SQ3zz - Economics 121 E. McDevitt Study Questions #3 1....

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Economics 121 E. McDevitt Study Questions #3 1. Factor Price Equalization . a. Given the assumptions of the Standard Trade Model, free trade leads to an outcome in which relative factor (input) prices are equalized across countries. A critical part of this argument is to show that relative input prices (r/w) are a function of relative output prices (P x /P y ), where here we assume that X is the capital intensive good. Derive an equation that explicitly shows the relationship between (r/w) and (P x /P y ) using the following assumptions (notice that these are the same assumptions used in SQ2): The production functions for goods X and Y in each country are X = L x 1/5 K x 4/5 and Y = L y 4/5 K y 1/5 . [Although not necessary for this question, we shall also continute to assume that country A’s endowment is L=1 and K =32 and that country B’s endowment is L = 32 and K = 1.] The Cobb-Douglas total cost functions for each good are TC x = [(a/b) b + (b/a) a ] (X)(w) a (r) b and TC y = [(a/b) b + (b/a) a ] (Y)(w) a (r) b where the “a” and “b” exponents are from the generalized Cobb-Douglas production function Q = A L a K b (for simplicity we shall assume the technology parameter— A —is equal to one, so we can write it as Q = L a K b ). b. What does this equation imply about the relationship between (r/w) and (P x /P y ) and how would you show this on a graph that places (P x /P y ) on the vertical axis and (r/w) on the horizontal axis? c. Recall from SQ2 that (P x /P y ) B > (P x /P y ) A in the pre-trade situation. What does this pre-trade inequality imply about the relative input price ratios in each country and what is the intuition behind this result? How would you show this on your graph from part (b)? d. What happens to (P x /P y ) in each country as trade opens?. ..what happens to (r/w) in each country? Show this on your graph from part (c). What is the intuition behind these changes and how would you show it on supply and demand graphs for the inputs? e. More generally, what does this result imply about which inputs gain from free trade and which inputs are hurt by free trade? f. Suppose trade barriers (tariffs, import quotas) prevent the full equalization of relative output prices (P x /P y ) across countries. What does this imply about (r/w) in each country? Use a graph to explain. g. From approximately 1980 to 2005 the U.S. witnessed a widening in the gap between the wage for high skilled workers (proxied by those with college degrees) and the wage for low skilled workers (those with high-school degrees). During this period the level of trade increased such that exports, intensive in high skilled labor, rose and imports, intensive in low skilled labor, also rose. How might our trade model help explain this outcome? Hint: Rather than K and L, think of L High and L Low as the two inputs with X being intensive in high skilled labor and Y being intensive in low skilled labor. h. Using data from 2004, we find that the U.S and Brazil were large net exporters of soybeans, whereas China,
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SQ3zz - Economics 121 E. McDevitt Study Questions #3 1....

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