ads_pricing.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# ORIE 5355/INFO 5370 HW 3: Algorithmic Pricing"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " - Name: Horizon Hou\n",
    " - Net-id: rh553\n",
    " - Date: 10/17/2022\n",
    " - Late days used for this assignment: 0\n",
    " - Total late days used (counting this assignment): 1\n",
    " - People with whom you discussed this assignment: "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "After you finish the homework, please complete the following (short, anonymous) post-homework survey: https://forms.gle/N2hdk8B4r7TF1RDG6 and include the survey completion code below."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Question 0 [1 point]\n",
    "<font color='blue'> Survey completion code: hw3_2021xyz"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We have marked questions in <font color='blue'> blue </font>. Please put answers in black (do not change colors). You'll want to write text answers in \"markdown\" mode instead of code. In Jupyter notebook, you can go to Cell > Cell Type > Markdown, from the menu. Please carefully read the late days policy and grading procedure [here](https://orie5355.github.io/Fall_2021/assignments/). "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Conceptual component [4 points]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Please complete the following pricing ethics scenario questionaire: https://forms.gle/dLq7mC32ft1NrhK69, and include the survey completion code below. **We will discuss these issues in class most likely on 10/5 (Exact date to be announced). You must complete the questionaire before the day of that class, even if you turn in the rest of the homework later. The questionaire will close the morning of the class that we discuss these issues.**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font color='blue'> Survey completion code: "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "hw3_pricingethics_2021"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font color='blue'> Survey completion code: Based on the first letter of your first name, explain your answers to the following questions, in at most three sentences each."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First letter A-C: 1, 6, 11, 16\n",
    "\n",
    "First letter D-H: 2, 7, 12, 17\n",
    "\n",
    "First letter I-M: 3, 8, 13, 18\n",
    "\n",
    "First letter N-S: 4, 9, 14, 19\n",
    "\n",
    "First letter T-Z: 5, 10, 15, 20\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font color='blue'> Be prepared to discuss your answers to at least these questions in class (I might randomly call on people), but you should also be willing/able to discuss your answers to other questions. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "2. A convenience store has been selling umbrellas for 5. Whenever it starts raining, the store raises the price to 8."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "I believe this is completely fair because when the weather is rainy, the demand curve for umbrella shift to the right. While supply remains the same, the price equilibrium increases. So it is completely fair for convenience store to raise the price of umbrella to the new equilibrium."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "7. A small factory produces tables and sells all that it can make at 200 each. Because of changes in the price of materials, the cost of making each table has recently decreased by 40. The factory reduces its price for the tables by only 20. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "I believe this is acceptable, because the decrease of cost is on the same material, and the quality of the table remains the same. The small factory do decrease the price by 20, which makes the benefit from cheaper material is shared half and half by the factory and the customers. I believe it is accepatble to split the benefit by half."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "12. A business in a community with high unemployment needs to hire a new computer programmer. Four candidates are judged to be completely qualified for the job. The manager asks the candidates to state the lowest salary they would be willing to accept, and then hires the one who demands the lowest salary. *"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "I believe this is unfair, because salary negotiation should be fair, and based on each side's interest. However, asking candidates to provide lowest salary and compare between those candidates generate unbalanced information between candidates and the company, and it acts like the company is treating candidates as commodities, which is unfair."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "17. On Uber/Lyft, drivers have to drive longer to pick up the passengers in certain suburbs or neighborhoods,  because they tend to be farther away. Is it acceptable for them to charge more to passengers from these neighborhoods? *"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "I believe this is acceptable, because the cost for those drivers to pick up passengers in certain suburbs or neighborhoods is higher, so it is accepatable to charge more. However, the price should only be increased if there is no available cars nearby. If there is available cars nearby, it is not fair to ask more money only based on the physical location of the neighborhood."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Programming component"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Helper code"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import os, sys, math\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 396,
   "metadata": {},
   "outputs": [],
   "source": [
    "df_train = pd.read_csv('HW3_data_train.csv')\n",
    "test_demand_curve = pd.read_csv('test_demand.csv')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Location</th>\n",
       "      <th>Income</th>\n",
       "      <th>Offered price</th>\n",
       "      <th>Purchased</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Africa</td>\n",
       "      <td>10.38</td>\n",
       "      <td>3.16</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Europe</td>\n",
       "      <td>26.33</td>\n",
       "      <td>3.47</td>\n",
       "      <td>True</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Europe</td>\n",
       "      <td>24.06</td>\n",
       "      <td>3.78</td>\n",
       "      <td>True</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Africa</td>\n",
       "      <td>16.18</td>\n",
       "      <td>3.74</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Asia Pacific</td>\n",
       "      <td>13.73</td>\n",
       "      <td>4.75</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       Location  Income  Offered price  Purchased\n",
       "0        Africa   10.38           3.16      False\n",
       "1        Europe   26.33           3.47       True\n",
       "2        Europe   24.06           3.78       True\n",
       "3        Africa   16.18           3.74      False\n",
       "4  Asia Pacific   13.73           4.75      False"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_train.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((4000, 4), (199, 5))"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_train.shape, test_demand_curve.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Problem 1: Demand estimation and pricing without covariates"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First, we will use the training data to construct estimates of the demand at each price without leveraging the covariates, and then use that estimated function to calculate optimal prices. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1a) Naive method: empirical estimate of demand $d(p)$ at each price"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font color='blue'> Fill in the below function, that takes in a dataframe and the number of bins into which to separate the historical prices. The function should output a dataframe that has one row for each price bin, with two columns: the bin interval, and the estimated demand $d(p)$ (the fraction of potential customers who purchase at price $p$) in that bin.  \n",
    "    \n",
    "Use the following function to create bins:\n",
    "https://pandas.pydata.org/pandas-docs/stable/reference/api/pandas.qcut.html"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/html": [
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Location</th>\n",
       "      <th>Income</th>\n",
       "      <th>Offered price</th>\n",
       "      <th>Purchased</th>\n",
       "      <th>bin_with_10_bins</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Africa</td>\n",
       "      <td>10.38</td>\n",
       "      <td>3.16</td>\n",
       "      <td>False</td>\n",
       "      <td>(2.95, 3.54]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Europe</td>\n",
       "      <td>26.33</td>\n",
       "      <td>3.47</td>\n",
       "      <td>True</td>\n",
       "      <td>(2.95, 3.54]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Europe</td>\n",
       "      <td>24.06</td>\n",
       "      <td>3.78</td>\n",
       "      <td>True</td>\n",
       "      <td>(3.54, 4.19]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Africa</td>\n",
       "      <td>16.18</td>\n",
       "      <td>3.74</td>\n",
       "      <td>False</td>\n",
       "      <td>(3.54, 4.19]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Asia Pacific</td>\n",
       "      <td>13.73</td>\n",
       "      <td>4.75</td>\n",
       "      <td>False</td>\n",
       "      <td>(4.19, 4.77]</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       Location  Income  Offered price  Purchased bin_with_10_bins\n",
       "0        Africa   10.38           3.16      False     (2.95, 3.54]\n",
       "1        Europe   26.33           3.47       True     (2.95, 3.54]\n",
