An economy has two types of jobs, Good and Bad, and two types of workers, Qualified and Unqualified. The population consists of 60% Qualified and 40% Unqualified. In a Bad job, either type of worker produces 10 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 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) What is the minimum level of n that will achieve separation?
b) Now suppose the signal is made unavailable. Which kind of jobs will be filled by which kinds of workers and at what wages? Who will gain and who will lose from this change?