## (Solution Document) Suppose there are two consumers, A and B. The utility functions of each consumer

Suppose there are two consumers, A and B.

The utility functions of each consumer are given by:

UA(X,Y) = XY3
UB(X,Y) = X*Y

Therefore:

• For consumer A: MUX= Y3; MUY= 3XY2
• For consumer B: MUX= Y; MUY= X

The initial endowments are:

A: X = 16; Y = 28
B: X = 54; Y = 12

a)  (20 points) Suppose the price of Y, PY = 1.  Calculate the price of X, PX that 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?

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