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Industrial Organization: EC460
Spring 2009
Notes on 2nd Degree Price Discrimination—Example from class
A ski resort has two types of customers: hardcore and leisurely. The demand curve for
skiing—as measured by how many lift rides up the mountain a skier would like to have
given diﬀerent prices—is given by
P
h
= 5

.
5
Q
h
for hardcore skiers; and
P
l
= 9

2
Q
l
for leisurely skiers. Suppose once the lift is in operation the marginal cost of taking a skier
up the mountain is zero, i.e.,
MC
= 0.
1. Calculate the proﬁt maximizing prices per singletrip liftticket if hardcore skiers
can be distinguished and charged separately from leisure skiers. What is the ﬁrm’s
overall proﬁt when there is exactly one skier of each type?
2. Calculate the optimal twopart tariﬀs, that is, suppose that the resort decides to sell
daypasses (tier 1) in conjunction with a marginal price per lift ride (tier 2). When
distinguishing hardcore and leisure skiers, what price should it charge for a day pass
for each type of skier and what is the optimal marginal price to be charged? What
is the ﬁrm’s proﬁt when there is exactly one skier of each type?
3. Can the plan calculated under 2 be modiﬁed in such a way that it can be implemented
if the resort cannot distinguish between the two types of skiers? That is, which
modiﬁcation to the plan will make it
incentive compatible
so that skiers
selfselect
into the plans designed for them? Explain.
Answer:
1. The solution to this question gives the standard
thirddegree
price discrimination
scenario for
uniform pricing
across the two groups. Consider the two groups sepa
rately:
•
For hardcore skiers:
Rev
h
= 5
Q
h

.
5(
Q
h
)
2
, so
MR
h
= 5

Q
h
. Setting
MR
h
=
MC
(= 0) yields
Q
h
*
= 5, hence
P
h
*
= 2
.
50 and the ﬁrm obtains
Q
h
*
×
P
h
*
= 12
.
50 from the hardcore skier.
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This note was uploaded on 03/29/2009 for the course ECON 460 taught by Professor Boyer during the Spring '08 term at Michigan State University.
 Spring '08
 Boyer
 Price Discrimination

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