Question: 1. An economy has two types of jobs, Good and Bad, and two types of workers, Qualified and Unqualified The population consists of 50% Qualified and 50% Unqualified. In a Bad job, either type of worker produces 40 units of output. In a Good job, a Qualified worker produces 100 units, and an Unqualified worker produces 0. There is enough demand for workers that for each type of job, companies must pay what they expect the appointee to produce. Companies must hire each worker without observing his type and pay him before knowing his actual output. But Qualified workers can signal their qualification by getting educated. For a Qualified worker, the cost of getting educated to level n is n2/2, whereas for an Unqualified worker, it is n2. These costs are measured in the same units as output, and n must be an integer

a. Find out the minimum level of n that will achieve separation (use the two incentive compatibility conditions)

b. Now, suppose the signal is made unavailable (so that only pooling equilibrium is possible). Will a company fill its Good job or Bad job? What will be a worker's wage?

c. Continuing b above. Will Qualified workers gain or lose? Will Unqualified workers gain or lose? Explain.