Question: Suppose there are two consumers, A and B. The utility functions of each consumer are given by: UA(X,Y) = X 2 Y UB(X,Y) = X*Y

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?

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