Adam and Eve are consumers in a 2-consumer, 2-good exchange economy. The price of X is PX, and the price of Y is $1. Each one has an initial endowment of (X=6, Y=6); therefore, each one has a "budget line" of X•PX + Y = 6•PX + 6. • Adam’s utility function is U = XY. The expression for Adam’s marginal rate of substitution (i.e., ∂U/∂X ÷ ∂U/∂Y) is Y/X, which at his initial endowment of (6, 6) has the value of 1. Adam’s demand for X as a function of the price of X is X = 3 + 3/PX.
(i) If Eve’s utility function is X2Y, find: (i) the expression for Eve’s marginal rate of substitution; (ii) the value of Eve’s marginal rate of substitution at her initial endowment; and (iii) Eve’s demand for X as a function of the price of X. (ii) What is the price of X in equilibrium?