ECO 364 International Trade Theory Problem set 2

Problem 1Canada and U.S. trade two products with each other – Cars (C) and Textile (T ). Denote all US variables with . Each product is produced using labour only but there are two types of workers in each industry: low-skilled workers (L) and high-skilled ones (H). Unskilled workers can easily change occupation and move from one industry to another if they can earn more there. Skilled workers, however, cannot change occupation because their skills are specic to the industry in which they work. For example, in the clothing industry there is no demand for skilled mechanics who spent most of their lives assembling cars. Denote with L low-skilled labor, so that LC and LT are employment of low-skilled workers in auto and textile  industries and LC + LT = L is the full employment condition for unskilled labor with L being the total number of unskilled workers. For skilled labor, employment levels are given exogenosuly by H C and H T .Production technologies in the two industries are the same in both countries and are given by the following production functions:1YC = LC H CYT = L T + H Twhere YC and YT are output levels. Consumers in both countries have the same preferences given by utility function43U = DC DTwhere DC and DT are consumption levels of the two goods. Also suppose that Canada has more skilled workers in auto industry but less in textiles than US: H C > H C ; H T < H T .a. Derive the equation for production possibility frontier in Canada. Prove that if Canada has more skilled workers in Auto industry but less in textiles than US, its PPF will be skewed towards output of cars (Hint: PPF can be derived from equations (1) and (2) in class notes. This is the system of three equations with four unknowns, YC ; YT ; LC ; LT , which we can always be transformed to a single equation with two unknowns YC and YT )1b. Calculate relative autarky prices in both countries. Prove that in the absence of trade cars are relatively cheaper in Canada. c. For the following factor endowments and production technology, calculate autarky equilibrium output and relative price in Canada:H C = 100; H T = 50; L = 50;= 0:5d. Now Canada started trading with the U.S. and trade costs are zero. How trade would aect the relative price of cloth in Canada? Assume that the equilibrium price of cloth change from the autarky level to 0:6, by how much the output of cars and textiles change in Canada?e. Using a diagram, illustrate the eect of trade on production and consumption in Canada. Which good would Canada export? Illustrate gains from trade (no calculations are required for this question).f. Now suppose that as Canada opened its markets for free with the US, the price of cars remain constant and equal to 1, while the price of textile decrease from 0.9 to 0.8. Useing a diagram similar to Figure 3.8 in the class notes (Class 3), illustrate the eect of openness to trade on the wage rate of unskilled workers in Canada. Calculate the eect of trade on real income of unskilled workers (Hint: for that you would need to solve for unskilled labor market equilibrium with and without trade using four equilibrium conditionson pp.27-28 of Class notes #3. Note that the marginal product of labor in sector i is a partial derivative of production function with respect to labor:@YM P Li = @Lii ).g. Calculate the impact of trade with the U.S. on earnings of skilled workers in Canadian auto and textile industries?