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 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) What is the minimum level of n that will achieve
(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?