1. Consider the 2x2x2 HeckscherOhlin model (two goods, 2' = 1, 2, two factors and two countries, 3' = 1, 2). The production technologies are as follows; 331 = EL}? (1) y}, = KELEB (2) where Y,-,- is output of good 2' in country 3', K5,,- is capital used in the production of good 1' in country 3', and L5,, is labor used in the production of good i in countryj. 0 or. The endowments of_capital (Kj, j : 1, 2) and labor (Lj, j : 1, 2) in the two countries are such that f1: > %. Consumers in both countries have identical, homothetic preferences. All markets are perfectly competitive. a) Write down the prot maximization problem for rms operating in sector 3' in coun try j. (2 marks) b) From the rst order conditions to rms' prot 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) (1) Further manipulate the rst order conditions in order to nd 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) 3olumbia University Professor Rka J uhasz Department of Economics email: rj 2446columbiaedu 3U4500 International Trade Fall 2017 g) Illustrate your ndings 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 nd