Question

1. (40 marks) Sylvania is a small open economy producing two products, X and Y, using two factors of production, capital and labour, under constant returns to scale. Capital is sector-specific, while labour is freely mobile between production sectors. Let Qx and Qy be the output quantities, Kx and Ky the capital endowments specific to the two sectors, and Lx and Ly the labour allocations to the two sectors subject to the constraint im- posed by the total endowment, namely Lx Ly L. Consumers have a utility function U(Dx, Dy) = D炙* Dy, where Dx and DY are consumptions of X and Y. The price ratio is defined as P Sylvania's production possibility frontier (PPF) is defined by the equation Kx Ky which has slope given by the marginal rate of transformation MRT=--= The production functions in the two sectors are Q-Lwkỷ2 and QY-42㎸2, so that the marginal products of labour in the two sectors are given by MPL,-3(수) Finally, suppose that the variables take the following values Kx = 1, KY-1, L=9 (a) Derive the relative supply and demand functions. Hence, compute the autarky equi- librium price ratio, I (b) Now suppose that Sylvania opens up to free trade at the world price ratio PF 1 Compute Sylvania's productions and consumptions of the two goods. Which good is (c) Compute the autarky and free trade real incomes for the owners of capital - capital specific to sector X and capital specific to sector Y. Which capital owners gain from trade and which capital owners lose from trade, and why? (d) Compute the autarky and free trade utility levels for labour. Does labour gain from trade or lose from trade, and why?