Economics 302
Silve Parviainen
Intermediate Microeconomics
Spring 2006
Answers to Mock Final
1
Duopoly with Product Differentiation
(a) To find the price reaction function for AA, we start by changing the demand function to inverse form:
p
A
= (400 +
1
2
p
N
)
−
1
2
q
A
. Note that the first term (in parenthesis) which consists of a constant and
Northwest’s price is beyond the control of AA, so the company takes that as given. Given the linear
inverse demand function, the marginal revenue function is
MR
A
= (400 +
1
2
p
N
)
−
q
A
. Since
MR
=
MC
in the equilibrium, we get
400 +
1
2
p
N
−
q
A
= 60
=
⇒
q
A
= 340 +
1
2
p
N
,
which gives us the price reaction function
p
A
= (400 +
1
2
p
N
)
−
1
2
340 +
1
2
p
N
= 230 +
1
4
p
N
(b) To solve for the equilibrium prices, we need the price reaction functions for both companies.
AA’s
price reaction function is given above, and NW’s is found with the same technique:
q
N
= 750 +
p
A
−
3
p
N
=
⇒
p
N
= (250 +
1
3
p
A
)
−
1
3
q
N
,
and
MR
N
= (250 +
1
3
p
A
)
−
2
3
q
N
= 40 =
MC
N
=
⇒
q
N
= 315 +
1
2
p
A
.
Inserting this into the perceived demand curve gives the NW’s price reaction function as
p
N
= (250 +
1
3
p
A
)
−
1
3
(315 +
1
2
p
A
)
= 145 +
1
6
p
A
.
Now, the equilibrium prices can be found by solving for the two unknowns (prices) in the two price
reaction functions. This gives us
p
N
=
4
,
400
23
≈
$191
and
p
A
= 230 +
1
,
100
23
≈
$278
.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
(c) With the equilibrium prices, the demand for AA tickets is
q
A
= 340 +
2
,
200
23
≈
436
,
and for NW tickets
q
N
= 980
−
12
,
100
23
≈
454
,
making the total number of passengers 890.
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '08
 TOOSSI
 Microeconomics, Supply And Demand, price reaction function

Click to edit the document details