A simple model of job market signaling
Let's assume that there are two groups of workers:
low-productivity workers (Group I), whose average and marginal
product is 1, and high-productivity workers (Group II), whose
average and marginal product is 2.
Workers will be employed by competitive firms whose products
sell for $10,000, and who expect an average of 10 years' work from
each employee. We also assume that half the workers in the
population are in Group I and the other half in Group II, so that
the average productivity of all workers is 1.5. Note that the
revenue expected to be generated from Group I workers is $100,000
($10,000/year * 10 years) and from Group II workers is $200,000
($20,000/year * 10 years).
Education as a Productivity Signal: The key
assumption is that the cost of education is greater for
the low-productivity group than for the high-productivity
group.
Suppose that for each group the cost of attaining educational
level y (say, years of schooling) is
CI(y) = 40,000y for type I
CII(y) = 20,000y
for Type II workers.
Education is costly because of tuition fees, opportunity costs
of time, psychological pressure for good grades, etc.
Now suppose (to keep things simple and to dramatize the
importance of signaling) that education does nothing to
increase one's productivity; its only value is as a signal.
Consider the Job Market Signaling model discussed in the slides.
a) Suppose that the costs of education for low type workers are $60,000 for every year of education. For
which values of y* do we obtain a Separating equilibrium? Compared to the original case, what happens
to Pareto efficiency? Provide an intuitive explanation of your answers.
b) Suppose that the costs of education for high type workers are $30,000 per year (and for low type
$40,000/year). For which values of y* do we obtain a Separating equilibrium? Compared to the original
case, what happens to Pareto efficiency? Provide an intuitive explanation of your answers.
c) Suppose that the costs of education are the same for both workers. Can education still be used as a
productivity signal? Explain your answer carefully.