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 = 8; Y = 6
B: X = 14; Y = 17
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?