Problems on Third degree price discrimination
1.
An event in a stadium was sold out.
While 60% of the participants
paid full price, the other 40% paid only half price.
Some people that
were willing to pay more than half price were left out. Conclusion : the
organizers could have made more money. True or False. Explain.
False.
If the consumers that were left out generated lower
marginal revenue than the ones that were included, this is con
sistent with pro°t maximization. For example, if there are two
groups of consumers with aggregate demands
p
= 100
°
q
h
and
p
= 60
°
q
l
, pro°t maximization with third degree price dis
crimination requires equating marginal revenues between the two
groups:
100
°
2
q
h
= 60
°
2
q
l
which implies that
q
l
=
q
h
°
20
:
So for example if the capacity
of the stadium is 60, then pro°ts are maximized setting
q
h
= 40
and
q
l
= 20
:
This implies
p
h
= 60
and
p
l
= 40
;
so there are
some consumers from the
h
group (those with reservations values
between
40
and
60
that are excluded even though their willingess
to pay is higher than the lower end of the included consumers of
the
l
group.
2.
A °rm sells in two separate markets. There is an additional marginal
cost of selling in the second market. Therefore, the price in the second
market must be higher. True or False. Explain.
False.
The price in each market also depends on demand
elasticity. In other words, if the two costs are
c
1
< c
2
and market
elasticities are
°
1
and
°
2
;
p
1
°
1
°
1
°
1
±
=
c
1
p
2
°
1
°
1
°
2
±
=
c
2
so it follows that
p
1
p
2
=
c
1
(1
°
1
=°
1
)
c
2
(1
°
1
=°
2
)
:
So even if
c
1
< c
2
it could still be true that
p
1
> p
2
:
1
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
3.
A monopolist sells to several markets and is able to do third degree price
discrimination. It will choose quantities so that elasticities are equated
across these markets. True or False? Explain.
False.
This is not necessarily true even if marginal cost is the
same in both markets. In that case it will choose quantities until
marginal revenues are equal across the °rms:
p
1
°
1
°
1
°
1
±
=
p
2
°
1
°
1
°
2
±
=
c
elasticities can be di/erent and prices also di/erent so that it is
still true that marginal revenues are equal.
4.
Demand elasticity in market
A
is half the demand elasticity in market
B
and the price a monopolist is charging twice as high. Show that the
price in market
B
is 50% higher than marginal cost.
p
A
°
c
p
A
=
1
°
A
p
B
°
c
p
B
=
1
°
B
Dividing the °rst equation by the second one:
°
p
A
°
c
p
B
°
c
± °
p
B
p
A
±
=
°
B
°
A
and using
p
A
= 2
p
B
and
°
A
=
°
B
=
2
4(
p
B
°
c
) =
p
A
°
c
= 2
p
B
°
c
so it follows that:
2
p
B
= 3
c
and hence
p
B
= 1
:
5
c:
5.
There are two groups of consumers. A monopolist is using third degree
price discrimination (group pricing). Marginal cost
c
= 1
is the same
in both markets. One of the markets have twice the demand elasticity
of the other market. The price in the market with low elasticity
p
= 2
:
What can you infer about the ratio of the prices? Explain your answer.
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '07
 Hopenhayn
 Price Discrimination, Supply And Demand

Click to edit the document details