BC3035: Microeconomic Theory, Problem Set #5

1. Jack Sprat can eat no fat, his wife can eat no lean.” Construct an Edgeworth box

diagram for this pair (assuming fixed quantities of “fat” and “lean”) and indicate the

contract curve.

2. Nothing in our analysis of exchange requires that the equilibrium be unique. Draw

an example of an Edgeworth box diagram in which there are two different, interior

equilibria arising from the same initial endowments. Explain intuitively why can

these occur.

3. Suppose there are only two individuals (Sally and Jenny) and two goods (ham and

cheese) in an exchange economy. Sally chooses to consume ham and cheese in fixed

proportions of 2 C and 1 H. Sally’s utility function is therefore U S = min( H , C / 2) .

Jenny has flexible preferences and utility is given by U J = 4H + 3C . Initial

endowments for Sally are H = 60, C = 80 and for Jenny H = 40, C = 120.

a. Graph the Edgeworth box diagram for this exchange economy and indicate the

core of the economy given the initial endowments specified

b. At the competitive equilibrium, what will be the equilibrium price ratio? Who

will obtain the gains from Trade?

4. Consider an exchange economy in which there are exactly 1000 soft drinks (x) and

100 hamburgers (y). Let Smith’s utility be represented by U S (X S , YS ) = X S 2/3 YS 1/3 . And

Jones’ utility by U J (X J , YJ ) = X J 1/3 YJ 2/3 . Each individual has an initial endowment of

500 units of each good.

a. Express the demand for Smith and Jones for goods x and y as functions of PX, PY

and their initial endowments.

b. Use the demand functions from part (a) together with the observation that total

demand for each good must be 1000 to calculate the equilibrium price ratio, PX

/PY, in this situation. What are the equilibrium consumption levels of each good

by each person?

c. How would the answers to this problem change for the following initial

endowments?i

ii

iii

iv

Smith’s endowment

X

Y

0

1000

600

600

400

400

1000

1000

Jones’ endowment

X

Y

1000

0

400

400

600

600

0

0