       "2        Europe   24.06           3.78       True     (3.54, 4.19]\n",
       "3        Africa   16.18           3.74      False     (3.54, 4.19]\n",
       "4  Asia Pacific   13.73           4.75      False     (4.19, 4.77]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Example with 10 bins:\n",
    "df_train['bin_with_10_bins'] = pd.qcut(df_train['Offered price'], 10)\n",
    "df_train.head()"
   ]
  },
  {
   "attachments": {
    "ac4e165a-3e02-4d40-a8cc-ef8591ad8e7e.png": {
     "image/png": "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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For example, with 2 bins and passing in df_train to the function, you should see the following output:\n",
    "\n",
    "![image.png](attachment:ac4e165a-3e02-4d40-a8cc-ef8591ad8e7e.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [],
   "source": [
    "def create_empirical_estimate_demand_df(df, number_of_pricing_bins):\n",
    "    df_train_bins = df.copy()\n",
    "    my_bins = str('bin_with_'+str(number_of_pricing_bins)+'_bins')\n",
    "    df_train_bins[my_bins] = pd.qcut(df_train['Offered price'], number_of_pricing_bins)\n",
    "    df_train_bins['Purchased_numeric'] = np.where(df_train_bins['Purchased']==True, 1, 0)\n",
    "    my_demand = df_train_bins.groupby(my_bins).sum()['Purchased_numeric']/df_train_bins.groupby(my_bins).count()['Purchased_numeric']\n",
    "    my_demand = pd.DataFrame(my_demand)\n",
    "    my_demand = my_demand.reset_index()\n",
    "    my_demand.columns = ['Price_bin','Demand_at_price']\n",
    "    \n",
    "    return my_demand"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "bin_with_10_bins\n",
       "(0.499, 1.05]    0.931373\n",
       "(1.05, 1.66]     0.795970\n",
       "(1.66, 2.29]     0.591584\n",
       "(2.29, 2.95]     0.398477\n",
       "(2.95, 3.54]     0.190476\n",
       "(3.54, 4.19]     0.115000\n",
       "(4.19, 4.77]     0.054591\n",
       "(4.77, 5.36]     0.050505\n",
       "(5.36, 5.91]     0.024691\n",
       "(5.91, 6.5]      0.005076\n",
       "Name: Purchased, dtype: float64"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_train.groupby('bin_with_10_bins').sum()['Purchased']/df_train.groupby('bin_with_10_bins').count()['Purchased']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Price_bin</th>\n",
       "      <th>Demand_at_price</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>(0.499, 1.05]</td>\n",
       "      <td>0.931373</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>(1.05, 1.66]</td>\n",
       "      <td>0.795970</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>(1.66, 2.29]</td>\n",
       "      <td>0.591584</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>(2.29, 2.95]</td>\n",
       "      <td>0.398477</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>(2.95, 3.54]</td>\n",
       "      <td>0.190476</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>(3.54, 4.19]</td>\n",
       "      <td>0.115000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>(4.19, 4.77]</td>\n",
       "      <td>0.054591</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>(4.77, 5.36]</td>\n",
       "      <td>0.050505</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>(5.36, 5.91]</td>\n",
       "      <td>0.024691</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>(5.91, 6.5]</td>\n",
       "      <td>0.005076</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       Price_bin  Demand_at_price\n",
       "0  (0.499, 1.05]         0.931373\n",
       "1   (1.05, 1.66]         0.795970\n",
       "2   (1.66, 2.29]         0.591584\n",
       "3   (2.29, 2.95]         0.398477\n",
       "4   (2.95, 3.54]         0.190476\n",
       "5   (3.54, 4.19]         0.115000\n",
       "6   (4.19, 4.77]         0.054591\n",
       "7   (4.77, 5.36]         0.050505\n",
       "8   (5.36, 5.91]         0.024691\n",
       "9    (5.91, 6.5]         0.005076"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "create_empirical_estimate_demand_df(df_train, 10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 401,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Price_bin</th>\n",
       "      <th>Demand_at_price</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>(0.499, 3.54]</td>\n",
       "      <td>0.583417</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>(3.54, 6.5]</td>\n",
       "      <td>0.050050</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       Price_bin  Demand_at_price\n",
       "0  (0.499, 3.54]         0.583417\n",
       "1    (3.54, 6.5]         0.050050"
      ]
     },
     "execution_count": 401,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "create_empirical_estimate_demand_df(df_train, 2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font color='blue'> Fill in the below function, that takes in a single price and your empirical df from the above function and outputs the prediction for the demand $d(p)$ at that price. For example, with 2 bins, at price = 3 the function should output 0.583417.\n",
    "\n",
    "If the price is lower than the smallest bin, then use the value of the smallest bin. If it is higher than the highest bin, use the value of the highest bin."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 411,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_prediction_empirical(empirical_df, price):\n",
    "    my_pred = 0\n",
    "    for i in range(len(empirical_df)):\n",
    "        if price in empirical_df['Price_bin'][i]:\n",
    "            my_pred = empirical_df['Demand_at_price'][i]\n",
    "    if price <= 0.499:\n",
    "        my_pred = empirical_df['Demand_at_price'][0]\n",
    "    if price > 6.5:\n",
    "        my_pred = empirical_df['Demand_at_price'][len(empirical_df)-1]\n",
    "    return my_pred"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 412,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.5834165834165834"
      ]
     },
     "execution_count": 412,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "get_prediction_empirical(create_empirical_estimate_demand_df(df_train, 2), 3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 413,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "pandas._libs.interval.Interval"
      ]
     },
     "execution_count": 413,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "my_df = create_empirical_estimate_demand_df(df_train, 10)\n",
    "type(my_df['Price_bin'][0])\n",
    "#1 < my_df['Price_bin'][0].min()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 414,
   "metadata": {},
   "outputs": [],
   "source": [
    "prices_to_predict = np.linspace(min(df_train['Offered price']), max(df_train['Offered price']), 200)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font color='blue'> Plot in a single figure the outputs of your function as a line plot -- where the X axis corresponds to prices in `prices_to_predict` and the Y axis the predicted Demand at that price -- for the following three inputs to the function:\n",
    "    \n",
    "    1. the dataframe is the first 100 rows of df_train, with 10 bins.\n",
    "    \n",
    "    2. the dataframe is the first 500 rows of df_train, with 10 bins.\n",
    "    \n",
    "    3. the dataframe is all the rows of df_train, with 10 bins.\n",
    "\n",
    "<font color='blue'> In the same figure, include the \"true\" test-time demand curve, `test_demand_curve` -- plot the mid-point of each bin on the X axis, and the demand for that bin on the Y axis. So your plot will contain 4 curves in total.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 419,
   "metadata": {},
   "outputs": [],
   "source": [
    "df1 = create_empirical_estimate_demand_df(df_train.iloc[0:100], 10)\n",
    "df2 = create_empirical_estimate_demand_df(df_train.iloc[0:500], 10)\n",
    "df3 = create_empirical_estimate_demand_df(df_train, 10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 420,
   "metadata": {},
   "outputs": [],
   "source": [
    "my_pred1 = []\n",
    "my_pred2 = []\n",
    "my_pred3 = []"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 421,
   "metadata": {},
   "outputs": [],
   "source": [
    "for p in range(len(prices_to_predict)):\n",
    "    my_pred1.append(get_prediction_empirical(df1, prices_to_predict[p]))\n",
    "    my_pred2.append(get_prediction_empirical(df2, prices_to_predict[p]))\n",
    "    my_pred3.append(get_prediction_empirical(df3, prices_to_predict[p]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 422,
   "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"
    }
   ],
   "source": [
    "plt.plot(prices_to_predict, my_pred1, color = 'red')\n",
    "plt.plot(prices_to_predict, my_pred2, color = 'orange')\n",
    "plt.plot(prices_to_predict, my_pred3, color = 'green')\n",
    "plt.plot(test_demand_curve['Price_bin_mid'], test_demand_curve['Demand_at_price'], color = 'blue')\n",
    "plt.xlabel('price')\n",
    "plt.ylabel('demand')\n",
    "plt.legend(['100 rows', '500 rows', 'all', 'test'])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 410,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Price_bin</th>\n",
       "      <th>Demand_at_price</th>\n",
       "      <th>Price_bin_left</th>\n",
       "      <th>Price_bin_right</th>\n",
       "      <th>Price_bin_mid</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>(0.5, 0.53]</td>\n",
       "      <td>0.985075</td>\n",
       "      <td>0.500</td>\n",
       "      <td>0.530</td>\n",
       "      <td>0.5150</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>(0.53, 0.56]</td>\n",
       "      <td>0.966102</td>\n",
       "      <td>0.530</td>\n",
       "      <td>0.560</td>\n",
       "      <td>0.5450</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>(0.56, 0.59]</td>\n",
       "      <td>0.963768</td>\n",
       "      <td>0.560</td>\n",
       "      <td>0.590</td>\n",
