{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "tags": [
     "remove_cell"
    ]
   },
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from datascience import *\n",
    "%matplotlib inline\n",
    "plt.style.use('seaborn-muted')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Measurements of Inequality"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The Lorenz Curve\n",
    "The Lorenz Curve visually presents income inequality by plotting household income percentile on the $x$-axis, and the cumulative income share that the bottom $x$ percentile own on the $y$-axis. The households are sorted by income, so that the first household at the 0th percentile has the least amount of income, while the household at the 100th percentile has the greatest income.\n",
    "\n",
    "For any point $(x,y)$ on the Lorenz curve, “the bottom x percent own y% of the income”. For example, if the $x$-axis reads 0.30 and $y$-axis reads 0.10, then it means that the bottom 30% of the population received 10% of the total population's income. This yields 2 implications for the Lorenz Curve:\n",
    "- The points $(0,0)$ and $(1,1)$ are always on the curve. $(0,0)$ represents the 0% of the population owning 0% of the income and $(1,1)$ represents 100% of the population owning 100% of the income.\n",
    "- The slope is always increasing. This is because households are sorted by income as percentiles: for a slight increase in $x$, households become richer and hence provide a larger share of total income.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Line of Perfect Equality\n",
    "In a world of perfect equality, everyone would have the exact same income. In this case, the Lorenz curve would just be a 45-degree straight line that runs through $(0,0)$ and $(1,1)$, i.e. $y=x$. Mathematically, this is because the derivative is constant: for a slight increase in $x$, the total share of income increases at a constant rate. Another way to think about this is that the bottom 10% of the population will own 10% of the total income, the bottom 50% of the population will own 50% of the total income, and so on. This line is known as the *line of perfect equality*, and we typically display this line when plotting our Lorenz curves as a reference."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### A Toy Example\n",
    "Let's suppose country 1 has the following income distribution: \n",
    "- The bottom 10% owns a cumulative 2% of total income \n",
    "- The bottom 20% owns 5% of total income\n",
    "- The bottom 30% owns 9% of total income\n",
    "- The bottom 40% owns 15% of total income \n",
    "- The bottom 50% owns 23% of total income\n",
    "- The bottom 60% owns 33% of total income\n",
    "- The bottom 70% with 45% of total income\n",
    "- The bottom 80% with 59% of total income \n",
    "- The bottom 90% with 75% of total income\n",
    "- The bottom 100% with 100% of total income\n",
    "\n",
    "We will create an array of income shares and call it `Country1`. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "Country1 = make_array(0, 0.02, 0.05, 0.09, 0.15, 0.23, 0.33, 0.45, 0.59, 0.75, 1.0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To better see this information, we will create a table containing population percentage and cumulative income share. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table border=\"1\" class=\"dataframe\">\n",
       "    <thead>\n",
       "        <tr>\n",
       "            <th>Population Percentage (%)</th> <th>Cumulative Income Share (%)</th> <th>Perfect Equality Income Share (%)</th>\n",
       "        </tr>\n",
       "    </thead>\n",
       "    <tbody>\n",
       "        <tr>\n",
       "            <td>0                        </td> <td>0                          </td> <td>0                                </td>\n",
       "        </tr>\n",
       "        <tr>\n",
       "            <td>10                       </td> <td>2                          </td> <td>10                               </td>\n",
       "        </tr>\n",
       "        <tr>\n",
       "            <td>20                       </td> <td>5                          </td> <td>20                               </td>\n",
       "        </tr>\n",
       "        <tr>\n",
       "            <td>30                       </td> <td>9                          </td> <td>30                               </td>\n",
       "        </tr>\n",
       "        <tr>\n",
       "            <td>40                       </td> <td>15                         </td> <td>40                               </td>\n",
       "        </tr>\n",
       "        <tr>\n",
       "            <td>50                       </td> <td>23                         </td> <td>50                               </td>\n",
       "        </tr>\n",
       "        <tr>\n",
       "            <td>60                       </td> <td>33                         </td> <td>60                               </td>\n",
       "        </tr>\n",
       "        <tr>\n",
       "            <td>70                       </td> <td>45                         </td> <td>70                               </td>\n",
       "        </tr>\n",
       "        <tr>\n",
       "            <td>80                       </td> <td>59                         </td> <td>80                               </td>\n",
       "        </tr>\n",
       "        <tr>\n",
       "            <td>90                       </td> <td>75                         </td> <td>90                               </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "</table>\n",
       "<p>... (1 rows omitted)</p>"
      ],
      "text/plain": [
       "Population Percentage (%) | Cumulative Income Share (%) | Perfect Equality Income Share (%)\n",
