Jack Sprat can eat no fat, his wife can eat no lean

| November 24, 2016

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

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