demand and supply - 2. supply.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": 2,
   "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": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "p, ph = symbols('p ph')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 2.1. Supply function and supply curve"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Define a supply function"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Define a supply function:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
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      "text/latex": [
       "$\\displaystyle 40 p - 60 ph + 178$"
      ],
      "text/plain": [
       "40⋅p - 60⋅ph + 178"
      ]
     },
     "execution_count": 4,
     "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": [
    "Calculate derivative of the supply function with respect to $p$ by hand. \n",
    "\n",
    "Note: \n",
    "* the partial derivative sign in LaTeX math is: \\partial\n",
    "* the fraction in LaTeX math is: \\frac{numerator}{denominator}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$\\frac{\\partial Q_s}{\\partial p} = 40$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Calculate derivative of the supply function with respect to $p$ using sympy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
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      "text/latex": [
       "$\\displaystyle 40$"
      ],
      "text/plain": [
       "40"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Note: in sympy, you can calculate derivative of a sympy object using the \"diff\" method\n",
    "Qs.diff(p)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Plot the supply curve with $p_h$ explicitly substituted later on"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Step 1: inverse the supply. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\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": 6,
     "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": "markdown",
   "metadata": {},
   "source": [
    "Step 2: plot the supply curve"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "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 0x1a965845cc8>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# use plot function\n",
    "plot(SInverse.subs([(ph,1.5)]), (q,0,286), xlabel=\"$q$\", ylabel=\"$p$\")"
   ]
  },
  {
   "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": 112,
   "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": 111,
   "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)"
   ]
  }
 ],
 "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": "3.7.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}