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Consider the following 2 economies, Home and Foreign, endowed with different
quantities of two goods, Apples and Blackberries. The respective demands in the two countries are
characterized by the following preferences. Consumers at Home have preferences representable by
the following utility function: U(xA,xB)=xA1/2 xB1/2, while consumers in Foreign have preferences
representable by the following utility function: U*(x*A,x*B)=x*A1/3 x*B2/3. Trade is the only
“production technology” available to the two countries, which have the following fruit endowments:
Home has 100 Apples and 70 Blackberries, while Foreign has 50 Apples and 80 Blackberries.
Assume countries are in autarky.
1. Homothetic preferences are characterized by the fact that marginal rate of substitution (MRS) is
constant along any ray from the origin, i.e. consumers always prefer to consume the two goods in
the same ratio. Show that both countries’ utility functions represent homothetic preferences. Why
do you think this type of preferences is appealing in international trade models?
2. Draw a graph representing Home country’s autarkic equilibrium, and one representing Foreign’s
2 autarkic equilibrium. Explain how this equilibrium is determined.
3. Compare autarky prices in the two countries and explain what are the factors that determine
them. Why is autarkic p in this particular relationship with autarkic p*, given the above
assumptions? Assume countries open up to trade with each other.
4. Calculate the demand for the two goods for both countries and the equilibrium relative price pw at
which the two countries trade Apples for Blackberries.
5. What is the trade pattern between the two countries? Explain the pattern of trade by looking at
the initial endowments and tastes?
6. Imagine there are 2 groups in each of the two countries: Apple-owners and Blackberry-owners.
Show that if when income redistribution is not possible, one interest group is hurt due to trade.
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