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Question 3 (14 marks) There are three types of workers in the market, H, M, and L. Each type H worker has a marginal product of $20, each type M worker has a marginal product of $16, and each type L worker has a marginal product of $10. The output market and the labor market are both perfectly competitive. All workers are risk neutral. It is common knowledge that 20% of the workers are type H, 40% are type M, and 40% are type L. Firms do not observe a worker's type. a) (4 marks) What is the wage for a type H worker, a type M worker, and a type L worker respectively? b) (4 marks) Suppose the workers have the option of taking a course "Workplace Ethics". The course has no effect on the marginal product of each worker. The utility loss of taking the course is equivalent to a $1 wage cut for type H workers, a $8 wage cut for type M workers, and a $12 wage cut for type L workers. Suppose type H workers take the course while the other two types do not take it. Firms observe whether a worker has taken the course or not. For a worker who took the course, firms believe that the worker is type H. For a worker who did not take the course, firms believe that the worker is type M with probably 0.5 and type L with probability 0.5. Given this belief, what wage will be offered to a worker who took the course? What wage will be offered to a worker who did not take the course? c) (6 marks) Continuing from part b), given the belief and the wages, is there an equilibrium where type H workers take the course while the other two types do not take it? Briefly explain