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Question 1 (5 Points): This question is based on the Specic Factor (Short Run) Model Portland can produce two goods: manufacturing (M) and Agriculture (A). The production functions of the manufacturing and Agriculture industries are given by QM = KIM LMIJJ and QA = 1-5 Laos where: K is capital, T is land, and L is labor. Capital is specic to manufacturing and land is specic to agriculture whereas labor is used in both the industries: Labor supply is Lu + L5 = 1000 and T = K = 1000. Prices of manufacturers (PM) and of agriculture (PA) are both equal to 1: PM = P... = 1. A. Derive the marginal products of labor (MPLM) and (MPLa) for the two industries. (1 point) B. Graph the labor demand curves in the manufacture and agriculture industries. Show the allocation of labor across industries and calculate the equilibrium wage rate in autarky. (1 point) C. Now suppose, Portland opens up to free trade and faces a relative price of Phil's = 2. How do the allocation of labor and wages change? (2 points) D. Using the general labor demand relationships for the two sectors, show that the production possibility frontier is given by - MPLJMPLM = - PMIPA. (1 point) E. Due to technological advancement the price of manufactures in the Portland falls to $0.5. Calculate new labor allocation across sectors and new wage and determine the gaim'loss to factors of productions. (Hint: compare real returns before and after price change.) (2 points) Question 2. (5 points): This question is based on Heekseher-Ohlln (HO) Model Suppose two countries. Grainland and Carsland, use only capital and labor to produce two goods, Grain (G) and Cars (C). Grainland has 2,050 units of capital and 916 units of labor, and Garland has 816 units of capital and 23"0 units of labor. In Carsland, there are 366 units of capital and 135 units of labor employed in the Grain industry. In Grainland, there are 926 units of capital and 613 units of labor employed in the Grain industry. A. Which country is labor-abundant? Which country is capital-abundant? In Carsland which industry is labor-intensive and why? B. Suppose that Grainland and Carsland do not engage in international trade. Assuming the countries have identical preferences, which country would have the cheaper relative price of Grain? C. Now suppose the two countries trade with one another. What will happen to the relative price of Grain in Grainland? What is the effect of he trade on labor and capital owners in Grainland? D. Now suppose. Cars use 4 units of capital for each worker (K1: m: = 4 or Kc = 4Lc) whereas Grains use 0.2 units of capital for each worker (Kn (Ln = 0.2 or Kn = 0.2 La). There are 200 workers and 200 units of capital in the economy. Solve for labor and capital in each industry. (hint: Kc + Kg = 200 and L: + La = 200. First solve for or Lc and Lo using these two equations and then for Kr: and Ks) E. Next, suppose number of workers increase to 250 because of immigration, keeping total capital xed at 200. Solve for labor and capital used in each industry. W'hich theorem is consistent with this result? Why and why not