Suppose there are two consumers, A and B.
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*Y3
Therefore:
? For consumer A: MUX = Y; MUY = X
? For consumer B: MUX = Y3; MUY = 3XY2
The initial endowments are:
A: X = 6; Y = 7
B: X = 14; Y = 13
a) (40 points) Suppose the price of Y, PY = 1. Calculate the price of X, PX that will lead to a competitive equilibrium.
b) (16 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) (8 points) What is the marginal rate of substitution for consumer A at the competitive equilibrium?

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Solution: Suppose there are two consumers, A and B.