Based on your answers to Problems 29-13 and 29-14, when A increased, did the degree of income inequality increase or decrease? Explain why your answer makes sense by referring to the implied change in the shape of the Lorenz curve.

Problem 29-13

Suppose that in Figure 29-1 the area labeled A is one-fourth of the area denoted B. What is the value of the Gini coefficient?

Problem 29-14

Now suppose that in the situation described in Problem 29-13, the distribution of income changes in such a way that A increases to one-third of the area denoted B. What is the new value of the Gini coefficient?

Transcribed Image Text:

FIGURE 29-1 The Lorenz Curve The horizontal axis measures the cumulative percentage of households, with lowest-income households first, from 0 to 100 percent. The vertical axis measures the cumulative percentage of money income, from 0 to 100. A straight line at a 45-degree angle cuts the box in half and represents a line of complete income equality, along which 25 percent of the families get 25 percent of the money income, 50 percent get 50 percent, and so on. The observed Lorenz curve, showing the actual U.S. money income distribution, is not a straight line but rather a curved line, as shown. The difference between complete money income equality and the Lorenz curve is the inequality gap. 100 Cumulative Percentage of Money Income 59 75 22 0 45 Inequality gap. Complete equality B Actual money income distribution 25 50 75 Cumulative Percentage of Households 100