3. Use quintiles to briefly summarize the degree of income in-equality in the United States. How and to what extent does government reduce income inequality?

a. Assume that Al, Beth, Carol, David, and Ed receive incomes of $500, $250, $125, $75, and $50, respectively. Construct and interpret a Lorenz curve for this five-person economy. What percentage of total income is received by the richest quintile and by the poorest quintile?

b. How does the Gini ratio relate to the Lorenz curve? Why can't the Gini ratio exceed 1? What is implied about the direction of income inequality if the Gini ratio declines from 0.42 to 0.35? How would one show that change of inequality in the Lorenz diagram?

c. Why is the lifetime distribution of income more equal than the distribution in any specific year?