1. Cali and David both collect stamps (??) and fancy spoons (??). They have the following preferences
and endowments.
????(??, ??) = ???? ∙ ????
2 ????(??, ??) = ???? ∙ ????
???? = (10, 5.2) ???? = (14, 6.8)
a. Write down the resource constraints and draw an Edgeworth box that shows the set of
feasible allocations.
b. Label the current allocation inside the box. How much utility does each person have?
c. Show that the current allocation of stamps and fancy spoons is not efficient. (Hint: Define the
contract curve, or the set of Pareto optimal allocations.)
d. Show that the following allocation would make both Cali and David better off compared to
the original allocation. Is it possible to make any further pareto improvements?
???? = (8, 6) ???? = (16, 6)
2. Suppose the economy consists of two individuals, Ariel and Brad, who consume two goods, ?? and ??,
with the following preferences and initial endowments.
????(??, ??) = ???? ∙ ???? ????(??, ??) = ???? + ????
???? = (4, 2) ???? = (2, 3)
a. In an Edgeworth Box label the initial endowment, draw an indifference curve through the initial
endowment for each individual, and shade the region of allocations that would be a Pareto
improvement to the initial endowment.
b. Derive an equation to describe the set of Pareto-optimal allocations, and draw it in the
Edgeworth Box.
c. Define the competitive equilibrium allocation [(????, ????), (????, ????) ] and price ratio ????⁄????.
(Remember that without loss of generality, you may set ??1 ≡ 1.)

d. Find a set of transfers, ???? and ????, where ???? + ???? = 0, such that the competitive equilibrium
becomes [(1, 1), (5, 4) ]

DETAILED ASSIGNMENT

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