       "0                         | 0                           | 0\n",
       "10                        | 2                           | 10\n",
       "20                        | 5                           | 20\n",
       "30                        | 9                           | 30\n",
       "40                        | 15                          | 40\n",
       "50                        | 23                          | 50\n",
       "60                        | 33                          | 60\n",
       "70                        | 45                          | 70\n",
       "80                        | 59                          | 80\n",
       "90                        | 75                          | 90\n",
       "... (1 rows omitted)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "income_distribution = Table().with_columns(\n",
    "    \"Population Percentage (%)\", np.arange(11) * 10, \n",
    "    \"Cumulative Income Share (%)\", Country1 * 100, \n",
    "    \"Perfect Equality Income Share (%)\", np.arange(11) * 10\n",
    ")\n",
    "income_distribution"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "How will the Lorenz Curve for this income distribution look? "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "tags": [
     "remove_input"
    ]
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 792x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "income_distribution.scatter(0, 1, width=11, height=7)\n",
    "plt.plot([0,100], [0,100], color='k');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Comparing Lorenz Curves\n",
    "Now let's compare 2 countries' Lorenz curves. Suppose country 2 has the following income distribution:\n",
    "- The bottom 10% owns a cumulative 3% of total income \n",
    "- The bottom 20% owns 7% of total income\n",
    "- The bottom 30% owns 13% of total income\n",
    "- The bottom 40% owns 19% of total income \n",
    "- The bottom 50% owns 27% of total income\n",
    "- The bottom 60% owns 37% of total income\n",
    "- The bottom 70% with 50% of total income\n",
    "- The bottom 80% with 65% of total income \n",
    "- The bottom 90% with 81% of total income\n",
    "- The bottom 100% with 100% of total income"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table border=\"1\" class=\"dataframe\">\n",
       "    <thead>\n",
       "        <tr>\n",
       "            <th>Population Percentage (%)</th> <th>Cumulative Income Share (%)</th> <th>Perfect Equality Income Share (%)</th>\n",
       "        </tr>\n",
       "    </thead>\n",
       "    <tbody>\n",
       "        <tr>\n",
       "            <td>0                        </td> <td>0                          </td> <td>0                                </td>\n",
       "        </tr>\n",
       "        <tr>\n",
       "            <td>10                       </td> <td>3                          </td> <td>10                               </td>\n",
       "        </tr>\n",
       "        <tr>\n",
       "            <td>20                       </td> <td>7                          </td> <td>20                               </td>\n",
       "        </tr>\n",
       "        <tr>\n",
       "            <td>30                       </td> <td>13                         </td> <td>30                               </td>\n",
       "        </tr>\n",
       "        <tr>\n",
       "            <td>40                       </td> <td>19                         </td> <td>40                               </td>\n",
       "        </tr>\n",
       "        <tr>\n",
       "            <td>50                       </td> <td>27                         </td> <td>50                               </td>\n",
       "        </tr>\n",
       "        <tr>\n",
       "            <td>60                       </td> <td>37                         </td> <td>60                               </td>\n",
       "        </tr>\n",
       "        <tr>\n",
       "            <td>70                       </td> <td>50                         </td> <td>70                               </td>\n",
       "        </tr>\n",
       "        <tr>\n",
       "            <td>80                       </td> <td>65                         </td> <td>80                               </td>\n",
       "        </tr>\n",
       "        <tr>\n",
       "            <td>90                       </td> <td>81                         </td> <td>90                               </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "</table>\n",
       "<p>... (1 rows omitted)</p>"
      ],
      "text/plain": [
       "Population Percentage (%) | Cumulative Income Share (%) | Perfect Equality Income Share (%)\n",
       "0                         | 0                           | 0\n",
       "10                        | 3                           | 10\n",
       "20                        | 7                           | 20\n",
       "30                        | 13                          | 30\n",
       "40                        | 19                          | 40\n",
       "50                        | 27                          | 50\n",
       "60                        | 37                          | 60\n",
       "70                        | 50                          | 70\n",
       "80                        | 65                          | 80\n",
       "90                        | 81                          | 90\n",
       "... (1 rows omitted)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Country2 = make_array(0, 0.03, 0.07, 0.13, 0.19, 0.27, 0.37, 0.5, 0.65, 0.81, 1.0)\n",
    "income_distribution2 = Table().with_columns(\n",
    "    \"Population Percentage (%)\", np.arange(11) * 10, \n",
    "    \"Cumulative Income Share (%)\", Country2 * 100, \n",
