Consider a simple Heckscher-Ohlin model in which the production functions are the following: Y1 = L1/2K Y2 = L1/312/3 While the representative consumer's preferences are given by the following Cobb- Douglas utility function: U = 61 C2- (f) Derive the unit-cost functions for each industry, c;(w, r) with i = 1,2, and the amount of factors (labour and capital) used to produce one unit of each product, air, aix. Which industry is labour intensive and which one is capital intensive? [5 marks] (g) Explain the conditions that determine the equilibrium in the closed economy (no trade), find the relative wage, w/r, and the relative price in the equilibrium. [8 marks] (h) Assume now that trade is allowed between two countries (named H and F). H's endowment is _ units of labor and K units of capital, while F's endowment is L* and K*. These endowments are such that L=L* and K>K*. Furthermore, assume that the factor endowments in the two countries imply that the factor price equalisation holds. Find the relative wage, w/r, in the free trade equilibrium. [4 marks] Compare the relative price of the products between the case of free trade and the case of autarky. [5 marks] (j) Who gains from trade in country F? [3 marks]