There are two types of jobs in the economy, good and bad, and two types of workers, qualified and unqualified. The population consists of 60 percent qualified and 40 percent unqualified. In a bad job, either type of worker produces the same 10 units of output. In a good job, a qualified worker produces 100 and an unqualified worker produces 0. There are numerous job openings of each type, and companies must pay for each type of job what they expect the appointee to produce. The worker's type is unknown before hiring, but the qualified workers can signal their type (e.g., by getting educated or some other means). The cost of signaling to level s for a qualified worker is s2/2 and for an unqualified worker is s2. The signaling costs are measured in the same units as output, and s must be an integer (e.g., number of years of education).
a. What is the minimum level of s that will achieve separation?
b. Suppose that the signal is no longer available. Which kinds of job will be filled by which types of workers, and at what wages? Who gains and who loses?