Suppose there is a rm operating in perfectly competitive output and labour markets and the output price is $ 1 00. Also assume that there are two types of workers: high-ability workers with a marginal product of 45 and low- ability workers with a marginal product of 20. a. Assume that the rm can easily distinguish between the two types of worker. Calculate the equilibrium wage rate for each type. (4 marks) In reality, rms cannot easily distinguish between the types. Therefore, this rm uses education as a screening device. Now workers can invest in their education but at a cost. The respective cost of acquiring S years of education for high and low-ability workers are CH (SH) = S2 and CL (3]) = 4- * S2 dollars. Further assume that education has no impact on a worker's marginal product. b. Calculate the optimal education level (5*) set by the rm to distinguish between the two types. Given the rm's 5*, what is the number of years of education that each type chooses? (7 marks) c. If the rm chooses S* = 24, then what level of education does each type choose? What is the disadvantage of this choice for the rm? (4 marks)