# assign colors for each line\n",
    "Eqplot_combo[0].line_color='salmon'\n",
    "Eqplot_combo[1].line_color='orchid'\n",
    "\n",
    "# show plot\n",
    "Eqplot_combo.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 3.3 Solve for the equilibrium"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Solve for the equilibrim price"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\frac{pb}{3} + ph + \\frac{pk}{20} + \\frac{y}{30} - \\frac{7}{60}$"
      ],
      "text/plain": [
       "pb        pk   y    7 \n",
       "── + ph + ── + ── - ──\n",
       "3         20   30   60"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Eq_p = solve(Qd - Qs, p)[0]\n",
    "Eq_p"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Solve for the equilibrium quantity using supply function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\frac{40 pb}{3} - 20 ph + 2 pk + \\frac{4 y}{3} + \\frac{520}{3}$"
      ],
      "text/plain": [
       "40⋅pb                  4⋅y   520\n",
       "───── - 20⋅ph + 2⋅pk + ─── + ───\n",
       "  3                     3     3 "
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Eq_q = Qs.subs([(p, Eq_p)])\n",
    "Eq_q"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Solve for the equilibrium quantity using demand function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\frac{40 pb}{3} - 20 ph + 2 pk + \\frac{4 y}{3} + \\frac{520}{3}$"
      ],
      "text/plain": [
       "40⋅pb                  4⋅y   520\n",
       "───── - 20⋅ph + 2⋅pk + ─── + ───\n",
       "  3                     3     3 "
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Eq_q = Qd.subs([(p, Eq_p)])\n",
    "Eq_q"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Find the equilibrium price when $p_b = 4, p_k = 10/3, y = 12.5, p_h = 1.5$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle 3.3$"
      ],
      "text/plain": [
       "3.30000000000000"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Eq_p.subs([(pb,4),(pk,Rational(10,3)),(y,Rational(25,2)),(ph,1.5)])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Find the equilibrium quantity when $p_b = 4, p_k = 10/3, y = 12.5, p_h = 1.5$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle 220.0$"
      ],
      "text/plain": [
       "220.000000000000"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Eq_q.subs([(pb,4),(pk,Rational(10,3)),(y,Rational(25,2)),(ph,1.5)])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 3.4 Comparative Statics"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "How $p_b$ affects the equilibrium price and quantity?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\frac{pb}{3} + ph + \\frac{pk}{20} + \\frac{y}{30} - \\frac{7}{60}$"
      ],
      "text/plain": [
       "pb        pk   y    7 \n",
       "── + ph + ── + ── - ──\n",
       "3         20   30   60"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Eq_p"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAAsAAAArCAYAAACuAHIQAAAACXBIWXMAAA7EAAAOxAGVKw4bAAABNElEQVQ4Ee2V4REBMRCFE6MAWlCCoQMl0AIdnBqUYJSgBEpAB1pAB/G9uM3FZQw/jbEzb7J52ezubTY5F0JwOZxzQ3AGvZyX3oV03vsewwZcwAgMQCnt3VhUIIDCc6fc/pr5G+e1+ZJqpCYity3YgSvQcauZxFXWEl7Kp/IlH/jzaXgO5ONT+fkTjG+dWpT3bsCwkI7o7dN8RQvvRUSp+1mLa2vympvDqaxT4+NNgbDHsFl4eJfx0Yyt606QtxoMuAxB82exXe0RqymQ57mtpQtrhEZkAnRhk6H4VA1ZUBH9ImQ4BkrtABrJPeY6FpZG89G5QVtng70h8ZcRq6HwdQpNyIdmaSg118VIB3LUBL2P97JkWpQoNKJw23dpWDWW2pELUfSBirqwaOmmsKi8ZtmGopHumiIRW5N4xcgAAAAASUVORK5CYII=\n",
      "text/latex": [
       "$\\displaystyle \\frac{1}{3}$"
      ],
      "text/plain": [
       "1/3"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# derivative of equil. p w.r.t. to p_b\n",
    "Eq_p.diff(pb)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\frac{40 pb}{3} - 20 ph + 2 pk + \\frac{4 y}{3} + \\frac{520}{3}$"
      ],
      "text/plain": [
       "40⋅pb                  4⋅y   520\n",
       "───── - 20⋅ph + 2⋅pk + ─── + ───\n",
       "  3                     3     3 "
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Eq_q"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\frac{40}{3}$"
      ],
      "text/plain": [
       "40/3"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# derivative of equil. q w.r.t. to p_b\n",
    "Eq_q.diff(pb)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "How $p_h$ affects the equilibrium price and quantity?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAAgAAAAOCAYAAAASVl2WAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAWUlEQVQYGWP4//8/AwwzMDAYAfFdIBaAibEwMjIKAAVmA/E7IDYBYiUgRgCYShANBGVADGLATWACieIDowogoUMwHBhBQQyMj9VA9aA4AcUFiL4HxOeA+DQAT1cpCApe64MAAAAASUVORK5CYII=\n",
      "text/latex": [
       "$\\displaystyle 1$"
      ],
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# derivative of equil. p w.r.t. to p_h\n",
    "Eq_p.diff(ph)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle -20$"
      ],
      "text/plain": [
       "-20"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# derivative of equil. q w.r.t. to p_h\n",
    "Eq_q.diff(ph)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Questions and challenges"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Q1: By hand\n",
    "\n",
    "* calculate the derivative of the supply function with respect to $p_h$\n",
    "\n",
    "Write up your answer below in markdown."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "(answer here)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Q2: Verify your answers using sympy\n",
    "\n",
    "* calculate the derivative of the supply function with respect to $p_h$\n",
    "\n",
    "Write up your answer below in code."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [],
   "source": [
    "# code here"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Q3: What is the interpretation of the derivatives above? Interpret both its magnitude and its sign. \n",
    "\n",
    "Write up your answer below in markdown."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "(answer here)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Q4: Plot two supply curves in one graph, one with $p_h = 1.5$, the other with $p_h=2$.\n",
    "\n",
    "Use different colors for each curve."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [],
   "source": [
    "# code here"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Q5: How does the supply curve move after $p_h$ increased by $0.5$? Specifically,\n",
    "\n",
    "* Does the supply curve shift outward (right) or inward (left)?\n",
    "* Does the slope of the supply curve change? Explain in terms of derivatives of the supply function.\n",
    "* How much is the horizontal distance between the two supply curves? Explain.\n",
    "\n",
    "Write up your answer below in markdown."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "(answer here)"
   ]
  }
 ],
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