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Econ 302

Homework #2

2022

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 = 4

· Y = 4

· U_A (X,Y) = MIN (2X,Y)

Consumer B:

· X = 4

· Y = 4

· U_B = X^1/4*Y^3/4

Suppose the Price of X is P_X = $2, and the Price of Y is P_Y = $1.

a) (16 points) 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) (8 points) 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. (26 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^1/2*Y^1/2,

And consumer B’s utility function is given by

U_B(X,Y) = X^1/4*Y^3/4.

a) (8 points) 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 = _____________________

b) (4 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) (14 points) Using an Edgeworth Box, illustrate

· The Budget Constraint

· The Initial Endowment (W)

· The Competitive Equilibrium (D)

Label the initial endowment “W” and label the Competitive Equilibrium “D”.  Make sure your graph is clearly and accurately labeled.