       "      <td>0.5750</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>(0.59, 0.621]</td>\n",
       "      <td>0.963235</td>\n",
       "      <td>0.590</td>\n",
       "      <td>0.621</td>\n",
       "      <td>0.6055</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>(0.621, 0.651]</td>\n",
       "      <td>0.956522</td>\n",
       "      <td>0.621</td>\n",
       "      <td>0.651</td>\n",
       "      <td>0.6360</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        Price_bin  Demand_at_price  Price_bin_left  Price_bin_right  \\\n",
       "0     (0.5, 0.53]         0.985075           0.500            0.530   \n",
       "1    (0.53, 0.56]         0.966102           0.530            0.560   \n",
       "2    (0.56, 0.59]         0.963768           0.560            0.590   \n",
       "3   (0.59, 0.621]         0.963235           0.590            0.621   \n",
       "4  (0.621, 0.651]         0.956522           0.621            0.651   \n",
       "\n",
       "   Price_bin_mid  \n",
       "0         0.5150  \n",
       "1         0.5450  \n",
       "2         0.5750  \n",
       "3         0.6055  \n",
       "4         0.6360  "
      ]
     },
     "execution_count": 410,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "test_demand_curve.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font color='blue'> Do the same plot, except now you're using 50 bins for each of the three data frames."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 317,
   "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"
    }
   ],
   "source": [
    "df1 = create_empirical_estimate_demand_df(df_train[0:100], 50)\n",
    "df2 = create_empirical_estimate_demand_df(df_train[0:500], 50)\n",
    "df3 = create_empirical_estimate_demand_df(df_train, 50)\n",
    "\n",
    "my_pred1 = []\n",
    "my_pred2 = []\n",
    "my_pred3 = []\n",
    "\n",
    "for p in prices_to_predict:\n",
    "    my_pred1.append(get_prediction_empirical(df1, p))\n",
    "    my_pred2.append(get_prediction_empirical(df2, p))\n",
    "    my_pred3.append(get_prediction_empirical(df3, p))\n",
    "    \n",
    "plt.plot(prices_to_predict, my_pred1, color = 'red')\n",
    "plt.plot(prices_to_predict, my_pred2, color = 'orange')\n",
    "plt.plot(prices_to_predict, my_pred3, color = 'green')\n",
    "plt.plot(test_demand_curve['Price_bin_mid'], test_demand_curve['Demand_at_price'], color = 'blue')\n",
    "plt.xlabel('price')\n",
    "plt.ylabel('demand')\n",
    "plt.legend(['100 rows', '500 rows', 'all', 'test'])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font color='blue'> Comment on your output in no more than 3 sentences. What is the effect of using more data and more bins?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If we use more data associates with more bins, our prediction is going to be more close to the true demand curve. However, if we use a small amount of data and a large number of bins, our prediction will flactuate a lot and become inaccurate because there are only a little samples are in each bin."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1b) Demand estimation using logistic regression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font color='blue'> First, Fill in the below function that fits a logistic regression to predict the probability of purchase at a price ($d(p)$). The logistic regression should just have two coefficients: one for the intercept, and one for the price. The function takes in a dataframe that you will use as your training data for your model, and should return your fitted model. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 332,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.linear_model import LogisticRegression\n",
    "from sklearn import preprocessing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 333,
   "metadata": {},
   "outputs": [],
   "source": [
    "def fit_logistic_regression_demand_just_on_price(df):\n",
    "    X = df['Offered price']\n",
    "    Y = df['Purchased']\n",
    "    X = np.array(X).reshape(-1, 1)\n",
    "    model = LogisticRegression(fit_intercept=True)\n",
    "    model.fit(X, Y)\n",
    "    \n",
    "    return model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 334,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 1, 1, ..., 1, 0, 0])"
      ]
     },
     "execution_count": 334,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.where(df_train['Purchased']==True,1,0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 335,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Location</th>\n",
       "      <th>Income</th>\n",
       "      <th>Offered price</th>\n",
       "      <th>Purchased</th>\n",
       "      <th>bin_with_10_bins</th>\n",
       "      <th>is_America</th>\n",
       "      <th>wealth_status</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Africa</td>\n",
       "      <td>10.38</td>\n",
       "      <td>3.16</td>\n",
       "      <td>False</td>\n",
       "      <td>(2.95, 3.54]</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Europe</td>\n",
       "      <td>26.33</td>\n",
       "      <td>3.47</td>\n",
       "      <td>True</td>\n",
       "      <td>(2.95, 3.54]</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Europe</td>\n",
       "      <td>24.06</td>\n",
       "      <td>3.78</td>\n",
       "      <td>True</td>\n",
       "      <td>(3.54, 4.19]</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Africa</td>\n",
       "      <td>16.18</td>\n",
       "      <td>3.74</td>\n",
       "      <td>False</td>\n",
       "      <td>(3.54, 4.19]</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Asia Pacific</td>\n",
       "      <td>13.73</td>\n",
       "      <td>4.75</td>\n",
       "      <td>False</td>\n",
       "      <td>(4.19, 4.77]</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       Location  Income  Offered price  Purchased bin_with_10_bins  \\\n",
       "0        Africa   10.38           3.16      False     (2.95, 3.54]   \n",
       "1        Europe   26.33           3.47       True     (2.95, 3.54]   \n",
       "2        Europe   24.06           3.78       True     (3.54, 4.19]   \n",
       "3        Africa   16.18           3.74      False     (3.54, 4.19]   \n",
       "4  Asia Pacific   13.73           4.75      False     (4.19, 4.77]   \n",
       "\n",
       "   is_America  wealth_status  \n",
       "0           0              1  \n",
       "1           0              1  \n",
       "2           0              1  \n",
       "3           0              1  \n",
       "4           0              1  "
      ]
     },
     "execution_count": 335,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_train.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 336,
   "metadata": {},
   "outputs": [],
   "source": [
    "scaler = preprocessing.MinMaxScaler(feature_range=(-1,1))\n",
    "\n",
    "df_scaled = scaler.fit_transform(df_train[['Offered price','Income']])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 337,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-0.11333333, -0.81018777],\n",
       "       [-0.01      , -0.51366425],\n",
       "       [ 0.09333333, -0.5558654 ],\n",
       "       ...,\n",
       "       [-0.69333333, -0.73824131],\n",
       "       [ 0.85666667, -0.2664064 ],\n",
       "       [-0.1       , -0.93344488]])"
      ]
     },
     "execution_count": 337,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_scaled"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font color='blue'> Fill in the below function, that takes in a single price and your trained model and outputs the prediction for the demand $d(p)$ at that price.\n",
    "\n",
    "Note that you do not want to treat logistic regression as a binary classifier that outputs either 0 or 1. Rather, you want to get the probability of being a 1. You can extract this using the predict_proba(X) function. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 338,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_prediction_logistic(fitted_model, price):\n",
    "    price = np.array(price).reshape(-1,1)\n",
    "    prediction = fitted_model.predict_proba(price)\n",
    "    \n",
    "    prediction = pd.DataFrame(prediction)[1]\n",
    "    return prediction"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font color='blue'> For each of the three training dataframes as in part A, fit a model and get the predictions for each of the prices in `prices_to_predict` using your above function. Generate the same lineplot as above. Also include the \"true\" test-time demand curve, `test_demand_curve`. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 339,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0      0.923410\n",
       "1      0.920484\n",
       "2      0.917457\n",
       "3      0.914325\n",
       "4      0.911086\n",
       "         ...   \n",
       "195    0.004324\n",
       "196    0.004152\n",
       "197    0.003987\n",
       "198    0.003829\n",
       "199    0.003677\n",
       "Name: 1, Length: 200, dtype: float64"
      ]
     },
     "execution_count": 339,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df1 = df_train[0:100]\n",
    "df2 = df_train[0:500]\n",
    "df3 = df_train.copy()\n",
    "\n",
    "model1 = fit_logistic_regression_demand_just_on_price(df1)\n",
    "model2 = fit_logistic_regression_demand_just_on_price(df2)\n",
    "model3 = fit_logistic_regression_demand_just_on_price(df3)\n",
    "\n",
    "prediction1 = get_prediction_logistic(model1, prices_to_predict)\n",
    "prediction2 = get_prediction_logistic(model2, prices_to_predict)\n",
    "prediction3 = get_prediction_logistic(model3, prices_to_predict)\n",
    "\n",
    "prediction1\n",
    "prediction2\n",
    "prediction3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 340,
   "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"
    }
   ],
   "source": [
    "plt.plot(prices_to_predict, pd.DataFrame(prediction1), color = 'red')\n",
