Homework 1 - Leshui He & Leshui Hee & Leshui Heeeee.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note: this is an example file for homework setup"
   ]
  },
  {
   "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": [
    "Q1 (a) The demand function is \n",
    "\\begin{align}\n",
    "Q_d &= 52 - 5p + 4p_f + 0.1 Y \\\\ \n",
    "    &= 52 - 5p + 8 + 20 \\\\\n",
    "    &= 80 - 5p\n",
    "\\end{align}\n",
    "\n",
    "The inverse demand function is..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# define symbols\n",
    "p, pf, Y = symbols('p, p_f, Y')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle 0.1 Y - 5 p + 4 p_{f} + 52$"
      ],
      "text/plain": [
       "0.1⋅Y - 5⋅p + 4⋅p_f + 52"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# define demand function\n",
    "Qd = 52-5*p + 4*pf + 0.1*Y\n",
    "Qd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle 80.0 - 5 p$"
      ],
      "text/plain": [
       "80.0 - 5⋅p"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Qd.subs([(pf,2), (Y,200)])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Q1 (b) blabla..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Q6 (d)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "# define demand function\n",
    "Qd = exp(ln(6) - 2* ln(p) + 5*ln(Y))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\frac{6 Y^{5}}{p^{2}}$"
      ],
      "text/plain": [
       "   5\n",
       "6⋅Y \n",
       "────\n",
       "  2 \n",
       " p  "
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Qd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle - \\frac{12 Y^{5}}{p^{3}}$"
      ],
      "text/plain": [
       "     5 \n",
       "-12⋅Y  \n",
       "───────\n",
       "    3  \n",
       "   p   "
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# calculate partial derivative\n",
    "Qd.diff(p)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAABkAAAAOCAYAAADaOrdAAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA9klEQVQ4Ea2UDQ3CMBBGV4KABQmbgwEOkAAWQAIakDANSAAkDAcgYcNBed/WJuVnCaFtcmvuOt5r1xZjrc1imzGmgLF3nAV9qxz2ta9JEhNAJDiGDPIDodmvVI8S9AAEwPJQ4uod9S6VRDDN+kVELrnqxYRHbDsDuDPjxwgoN25pI+P/lzkMN35dwDcpVvIxEwSVBMRw4rSS1AFcq6g915DkxMX1dD+1DYDhDry9zipqlRjf+aGke4JgC3geCiSaeltsj2ANowwF1LQvWZKNB6aNXiLwfy1iq0ncRn8uN9sTMN2XsM1IKsRl9MkC1BC62d+iQZI9ARiFdHIvjkVMAAAAAElFTkSuQmCC\n",
      "text/latex": [
       "$\\displaystyle -2$"
      ],
      "text/plain": [
       "-2"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# calculate elasticity\n",
    "Qd.diff(p) * p/Qd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAABkAAAAOCAYAAADaOrdAAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA9klEQVQ4Ea2UDQ3CMBBGV4KABQmbgwEOkAAWQAIakDANSAAkDAcgYcNBed/WJuVnCaFtcmvuOt5r1xZjrc1imzGmgLF3nAV9qxz2ta9JEhNAJDiGDPIDodmvVI8S9AAEwPJQ4uod9S6VRDDN+kVELrnqxYRHbDsDuDPjxwgoN25pI+P/lzkMN35dwDcpVvIxEwSVBMRw4rSS1AFcq6g915DkxMX1dD+1DYDhDry9zipqlRjf+aGke4JgC3geCiSaeltsj2ANowwF1LQvWZKNB6aNXiLwfy1iq0ncRn8uN9sTMN2XsM1IKsRl9MkC1BC62d+iQZI9ARiFdHIvjkVMAAAAAElFTkSuQmCC\n",
      "text/latex": [
       "$\\displaystyle -2$"
      ],
      "text/plain": [
       "-2"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "simplify(Qd.diff(p) * p/Qd)"
   ]
  },
  {
   "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": 2
}