    "    \"Perfect Equality Income Share (%)\", np.arange(11) * 10\n",
    ")\n",
    "income_distribution2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Comparing the 2 countries' income distributions side by side:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table border=\"1\" class=\"dataframe\">\n",
       "    <thead>\n",
       "        <tr>\n",
       "            <th>Population Percentage (%)</th> <th>Perfect Equality Income Share (%)</th> <th>Country 1 Cumulative Income Share (%)</th> <th>Country 2 Cumulative Income Share (%)</th>\n",
       "        </tr>\n",
       "    </thead>\n",
       "    <tbody>\n",
       "        <tr>\n",
       "            <td>0                        </td> <td>0                                </td> <td>0                                    </td> <td>0                                    </td>\n",
       "        </tr>\n",
       "        <tr>\n",
       "            <td>10                       </td> <td>10                               </td> <td>2                                    </td> <td>3                                    </td>\n",
       "        </tr>\n",
       "        <tr>\n",
       "            <td>20                       </td> <td>20                               </td> <td>5                                    </td> <td>7                                    </td>\n",
       "        </tr>\n",
       "        <tr>\n",
       "            <td>30                       </td> <td>30                               </td> <td>9                                    </td> <td>13                                   </td>\n",
       "        </tr>\n",
       "        <tr>\n",
       "            <td>40                       </td> <td>40                               </td> <td>15                                   </td> <td>19                                   </td>\n",
       "        </tr>\n",
       "        <tr>\n",
       "            <td>50                       </td> <td>50                               </td> <td>23                                   </td> <td>27                                   </td>\n",
       "        </tr>\n",
       "        <tr>\n",
       "            <td>60                       </td> <td>60                               </td> <td>33                                   </td> <td>37                                   </td>\n",
       "        </tr>\n",
       "        <tr>\n",
       "            <td>70                       </td> <td>70                               </td> <td>45                                   </td> <td>50                                   </td>\n",
       "        </tr>\n",
       "        <tr>\n",
       "            <td>80                       </td> <td>80                               </td> <td>59                                   </td> <td>65                                   </td>\n",
       "        </tr>\n",
       "        <tr>\n",
       "            <td>90                       </td> <td>90                               </td> <td>75                                   </td> <td>81                                   </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "</table>\n",
       "<p>... (1 rows omitted)</p>"
      ],
      "text/plain": [
       "Population Percentage (%) | Perfect Equality Income Share (%) | Country 1 Cumulative Income Share (%) | Country 2 Cumulative Income Share (%)\n",
       "0                         | 0                                 | 0                                     | 0\n",
       "10                        | 10                                | 2                                     | 3\n",
       "20                        | 20                                | 5                                     | 7\n",
       "30                        | 30                                | 9                                     | 13\n",
       "40                        | 40                                | 15                                    | 19\n",
       "50                        | 50                                | 23                                    | 27\n",
       "60                        | 60                                | 33                                    | 37\n",
       "70                        | 70                                | 45                                    | 50\n",
       "80                        | 80                                | 59                                    | 65\n",
       "90                        | 90                                | 75                                    | 81\n",
       "... (1 rows omitted)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "income_distribution.join(\n",
    "    [\"Population Percentage (%)\", \"Perfect Equality Income Share (%)\"], \n",
    "    income_distribution2, [\"Population Percentage (%)\", \"Perfect Equality Income Share (%)\"]\n",
    ").relabel(\n",
    "    \"Cumulative Income Share (%)\", \"Country 1 Cumulative Income Share (%)\"\n",
    ").relabel(\n",
    "    \"Cumulative Income Share (%)_2\", \"Country 2 Cumulative Income Share (%)\"\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plotting both countries' Lorenz curves, can you tell which country has a higher level of income inequality?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "tags": [
     "remove_input"
    ]
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=[7,7])\n",
    "plt.plot(income_distribution.column(0), income_distribution.column(1), \"-o\", c = 'b')\n",
    "plt.plot(income_distribution.column(0), income_distribution2.column(1), \"-o\", c = 'r')\n",
    "plt.legend([\"Country 1\", \"Country 2\"])\n",
