== 1. Consider the 2x2x2 Heckscher-Ohlin model (two goods, i countries, j 1,2). The production technologies are as follows; = 1, 2, two factors and two Y = Ka 1-a (1) Y = K2L1 Yj2 1-B (2) == where Yji is output of good i in country j, K; is capital used in the production of good i in country j, and Lj is labor used in the production of good i in country j. 0 < a < 1, and 0 < < 1, moreover, > a. The endowments of capital (K;, j 1, 2) and labor (L;, j = 1, 2) in the two countries are such that > K2 Consumers in both countries have identical, homothetic preferences. All markets are perfectly competitive. L1 L2 a) Write down the profit maximization problem for firms operating in sector i in coun- try j. (2 marks) b) From the first order conditions to firms' profit maximization problem in each sector, solve for the algebraic equilibrium relationship between the factor intensity and relative factor prices. (5 marks) c) Based on your answer to part (b), what can you say about the relative factor intensities of the two sectors? Why? (3 marks) d) Further manipulate the first order conditions in order to find the algebraic equi- librium relationship between relative goods prices and relative factor prices when both goods are produced. (5 marks) e) Suppose that the two countries open up to free trade. What will the move from autarky to free trade imply for the relative price of good 1 in country 2? What will the pattern of trade be? NB. You do not need to derive anything in this subquestion. (5 marks) f) Based on your prediction for the movement in relative goods prices in country 2, together with your answer to part d), show what will happen to relative factor prices in country 2. What will happen to relative factor intensities in country 2? (5 marks) g) Illustrate your findings to part (f) using a Lerner diagram. Show how the relative price change of the commodities affects the nominal returns to the two factors and the relative factor intensities of the two sectors. Make sure to carefully label the graph and explain the changes you find. (5 marks)