pricing/market-response-functions.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "copyrighted-mother",
   "metadata": {},
   "source": [
    "# Market Response Functions\n",
    "\n",
    "This notebook provides simple illustrative examples of how individual customer price response aggregate into the total market response function. \n",
    "\n",
    "### Use Case\n",
    "We have a model that specifies how individual customers respond on price changes (yes/no purchasing decisions, variable quantity, etc.). We want to derive an aggregated market response model from individual response models.\n",
    "\n",
    "### Prototype: Approach and Data\n",
    "We demonstrate how the standard aggregated market response models such as linear and constant-elasticity can be derived from basic assumptions about individual responses.\n",
    "\n",
    "### Usage and Productization\n",
    "This prototype is provided mainly for educational purposes, but it can also be used to design custom response models."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "powered-account",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Python 3.9.1\n"
     ]
    }
   ],
   "source": [
    "#\n",
    "# Imports and settings\n",
    "#\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "from matplotlib import pylab as plt\n",
    "plt.style.use('seaborn-white')\n",
    "pd.options.mode.chained_assignment = None\n",
    "plt.rcParams.update({'pdf.fonttype': 'truetype'})\n",
    "\n",
    "import platform\n",
    "print(f'Python {platform.python_version()}')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "thousand-reproduction",
   "metadata": {},
   "source": [
    "# Market Response Function for Yes-No Customer Choice\n",
    "\n",
    "We first consider the case of yes-no customer choice. Each customer has a maximum price she is willing to pay for a certain product or service, and she buys exactly one unit when the offered price is below her willingness to pay. This is typcial for services and durable goods.\n",
    "\n",
    "We generate uniformly distributed willingness-to-pay points for a small population of customers, and aggregate them into the overall market response that approaches the linear price-demand function as the number of customers grows. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "executed-synthetic",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 576x1152 with 17 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n = 100\n",
    "n_customers = 16\n",
    "\n",
    "#\n",
    "# Generate response functions\n",
    "#\n",
    "willingness_to_pay = np.random.randint(0, n, size=n_customers)\n",
    "y = np.zeros((n_customers, n))\n",
    "for i, wtp in enumerate(willingness_to_pay):\n",
    "    y[i, :] = np.hstack([np.ones(wtp), np.zeros(n - wtp)])\n",
    "    \n",
    "market_response = np.sum(y, axis=0)\n",
    "\n",
    "#\n",
    "# Visualization\n",
    "#\n",
    "x = np.linspace(1, n, n)\n",
    "fig, ax = plt.subplots(len(willingness_to_pay) + 1, 1, figsize=(8,  16), gridspec_kw={'height_ratios': [1]*n_customers + [10]})\n",
    "for i, wtp in enumerate(willingness_to_pay):\n",
    "    ax[i].plot(x, y[i])\n",
    "    ax[i].tick_params(axis='x', which='both', bottom=True, top=True, labelbottom=False)\n",
    "    ax[i].set_yticks([])\n",
    "    ax[i].set_ylim([-0.5, 1.5])\n",
    "    ax[i].grid(True)\n",
    "    \n",
    "ax[-1].plot(x, market_response)\n",
    "ax[-1].grid(True)\n",
    "ax[-1].set_xlabel('Price')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "careful-samba",
   "metadata": {},
   "source": [
    "# Market Response Function for Variable Quantity Choice\n",
    "\n",
    "Second, we repeat the simulation with variable-quantity responses. Each customer has a randomly parametrized linear response function: she buys more units at lower prices, and fewer units at higher prices."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "strong-visit",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 576x1152 with 9 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n = 100\n",
    "n_customers = 8\n",
    "max_units = 10\n",
    "\n",
    "#\n",
    "# Generate response functions\n",
    "#\n",
    "max_units_customer = np.random.randint(0, max_units, size=n_customers)\n",
    "willingness_to_pay = np.random.randint(0, n, size=n_customers)\n",
    "y = np.zeros((n_customers, n))\n",
    "for i in range(n_customers):\n",
    "    y[i, :] = np.hstack([np.linspace(max_units_customer[i], 0, willingness_to_pay[i]), np.zeros(n - willingness_to_pay[i])])\n",
    "market_response = np.sum(y, axis=0)\n",
    "\n",
    "#\n",
    "# Visualization\n",
    "#\n",
    "x = np.linspace(1, n, n)\n",
    "fig, ax = plt.subplots(n_customers + 1, 1, figsize=(8,  16), gridspec_kw={'height_ratios': [1]*n_customers + [10]})\n",
    "for i in range(n_customers):\n",
    "    ax[i].plot(x, y[i])\n",
    "    ax[i].tick_params(axis='x', which='both', bottom=True, top=True, labelbottom=False)\n",
    "    ax[i].set_ylim([-0.5, max_units])\n",
    "    ax[i].set_yticks(np.arange(0, max_units, 2), minor=True)\n",
    "    ax[i].grid(which='both')\n",
    "    \n",
    "ax[-1].plot(x, market_response)\n",
    "ax[-1].grid(True)\n",
    "ax[-1].set_xlabel('Price')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "relative-declaration",
   "metadata": {},
   "source": [
    "# Standard Market-Response Functions\n",
    "\n",
    "In this section, we plot several standard market response functions and the corresponding price elasticities computed emperically. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "actual-mexico",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "<ipython-input-13-8d164d3725a8>:31: RuntimeWarning: divide by zero encountered in power\n",
      "  demand_function = lambda p: 5*np.power(p, epsilon)\n",
      "<ipython-input-13-8d164d3725a8>:31: RuntimeWarning: divide by zero encountered in power\n",
      "  demand_function = lambda p: 5*np.power(p, epsilon)\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 720x360 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(1, 2, figsize=(10, 5))\n",
    "\n",
    "#\n",
    "# Calculate the empirical price elasticity of demand\n",
    "#\n",
    "def empirical_elasticity(p, q):\n",
    "    e = np.zeros(len(q))\n",
    "    for i in range(1, len(q)):\n",
    "        e[i] = -(q[i] - q[i-1])/(p[i] - p[i-1]) * (p[i] / q[i])\n",
    "    return e\n",
    "\n",
    "#\n",
    "# Linear function\n",
    "#\n",
    "a, b = 10, 0.99\n",
    "demand_function = lambda p: a - b*p\n",
    "\n",
    "p = np.linspace(0, 10, 100)\n",
    "ax[0].plot(p, demand_function(p), label='demand')\n",
    "ax[0].plot(p, empirical_elasticity(p, demand_function(p)), label='elasticity')\n",
    "ax[0].grid(True)\n",
    "ax[0].set_xlabel('p')\n",
    "ax[0].set_ylabel('q')\n",
    "ax[0].legend()\n",
    "ax[0].set_ylim([-1, a+1])\n",
    "\n",
    "#\n",
    "# Constant-elasticity function\n",
    "#\n",
    "epsilon = -0.25\n",
    "demand_function = lambda p: 5*np.power(p, epsilon)\n",
    "\n",
    "p = np.linspace(0, 10, 100)\n",
    "ax[1].plot(p, demand_function(p), label='demand')\n",
    "ax[1].plot(p, empirical_elasticity(p, demand_function(p)), label='elasticity')\n",
    "ax[1].grid(True)\n",
    "ax[1].set_xlabel('p')\n",
    "ax[1].set_ylabel('q')\n",
    "ax[1].legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "engaging-nicholas",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "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": "3.10.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}