1. Suppose there are two consumers, A and B.

The utility functions of each consumer are given by:

UA (X,Y) = X*Y

UB (X,Y) = X*Y^3

Therefore:

For consumer A: MUX = Y; MUY = X

For consumer B: MUX = Y^3; MUY = 3X Y^2

The initial endowments are:

A: X = 10; Y = 6

B: X = 14; Y = 19

a) Suppose the price of Y, PY = 1. Calculate the price of X, PXthat will lead to a competitive equilibrium.

b) How much of each good does each consumer demand in equilibrium?

Consumer A's Demand for X:

Consumer A's Demand for Y

Consumer B's demand for X

Consumer B's demand for Y

c) What is the marginal rate of substitution for consumer A at the competitive

equilibrium?