    "plt.plot(prices_to_predict, prediction2, color = 'orange')\n",
    "plt.plot(prices_to_predict, prediction3, color = 'green')\n",
    "plt.plot(test_demand_curve['Price_bin_mid'], test_demand_curve['Demand_at_price'], color = 'blue')\n",
    "plt.xlabel('price')\n",
    "plt.ylabel('demand')\n",
    "plt.legend(['100 rows', '500 rows', 'all', 'test'])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 341,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9396783939710353"
      ]
     },
     "execution_count": 341,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "prediction1[0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font color='blue'> Comment on your output in no more than 3 sentences. What is the effect of using logistic regression instead of the empirical distribution? "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Logistic regression gives us a more smooth curve than using empirical distribution. Also, it avoids predictions that with higher demand for higher price as the curve is monotonically decreasing."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1c) Optimal pricing using your demand estimates"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font color='blue'> Fill in the following function that takes in two lists: a list of prices, and a list of predicted demand d(p) at that price. The function outputs the revenue maximizing price given the data and the corresponding revenue. You may use a \"brute force\" technique, that loops through all the possible prices and calculates the revenue using that price. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 342,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_revenue_maximizing_price_and_revenue(price_options, demand_predictions):\n",
    "    all_revenue = []\n",
    "    for i in range(len(price_options)):\n",
    "        all_revenue.append(price_options[i]*demand_predictions[i])\n",
    "    max_index = np.argmax(all_revenue)\n",
    "    \n",
    "    return price_options[max_index], all_revenue[max_index]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font color='blue'> Print out the optimal price and the predicted optimal revenue from the predictions for your naive and logistic models, using 100 rows and all the data, each. \n",
    "\n",
    "For example, we got the following (your numbers may differ slightly):\n",
    "\n",
    "logistic, 100 points:  2.580402010050251 1.2143341610705582\n",
    "\n",
    "naive, all points:  2.278894472361809 1.348157868550674"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 343,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(2.1884422110552766, 1.4070878495510661)"
      ]
     },
     "execution_count": 343,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# logistic 100 points\n",
    "train = df_train[0:100]\n",
    "model_log_100 = fit_logistic_regression_demand_just_on_price(train)\n",
    "prediction_log_100 = get_prediction_logistic(model_log_100, prices_to_predict)\n",
    "\n",
    "best_rev_log100 = get_revenue_maximizing_price_and_revenue(prices_to_predict, prediction_log_100)\n",
    "best_rev_log100"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 344,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1.9773869346733668, 1.2295480454251977)"
      ]
     },
     "execution_count": 344,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# logistic all points\n",
    "train = df_train.copy()\n",
    "model_log_100 = fit_logistic_regression_demand_just_on_price(train)\n",
    "prediction_log_100 = get_prediction_logistic(model_log_100, prices_to_predict)\n",
    "\n",
    "best_rev_logAll = get_revenue_maximizing_price_and_revenue(prices_to_predict, prediction_log_100)\n",
    "best_rev_logAll"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 423,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(2.278894472361809, 1.9940326633165828)"
      ]
     },
     "execution_count": 423,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# naive 100 points\n",
    "train = df_train[0:100]\n",
    "df1 = create_empirical_estimate_demand_df(train, 10)\n",
    "\n",
    "my_pred1 = []\n",
    "\n",
    "for p in prices_to_predict:\n",
    "    my_pred1.append(get_prediction_empirical(df1, p))\n",
    "    \n",
    "best_rev_naive100 = get_revenue_maximizing_price_and_revenue(prices_to_predict, my_pred1)\n",
    "best_rev_naive100"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 346,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(2.278894472361809, 1.348157868550674)"
      ]
     },
     "execution_count": 346,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# naive all points\n",
    "train = df_train.copy()\n",
    "df1 = create_empirical_estimate_demand_df(train, 10)\n",
    "\n",
    "my_pred1 = []\n",
    "\n",
    "for p in prices_to_predict:\n",
    "    my_pred1.append(get_prediction_empirical(df1, p))\n",
    "    \n",
    "best_rev_naiveAll = get_revenue_maximizing_price_and_revenue(prices_to_predict, my_pred1)\n",
    "best_rev_naiveAll"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font color='blue'> Now, we're going to use the \"true\" test-time demand curve, `test_demand_curve`. For each of the above predicted optimal prices, calculate the revenue resulting from that price used on the true demand curve. Also print out the true optimal price and corresponding revenue for that curve.  \n",
    "\n",
    "For example, we got:\n",
    "\n",
    "true revenue using logistic 100 price:  0.9729384628058323"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 347,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Price_bin</th>\n",
       "      <th>Demand_at_price</th>\n",
       "      <th>Price_bin_left</th>\n",
       "      <th>Price_bin_right</th>\n",
       "      <th>Price_bin_mid</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>(0.5, 0.53]</td>\n",
       "      <td>0.985075</td>\n",
       "      <td>0.500</td>\n",
       "      <td>0.530</td>\n",
       "      <td>0.5150</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>(0.53, 0.56]</td>\n",
       "      <td>0.966102</td>\n",
       "      <td>0.530</td>\n",
       "      <td>0.560</td>\n",
       "      <td>0.5450</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>(0.56, 0.59]</td>\n",
       "      <td>0.963768</td>\n",
       "      <td>0.560</td>\n",
       "      <td>0.590</td>\n",
       "      <td>0.5750</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>(0.59, 0.621]</td>\n",
       "      <td>0.963235</td>\n",
       "      <td>0.590</td>\n",
       "      <td>0.621</td>\n",
       "      <td>0.6055</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>(0.621, 0.651]</td>\n",
       "      <td>0.956522</td>\n",
       "      <td>0.621</td>\n",
       "      <td>0.651</td>\n",
       "      <td>0.6360</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        Price_bin  Demand_at_price  Price_bin_left  Price_bin_right  \\\n",
       "0     (0.5, 0.53]         0.985075           0.500            0.530   \n",
       "1    (0.53, 0.56]         0.966102           0.530            0.560   \n",
       "2    (0.56, 0.59]         0.963768           0.560            0.590   \n",
       "3   (0.59, 0.621]         0.963235           0.590            0.621   \n",
       "4  (0.621, 0.651]         0.956522           0.621            0.651   \n",
       "\n",
       "   Price_bin_mid  \n",
       "0         0.5150  \n",
       "1         0.5450  \n",
       "2         0.5750  \n",
       "3         0.6055  \n",
       "4         0.6360  "
      ]
     },
     "execution_count": 347,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "test_demand_curve.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 348,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "true revenue using logistic 100 price: 1.141795936202753\n"
     ]
    }
   ],
   "source": [
    "# logistic 100 points\n",
    "price = best_rev_log100[0]\n",
    "true_best_rev = 0\n",
    "for i in range(len(test_demand_curve)):\n",
    "    if price > test_demand_curve['Price_bin_left'][i] and price <= test_demand_curve['Price_bin_right'][i]:\n",
    "        true_best_rev = price*test_demand_curve['Demand_at_price'][i]\n",
    "print('true revenue using logistic 100 price:', true_best_rev)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 349,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "true revenue using logistic all price: 1.1413105797443595\n"
     ]
    }
   ],
   "source": [
    "# logistic all points\n",
    "price = best_rev_logAll[0]\n",
    "true_best_rev = 0\n",
    "for i in range(len(test_demand_curve)):\n",
    "    if price > test_demand_curve['Price_bin_left'][i] and price <= test_demand_curve['Price_bin_right'][i]:\n",
    "        true_best_rev = price*test_demand_curve['Demand_at_price'][i]\n",
    "print('true revenue using logistic all price:', true_best_rev)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 350,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "true revenue using naive 100 price: 1.1655414476964976\n"
     ]
    }
   ],
   "source": [
    "# naive 100 points\n",
    "price = best_rev_naive100[0]\n",
    "true_best_rev = 0\n",
    "for i in range(len(test_demand_curve)):\n",
    "    if price > test_demand_curve['Price_bin_left'][i] and price <= test_demand_curve['Price_bin_right'][i]:\n",
    "        true_best_rev = price*test_demand_curve['Demand_at_price'][i]\n",
    "print('true revenue using naive 100 price:', true_best_rev)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 351,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "true revenue using naive all price: 1.1655414476964976\n"
     ]
    }
   ],
   "source": [
    "# naive all points\n",
    "price = best_rev_naiveAll[0]\n",
    "true_best_rev = 0\n",
    "for i in range(len(test_demand_curve)):\n",
    "    if price > test_demand_curve['Price_bin_left'][i] and price <= test_demand_curve['Price_bin_right'][i]:\n",
