Intermediate Microeconomic Theory (3550)
Homework 5 – Answers
Due Thursday, October 30, 2008
1. Suppose the firm is in the short run, and consider the first stage of production.
a. What happens to the average product of labor when the firm adds an additional
worker?
In the first stage of production, an additional worker will raise the average
product of labor.
b. What causes this change in labor productivity?
The additional worker creates more opportunities for specialization and thus
makes the other workers more productive.
c. What happens to the average product of labor in the second stage of production when
the firm adds another worker?
In the second stage of production, an additional worker will reduce the average
product of labor.
d. What causes this change in average product of labor?
In this case, the additional worker creates additional crowding. The firm’s fixed
capital must be shared among more workers, which makes the workers less
productive.
2. The manager of a firm receives an engineering report claiming that an additional hour of
capital would add twice as much output as would an additional hour of labor. According to
the firm’s accountants, an hour of capital costs 3 times more than an hour of labor.
a. Is the firm on its expansion path? Why or why not?
The firm is not on its expansion path. The engineering report shows that the
value of MPk is twice that of MPl, so MRTSlk = MPl/MPk = ½ hour of capital
per hour of labor. The accounting report shows that the value of Pk is 3 times
that of Pl, so Pl/Pk = 1/3 hour of capital per hour of labor. Thus, MRTS
Pl/Pk, but the two values must be equal for the firm to be on its expansion path.
b. Suppose the firm is under contractual obligations to keep its output at current levels.
What long-run adjustment (if any) should the manager make in the firm’s
employment of labor and capital?
We can conclude that the isoquant is steeper than the isocost since MRTSlk >
Pl/Pk, so the manager should employ more labor and less capital in the long
run.
c. Sketch an isoquant – isocost diagram that illustrates the situation described in part b.
Label the initial situation A and the post-adjustment situation B. The scale of your
diagram does not need to be accurate. (Although we have not finished covering
isocost and isoquant diagrams in class lectures, their similarity to budget line /
indifference curve diagrams should enable you to complete this problem).
A
B
3. a. State the law of diminishing marginal returns.
Slope = ½ machine-hour per
man-hour.
Slope = 1/3 machine-hour per
man-hour.
Capital
Labor
