Problem 1 [Specic Factors Model}. Canada and U .S. trade two products with each other - Cars [C] and Textile {T}. Denote all US variables with a. 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]. Low-skilled 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. Denote with L low-skilled labor, so that L3;- and by are employment of low-skilled workers in auto and textile industries and LC+LT : E is the full employment condition for unskilled labor, with 3 being the total number of unskilled workers. For skilled labor, employment levels are given exogenosuly by He and HT. Production technologies in the two industries are the same in both coun- tries and are given by the following production mctions: l a Yp = LEI-[c .r YT = LT'i'H-T where Y}; and YT are output levels. Consinners in both colmtries have the same preferences given by utility function U = CECT where C5;- and CT are consumption levels of the two goods. Also suppose that Canada has more skilled workers in auto industry but less in textiles than US: He- 3: FEET sf. H; 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 the US, its l'l'F will be skewed towards output of cars (Hint: l'l'F can be derived from equations (1} and [2] in class notes. This is the system of three equations with four unknowns, Ya, Yale, by, which can alsways be transformed into a single equation with two unknowns l'}; and YT] b. Calculate relative autarky prices in both countries. Prove that in the absence of trade cars are relatively cheaper in Canada. 1 c. For the following factor endowments and production technology, cal- culate autarky equilibrium output and relative price in Canada: as = wear 2 50;: = so; a = 0.5 d. Next, consider the free-trade scenario. How free trade between Canada and the US would affect the relative price of cloth in Canada? Assume that the equilibrium price of cloth changes from the autark},r level to 0.6. what would be the change in output of cars and textiles in Canada? e. Using a diagram, illustrate the effect of trade on production and con- sumption in Canada. 1Which good would Canada export? Illustrate gains from trade (no calcaations are required for this question]. f. Now suppose that as Canada opened its markets for free trade with the US, the price of cars remain constant and equal to 1, while the price of textile decrease from 0.9 to [1.8. Useing a diagram similar to Figure 3.8 in the class notes [Class 3], illustrate the effect of openness to trade on the wage rate of lmskilled workers in Canada. Calculate the effect of trade on real income of lmskilled workers (Hint: for that you would need to solve for unskilled labor market equilibrium with and without trade using four equilibrium conditions on pp.ZT-28 of Class notes #3. Note that the marginal product of labor in sector 1' is the partial derivative of production function with respect to labor: MPL, = gs }. g. Calculate the impact of trade with the US. on earnings of skilled workers in Canadian auto and textile industries? Problem 2 [HeckscherChlin model]. Suppose two countries can produce and trade two goods - food [F] and cloth [C]. Production technologies for the two industries are given below and are identical across coimtries: i a a = Km 3 i Qt\": = HCLC where Q denotes output and K, and L, are the amolmt of capital and labor used in the production of good i. a. Using prot-maximization conditions for each industry, derive relative demand for capital [%} as a mction of the relative factor prices L 'll'J' 2 b. Suppose the SS curve is given by the following function: PE = PC Also assume that the relative price of food is equal to one. Calculate capital intensity of each industry. c. Now we add information on factor endowment. Suppose a country has K = 90 units of capital and Z = 60 units of labor and the following full employment conditions are satisfied: KF+ Ko = K LF+ Lo = L Find equilibrium allocation of resources across industries and output of each good. d. Suppose labor endowment increase to Z = 90. How would it affect output of capital-intensive and labor-intensive goods? e. Going back to the case when Z = 60, demonstrate the effect of a decrease in price of food to 2 = (0.8). Solve for the new production patterns and w/r and confirm the Stolper-Samuelson theorem