Dr. Stonebraker

Sample comparative advantage problems

Try to complete the questions below. The answers are
listed at the end.

Suppose Tom can produce either 5 units of good X or 15
units of good Y in one day while Harry can produce either 2 units of X or 10
units of Y in one day.

a. If no specialization is possible, what is the opportunity cost to Tom of one unit of good X? Of one unit of good Y?

b. If specialization is possible, in which good should Tom specialize? In which should Harry specialize? Explain.

c. At what sort of ratio will Tom and Harry trade good X for good Y? Explain how such a ratio could benefit both.

Answers:

a. Tom can produce either 5 units of X or 15 units of Y in a day. In the time it takes him to produce an X he could have produced three times as many units of Y. Therefore, the opportunity cost of one X = 3Y, and the opportunity cost of one Y = (1/3)X.

b. Tom should specialize in X and Harry in Y. Tom can produce more than twice the amount X as Harry (5 vs. 2), but only 50% more Y (15 vs. 10). Alternatively, the opportunity cost of good X for Tom is lower than for Harry (3Y vs. 5Y) and the opportunity cost of Y for Harry is lower than for Tom (1/5 vs. 1/3 of an X).

c. Any ratio between 1:3 and 1:5 works. For example, at 1X = 4Y, Tom can get 4Y per X through trade while he could get only 3Y per X by himself. Harry could get an X for 4Y through trade, but must sacrifice 5Y for an X by himself.