Problem 2: Income distribution (and redistribution?)

Consider a small ten-household economy in which four households each have an annual income of $20,000; four each have an annual income of $70,000; and two each have an annual income of $320,000.

a. What is the median annual income in this economy? The mean (average) annual income? What percentage of households have incomes that are less than the mean?

b. Sketch a Lorenz curve for this country, and (use what you know about the areas of triangles and rectangles to) compute the Gini coefficient. Show your calculations.

c. Suppose the government assesses a 20% tax on all incomes (the ones listed at the beginning of the problem!), and then distributes the revenues equally to all ten households as a basic-income program. Compute each household's income after taxes and transfers, and use these new numbers to repeat your analysis from parts a) and b).