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Problem Set 2 - questions - Ricardian Model
International Trade (University of Notre Dame)
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Economics 40710: International Trade
University of Notre Dame
Practice problems 2 - Ricardian Model
Question 1: Suppose that in the United States 4 man-hours are required to produce each
unit of clothing (C) and each unit of food (F). In Canada, 1 man-hour is required for each
unit of clothing and 2 man-hours are required for a unit of food.
a. Which country has an absolute advantage in each good?
b. Which country has a comparative advantage in each good?
c. Assuming that each country has 40 man-hours of labor available for production, draw
the production possibilities frontiers for each country. (Put food on the vertical axis.) What
do the slopes of these frontiers indicate?
d. Draw the world production possibilities frontier (defined as the maximum amount of
goods that can be produced worldwide for a fixed amount of resources). What does its slope
indicate?
e. If consumers in both countries have identical Leontief preferences, consuming clothing
and food in the fixed proportion of one-to-one, what is the trade pattern? Note: when
U = min{C, F } the indifference curves associated with Leontief preferences are right anglesso
there are no substitution effects between the goods.
f. If the labor force of the United States increases by a factor of 20, will anything happen
to the pattern of trade? You do not need to provide numerical details. Will the gains of trade
for the U.S. be higher or lower than when the two countries have the same labor force?
Question 2: Suppose that each worker in the home country can produce three cars or two
televisions. Assume that Home has four workers.
a. Graph the production possibilities frontier for the home country.
b. What is the no-trade relative price of cars at Home?
Suppose that each worker in the foreign country can produce two cars or three televisions.
Assume that Foreign also has four workers.
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c. Graph the production possibilities frontier for the foreign country.
d. What is the no-trade relative price of cars in Foreign?
e. In which good does Foreign have a comparative advantage and why?
f. Suppose that in the absence of trade, Home consumes nine cars and two televisions and
Foreign consumes two cars and nine televisions. Add the indifference curve for each country
to the figures in part (a) and (b). Label the production possibilities frontier (PPF), the
indifference curve (U1 ), and the no-trade equilibrium consumption and production for each
country. Label Home and Foreign’sno-trade consumption points as A and A*, respectively.
Now suppose the world relative price of cars is PC / PT V = 1.
g. What good will each country specialize in? Briefly explain why.
h. Graph the new world price line for each country (in the same figure), and add a new
indifference curve (U2 ) for each country in the trade equilibrium.
i. Label the exports and imports for each country. How does the amount of Home exports
compare with Foreign imports?
j. Does each country gain from trade? Briefly explain why or why not.
Question 3: Two countries, Home and Foreign, use one factor, labor, to produce two goods,
wheat and clothing. Home can produce 4 bushels of wheat or 2 yards of cloth with one unit
of labor. Meanwhile, Foreign can produce 1 bushel of wheat or 1 yard of cloth with one unit
of labor. Home is endowed with 25 units of labor and Foreign with 75. Preferences in both
countries are the same and described by the following utility function:
1/2
1/2
U = Cw Cc .
a. Assume that Home produces both goods. Use the wage equality condition to find Home
autarky relative price of cloth Pc /Pw .
b. Set up the utility maximization Lagrangian and derive the first order conditions.
Provide an expression for the relative demand for wheat (CW /CC ) as a function of the
relative price of wheat (PW /PC ).
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c. Use your answers from (a) and (b) to solve for the autarky equilibrium consumption
(Cw and Cc ) and labor allocation (Lw and Lc ).
d. Repeat part (a), (b) and (c) for Foreign. Use ∗ to denote Foreign values (e.g. Cw∗ to
denote Foreign consumption of wheat). Compare the two autarky equilibrium and predict
the trade pattern.
e. Assume full specialization and solve for the equilibrium free trade relative price as well
as the production and consumption in each country. Describe the trade pattern.
f. We now look at the impact of trade on welfare. Compute consumption per worker in
each country before and after trade. Is welfare higher or lower with trade?
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