    "plt.plot([0,100], [0,100], color='k');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this case, we can see that country 2's Lorenz curve is closer to the line of equality than that of country 1, which intuitively would suggest that country 2 is more equal. If we were to look at the numbers, we see that the bottom percentiles own a higher % of total national income in country 2 than in country 1, while top percentiles own less in country 2 than in country 1. This would suggest that country 2 is more equal in income than country 1, so that country 1 has a higher level of income inequality."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "But now let's consider a different case; suppose country 3 has the following distribution: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table border=\"1\" class=\"dataframe\">\n",
       "    <thead>\n",
       "        <tr>\n",
       "            <th>Population Percentage (%)</th> <th>Perfect Equality Income Share (%)</th> <th>Country 1 Cumulative Income Share (%)</th> <th>Country 3 Cumulative Income Share (%)</th>\n",
       "        </tr>\n",
       "    </thead>\n",
       "    <tbody>\n",
       "        <tr>\n",
       "            <td>0                        </td> <td>0                                </td> <td>0                                    </td> <td>0                                    </td>\n",
       "        </tr>\n",
       "        <tr>\n",
       "            <td>10                       </td> <td>10                               </td> <td>2                                    </td> <td>3                                    </td>\n",
       "        </tr>\n",
       "        <tr>\n",
       "            <td>20                       </td> <td>20                               </td> <td>5                                    </td> <td>7                                    </td>\n",
       "        </tr>\n",
       "        <tr>\n",
       "            <td>30                       </td> <td>30                               </td> <td>9                                    </td> <td>12                                   </td>\n",
       "        </tr>\n",
       "        <tr>\n",
       "            <td>40                       </td> <td>40                               </td> <td>15                                   </td> <td>18                                   </td>\n",
       "        </tr>\n",
       "        <tr>\n",
       "            <td>50                       </td> <td>50                               </td> <td>23                                   </td> <td>25                                   </td>\n",
       "        </tr>\n",
       "        <tr>\n",
       "            <td>60                       </td> <td>60                               </td> <td>33                                   </td> <td>33                                   </td>\n",
       "        </tr>\n",
       "        <tr>\n",
       "            <td>70                       </td> <td>70                               </td> <td>45                                   </td> <td>42                                   </td>\n",
       "        </tr>\n",
       "        <tr>\n",
       "            <td>80                       </td> <td>80                               </td> <td>59                                   </td> <td>54                                   </td>\n",
       "        </tr>\n",
       "        <tr>\n",
       "            <td>90                       </td> <td>90                               </td> <td>75                                   </td> <td>73                                   </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "</table>\n",
       "<p>... (1 rows omitted)</p>"
      ],
      "text/plain": [
       "Population Percentage (%) | Perfect Equality Income Share (%) | Country 1 Cumulative Income Share (%) | Country 3 Cumulative Income Share (%)\n",
       "0                         | 0                                 | 0                                     | 0\n",
       "10                        | 10                                | 2                                     | 3\n",
       "20                        | 20                                | 5                                     | 7\n",
       "30                        | 30                                | 9                                     | 12\n",
       "40                        | 40                                | 15                                    | 18\n",
       "50                        | 50                                | 23                                    | 25\n",
       "60                        | 60                                | 33                                    | 33\n",
       "70                        | 70                                | 45                                    | 42\n",
       "80                        | 80                                | 59                                    | 54\n",
       "90                        | 90                                | 75                                    | 73\n",
       "... (1 rows omitted)"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Country3 = make_array(0, 0.03, 0.07, 0.12, 0.18, 0.25, 0.33, 0.42, 0.54, 0.73, 1.0)\n",
    "income_distribution3 = Table().with_columns(\n",
    "    \"Population Percentage (%)\", np.arange(11) * 10, \n",
    "    \"Cumulative Income Share (%)\", Country3 * 100, \n",
    "    \"Perfect Equality Income Share (%)\", np.arange(11) * 10\n",
    ")\n",
    "income_distribution.join(\n",
    "    [\"Population Percentage (%)\", \"Perfect Equality Income Share (%)\"], \n",
    "    income_distribution3, [\"Population Percentage (%)\", \"Perfect Equality Income Share (%)\"]\n",
    ").relabel(\n",
    "    \"Cumulative Income Share (%)\", \"Country 1 Cumulative Income Share (%)\"\n",
    ").relabel(\n",
    "    \"Cumulative Income Share (%)_2\", \"Country 3 Cumulative Income Share (%)\"\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "tags": [
