1.(24 points) Suppose there are two consumers, A and B, and two goods, X and Y. The consumers have

the following initial endowments and utility functions.

Consumer A:

X = 1

Y = 7

UA(X,Y) = MIN (X,Y)

Consumer B:

X = 7

Y = 1

UB= X^1/4*Y^3/4

Suppose the Price of X is Px= $1, and the Price of Y is PY= $1.

a) Suppose each consumer sells their initial endowment and buys back their optimal bundle.

Using an Edgeworth Box, illustrate

The Budget Constraint

The Initial Endowment (W)

A's Optimal Bundle (A)

B's Optimal Bundle (B)

Label the initial endowment W, label A's optimal bundle A, and label B's optimal bundle B. Make sure

your graph is clearly and accurately labeled.

b. For the situation above, determine for each market if there is excess demand, excess supply, or the market is in equilibrium (circle the correct answer). If there is excess demand or excess supply, determine how much it is.

Market for Good X:

Excess Demand = __________________

Excess Supply = ___________________

The market is in equilibrium

Market for Good Y:

Excess Demand = __________________

Excess Supply = ___________________

The market is in equilibrium

2. 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:

UA(X,Y) = X*Y,

And consumer B's utility function is given by

UB(X,Y) = X*Y^3

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

MUX= Y

MUY= X

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

MUX= Y^3

MUY= 3XY^2

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

competitive equilibrium.

PX= _____________________

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?

MRSA= ____________

3. Suppose there are two consumers, A and B. There are two goods, X and Y. There is a TOTAL of 8 units of X and a TOTAL of 8 units of Y. The consumers' utility functions are given by:

UA(X,Y) = 4X + Y

UB(X,Y) = X*Y

For each of the following allocations, write TRUE if it is Pareto Efficient and FALSE if it is not:

i) Consumer A gets 6 units of X and 2 units of Y, and Consumer B gets 2 units of X and 6 units of Y.

ii) Consumer A gets 4 units of X and 6 units of Y, and Consumer B gets 4 units of X and 2 units of Y.

iii) Consumer A gets 7 units of X and 0 units of Y, and Consumer B gets 1 units of X and 8 units of Y.

iv) Consumer A gets 4 units of X and 0 units of Y, and Consumer B gets 4 units of X and 8 units of Y.