Suppose there are two consumers a and bthe utility

Question

Suppose there are two consumers, A and B.

The utility functions of each consumer are given by:

U_A = X²Y

U_B = X*Y

Therefore:

?           Consumer A: MU_X = 2XY; MU_Y = X²

?           Consumer B: MU_X = Y; MU_Y = X

The initial endowments are:

A: X = 120; Y =6

B: X = 30; Y =14

a)  Suppose the price of good Y,  Py=1. Calculate the price of good X, Px  that 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?