Question

Assume that there are two types of workers in a perfectly competitive labour marker: type H is the high ability worker with lifetime productivity of $550,000 and type L is the low ability worker with lifetime productivity of $370,000. Suppose 60 percent of the workers are type H and 40 percent are type L. Both types already have 9 years of schooling. Also, further education can be used as a signal for productivity in the labour market. In this case, firm uses the following rule to pay workers' wage if E < 9 then pay the worker $370,000 if E 2 9 then pay the worker $550,000 where E is the number of years of further edu $25,000 and $18,000 for the low and high ability workers, respectively cation. Suppose cost of an additional year of education is a) What is the wage for each type of worker if the firm can distinguish the type of workers easily at no cost? (4 marks) Now assume that the firm cannot distinguish between the two types b) One option is that the firm pays the same wage to everyone, equal to the average productivity Calculate the equilibrium wage for high and low ability workers and determine their level of education. (6 marks) Now suppose that education is available as described above. Set up the self-selection constraints for both types and determine the education level and wage for each type. (6 marks) c) Suppose that the government gives a subsidy of $8,500 per year to decrease the cost of education for both types. d) e) f) Show that the pay scheme adopted by the firm does not yield an equilibrium anymore. Briefly explain your result. (3 marks) Use the self-selection constraints for both types and calculate a range for E that yields an equilibrium. (4 marks) Use your answer in the previous part and pick the most efficient value as a threshold for E. Briefly explain why you chose this value. (Note that the range is continuous.) (2 marks)

Answer 1

If firm can distinguish the type of workers easily at no cost then it will pay $550,000 to high ability workerand $370,000 to low ability worker.

b) The equilibriumwage for high and low ability worker will be

0.60*550,000 + 0.40*370,000 = $478,000

c) The wage for high ability worker will be $ $550,000 - $18,000 = $532,000and for low ability worker will be $370,000 - $25,000 = $345,000