There are two countries, Canada (CAN) and Mexico (MEX). Consumers in both coun- tries have identical preferences over two goods, oil and corn, with utility given by: c c S C 13 U = (Coil) (acorn) where 0;; and 0:0,.\" denote consumption of oil and corn respectively in country c. The parameter S E (0, 1) indicates how much consumers like oil relative to corn. We will denote the prices of oil and corn by p0,; and 3960,.\" respectively, with p, E pas/{pm denoting the relative price of oil to corn. Each country is also endowed with stocks of two productive factors, capital (K) and labor (L), which are owned by consumers. Endowments of capital and labor are: EGAN = 10' EGAN = 5 RMEX = 2' EMEX = 8 We will denote the prices of capital and labor by 'r and w respectively. In country c E {CAN , MEX} and sector 2' E {0% com}, production uses the following Cobb-Douglas tech- nology: X: = T: (K:)1'*' (L:)"* where Xf, Kf, and LE denote output, capital input, and labor input respectively in sector 15 in country c. All output is produced under perfect competition. Note that the parameter Tf allows for productivity dierences across both countries c and sectors 2', while the parameter A, allows for differences in factor intensities across sectors. Below, you will consider four scenarios that differ in terms of how mobile factors are across sectors and in terms of the parameters {3,119, A,} of the utility and production functions. Treat each scenario independently. Each scenario has questions that are worth 30 points in total, for a grand total of 120 points. Answer all questions. Scenario 1 Both capital and labor are specic to individual sectors and cannot be reallocated across sectors. In Canada, the allocation of factors is: Kata, LEN3 K31? _ 4: L302}: _ 2 while in Mexico, the allocation of factors is: xx\" = 1, L3\" = 2 Kax = 1, La? = 5 Assume that A0,; = Am...\" = and that 1'1? = 1 in all countries and sectors. Assume that S = l 3. (a) What is the relative price of oil to corn, pr E pal/p20,\Scenario 2 Suppose that A011 = Am = 1, so that capital is not a productive factor and earns zero income. Labor is freely mobile across sectors but is immobile across countries. Productivities in Canada are: TOE'IAN = 5:| TCAN = 4 COT\" while productivities in Mexico are: MEX = 2, Tfx = 1 m Assume that S = %- (a) What is total consumer utility U C in each country c under autarky? (15 points) (b) Suppose that under free trade, there is complete specialization, so that each country only produces in one sector. What is the world relative price of oil to corn under free trade, pr E pig/pg\"? (15 points) Scenario 3 Suppose that A0,; = AW\" = g. Capital is freely mobile across sectors but is immobile across countries. Labor is specic to individual sectors and cannot be reallocated across sectors. In Canada, the allocation of labor is: O 3 COT\" while in Mexico, the allocation of labor is: LEX = 2: LgX = 6 Assume that If = 1 in all countries and sectors. Assume that S = CollI a What are real incomes for ca ital owners 5"\" 9 in each countr c under autark '? Note: P 10% y 3' you should calculate real capital incomes in each country using goods prices in both sectors.) (20 points) (b) Now suppose that Canada and Mexico open up to free trade with each other. How would you expect the real capital incomes that you compute in part (a) to change (is. would real incomes increase, decrease, or stay the same)? Explain clearly the economic reasoning behind your answer. (10 points)