     "remove_input"
    ]
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=[7,7])\n",
    "plt.plot(income_distribution.column(0), income_distribution.column(1), \"-o\", c = 'b')\n",
    "plt.plot(income_distribution.column(0), income_distribution3.column(1), \"-o\", c = 'r')\n",
    "plt.legend([\"Country 1\", \"Country 3\"])\n",
    "plt.plot([0,100], [0,100], color='k');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, ambiguity arises; while bottom income percentiles earn a larger share of national income in country 3, top income percentiles also have a larger share. We can visualize this phenomenon by the 'crossing' of Lorenz curves on the plot. As a result, we do cannot easily tell which country has a higher level of income inequality.\n",
    "\n",
    "As you may see, the Lorenz curve is not able to produce a 'quantitative' measure of income inequality, making the scenario above hard for us to compare the 2 countries. For this, we turn to the Gini coefficient."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The Gini Coefficient"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can use the Gini coefficeint to quantify the level of income inequality."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```{figure} Gini.png\n",
    "---\n",
    "width: 500px\n",
    "name: gini-coefficient\n",
    "---\n",
    "The Gini coefficient\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```{admonition} Definition\n",
    "\n",
    "The **Gini coefficient** is the ratio of the area between the line of equality and the Lorenz curve to the total area under the line of equality. Referring to $A$ and $B$ from {numref}`gini-coefficient`:\n",
    "\n",
    "$$\\text{Gini} = \\frac{\\text{Area between line of equality and Lorenz curve}}{\\text{Area under line of equality}} = \\frac{A}{A+B}$$\n",
    "\n",
    "If we express the Lorenz curve as $L(x)$, we can use calculus to derive an equation for the Gini coefficient:\n",
    "\n",
    "$$\\text{Gini} = \\frac{\\frac{1}{2} - \\int_0^1 L(x)\\text{d}x}{\\frac{1}{2}} = 1 - 2\\int_0^1 L(x)\\text{d}x$$\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Intuitively, the closer the Lorenz curve is to the line of equality, the lower income inequality exists. Hence, the smaller the area of A, the lower the inequality. **This means that the smaller the Gini coefficient, the lower the income inequality.** Also note that the Gini coefficient will always be between 0 and 1. Mathematically, since $A$ and $B$ are both positive, $0<\\frac{A}{A+B}<1$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "# This function estimates the Gini coefficient. You don't have to understand how this code works below.\n",
    "def gini(distribution):\n",
    "    sorted_distribution = sorted(distribution)\n",
    "    height = 0\n",
    "    area = 0\n",
    "    for i in sorted_distribution:\n",
    "        height += i\n",
    "        area += height - i / 2\n",
    "    fair_area = height * len(distribution) / 2.\n",
    "    return (fair_area - area) / fair_area"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "When we use our population as the parameter to the `gini` function, we get: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.518628912071535"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gini_coefficient_country1 = gini(Country1)\n",
    "gini_coefficient_country1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.48756218905472637"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gini_coefficient_country2 = gini(Country2)\n",
    "gini_coefficient_country2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.4934357195937577"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gini_coefficient_country3 = gini(Country3)\n",
    "gini_coefficient_country3"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "These results confirm our intuition from the analysis we did previously via Lorenz curves. Previously, we concluded that country 1 had a higher level of income inequality than country 2, and this is supported by country 1's higher gini coefficient. On the other hand, we had trouble comparing levels of inequality between country 1 and country 3. Here, the gini coefficient would indicate that country 1 has a higher level of income inequality than country 3."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Other Forms of Measurement"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The Gini coefficient is a fairly comprehensive and robust measure of inequality with just a single value: as we've seen above, we look at the entire population's income distribution to determine the Gini coefficient. As a result, calculating the Gini is often a challenging task. In reality, we will never observe the true population Lorenz curve without conducting a census to know how much exactly each household earns. As a result, economists will often attempt to interpolate the Lorenz curve and consequent Gini coefficient from the data they have available. The Gini coefficient is also not as easy to understand or explain; the value by itself does not have significant meaning.\n",
    "\n",
    "Instead, another common measure of income inequality is the share of income earned by the \"top $x$%\" or the \"bottom $y$%\". These measures are more often used in the media or by politicians in discussing the extent of inequality, since they are much easier to understand. Consider the chart below, which plots the share of income earned by the top 1%, bottom 90%, and the 90-99%:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```{figure} alt_measure.png\n",
    "---\n",
    "---\n",
    "Alternative forms of measurement\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " "
   ]
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