1.Suppose there are two consumers, A and B.

The utility functions of each consumer are given by:

U_A(X,Y) = X^*Y

U_B(X,Y) = X*Y³

Therefore:

For consumer A: MU_X = Y; MU_Y = X

For consumer B: MU_X = Y³; MU_Y = 3XY²

The initial endowments are:

A: X = 10; Y = 6

B: X = 14; Y = 19

a)(40 points) Suppose the price of Y, P_Y = 1.Calculate the price of X, P_X 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?

1. Suppose there are two consumers, A and B. The utility functions of each consumer are given by: magi) = X'Y magi) = X'Y3 Therefore: a For consumer A: MU); = Y; MUY = X a For consumer B: MU); = Y3; MUY = BXY2 The initial endowments are: A: X = 10; Y = 6 B: X = 14; Y =19 Q40 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