Suppose France needs 4 units of labor to produce 2 unit of cheese (C), and 3 units of labor to produce 2 units of wine (W). Spain needs 3 units of labor to produce 1 unit of cheese, and 4 units of labor to produce 5 units of wine. Assume the marginal productivities of labor are constant in each country. Assume both countries have populations of 90 million.
France has a Cobb-Douglas utility function of U(C,W)=C^.3W^.7, making its MUc=.3(W/C)^.7 and MUw=.7(C/W)^.3
Spain has a Cobb-Douglas utility function of U(C,W)=C^.6W^.4, making its MUc=.6(W/C)^.4 and MUw=.4(C/W)^.6
Throughout the problem, treat Cheese as the good on the X-axis. To make your notation easier, your numbers should be in millions of units when necessary. That is, if the answer to a question is "5 million units," then write down just "5." Finally, to facilitate grading, ANSWER IN ORDER AND CIRCLE YOUR ANSWERS.
a.) Which good does France have a comparative advantage in producing?
b.) What is the autarky price ratio in Spain?
c.) Graph the PPFs for France and Spain. Be sure to indicate the slopes.
d.) What is the MRS for France?
e.) In autarky, how much cheese does France produce?
f.) In autarky, how much wine does Spain consume?
g.) What is Spain's utility level in Autarky?
h.) If France and Spain have free trade, how many units of cheese will France produce?
i.) How many units of cheese will France consume? This will be true at any price.
j.) What will France's exports of cheese be? This will be true at any price.
k.) How many units of cheese will Spain consume, as a function of the world price ratio P=Pc/Pw?
l.) At what value of P will the market for cheese clear? That is, what is the international equilibrium price?
m.) What is Spain's consumption of i) cheese and ii) wine?
n.) What is Spain's utility after trade?