    "        true_best_rev = price*test_demand_curve['Demand_at_price'][i]\n",
    "print('true revenue using naive all price:', true_best_rev)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 352,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(2.083, 1.1922434210526316)"
      ]
     },
     "execution_count": 352,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "best_rev_true = get_revenue_maximizing_price_and_revenue(test_demand_curve['Price_bin_mid'], test_demand_curve['Demand_at_price'])\n",
    "best_rev_true"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font color='blue'> How do your estimates compare to the actual revenue? Discuss in no more than 3 sentences. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Our estimates do not reach the true optimal revenue, but all of them are pretty close to the true optimal. Naive method out perform logistic regression by a little."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Problem 2: Demand estimation and pricing with covariates "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, we are going to ask you to do personalized pricing, based on just a two binarized covariates. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First, take `df_train` and create a new column for \"low\" and \"high\" wealth, based on if the income level is above or below the median income level. Second, create a new column for Location: `1` if the location is either America, and `0` if the location is anything else.\n",
    "\n",
    "For this section, we will use all the df_train data, as opposed to just the first few rows."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 353,
   "metadata": {},
   "outputs": [],
   "source": [
    "df_train['is_America'] = np.where(df_train['Location']=='America', 1, 0)\n",
    "df_train['wealth_status'] = np.where(df_train['Income']>= np.median(df_train['Income']), 1, 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 354,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Location</th>\n",
       "      <th>Income</th>\n",
       "      <th>Offered price</th>\n",
       "      <th>Purchased</th>\n",
       "      <th>bin_with_10_bins</th>\n",
       "      <th>is_America</th>\n",
       "      <th>wealth_status</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Africa</td>\n",
       "      <td>10.38</td>\n",
       "      <td>3.16</td>\n",
       "      <td>False</td>\n",
       "      <td>(2.95, 3.54]</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Europe</td>\n",
       "      <td>26.33</td>\n",
       "      <td>3.47</td>\n",
       "      <td>True</td>\n",
       "      <td>(2.95, 3.54]</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Europe</td>\n",
       "      <td>24.06</td>\n",
       "      <td>3.78</td>\n",
       "      <td>True</td>\n",
       "      <td>(3.54, 4.19]</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Africa</td>\n",
       "      <td>16.18</td>\n",
       "      <td>3.74</td>\n",
       "      <td>False</td>\n",
       "      <td>(3.54, 4.19]</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Asia Pacific</td>\n",
       "      <td>13.73</td>\n",
       "      <td>4.75</td>\n",
       "      <td>False</td>\n",
       "      <td>(4.19, 4.77]</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       Location  Income  Offered price  Purchased bin_with_10_bins  \\\n",
       "0        Africa   10.38           3.16      False     (2.95, 3.54]   \n",
       "1        Europe   26.33           3.47       True     (2.95, 3.54]   \n",
       "2        Europe   24.06           3.78       True     (3.54, 4.19]   \n",
       "3        Africa   16.18           3.74      False     (3.54, 4.19]   \n",
       "4  Asia Pacific   13.73           4.75      False     (4.19, 4.77]   \n",
       "\n",
       "   is_America  wealth_status  \n",
       "0           0              1  \n",
       "1           0              1  \n",
       "2           0              1  \n",
       "3           0              1  \n",
       "4           0              1  "
      ]
     },
     "execution_count": 354,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_train.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 355,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "10.34"
      ]
     },
     "execution_count": 355,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.median(df_train['Income'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2a) Demand estimation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font color='blue'> First, Fill in the below function that fits a logistic regression to predict the probability of purchase at a price ($d(p)$). The logistic regression should now have more coefficients than before: 1 for each covariate, and any interactions (including interactions between price and covariates) that you wish to add. If you add more interactions, you may wish to add regularization. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 356,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Location</th>\n",
       "      <th>Income</th>\n",
       "      <th>Offered price</th>\n",
       "      <th>Purchased</th>\n",
       "      <th>bin_with_10_bins</th>\n",
       "      <th>is_America</th>\n",
       "      <th>wealth_status</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Africa</td>\n",
       "      <td>10.38</td>\n",
       "      <td>3.16</td>\n",
       "      <td>False</td>\n",
       "      <td>(2.95, 3.54]</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Europe</td>\n",
       "      <td>26.33</td>\n",
       "      <td>3.47</td>\n",
       "      <td>True</td>\n",
       "      <td>(2.95, 3.54]</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Europe</td>\n",
       "      <td>24.06</td>\n",
       "      <td>3.78</td>\n",
       "      <td>True</td>\n",
       "      <td>(3.54, 4.19]</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Africa</td>\n",
       "      <td>16.18</td>\n",
       "      <td>3.74</td>\n",
       "      <td>False</td>\n",
       "      <td>(3.54, 4.19]</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Asia Pacific</td>\n",
       "      <td>13.73</td>\n",
       "      <td>4.75</td>\n",
       "      <td>False</td>\n",
       "      <td>(4.19, 4.77]</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       Location  Income  Offered price  Purchased bin_with_10_bins  \\\n",
       "0        Africa   10.38           3.16      False     (2.95, 3.54]   \n",
       "1        Europe   26.33           3.47       True     (2.95, 3.54]   \n",
       "2        Europe   24.06           3.78       True     (3.54, 4.19]   \n",
       "3        Africa   16.18           3.74      False     (3.54, 4.19]   \n",
       "4  Asia Pacific   13.73           4.75      False     (4.19, 4.77]   \n",
       "\n",
       "   is_America  wealth_status  \n",
       "0           0              1  \n",
       "1           0              1  \n",
       "2           0              1  \n",
       "3           0              1  \n",
       "4           0              1  "
      ]
     },
     "execution_count": 356,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_train.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 357,
   "metadata": {},
   "outputs": [],
   "source": [
    "def fit_logistic_regression_demand_with_covariates(df):\n",
    "    df1 = df.copy()\n",
    "    X = df1[['Offered price', 'is_America', 'wealth_status']]\n",
    "    Y = df1['Purchased']\n",
    "    #X = np.array(X).reshape(-1, 1)\n",
    "    model = LogisticRegression(fit_intercept=True)\n",
    "    model.fit(X, Y)\n",
    "    \n",
    "    return model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font color='blue'> Fill in the below function, that takes in a single price, covariates, and your trained model, and outputs the prediction for the demand $d(p)$ at that price. For example, one of the covariate inputs to the function can be `['NotAmerica', 'LowWealth']`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 358,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_prediction_logistic(fitted_model, price, covariates):\n",
    "    #price = np.array(price).reshape(-1,1)\n",
    "    my_x = [[p, covariates[0], covariates[1]] for p in price]\n",
    "    prediction = fitted_model.predict_proba(my_x)\n",
    "    \n",
    "    prediction = pd.DataFrame(prediction)[1]\n",
    "    return prediction"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 359,
   "metadata": {},
   "outputs": [],
   "source": [
    "test_demand_curve_America_HighWealth = pd.read_csv('test_demand_America_HighWealth.csv')\n",
    "test_demand_curve_NotAmerica_HighWealth = pd.read_csv('test_demand_NotAmerica_HighWealth.csv')\n",
    "test_demand_curve_America_LowWealth = pd.read_csv('test_demand_America_LowWealth.csv')\n",
    "test_demand_curve_NotAmerica_LowWealth = pd.read_csv('test_demand_NotAmerica_LowWealth.csv')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font color='blue'> Fit a model and get the predictions for each of the prices in `prices_to_predict` using your above function and each unique covariate combination.\n",
    "\n",
    "For example, `test_demand_NotAmerica_LowWealth`, we got:\n",
    "\n",
    "Group Not America, Low Wealth: Optimal price 1.314070, Revenue 0.913284, True revenue 0.788442\n",
    "\n",
    "\n",
    "<font color='blue'> For each covariate combination, generate the same lineplot as in 1a and 1b (separately for each covariate combination). Also include the \"true\" test-time demand curve for the appropriate covariate combination \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 360,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1.2537688442211055, 0.7346870013657666)"
      ]
     },
     "execution_count": 360,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Not America Low Wealth points\n",
