What is the average VMP in the population?

What is the average VMP in the population?

Question
1. There is a population of 100 workers, in which 20 per cent are of low ability,
and 80 per cent are of high ability. The high ability types have a VMP (value
of marginal product) = 50. The low quality types have VMP = 10. Firms will
pay workers their VMP, but cannot distinguish between the two types of
workers. If firms cannot distinguish between the two types of workers, they
pay all workers the same wage, equal to the population average VMP.
a. What is the average VMP in the population?
b. What is the equilibrium wage rate assuming that firms have no way of
distinguishing between workers?
c. Now assume that workers can buy education (E years). The cost of
acquiring that education differs among high and low ability workers.
The cost to high ability workers is 2E. The cost to low ability workers
is 4E. Education does not affect worker’s marginal product. Firms use
the following rules to pay workers:
if E<15, E(VMP) = wage = 10
if E>=15, E(VMP) = wage = 50
How much education will the low ability types obtain? How much
education will the high ability types obtain? Is this an equilibrium?
Why/why not? [A diagram might be help arrange your thoughts.]
d. Are the workers better off under the pooling or the separating
equilibrium?
e. Explain in general terms why if the signaling model is a good
description of reality, educational levels may be higher than socially
optimal.
2. In 2000, New Brunswick introduced legislation requiring that all youth be
enrolled in school until they reached the age of 18. Ontario did much the same
in 2006. Should BC introduce similar legislation? In addressing this question,
please explain the basic economic theory explaining optimal schooling
decisions, as well as any empirical evidence on the benefits of attaining
additional schooling.

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