Exercises -

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) Suppose the price of Y, P_Y = 1. Calculate the price of X, P_X 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?

2. 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) = Min(X, Y)

The initial endowments are:

A: X = 1; Y = 1

B: X = 5; Y = 5

Illustrate the initial endowments in and Edgeworth Box. Be sure to label the Edgeworth Box carefully and accurately, and make sure the dimensions of the box are correct. Also, draw each consumer's indifference curve that runs through the initial endowments. Is this initial endowment Pareto Efficient?

3. For each of the following production functions, determine whether it exhibits increasing, constant or decreasing returns to scale:

a) Q = K + L

b) Q = L + L/K

c) Q = Min(2K,2L)

d) Q = (L^.5)(K^.5)