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 = 3Lx

where Ly and Lx 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/MPLx.

(b) All consumers in Ricardia have identical tastes which can be represented by a utility

function

U(X, Y) = 5X2/3Y 1/3

What are the Pareto optimal levels of output of X and Y and corresponding labor inputs Lx

and Ly