PRODUCTION ANALYSIS SAMPLE PROBLEMS
Analytical Questions
1) The table above shows the weekly relationship between output and number of workers for a
factory with a fixed size of plant.
a. Calculate the marginal product of labor.
b. At what point does diminishing returns set in?
c. Calculate the average product of labor.
d. Find the three stages of production.
Answer:
2) Based on the table above, if the wage rate is $500 and the price of output is $5, how many
workers should the firm hire?
3) A firm has two plants, one in the United States and one in Mexico, and it cannot change the
size of the plants or the amount of capital equipment. The wage in Mexico is $5. The wage in the
U.S. is $20. Given current employment, the marginal product of the last worker in Mexico is
100, and the marginal product of the last worker in the U.S. is 500.
a. Is the firm maximizing output relative to its labor cost? Show how you know.
b. If it is not, what should the firm do?
Answer:
a. Maximizing output between plants requires that (MPL/w)U.S. = (MPL/w)MEXICO. Since
100/5 (=20) is not equal to 500/20 (=25), the firm is not maximizing output relative to its labor
cost.
b. The firm should hire more U.S. workers and fewer Mexican workers, all other things equal.
4) From your knowledge of the relationships among the various functions, complete the ff. table:
Answer:
5)
Answer:
a. (i) two to five workers generate increasing returns, (ii) four and six workers generate constant
returns, (iii) six to eleven workers generate decreasing returns, and (iv) twelve workers generate
negative returns.
b. How large a crew should be used if the trawler owner is interested in maximizing the total
amount of fish caught? – either ten or 11 workers.
c. How large a crew should be used if the trawler owner is interested in maximizing the average
amount of fish caught? – either six or seven workers.