The Lorenz curve is the curve that represents the income (or wealth) distribution of a society. Consider a graph where the x-axis represents the percentage of the population and the y-axis the percentage of income. The Lorenz curve, y = L(r), contains points (r, y) where the bottom r percentage of the population have y percentage of total income of the society. By definition, we know that every Lorenz curve has the following properties: L(0) = 0, L(1) 1. y= L(x) is non-decreasing. In this worksheet, you will explore some examples and investigate more interesting properties about Lorenz curves. 1. Suppose that everyone has the same income. What percentage of income would the bottom z percentage of the population have? Write down the Lorenz curve equation, L(x), for this perfectly equal distribution. 2. Suppose that one person has all the income and everyone else has none. Write down the Lorenz curve equation, L(x), for this perfectly unequal distribution. 3. Suppose that the top 50% and the bottom 50% of the population each have the same amount of income (within each group), and the top 50% have income which is 5 times the bottom's income. Write down the Lorenz curve equation. 4. Draw the Lorenz curves of problem 1 to problem 3 in the same figure.