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ECON 398 HOMEWORK 3
Professor Ozdenoren
1.
In a small town called Ham Harbour there are two shops. Wingerman’s has great
cheese and Trader Moe’s has good wine. Demand for Wingerman’s cheese is given
by Q
W
= 32  2P
W
 P
M
and demand for Trader Moe’s wine is given by Q
M
= 20 – 2P
M
 P
W
where Q
W
is pounds of cheese per day sold by Wingerman’s, Q
M
is cases of
wines per day sold by Moe’s and P
W
and P
M
are prices in dollars for cheese and wine
respectively. Suppose that a pound of cheese and a case of wine both cost 2 dollars to
the shops.
a.
If both firms set their prices simultaneously, what are the equilibrium prices
and profits for each shop?
b.
If the firms can set prices together (i.e., collude), what are the equilibrium
prices and profits in this case?
c.
Compare this with the Donna’s and Pierce’s example solved in class. What is
the main difference?
Answer a)
Profit function of Wingerman’s is (32  2 P
W

P
M
)( P
W
 2) and the profit
function for Moe’s is (20  2P
M

P
W
)( P
M
 2). Taking the derivative of Wingerman’s
profit fuction with respect to P
M
and setting it to zero we find that Wingerman’s best
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This note was uploaded on 04/02/2008 for the course ECON 398 taught by Professor Emre during the Winter '07 term at University of Michigan.
 Winter '07
 Emre

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