Reconcile these facts with the theory of human capital.


1. General OJT. (Milgrom & Roberts, revised) Actuaries perform the crucial task of estimating the time
paths and probability distributions of costs and revenues for different insurance contracts. Becoming
an actuary takes several years, and involves passing a series of rigorous examinations given either by
the Society of Actuaries or by the Casualty Actuarial Society. Usually the individual works for an
insurance company while studying for the exams, and the company gives the individual time off to
study for the exams. Passing an exam usually results in a significant pay increase.
(a) Actuaries have general human capital. Explain why.
(b) Who pays for the workers time off to study for the exams? Choose one answer and explain.
i. the worker does, by accepting a lower salary
ii. the firm does, to invest in the workers human capital
(c) Why does the individual get a pay increase after passing each exam? Why not evaluate the
employee once per year, like many companies do?
2. Specific OJT. (Milgrom & Roberts, revised) Workers who are laid off from their jobs generally
receive lower wages once they find new jobs (Fact 1). Moreover, the wage reduction appears to be
persistent–for many years, wages are lower than they would have been had the worker keep his/her
old job (Fact 2). Moreover, the wage loss differs by the type of job–relatively unskilled laborers such
as fast-food workers or retail clerks suffered a smaller wage decline than did certain kinds of skilled
labor, such as production workers in automobile or airplane manufacturing plants (Fact 3). What
key insight explains all three of these facts?
3. On the Job Training. Three basic facts about men and women in the labor market are these:
• As a group, women now get just as much schooling as men do (actually, a little more).
• Upon graduating from college, women receive salary offers that are the same as mens offers, on
• As they age, mens average wages and womens average wages diverge, with women lagging behind
men, even when they have the same amount of education.
(a) Reconcile these facts with the theory of human capital.
(b) Under one standard theory of labor market discrimination, “employer discrimination,” employers
are willing to pay a fixed premium to hire members of a preferred group instead of members of
a non-preferred group. What pattern of facts should you observe if women were discriminated
against in this way?
(c) Under another theory of discrimination, families are reluctant to invest in the education of their
daughters. What pattern of facts should you observe if women were discriminated against in
this way?
4. Human Capital Investments. Suppose that the marginal cost of an additional unit of human capital
is given by MC = 400 and the marginal benefit is given by MB = 800 ? 25HC , where HC is the
number of units of human capital.
(a) Graph MB and MC as a function of HC. Calculate the optimal level of human capital investment,
(b) The growing importance of computer skills in todays economy leads firms to place a greater
premium on human capital investments. As a result, the marginal benefit of an additional unit
of human capital increases to MB = 800 ? 20HC. Re-answer part (a).
5. Human Capital Investment. Billy and Bob are both 50 years old and work at the same firm. Billy is
a more able individual and presently earns $90,000 per year; Bob earns $50,000 per year. They have
the opportunity to enroll in a job-training course for a one-time cost of $10,000. The raise they are
entitled to depends on how much they learn in the course.
Since Billy is more able, he expects to earn an additional $2,000 per year, while Bob expects to
earn only an additional $1,000 per year. Both workers have a discount rate of 5%.
(a) If both workers expect to work until age 60 (i.e., ten more years), will either opt to take the
(b) What is the minimum number of years each worker needs to work before retiring if the course
is to be a wise investment?

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