Suppose there are two consumers, A and B.

The utility functions of each consumer are given by:

UA(X,Y) = X2Y

UB(X,Y) = X*Y

Therefore:

• For consumer A: MUX= 2XY; MUY= X2
• For consumer B: MUX= Y; MUY= X

The initial endowments are:

A: X = 120; Y = 6

B: X = 30; Y = 14

a)(20 points) Suppose the price of Y, PY= 1.Calculate the price of X, PXthat will lead to a competitive equilibrium.

b) (8 points) 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) (4 points) What is the marginal rate of substitution for consumer A at the competitive equilibrium?