    "train = df_train.copy()\n",
    "model_log = fit_logistic_regression_demand_with_covariates(train)\n",
    "prediction_log_notA_lowW = get_prediction_logistic(model_log, prices_to_predict, [0,0])\n",
    "\n",
    "best_rev_log_notA_lowW = get_revenue_maximizing_price_and_revenue(prices_to_predict, prediction_log_notA_lowW)\n",
    "best_rev_log_notA_lowW"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 361,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "true revenue using logistic all price: 0.8059942569992822\n"
     ]
    }
   ],
   "source": [
    "# logistic all points\n",
    "price = best_rev_log_notA_lowW[0]\n",
    "true_best_rev = 0\n",
    "for i in range(len(test_demand_curve_NotAmerica_LowWealth)):\n",
    "    if price > test_demand_curve_NotAmerica_LowWealth['Price_bin_left'][i] and price <= test_demand_curve_NotAmerica_LowWealth['Price_bin_right'][i]:\n",
    "        true_best_rev = price*test_demand_curve_NotAmerica_LowWealth['Demand_at_price'][i]\n",
    "print('true revenue using logistic all price:', true_best_rev)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 362,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Price_bin</th>\n",
       "      <th>Demand_at_price</th>\n",
       "      <th>Price_bin_left</th>\n",
       "      <th>Price_bin_right</th>\n",
       "      <th>Price_bin_mid</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>(0.5, 0.53]</td>\n",
       "      <td>0.969231</td>\n",
       "      <td>0.500</td>\n",
       "      <td>0.530</td>\n",
       "      <td>0.5150</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>(0.53, 0.56]</td>\n",
       "      <td>0.926471</td>\n",
       "      <td>0.530</td>\n",
       "      <td>0.560</td>\n",
       "      <td>0.5450</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>(0.56, 0.59]</td>\n",
       "      <td>0.924528</td>\n",
       "      <td>0.560</td>\n",
       "      <td>0.590</td>\n",
       "      <td>0.5750</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>(0.59, 0.621]</td>\n",
       "      <td>0.906977</td>\n",
       "      <td>0.590</td>\n",
       "      <td>0.621</td>\n",
       "      <td>0.6055</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>(0.621, 0.651]</td>\n",
       "      <td>0.901408</td>\n",
       "      <td>0.621</td>\n",
       "      <td>0.651</td>\n",
       "      <td>0.6360</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        Price_bin  Demand_at_price  Price_bin_left  Price_bin_right  \\\n",
       "0     (0.5, 0.53]         0.969231           0.500            0.530   \n",
       "1    (0.53, 0.56]         0.926471           0.530            0.560   \n",
       "2    (0.56, 0.59]         0.924528           0.560            0.590   \n",
       "3   (0.59, 0.621]         0.906977           0.590            0.621   \n",
       "4  (0.621, 0.651]         0.901408           0.621            0.651   \n",
       "\n",
       "   Price_bin_mid  \n",
       "0         0.5150  \n",
       "1         0.5450  \n",
       "2         0.5750  \n",
       "3         0.6055  \n",
       "4         0.6360  "
      ]
     },
     "execution_count": 362,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "test_demand_curve_NotAmerica_LowWealth.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 363,
   "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"
    }
   ],
   "source": [
    "plt.plot(prices_to_predict, prediction_log_notA_lowW, color='red')\n",
    "plt.plot(test_demand_curve_NotAmerica_LowWealth['Price_bin_mid'], test_demand_curve_NotAmerica_LowWealth['Demand_at_price'])\n",
    "plt.xlabel('price')\n",
    "plt.ylabel('demand')\n",
    "plt.title('Not America Low Wealth')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 364,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Group America, Low Wealth: Optimal price and Revenue are: (1.7060301507537687, 1.1685625179462906)\n",
      "true revenue using logistic all price: 1.0236180904522612\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# America Low Wealth points\n",
    "train = df_train.copy()\n",
    "model_log = fit_logistic_regression_demand_with_covariates(train)\n",
    "prediction_log_A_lowW = get_prediction_logistic(model_log, prices_to_predict, [1,0])\n",
    "\n",
    "best_rev_log_A_lowW = get_revenue_maximizing_price_and_revenue(prices_to_predict, prediction_log_A_lowW)\n",
    "print('Group America, Low Wealth: Optimal price and Revenue are:',best_rev_log_A_lowW)\n",
    "\n",
    "# logistic all points\n",
    "price = best_rev_log_A_lowW[0]\n",
    "true_best_rev = 0\n",
    "for i in range(len(test_demand_curve_America_LowWealth)):\n",
    "    if price > test_demand_curve_America_LowWealth['Price_bin_left'][i] and price <= test_demand_curve_America_LowWealth['Price_bin_right'][i]:\n",
    "        true_best_rev = price*test_demand_curve_America_LowWealth['Demand_at_price'][i]\n",
    "print('true revenue using logistic all price:', true_best_rev)\n",
    "\n",
    "plt.plot(prices_to_predict, prediction_log_A_lowW, color='red')\n",
    "plt.plot(test_demand_curve_America_LowWealth['Price_bin_mid'], test_demand_curve_America_LowWealth['Demand_at_price'])\n",
    "plt.xlabel('price')\n",
    "plt.ylabel('demand')\n",
    "plt.title('America Low Wealth')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 365,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Group Not America, High Wealth: Optimal price and Revenue are: (2.42964824120603, 1.8972428666515946)\n",
      "true revenue using logistic all price: 1.8093125200470437\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Not America High Wealth points\n",
    "train = df_train.copy()\n",
    "model_log = fit_logistic_regression_demand_with_covariates(train)\n",
    "prediction_log_notA_highW = get_prediction_logistic(model_log, prices_to_predict, [0,1])\n",
    "\n",
    "best_rev_log_notA_highW = get_revenue_maximizing_price_and_revenue(prices_to_predict, prediction_log_notA_highW)\n",
    "print('Group Not America, High Wealth: Optimal price and Revenue are:',best_rev_log_notA_highW)\n",
    "\n",
    "# logistic all points\n",
    "price = best_rev_log_notA_highW[0]\n",
    "true_best_rev = 0\n",
    "for i in range(len(test_demand_curve_NotAmerica_HighWealth)):\n",
    "    if price > test_demand_curve_NotAmerica_HighWealth['Price_bin_left'][i] and price <= test_demand_curve_NotAmerica_HighWealth['Price_bin_right'][i]:\n",
    "        true_best_rev = price*test_demand_curve_NotAmerica_HighWealth['Demand_at_price'][i]\n",
    "print('true revenue using logistic all price:', true_best_rev)\n",
    "\n",
    "plt.plot(prices_to_predict, prediction_log_notA_highW, color='red')\n",
    "plt.plot(test_demand_curve_NotAmerica_HighWealth['Price_bin_mid'], test_demand_curve_NotAmerica_HighWealth['Demand_at_price'])\n",
    "plt.xlabel('price')\n",
    "plt.ylabel('demand')\n",
    "plt.title('Not America High Wealth')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 366,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Group America, High Wealth: Optimal price and Revenue are: (2.972361809045226, 2.442468257720609)\n",
      "true revenue using logistic all price: 2.1231155778894473\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# America High Wealth points\n",
    "train = df_train.copy()\n",
    "model_log = fit_logistic_regression_demand_with_covariates(train)\n",
    "prediction_log_A_highW = get_prediction_logistic(model_log, prices_to_predict, [1,1])\n",
    "\n",
    "best_rev_log_A_highW = get_revenue_maximizing_price_and_revenue(prices_to_predict, prediction_log_A_highW)\n",
    "print('Group America, High Wealth: Optimal price and Revenue are:',best_rev_log_A_highW)\n",
    "\n",
    "# logistic all points\n",
    "price = best_rev_log_A_highW[0]\n",
    "true_best_rev = 0\n",
    "for i in range(len(test_demand_curve_America_HighWealth)):\n",
    "    if price > test_demand_curve_America_HighWealth['Price_bin_left'][i] and price <= test_demand_curve_America_HighWealth['Price_bin_right'][i]:\n",
    "        true_best_rev = price*test_demand_curve_America_HighWealth['Demand_at_price'][i]\n",
    "print('true revenue using logistic all price:', true_best_rev)\n",
    "\n",
    "plt.plot(prices_to_predict, prediction_log_A_highW, color='red')\n",
    "plt.plot(test_demand_curve_America_HighWealth['Price_bin_mid'], test_demand_curve_America_HighWealth['Demand_at_price'])\n",
    "plt.xlabel('price')\n",
    "plt.ylabel('demand')\n",
    "plt.title('America High Wealth')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2b) Pricing"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font color='blue'> Now, use your code from 1c to output predicted optimal prices, predicted revenue, and and actual revenue using the test data curve, for each covariate combination. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 395,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Group Not America, Low Wealth: Optimal price and Revenue are: (1.2537688442211055, 0.7346870013657666)\n",
      "true revenue using logistic all price: 0.8059942569992822\n"
     ]
    }
   ],
   "source": [
    "# Not America Low Wealth points\n",
    "train = df_train.copy()\n",
    "model_log = fit_logistic_regression_demand_with_covariates(train)\n",
    "prediction_log_notA_lowW = get_prediction_logistic(model_log, prices_to_predict, [0,0])\n",
    "\n",
    "best_rev_log_notA_lowW = get_revenue_maximizing_price_and_revenue(prices_to_predict, prediction_log_notA_lowW)\n",
    "print('Group Not America, Low Wealth: Optimal price and Revenue are:',best_rev_log_notA_lowW)\n",
    "\n",
    "# logistic all points\n",
    "price = best_rev_log_notA_lowW[0]\n",
    "true_best_rev0 = 0\n",
    "for i in range(len(test_demand_curve_NotAmerica_LowWealth)):\n",
    "    if price > test_demand_curve_NotAmerica_LowWealth['Price_bin_left'][i] and price <= test_demand_curve_NotAmerica_LowWealth['Price_bin_right'][i]:\n",
