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Intermediate Microeconomics, 2010
Problem Set 20: Homework
Due Mon/Tue March 29/30
1. Reconsider question 2 from Homework 19 (Guard for a Mall). Suppose the two
stores choose the number of guards sequentially: ±rst store A chooses whether to
hire zero, one, two, or three guards and then store B chooses whether to hire zero,
one, two, or three guards.
Find all subgame perfect equilibria. For each subgame perfect equilibrium, write
down the complete equilibrium strategy of store B, i.e., write down how many
guards B would hire, after A has hired
X
guards.
2. Suppose the demand for Pepsi is
q
p
= 54
±
2
p
p
+ 1
p
c
. The demand for Coke is
q
c
= 54
±
2
p
c
+ 1
p
p
. Each ±rm faces a constant marginal cost of zero.
(a) Determine the Bertrand equilibrium prices.
(b) What happens to the Bertrand equilibrium prices and pro±ts if increased dif
ferentiation causes the demand for Pepsi to become
q
p
= 104
±
2
p
p
+1
p
c
while
the demand for Coke remains unchanged?
3. Suppose the (inverse) demand for pizza in a small isolated town is
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 Spring '08
 Malley

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