ECO 310, Fall 2007
Problem Set 5: Equilibrium Analysis
Due in class on November 20
Question 1
In this problem we will consider the fish industry on the island of San Serife.
For this purpose we will aggregate all the other goods into one composite, and
measure it in units of the island’s currency Arial. Thus the price of the other
good is 1.
(a) There are 160 consumers, each with the utility function
U
(
x, y
) = 10
x

5
x
2
+
y,
where
x
is the consumption of fish and
y
the consumption of the other
good. Let
P
denote the price of fish. Find one consumer’s demand func
tion (
x
expressed as function of
P
). Be careful about boundary solutions
with
x
= 0, but ignore boundary solutions with
y
= 0, i.e., assume that
each consumer has suﬃciently high income. Find the market demand for
fish.
Show this in a graph with
P
on the vertical axis and the market
quantity
Q
on the horizontal axis.
(b) The fishing industry consists of several firms. Each firm, to produce and
sell a positive amount of fish, must get a boat and hire a market stall.
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 Fall '08
 StephenE.Morris
 Economics, Supply And Demand, longrun equilibrium, longrun equilibrium price

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