    "        true_best_rev0 = price*test_demand_curve_NotAmerica_LowWealth['Demand_at_price'][i]\n",
    "print('true revenue using logistic all price:', true_best_rev0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 389,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Group America, Low Wealth: Optimal price and Revenue are: (1.7060301507537687, 1.1685625179462906)\n",
      "true revenue using logistic all price: 1.0236180904522612\n"
     ]
    }
   ],
   "source": [
    "# America Low Wealth points\n",
    "train = df_train.copy()\n",
    "model_log = fit_logistic_regression_demand_with_covariates(train)\n",
    "prediction_log_A_lowW = get_prediction_logistic(model_log, prices_to_predict, [1,0])\n",
    "\n",
    "best_rev_log_A_lowW = get_revenue_maximizing_price_and_revenue(prices_to_predict, prediction_log_A_lowW)\n",
    "print('Group America, Low Wealth: Optimal price and Revenue are:',best_rev_log_A_lowW)\n",
    "\n",
    "# logistic all points\n",
    "price = best_rev_log_A_lowW[0]\n",
    "true_best_rev1 = 0\n",
    "for i in range(len(test_demand_curve_America_LowWealth)):\n",
    "    if price > test_demand_curve_America_LowWealth['Price_bin_left'][i] and price <= test_demand_curve_America_LowWealth['Price_bin_right'][i]:\n",
    "        true_best_rev1 = price*test_demand_curve_America_LowWealth['Demand_at_price'][i]\n",
    "print('true revenue using logistic all price:', true_best_rev1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 390,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Group Not America, High Wealth: Optimal price and Revenue are: (2.42964824120603, 1.8972428666515946)\n",
      "true revenue using logistic all price: 1.8093125200470437\n"
     ]
    }
   ],
   "source": [
    "# Not America High Wealth points\n",
    "train = df_train.copy()\n",
    "model_log = fit_logistic_regression_demand_with_covariates(train)\n",
    "prediction_log_notA_highW = get_prediction_logistic(model_log, prices_to_predict, [0,1])\n",
    "\n",
    "best_rev_log_notA_highW = get_revenue_maximizing_price_and_revenue(prices_to_predict, prediction_log_notA_highW)\n",
    "print('Group Not America, High Wealth: Optimal price and Revenue are:',best_rev_log_notA_highW)\n",
    "\n",
    "# logistic all points\n",
    "price = best_rev_log_notA_highW[0]\n",
    "true_best_rev2 = 0\n",
    "for i in range(len(test_demand_curve_NotAmerica_HighWealth)):\n",
    "    if price > test_demand_curve_NotAmerica_HighWealth['Price_bin_left'][i] and price <= test_demand_curve_NotAmerica_HighWealth['Price_bin_right'][i]:\n",
    "        true_best_rev2 = price*test_demand_curve_NotAmerica_HighWealth['Demand_at_price'][i]\n",
    "print('true revenue using logistic all price:', true_best_rev2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 391,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Group America, High Wealth: Optimal price and Revenue are: (2.972361809045226, 2.442468257720609)\n",
      "true revenue using logistic all price: 2.1231155778894473\n"
     ]
    }
   ],
   "source": [
    "# America High Wealth points\n",
    "train = df_train.copy()\n",
    "model_log = fit_logistic_regression_demand_with_covariates(train)\n",
    "prediction_log_A_highW = get_prediction_logistic(model_log, prices_to_predict, [1,1])\n",
    "\n",
    "best_rev_log_A_highW = get_revenue_maximizing_price_and_revenue(prices_to_predict, prediction_log_A_highW)\n",
    "print('Group America, High Wealth: Optimal price and Revenue are:',best_rev_log_A_highW)\n",
    "\n",
    "# logistic all points\n",
    "price = best_rev_log_A_highW[0]\n",
    "true_best_rev3 = 0\n",
    "for i in range(len(test_demand_curve_America_HighWealth)):\n",
    "    if price > test_demand_curve_America_HighWealth['Price_bin_left'][i] and price <= test_demand_curve_America_HighWealth['Price_bin_right'][i]:\n",
    "        true_best_rev3 = price*test_demand_curve_America_HighWealth['Demand_at_price'][i]\n",
    "print('true revenue using logistic all price:', true_best_rev3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font color='blue'> Suppose each of the 4 covariate combinations make up an equal part of the population. What would be the resulting revenue achieved at test time if you use the optimal price for each group (so you look at their covariates, and then give them the optimal price for that group)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 394,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Actual revenue is: 1.4405101113470087\n"
     ]
    }
   ],
   "source": [
    "actual_revenue = 1/4*(true_best_rev0+true_best_rev1+true_best_rev2+true_best_rev3)\n",
    "print('Actual revenue is:',actual_revenue)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 392,
   "metadata": {},
   "outputs": [],
   "source": [
    "#test_demand_curve[100:150]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font color='blue'> Comment on your outputs in no more than 3 sentences. What is the effect of using different prices for differerent covariate groups?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see that using different prices for differerent covariate groups, we get a higher test revenue compared to our models using simple naive and logistic regressions. Using different prices for differerent covariate groups will allow us to reach a higher revenue."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Problem 3: Pricing under capacity constraints"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, we are going to build up to implementing the Bellman equation approach discussed in class, to price a single copy of an item to be sold over $T$ time periods. For simplicity, we will use `test_demand_curve` as $d(p)$. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 271,
   "metadata": {},
   "outputs": [],
   "source": [
    "price_options = list(test_demand_curve.Price_bin_mid)\n",
    "demand_predictions = list(test_demand_curve.Demand_at_price)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3a) Implementing one step of the Bellman equation\n",
    "\n",
    "Recall the \"Bellman equation\" taught in class. Suppose we have 1 copy of the item at time $t$. Then, my expected revenue given I price the item at $p_t$ is:\n",
    "$$ V_t = d(p_t)p_t + (1 - d(p_t))V_{t+1}$$\n",
    "\n",
    "<font color='blue'> Implement the following function that returns optimal price $p_t$ and the resulting value $V_t$, given the demand curve and $V_{t+1}$. \n",
    "\n",
    "For example, we find that the output of the following function call is: (2.083, 1.1922434210526316)\n",
    "\n",
    "`get_single_step_revenue_maximizing_price_and_revenue(0, price_options, demand_predictions)`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 269,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_single_step_revenue_maximizing_price_and_revenue(Vtplus1, price_options, demand_predictions):\n",
    "    Vt = []\n",
    "    for i in range(len(price_options)):\n",
    "        vt = demand_predictions[i]*price_options[i]+(1-demand_predictions[i])*Vtplus1\n",
    "        Vt.append(vt)\n",
    "    max_index = np.argmax(Vt)\n",
    "    \n",
    "    return price_options[max_index], Vt[max_index]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 272,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(2.083, 1.1922434210526316)"
      ]
     },
     "execution_count": 272,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "get_single_step_revenue_maximizing_price_and_revenue(0, price_options, demand_predictions)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3b) Calculating prices over time\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font color='blue'> Implement the following function that returns a list (of length $T$) of optimal prices for each time period, and a expected revenue number for those prices.\n",
    "    \n",
    "Hint: your function should loop through each time step, _starting_ at time $t=T-1$ (the last time period, since the first time period is time $t=0$). Each iteration of the loop should call the function from part 3a. Recall that we can define $V_T = 0$, since even if the item is unsold at time $T$, we have finished trying to sell it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 291,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_prices_over_time_and_expected_revenue(prices, demand_predictions, T):\n",
    "    T_lst = reversed(range(T))\n",
    "    vt = 0\n",
    "    prices = []\n",
    "    values = []\n",
    "    for i in range(T):\n",
    "        opt = get_single_step_revenue_maximizing_price_and_revenue(vt, price_options, demand_predictions)\n",
    "        prices.append(opt[0])\n",
    "        values.append(opt[1])\n",
    "        vt = opt[1]\n",
    "    prices.reverse()\n",
    "    \n",
    "    return prices, values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 292,
   "metadata": {},
   "outputs": [],
   "source": [
    "prices = get_prices_over_time_and_expected_revenue(price_options, demand_predictions, 100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 295,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "5.822 4.224\n"
     ]
    }
   ],
   "source": [
    "print(prices[0][0],prices[0][90])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 300,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "5.228684354819154\n"
     ]
    }
   ],
   "source": [
    "print(prices[1][99])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font color='blue'> Plot a line plot for your optimal prices over time when $T=100$ and $T=10$. Also print out the expected revenue using these prices and for each $T$. \n",
    "\n",
    "For example, when $T=100$, we find that prices[0] = 5.822, prices[90] = 4.224, and that revenue = 5.2287"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 330,
   "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"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Revenue is 5.228684354819154\n"
