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 = 90; Y = 12

B: X = 60; Y = 8

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?