2.(6 Total Points) Suppose a consumer's utility function is given by U(X,Y) = MIN (4X, Y). Also, the consumer has $40 to spend, and the price of Good X, P_X = $1. Let Good Y be a composite good whose price is P_Y = $1. So on the Y-axis, we are graphing the amount of money that the consumer has available to spend on all other goods for any given value of X.

Now suppose P_X increases to $4.

i) (3 points) Calculate the Compensating Variation:

CV = _____________________

ii) (3 points) Calculate the Equivalent Variation:

EV = _____________________

3. (14 points) Suppose there are two consumers, A and B.

The utility functions of each consumer are given by:

U_A(X,Y) = X^1/2*Y^1/2

U_B(X,Y) = X + 4Y

The initial endowments are:

A: X = 4; Y = 4

B: X = 12; Y = 4

a) (8 points) Using an Edgeworth Box, graph the initial allocation (label it "W") and draw the indifference curve for each consumer that runs through the initial allocation. Be sure to label your graph carefully and accurately.

b) (2 points) What is the marginal rate of substitution for consumer A at the initial allocation?

c) (2 points) What is the marginal rate of substitution for consumer B at the initial allocation?

d) (2 points) Is the initial allocation Pareto Efficient?

4.(6 points) Suppose there are two consumers, A and B, and two goods, X and Y. Consumer A is given an initial endowment of 6 units of good X and 1 units of good Y. Consumer B is given an initial endowment of 2 units of good X and 7 units of good Y.Consumer A's utility function is given by:

U_A(X,Y) = X*Y,

And consumer B's utility function is given by

U_B(X,Y) = X*Y³.

Therefore, consumer A's marginal utilities for each good are given by:

MU_X = Y

MU_Y = X

Also, consumer B's marginal utilities for each good are given by:

MU_X = Y³

MU_Y = 3XY²

Suppose the price of good Y is equal to one. Calculate the price of good X that will lead to a competitive equilibrium.

P_X = _____________________