3
Labor hours needed to produce
a
car in the United states 500 hrs
Labour hours needed
needed to produce a
chair in the United States: 200 hrs
What is the opportunity cost of one
chair in the United states
Answers
Answer:
on 116a (second half)
Yale University
Fall 2007
Prof. Tony Smith
HOMEWORK #7
Answer Key
Question 1
Please see the Aplia course site for suggested answers to this Aplia problem.
Question 2
(Mankiw Chapter 3 Problem 6, on page 60).
The following table describes the production possibilities of two cities in the country of
Baseballia:
Pairs of Red
Socks per
Worker per Hour
Pairs of White
Socks per
Worker per Hour
Boston 3 3
Chicago 2 1
(a) Without trade, what is the price of white socks (in terms of red socks) in
Boston? What is the price in Chicago?
From the table we see that 1 worker-hour (1 worker working for 1 hour) employed in the
production of white socks is necessary to produce 3 pairs of white socks in Boston. If
this worker-hour was employed instead in producing red socks, exactly 3 pairs of red
socks would be produced. Thus the price of 3 pairs of white socks is just 3 pairs of red
socks -- or equivalently -- the price of one pair of white socks is one pair of red socks.
Similarly, in Chicago, freeing up 1 worker-hour from producing 1 pair of white socks and
employing it instead in red socks production, 2 pairs of red socks can be produced.
Thus, the price of 1 pair of white socks is 2 pairs of red socks, or equivalently, the price
of a pair of white socks is two pairs of red socks.
Note that the price reflects the opportunity cost of worker-hours spent in the productio(b) Which city has an absolute advantage in the production of each color sock?
Which city has a comparative advantage in the production of each color sock?
Recall that a city has an absolute advantage over another in the production of a good if
it can produce the same good with fewer resources than the other country. A city has a
comparative advantage in the production of a good over another city if it has a lower
opportunity cost in its production relative to the other city.
To produce 1 pair of red socks, Boston requires 1/3 worker-hours whereas Chicago
needs 1/2 worker hours. Thus Boston has an absolute advantage in the production of
red socks since it needs fewer worker-hours per pair.
Similarly, Boston also has an absolute advantage in the production of white socks since
it needs fewer worker-hours per pair of white socks (1/3 to 1).
From part (a) above, we see that the opportunity cost of producing a pair of white socks
is higher in Chicago than in Boston. Thus Boston has a comparative advantage in white
socks production (give up only 1 pair of red socks as opposed to 2 pairs for Chicago).
Chicago has a comparative advantage in red socks production (give up 1/2 pair of white
socks as opposed to 1 pair for Boston).
Note: the comparative advantage result differing across cities is not an accident. In a
two-good, two-city case, if one city has a comparative advantage over another in the
production of one good, it necessarily means that the other city has a comparative
advantage in the production of the other good.
(c) If the cities trade with each other, which color sock will each export?
When opened up to trade, each city will specialize in the production of the good in
whose production it has a comparative advantage, and will export that same good. Thus
Boston will export white socks and Chicago will export red socks.
(d) What is the range of prices at which trade can occur?
A city will remain no worse-off from trade if its terms of trade (the ratio of the price of the
exported good to the price of the imported good) are higher than or equal to the ratio of
the domestic prices of the same two goods before opening up to trade. If the terms of
trade do not meet this condition for either or both of a pair of cities, the city for which
this is not met will prefer not to trade since it will be better off without trade. In such a
situation, mutually agreeable trade cannot take place.