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Economics 200b, Spring 200
5
M
idtermExamSo
lut
ion(uptotypos)
1. a. The
f
rm is a monopoly in each market. He chooses prices that maximize his pro
f
t in each country.
For a linear demand of
Q
=
a
−
bp,
the optimal price is determiend by:
max
p
(
p
−
c
)(
a
−
bp
)
.
First order condition implies that
p
=
a
+
bc
2
b
.
So the optimal prices are:
p
u
=27
,p
c
=12
.
The quantity sold in each country is:
q
u
=50
,q
c
=30
.
The
f
rm’s pro
f
tinUSis
:
π
u
=(27
−
2)
∗
50 = 1250
,
and his pro
f
t in Canada is:
π
c
=(12
−
2)
∗
30 = 300
.
His total pro
f
t is 1550.
Consumer suplus is:
CS
=
1
2
(
a
b
−
p
)
∗
q
=
1
2
π.
The consumer suplus is 625 in US, and 150 in Canada.
b. The monopolist will choose one single price to maximize his total pro
f
t in the two countries. At any
price
p,
the total quantity sold in both countries will be
Q
(
p
)=
Q
u
(
p
)+
Q
c
(
p
) = 170
−
5
p.
The monopolist solves the following problem:
max
p
(170
−
5
p
)(
p
−
2)
The
f
rst order condition is:
180
−
10
p
=0
,
so the optimal price
p
=18
.
Thequant
ityso
ldinUSis
:
Q
u
=68
.
The quantity sold in Canada is:
Q
c
.
The monopolist’s pro
f
:
π
=(18
−
2)
∗
68 = 1088
,
The monopolist’s pro
f
t in Canada is:
π
−
2)
∗
12 = 192
.
Again, consumer surplus is:
=
1
2
(
a
b
−
p
)
∗
q.
So we have:
u
=
1
2
(52
−
18)
∗
68 = 1156
,CS
c
=
1
2
(22
−
18)
∗
12 = 24
.
Compared with part a, consumers in Canada lose and consumers in US bene
f
t.
c. Notice that the price in US is at most $5 more than the price in Canada, otherwise US consumers will
simply import from Canada. From part a and b, we know that the optimal price for US is 27, much higher
than the optimal price in Canada and the price that would be charged if price discrimination is banned.
Therefore his pro
f
t in US is increasing for any price below 27. He should charge exactly $5 more in US (we
can varify later that this is true.)
Let
p
denote price in Canada, then
p
u
=
p
+5
.
The monopolist chooses the optimal
p
to maximize his
pro
f
tinbothcount
ies
:
max(
p
u
−
2)
∗
(104
−
2
∗
p
u
)+(
p
c
−
2)
∗
(66
−
3
p
c
)
=(
p
−
2)
∗
(104
−
2
∗
(
p
+5))+(
p
−
2)
∗
(66
−
3
p
)
(Remember, price in US is
p
.
)
The
f
rst order condition is:
160
−
10
p
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 Spring '08
 PHILIPHAILE
 Monopoly

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