     ]
    }
   ],
   "source": [
    "plt.plot(range(100),prices[0])\n",
    "plt.plot(range(100),prices[1])\n",
    "plt.show()\n",
    "print(\"Revenue is\", prices[1][99])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 306,
   "metadata": {},
   "outputs": [],
   "source": [
    "prices_10 = get_prices_over_time_and_expected_revenue(price_options, demand_predictions, 10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 329,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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NgceOKnQzGwYMA0hNTS1hZBGpkPbvwDbMpE/GbM6JmQmxi7GcIgqXGetjmpLS9kqiUjp75Z3UGqJi/E4cdopV6M65QqCjmdUE/mNm7ZxzS4645HjvRvxoLMc5NxoYDd6Qy+nHFZEKwTlv7DtjFmyY5X3OWuM9FxWHJXeFc35DYUoa726vx4MfruPiffV4sVNnIrSjY5k5rX/fOOf2mNkXwCXAkYW+CUg54utkYEup04lIxVBY4E0TzJgFG2ZCxmw4sMN7Lq4WpKZBl1ugUS+o1+F/d9+RwPUt4ABx/HnKMp74aDkP9mvt2x8j3J2y0M0sCcgPlHkccAHwxDGXTQLuMrO38d4Uzdb4uUgIy8uBzfO8As+YBRu/PbxBVc1UaHauV+Kpad6y+VPMOrmtd2M27DrAy1+tJfWMeAb3aFQOf4jKpzh36PWB1wLj6BHAeOfcFDMbDuCcGwVMxZvhshpv2uKtZZRXRMpCTpZ31/1DgW9ZCEX5gEGdNnDW9YcLPKHhaX97M+OP/duwMSuHP36wlORa8fQ5Mynof4zKTguLRCqjPRmHx74zZnmrMMGbfdKgMzQKlHdKd29IJUj2Hyrg2lGz2JiVw4Q702hVL4x2cCwnWikqUpkVFXkbVP3vDczZsHeT91yVGpDSA1J7euPfDTpDdGyZxtmafZABI78h0oyJI3pTp0bZ/rxwo0IXqUycg8wVsOYzWPslbJx9+Fi06vUPD500SvOGU3xYuLNkczaDXp5Fs6RqvHNHT+JjNP+8uHRItEi4y8mCtV94Jb5mundQMcAZzaHNlZDay7sLryB7nrRrmMDzN3TiZ+Pmcs/bCxk1pIsOqA4CFbpIKCrMh01zAwX+OWyeDzjvDMumfaHZfdDsPG9GSgV1fuu6PHx5Wx6etJTHp6bzh/5t/I4U8lToIqEia51X3ms+h3VfeXugWAQ07Ap9H4Bm53urMENo+fzNvRqzftcBxny9jkZnxHNTWmO/I4W00PlfXqSyObQP1s04fBeetdZ7PCEV2l3t3YE36QNxNX2NWVq/v8ybzvinSUtJqRXPua3q+B0pZOlNUZGKoqgIti48fBe+cY53+k50PDQ+G5qf792Fn9GsQoyDB9OBQwVcN3oW6zIPMH54Gm0bJPgdqcLSLBeRimrv1kCBB97MPJjlPV6vQ6DAz/OmFYbQmZcltX1vLgNGfoNzMHFEb+olaDrj8WiWi0hFkX/Q2wvlh7vwHcu8x6vWgRYXeSXetC9Uq3zDDnVrxDL2lm4MfGkmt/3rO94dnkbVKqqo06FXS6QsOeetwlz9mXcXvmEmFOR6KzJT0+CCR7wSr9su7IZRSqJ1/RqMHNyZn742l7vfWsArN3XVdMbToEIXCbbcbFj9KawO3IXvC2w8mtgSutzqFXijXhBT1d+cFVTflnX40xVt+cPEJfx5yjL+dEVbvyOFDBW6SDAc2AkrpkL6ZG+BT2GedxJ9077eOHiz86Bmyim+ifxgaM9GZOw6wCszvOmMt/Zu4nekkKBCFymp7M2w/ENInwQbvgFX5C3k6T4MWl8Oyd10HmYpPHhpazKycnh0yjKSa8VzYZu6fkeq8DTLReR0ZK317sKXTYLNgb+/Sa28Am99uTc7RWPhQXMwr5DrR89i5fb9jL8jjfbJms6oaYsiJeUc7Ej37sLTJ3un9oB3Kn3ry6H1FZB0pq8Rw92OfblcNXIm+YVFTBzRmwY14/yO5CsVusjpcA62zPfuwtMnB87KNG9zq9ZXQOv+FXqPlHC0Yts+Br40k4a14nh3eBrVY6P9juQbzUMXOZWiQm+/8PTJkD7F2y88IspbodnrLmh5GVTXGK5fWtarzotDOnPLq99x15sLGHNzV6IiT37sXWWkQpfKqyDP2+QqfZL35mbOToiK9ZbXn/d7OPNiiK/td0oJOLtFEo8NaMeD7y/m4UlLeWxAO0zvVxxFhS6VS16Ot8AnfTKs+AgOZUNMNa+8W18OzS+EKtX8TikncEP3VDbsymHUl2tokliV289u6nekCkWFLuEvNxtW/te7E1/9KeTneOdk/jAzpWnfMj92TYLnvotbkpF1gP+bmk5yrXguaVfP70gVhgpdwtMPC32WTfIW+hTlQ7V60PFG743NRr1Dat9wOSwiwnh6UEe27JnNve8s4J2ENM5Kqel3rApBs1wkfORkwZL3YNkHRyz0aQRtrvBKvGFXiNAbaeFi5/5DDBj5Dbn5RUwc0YvkWvF+RyoXmrYo4auoCNZOhwX/9t7YLMwLLPS5IrDQp70W+oSx1Tv2cdWLM6mfEMuEO3tRoxJMZyzVtEUzSwHGAfWAImC0c+7ZY67pC3wArAs89L5z7tFSZBY5ud0bYOEbsPBNyN7ojYl3vQ06DfFKXCqF5nWq8/KQLtw09ltGvDGfsbd0I7oST2csziBiAfBr59x8M6sOzDOzT5xzy465boZzrn/wI4oE5OfC8ine3fjaL73Hmp0LFz4KrS6rFIdAyI/1ap7I41e3574Ji/jDxCX85er2lXY64ykL3Tm3Fdga+PU+M0sHGgLHFrpI2dj6PSx4HRaNh9w93irNvg96b3BqB0MBBnVNIWNXDi9MX03jxKoM79PM70i+OK23+c2sMdAJmHOcp9PM7HtgC/Ab59zS0seTSuvgblg8AeaPg22LILKKNybeeSg0PkdvbsqP/OrCM9mQlcNfpy0ntXY8/drX9ztSuSt2oZtZNeA94F7n3N5jnp4PNHLO7TezfsBEoMVxvscwYBhAaqr2wpBjFBXBui+9u/H0yVB4yNu9sN/fod01WrUpJxURYTw5sANb9hzkl+8spF5CLJ1Ta/kdq1wVa5aLmUUDU4CPnXNPF+P69UBX59zOE12jWS7yP3s2em9uLnwd9mR4B0N0GOS9wVn/LL/TSYjZtf8QV780k/25BUwc0ZuU2uE1nbG0s1wMGAOkn6jMzawesN0558ysOxAB7CpFZgl3BYe8aYYL/u2ddo/zVmye/zC06q+Vm1JiZ1SrwthbunH1izO55dVvef/O3iTEh/90RijekEtvYCiw2MwWBh77HZAK4JwbBQwE7jSzAuAgcL3za4K7VGzblnglvugdb5y8RjL0uQ86DoZajfxOJ2GiWVI1Xh7ahaFj5nDnG/P4163diYkK//ddtLBIyt7BPbBkAsz/N2xd6J1436q/N6TStK+OaZMy8/78Tfxq/Pdc2yWZvw3sEBbTGbUfupS/oiLY8LVX4umToCAX6raDS57wxsf1BqeUg6s7J7NhVw7PfraKxolVGXFuc78jlSkVugRX9ubDb3DuXg9VErzhlM5DvWPbwuAOSULLvRe0ICMrhyc/XkHN+Ghu7J4aFnfqx6NCl9IrKoKV02Duq95e467IO+nn3Ie8uePRlfsMSPGXmfHXa9qzfW8uD/1nCRMXbObhy9vSrmH4HTitMXQpuaIibzjly7/BjqVQo6G3erPjYKjdxO90IkcpLHKMn7uRJz9ewe6cPK7vlsKvL2pJYrXQ2jJCuy1KcBUVwbKJ8NWTsGMZnNECzvmtt/hHe4xLBZd9MJ/nPlvFazPXExcTyT3nt+CmtMYhMwtGhS7BUVToFfmXf4PM5ZB4JpxzH7S7WjNVJOSs3rGPR6ek89XKTJomVeWP/dvQt2Udv2OdkgpdSqeoEJb+xyvynSu8/cbP+S20vUpFLiHNOcfny3fw5ynLWL8rh/Na1eEP/dvQJLGq39FOSIUuJVNU6J0A9NWTsHMlJLX2FgG1GaDNsSSs5BUU8a+Z63jus9UcKijktt5NuOu85lSvgAdmqNDl9BQWeAuBvnoSdq2GOm2gz/3eKUAqcgljO/bl8uRHK3h33iYSq1XhvktaMrBzMhERFWeaowpdiqewABa/6xV51hpvIVCf+6DV5SpyqVS+37iHRyYvZX7GHjokJ/Dw5W3p0qhi7NyoQpeTKyzw9laZ8XfIWusd4dbnfmh5mYpcKi3nHBMXbuav05azfe8hBnRswAOXtqZegr8bx2npvxxfYT58/7ZX5LvXe3uPX/8mtOynFZ1S6ZkZV3VK5qI29XjpizWMnrGWj5duZ8S5zbj97KbERle8CQG6Q6+MCvO95fkznoI9G7wl+X0fgDMvUZGLnEDGrhwen5rOR0u3kVI7jof6teHitnXLfRsBDbmIpyAPvn8TvnoKsjOgQSfvbM4WF6nIRYrpm9U7eXTyMlZs30evZmfw8OVtaVmvern9fBV6ZVeQ522WNeNpyN4IDbtAnwegxYUqcpESKCgs4s1vM3jqvyvZl5vPkJ6N+NWFZ1IzPqbMf7YKvbIqOOQdJjHjGdi7CZK7eUXe/HwVuUgQ7D6QxzOfruT12RuoERfNry48kxu7pxIVWXaTCVTolU1+rlfkXz8DezdDSg9v1kqz81TkImVg+ba9PDJpGbPW7qJl3eo8fHkbejVPLJOfpUKvLPJzYf44r8j3bYHUNK/Im/ZVkYuUMeccHy/dxmMfprNp90EuaVuPhy5rHfRDqjVtMdzlH4R5r8E3/4B9WyG1F1w1CpqcoyIXKSdmxiXt6tO3ZR3+OWMtI6ev4fMVOxh2dlN+fm4z4mPKvm51hx7KnIP5r8H0x2H/dmj0E+h7v3e4hIpcxFfbsnP567R0Ji7cQr0asTxwaSuu7Nig1NMcNeQSjrI3w6S7YM3n3h35eQ9B45/4nUpEjjFvQxZ/mrSMxZuz6dKoFg9f3oYOyTVL/P1OVuha1x1qnPNWd76YBhmz4bKn4NapKnORCqpLo9p8MKI3f7umAxt2HeDKkd/w3GeryuRnaQw9lOzPhCn3wvIp3hueV46EM5r5nUpETiEiwhjULYVL29fjhc9X0zm1bDb6UqGHimUfwJRfwqH9cNFj0PPnOlxCJMRUj43mwX6ty+z7n3LIxcxSzGy6maWb2VIzu+c415iZPWdmq81skZl1Lpu4ldDB3fDe7TD+JkhIgTu+hF53q8xF5EeKc4deAPzaOTffzKoD88zsE+fcsiOuuRRoEfjoAbwU+CylseoTmHQ3HMiEvr+Ds38FkRXvBBURqRhOWejOua3A1sCv95lZOtAQOLLQrwTGOW/KzGwzq2lm9QO/V07XoX3w8UPelMSk1nDD29Cgo9+pRKSCO60xdDNrDHQC5hzzVENg4xFfbwo8dlShm9kwYBhAamrqaUatJNbNgA9+Dns2Qu974NyHIKqK36lEJAQUe9qimVUD3gPudc7tPfbp4/yWH01wd86Nds51dc51TUpKOr2k4S7/IEx7AF7rDxFRcNvHcOGjKnMRKbZi3aGbWTRemb/hnHv/OJdsAlKO+DoZ2FL6eJXEprnwn+GwaxV0HwYX/AliqvqdSkRCTHFmuRgwBkh3zj19gssmATcFZrv0BLI1fl4MBXnw2aMw5kLvDn3oROj3pMpcREqkOHfovYGhwGIzWxh47HdAKoBzbhQwFegHrAZygFuDnjTcbFvs3ZVvXwIdh8Alj0Nsgt+pRCSEFWeWy9ccf4z8yGscMCJYocJaYQF88wx88QTE1fJmsLS81O9UIhIGtFK0PGWuhInDYfM8aHsVXPY0xNf2O5WIhAkVenkoKoI5o+CzRyA6DgaOhXbX+J1KRMKMCr2s7V4PE0fAhq/hzEvg8mehej2/U4lIGFKhl5UfDp/4+CHAvJ0ROw7WwRMiUmZU6GVh7xZvD5bVn3rHwF05EmpqZayIlC0VejA5B4vfham/8eaYX/okdLsdInSOiIiUPRV6sBzY6e1Xnj4Jkrt7hzTr8AkRKUcq9GBInwKT74FDe+GCR7RfuYj4QoVeGgf3wLT7YdHbUK8DXDUZ6rbxO5WIVFIq9JLa+C2Mvxn2b4c+98PZv4GoGL9TiUglpkIviW2L4fWB3irP2z+FhjpxT0T8p0I/XVlr4fVroEo1uHky1Ew59e8RESkHKvTTsW8b/PsqKMxTmYtIhaNCL66De7w78/2ZcPMkSGrpdyIRkaOo0IsjLwfeuh4yV8Dg8ZDc1e9EIiI/okI/lcJ8mHArZMz2dklsdp7fiUREjkuFfjJFRfDBXbDyI2/v8nZX+51IROSEtMnIiTgH//29t2jo3Ieg20/9TiQiclIq9BP5+mmYPRJ6DIdzfut3GhGRU1KhH8/cV+GzR6H9ILj4L9rDXERCggr9WMs+gA9/Bc0vhAEvautbEQkZaqsjrf0C3rsdkrvBoHEQGe13IhGRYlOh/2DzfHh7MJzRHG58B2Li/U4kInJaVOgAmSvhjcBmW0Peh7haficSETltpyx0MxtrZjvMbMkJnu9rZtlmtjDw8cfgxyxD2Zu8/VksAoZOhBr1/U4kIlIixVlY9C/gBWDcSa6Z4ZzrH5RE5SknC/59tXfS0C1TdGSciIS0U96hO+e+ArLKIUv5OrTfG2bZvR5ueAvqn+V3IhGRUgnWGHqamX1vZtPMrO2JLjKzYWY218zmZmZmBulHl0DBIXhnCGxZCNf+Cxr/xL8sIiJBEoxCnw80cs6dBTwPTDzRhc650c65rs65rklJSUH40SVQVAj/uQPWTocrnodW/fzJISISZKUudOfcXufc/sCvpwLRZpZY6mRlwTmY+htY+h+48M/QabDfiUREgqbUhW5m9cy8tfFm1j3wPXeV9vuWiemPw9yx0Pte6P0Lv9OIiATVKWe5mNlbQF8g0cw2AQ8D0QDOuVHAQOBOMysADgLXO+dcmSUuqdmj4Ku/QaehcMGf/E4jIhJ0pyx059wNp3j+BbxpjRXXovHw0f3Qqj/0/4c22xKRsBT+K0VX/hcm3gmNz4ZrxkCkzvQQkfAU3oWeMRvG3wR128L1b0J0rN+JRETKTPgW+val8OYgSGgIg9+D2Bp+JxIRKVPhWei713tL+qPjYeh/oJpPc95FRMpR+A0o798B4wZAQS7c9hHUTPU7kYhIuQivQs/Nhtevhv3b4aZJUKe134lERMpN+BR6/kF46wbYsRxufBtSuvmdSESkXIVHoRcWwITbYMNMuOaf0PwCvxOJiJS70C9052DyL2DFVOj3d2g/0O9EIiK+CP1ZLp/8ARa+AX0fhO4/8zuNiIhvQrvQv/4HzHweug+DPvf7nUZExFehW+jzx8GnD0O7gXDJE9qfRUQqvdAs9PTJMPkeaHY+DHgJIkLzjyEiEkyh14TrZsCEn0LDLnDdvyEqxu9EIiIVQugVetVEaNwbbhwPMVX9TiMiUmGE3rTFOq29/VlEROQooXeHLiIix6VCFxEJEyp0EZEwoUIXEQkTKnQRkTChQhcRCRMqdBGRMKFCFxEJE+ac8+cHm2UCG0r42xOBnUGME+r0ehxNr8dhei2OFg6vRyPnXNLxnvCt0EvDzOY657r6naOi0OtxNL0eh+m1OFq4vx4achERCRMqdBGRMBGqhT7a7wAVjF6Po+n1OEyvxdHC+vUIyTF0ERH5sVC9QxcRkWOo0EVEwkTIFbqZXWJmK8xstZk94HceP5lZiplNN7N0M1tqZvf4nclvZhZpZgvMbIrfWfxmZjXNbIKZLQ/8HUnzO5NfzOyXgf9GlpjZW2YW63emshBShW5mkcBI4FKgDXCDmbXxN5WvCoBfO+daAz2BEZX89QC4B0j3O0QF8SzwkXOuFXAWlfR1MbOGwC+Ars65dkAkcL2/qcpGSBU60B1Y7Zxb65zLA94GrvQ5k2+cc1udc/MDv96H9x9sQ39T+cfMkoHLgH/6ncVvZlYDOAcYA+Ccy3PO7fE1lL+igDgziwLigS0+5ykToVboDYGNR3y9iUpcYEcys8ZAJ2COz1H89A/gPqDI5xwVQVMgE3g1MAT1TzOrlKeqO+c2A38HMoCtQLZz7r/+pioboVbodpzHKv28SzOrBrwH3Ouc2+t3Hj+YWX9gh3Nunt9ZKogooDPwknOuE3AAqJTvOZlZLbx/yTcBGgBVzWyIv6nKRqgV+iYg5YivkwnTfzoVl5lF45X5G8659/3O46PewBVmth5vKO48M3vd30i+2gRscs798C+2CXgFXxldAKxzzmU65/KB94FePmcqE6FW6N8BLcysiZnF4L2xMcnnTL4xM8MbI013zj3tdx4/OecedM4lO+ca4/29+Nw5F5Z3YcXhnNsGbDSzloGHzgeW+RjJTxlATzOLD/w3cz5h+gZxlN8BTodzrsDM7gI+xnuneqxzbqnPsfzUGxgKLDazhYHHfuecm+pfJKlA7gbeCNz8rAVu9TmPL5xzc8xsAjAfb2bYAsJ0CwAt/RcRCROhNuQiIiInoEIXEQkTKnQRkTChQhcRCRMqdBGRMKFCFxEJEyp0EZEw8f82sbDuyy/V/wAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Revenue is 3.1976788395450586\n"
     ]
    }
   ],
   "source": [
    "plt.plot(range(10),prices_10[0])\n",
    "plt.plot(range(10),prices_10[1])\n",
    "plt.show()\n",
    "print(\"Revenue is\", prices_10[1][9])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3c) [Bonus, 3 points] Prices over time with multiple copies"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font color='blue'> Now, suppose that you have $K$ copies of the item, that you must sell over a time period $T$. Implement the two-dimensional dynamic program as discussed in class. Plot a line plot where the X axis is time as in 3b, but now you have $K$ lines where each line indicates the price at time $T$ if you have $K$ items left. \n",
    "    \n",
    "Hint: As in 3a and 3b, you may find it useful to first optimize the price $p_{t,k}$ given the values $V_{t+1, k}$, $V_{t+1, k-1}$. Then, have a 2nd function that loops through $t, k$ in an appropriate order. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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