In 2010, many unskilled workers in the United States earned the federal minimum wage of $7.25 per hour. By contrast, average earnings in 2010 were about $22 per hour, and certain highly skilled professionals, such as doctors and lawyers, earned $100 or more per hour.

a. If we assume that wage differences are caused solely by differences in productivity, how many times more productive was the average worker than a worker being paid the federal minimum wage? How many times more productive was a $100-per-hour lawyer compared to a worker earning minimum wage?

b. Assume that there are 20 minimum-wage workers in the economy for each $100-per-hour lawyer. Also assume that both lawyers and minimum-wage workers work the same number of hours per week. If everyone works 40 hours per week, how much does a $100-per-hour lawyer earn a week? How much does a minimum-wage worker earn a week?

c. Suppose that the government pairs each $100-per-hour lawyer with 20 nearby minimum-wage workers. If the government taxes 25 percent of each lawyer's income each week and distributes it equally among the 20 minimum wage workers with whom each lawyer is paired, how much will each of those minimum-wage workers receive each week? If we divide by the number of hours worked each week, how much does each minimum-wage worker's weekly transfer amount to on an hourly basis?

d. What if instead the government taxed each lawyer 100 percent before dividing the money equally among the 20 minimum-wage workers with whom each lawyer is paired. How much per week will each minimum-wage worker receive? How much is that on an hourly basis?