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

Question

Suppose there are two consumers, A and B. The utility functions of each consumer are given by: U_A(X, Y) = XY^3 U_B(X, Y) = X*Y Therefore: For consumer A: MU_X = Y^3; MU_Y = 3XY^2 For consumer B: MU_X = Y; MU_Y = X The initial endowments are: X = 16: Y = 28 X = 54: Y = 12 Suppose the price of Y. P_Y = 1. Calculate the price of X, P_X that will lead to a competitive equilibrium. 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 What is the marginal rate of substitution for consumer A at the competitive equilibrium?

Explanation / Answer

a)     Price of Y, PY= 3.107

Consumer

MUx

MUY

PY(MUY/MUX)

A

21952

37686

1.714

B

12

54

4.5

Competitive Equilibrium(PY)

3.107

b)    Consumer’s A demand for X= 21952

Consumer’s A demand for Y= 37686

Consumer’s B demand for X= 12

Consumer’s B demand for Y= 54

c)     Marginal rate of substitution for Consumer A= MUx/PX= MUY/PY

                    21592/1=37686/1.714

Consumer

MUx

MUY

PY(MUY/MUX)

A

21952

37686

1.714

B

12

54

4.5

Competitive Equilibrium(PY)

3.107

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