2. Consider the specific factors model. There are two sectors; cloth and food. Cloth production uses labor and capital. Food production uses land and labor. Labor is fully mobile between the two sectors. Production technologies for the two goods are as follows: Qc = ZCKI/QL(I;P (1) Qr = ZpT'2Ly? (2) where Z- and Zp are the productivities, K and 7" are the endowments of capital and land respectively, and L = Lo + L is the aggregate endowment of labor. Consumers' preferences are given by the following utility function; U(Qc, Qr) = min{Qc, Qr}. a) Derive the equation of relative supply for this economy (8% as a function of the relative price, gfj). Plot the relative supply curve. b) Assume this country opens up to trade at fixed world prices Pt =1 and P_,_:ft =1 (the country is sufficiently small relative to the world economy such that it has no effect on prices). How will the country's pattern of trade (which good is imported and which good is exported) depend on the parameters of the model (K, L, T', Z, Zr )7 To gain some intuition, answer this question in two parts. First, set Zo = Zp and describe how the pattern of trade will depend on the size of T relative to K. Second, set T'= K to describe how the pattern of trade will depend on the size of Z relative to Zp