EC 501: Problem Set 7 (Due in class on Tuesday, November 6) 1. In the economy of Ricardia, two consumer goods, X and Y, are produced from a single factor input, labor, according to the production functions: Y = 3Ly and X = 3Ly where Ly and Ly are the quantities of labor used in the production of Y and X respectively. The total amount of labor available is 66 units. (a) Derive the equation for the economy's production possibility frontier. Confirm that the marginal rate of transformation is equal to MPLy/MPL. (b) All consumers in Ricardia have identical tastes which can be represented by a utility function U(X, Y) = 5X2/3y1/3 What are the Pareto optimal levels of output of X and Y and corresponding labor inputs Lx and Ly