15. Consider a two-sector economy that employs a total of 80 units of a single input, labor.

N1 of these units are allocated to sector 1, where the wage is 100 for the top five workers in that sector and zero for all others. (Both the wage for the top workers and the number who receive that wage are invariant to changes in N1.) The remaining N2  80  N1 units of labor serve in sector 2, where every worker receives a wage of 10. All workers in sector 1 have an equal probability of being among the top five workers, 5N1, and all workers are risk neutral.

a. How many workers will work in sector 1?

b. What will be the value of GNP for the economy?

c. How would your answers differ if there were a 50 percent tax on the earnings of workers in sector 1?