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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 Sm, each type M worker has a marginal product of $16, and each type L worker has a marginal pro-duet of SID. The output market and the labor market are both perfectly competitive. All workers are risk neutral. It is eommon knowledge that save of the workers are type H, ditto 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 \"Workplaoe 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 $3 wage out 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, rms 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 National University of Singapore ECASIGI Microeconomic Analysis I Department DfEcmtomics Sterne-star I A'r'" 21111321322 with probability IIS. 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) {t3 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? Briey explain