Problem Set 2
Professor Kala Krishna
The Pennsylvania State University
Due September 20 in class.
Do all questions. Please write or type clearly. You do not need to calculate
the points on the graph, just label them as needed.
1: Consider a Ricardian Model of Trade. There are two countries, Home
and Foreign, who produce two goods Food and Clothing, using one factor of
production, Labor. The unit input requirements are given by the table below
in the two countries.
Goodn Country Home Foreign
Food 3 9
Clothing 9 3
Home has 30 units of labor while foreign has 90 units. Food is consumed in
a one to one ratio relative to clothing at all prices by both countries. Use graph
a: Draw the world PPF under trade. If the price of clothing is 1; what is
the price of food under free trade? What are equilibrium wages (what a unit of
labor earns) in each country?
b: Depict the trading equilibrium and the prices, production, imports and
exports by each country in your graph. You do not need to solve for it alge-
braically, just on graph paper.
c: What happens to equilibrium prices if labor migrates from foreign to home
so that home has 90 workers and foreign has 30. Labor that migrates then has
the same productivity as native labor.
d: Would labor that stayed behind in Foreign gain or lose from this mi-
gration? Why? (What happens to the budget set of a Foreign worker? If it
expands, he must gain.)
e: Suppose productivity abroad quadrupled, that is, the unit labor require-
ments fell to 1/4 of the levels above. (Note that in this case Foreign has an
absolute advantage in both goods.) What happens to world prices? Do home
workers gain from foreign becoming more productive ? Do foreign workers gain
from its productivity improvement? (Comparisons should be relative to the
outcome in part b)
f: Can the PPF when labor is mobile between countries lie strictly outside
the world PPF through trade or must it touch it somewhere? Can you give
conditions under which they would touch at some point and when they would
not? (Hint: consider what happens when one country has an absolute advantage
in both goods and when this is not the case.)
g: Given your answers to part f:, how would you respond to the following
Given the lack of trade barriers today, there are orders of magnitude more
gains to be had from permitting labor migration than trying to further liberalize
2. This problem asks you to think of issues using a relative demand and sup-
ply framework more generally. The U.S. and the rest of the world(ROW) are
the two countries in the world. They make two goods, Food (F) and Wine (W)
The U.S. exports W:
a: What would be the e¤ect of an advertising campaign to promote W in
the ROW? ( Assume that the advertising campaign makes foreigners demand
more W relative to F at any relative price.) What would shift? What would
happen to relative prices in the world? Would the U.S. gain or lose from such
advertising if advertising is essentially costless?
b: A war destroys half of ROWs productive capacity shrinking its Production
Possibility Frontier (PPF) uniformly inwards for all goods. What would shift?
What would happen to prices in the world? Would the U.S. gain or lose? What
c: Suppose that the US consumes mostly wine while the rest of the world
consumes mostly food. Would there be a secondary burden of foreign aid given
by the US to the ROW? Could the US reduce this secondary burden by giving
its aid in barrels of wine? Why/Why not?
3: This question asks you to think of how trade can result in gains due to
increasing competition and variety. You do not need to do any algebra. Just
draw the graphs needed.
Suppose there two countries of equal size, i.e., both have the same number
of people, S. There are n symmetric rms. Each individual has demand for
the output of a representative rm denoted by q(p; P; n) where p is the rms
price, P is the overall average price in the market, and n is the number of
rms. q(p; P; n) is decreasing in p, increasing in P and decreasing in n. With S
individuals, the demand for a rm is thus Sq(p; P; n): Let c be marginal cost and
F be the xed cost of production. Firms behave monopolistically competitively
and choose p to maximize prots taking P and n as given. Assume all rms are
symmetric so that in equilibrium p = P and that rms enter till price equals
average cost, i.e., prots are 0.
a: Depict the prot maximizing price charged by a representative rm for
given P and n. You do not need to do any algebra. Just to draw demand and
the prot maximizing price.
b: Show that the maximized prots of the rm are higher when its costs fall.
(Hint: variable prots are also the sum of the di¤erence in marginal cost and
marginal revenue over units produced)
c: As n rises, what happens to the prot maximizing price? What is the
intuition? Call this relation the PP curve.
d: Does an increase (or decrease) in S shift the PP curve? Why?
e: As n rises, what happens to output per rm in symmetric equilibrium and
therefore to average cost? What is the economic intuition here? Call this curve
f: Does an increase in S shift CC? Why?
g: Depict the equilibrium n and p without and with trade where trade is just
a doubling of S?
h: Explain what the e¤ects of trade are on prices, variety and welfare.