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

Suppose there are two consumers, A and B. The utility functions of each consumer are given by:

UA(X,Y) = X2*Y

UB(X,Y) = X*Y2

Therefore:

  • For consumer A: MUX = 2XY; MUY = X2
  • For consumer B: MUX = Y2; MUY = 2XY

The initial endowments are:

A: X = 20; Y = 95

B: X = 15; Y = 60

a) (16 points) Suppose the price of Y, PY = 1. Calculate the price of X (PX) that will lead to a competitive equilibrium. Put this equilibrium price of X in the blank below.

PX =

b) (8 points) How much of each good does each consumer demand in equilibrium? Consumer A's demand for X is Consumer A's demand for Y is Consumer B's demand for X is Consumer B's demand for Y is

c) (4 points) What is the marginal rate of substitution (MRS) for consumer A at the competitive equilibrium? MRS =

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