Question: 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*Y2 Therefore: For

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*Y2

Therefore:

  • For consumer A: MUX= Y; MUY= X
  • For consumer B: MUX= Y2; MUY= 2XY

The initial endowments are:

A: X = 140; Y = 61

B: X = 100; Y = 11

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?

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