So it wouldn't be economics if we didn't examine the graph, right? Now, let's discuss income inequality using the differences between the rich and the poor. It's going to show us this on a graph. When we talk about the Lorenz curve, it's a bit different than the graphs we've discussed throughout this course. On the horizontal axis, we have the cumulative percentage of households. "Cumulative" means that we're adding more and more. Think of a cumulative exam, where it includes topics from various chapters, uniting everything you've learned. So, on the horizontal axis, the x-axis, we have the cumulative amount of households in percentage format, and on the y-axis, the vertical axis, we also have a cumulative percentage of income.

We create our Lorenz Curve by dividing the population into quintiles. "Quint" meaning five, each quintile will represent 20%, thus dividing the economy into five 20% sections based on household income. We'll start with the poorest 20% and evaluate what percentage of the total income they're receiving. Then we look at each subsequent 20% up to the richest. Now, let's proceed to calculate this Lorenz curve. Notice on the graph, the x and y axes are labeled according to these quintiles. Now, we need to accumulate these percentages of income. So, the lowest 20% might earn 3.4% of the total income. As we combine this with the next tier, 8.6%, we accumulate these figures: 3.4% + 8.6% equals 12%. Continuing this way, we add increasingly larger percentages for each subsequent tier until the total population and income reach 100%.

Now, plotting this Lorenz curve on our graph, begin with the lowest 20% earning 3.4% of income, significantly less than their demographic proportion. Progressing cumulatively upward as we incorporate higher earning brackets, the curve will rise, illustrating inequality distribution as it moves away from the line of perfect equality. The line of perfect equality, where the percentage of income matches the percentage of the population, would graph as a straight diagonal line. This line reflects an ideal scenario where there is no income inequality where each 20% of the population earns a corresponding 20% of the total income.

Another hypothetical scenario to consider is one of complete inequality, where nearly all income is earned by the last percentage of the population, regardless of prior income zeros. Here, the inequality is starkly depicted by a flat line at the bottom that spikes only at the end.

The Gini Coefficient, calculated using the areas under the Lorenz curve and the line of perfect equality, quantifies these disparities in income distribution. It ranges between 0 (perfect equality) and 1 (maximum inequality), providing an intuitive measure of economic disparity.

In sum, the Lorenz curve and Gini Coefficient become necessary tools to visualize and quantify income inequality. By comparing these measures across different contexts, we can better understand the depth and nature of economic disparity within and across societies. Let's engage in some practice examples to solidify these concepts before moving on to our next topic.