Transcript price discrimination

Microeconomics, 2nd Edition
David Besanko and Ronald Braeutigam
Chapter 12: Pricing to Capture Surplus Value
Prepared by Katharine Rockett
© 2006 John Wiley & Sons, Inc.
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1. Introduction: Airline Tickets
2. Price Discrimination
• First Degree Price Discrimination
 Second Degree Price Discrimination
 Third Degree Price Discrimination
3. Tie-in Sales
Requirements Tie-ins
Package Tie-ins (Bundling)
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Prices for UA Flight 815
Ticket Price
Number of
Passengers
 $2000
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Average
Advance
Purchase
12 days
$1000-$1999
15
14 days
$800-$999
23
32 days
$600-$799
49
46 days
$400-$599
23
65 days
$200-$399
23
35 days
$1-$199
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26 days
$0
19
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Definition: A monopolist charges a uniform price if it sets
the same price for every unit of output sold.
While the monopolist captures profits due to an optimal
uniform pricing policy, it does not receive the consumer
surplus or dead-weight loss associated with this policy.
The monopolist can overcome this by charging more than
one price for its product.
Definition: A monopolist price discriminates if it charges
more than one price for its output.
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Price
Example: Uniform Pricing vs. Price Discrimination
Uniform Price Monopoly 1st Degree P.D. Monopoly
MC
D
MR
Quantity
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Price
Example: Uniform Pricing vs. Price Discrimination
Uniform Price Monopoly 1st Degree P.D. Monopoly
CS: E+F
0
PS: G+H+K+L
E+F+G+H+J+K+L+N
TS: E+F+G+H+K+L E+G+G+H+J+K+L+N
DWL: J+N
0
PU E F
H
G
P1
K
MC
J
N
L
D
MR
Quantity
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Definition: A policy of first degree (or perfect) price
discrimination prices each unit sold at the consumer's
maximum willingness to pay. This willingness to pay is
directly observable by the monopolist.
Definition: The consumer's maximum
willingness to pay is called the consumer's reservation
price.
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Recall…
We can think of the demand curve as a "willingness to pay"
curve.
If the monopolist can observe the willingness to pay of
each customer (based on, for example, residence,
education, "look", etc), then the monopolist can observe
demand perfectly and can "perfectly" price discriminate.
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Is this reasonable? Think of buying a car…
The monopolist will continue selling units until the
reservation price exactly equals marginal cost.
Therefore, a perfectly price discriminating
monopolist will produce and sell the efficient
quantity of output.
Note: Only if the monopolist can prevent resale
can the monopolist capture the entire surplus.
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Example:
Monopoly
MC = 2
P = 20 - Q
What is producer surplus if uniform pricing is followed?
MR = P + (P/Q)Q = 20 - Q - Q = 20 - 2Q
MR = MC => 20 - 2Q = 2 =>
Q* = 9
P* = 11
Mc=dvc/dq, 2=dvc/dq, 2=1/dq*dvc (*1/dq), 1/q*vc=2,
vc=2q
PS= Revenue-TVC = PQ-2Q = 11(9)-2(9) = 81
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What will producer surplus be if the monopolist perfectly
price discriminates?
P = MC => 20 - Q = 2 =>Q* = 18
Revenue - TVC = [18(20-2)(1/2) + 18(2)]-18(2) = 162
This is a gain in captured surplus of 81!
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Price
Example: First Degree Price Discrimination
20
11
MC
2
9
D
18
20
MR (uniform pricing)
Quantity
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What is the marginal revenue curve for a perfectly
price discriminating monopolist?
When the monopolist sells an additional unit, it does
not have to reduce the price on the other units it is
selling. Therefore, MR = P. (i.e., the marginal revenue
curve equals the demand curve.)
Definition: A policy of second degree price
discrimination allows the monopolist to
charge a different price to different consumers.
While different consumers pay different prices,
the reservation price of any one consumer
cannot be directly observed.
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Definition: A monopolist charges a two part tariff if it charges a
per unit fee, r, plus a lump sum fee (paid whether or not a
positive number of units is consumed), F.
This, effectively, charges demanders of a low quantity a different
average price than demanders of a high quantity.
Example: hook-up charge plus usage fee for a telephone….club
membership…
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Example:
All customers are identical and have demand
P = 100 - QI
MC = AC = 10
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P
Example: Two-Part Tariff
100
4050
10
90 100
Q
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What is the optimal two-part tariff?
Two steps: (1) maximize the benefits to the
consumers by charging r =
MC = 10.
(2) capture this benefit by setting
F = consumer benefits = 4050.
Why?
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Any higher usage charge would result in a deadweight loss that could not be captured by the
monopolist. Any lower usage charge would result in
selling at less than marginal cost.
In essence, the monopolist maximizes the size of the
"pie", then sets the lump sum fee so as to capture
the entire "pie" for itself.
The total surplus captured is the same as in the case
of perfect price discrimination.
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Definition: If a consumer pays one price for
one block of output and another price for
another block of output, the consumer faces a
block tariff
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P = 100 - Q
MC = AC = 10
Let Q1 be the largest quantity for which the first block rate
applies so that
p1(Q1) = 100 - Q1.
Let Q2 be the largest quantity purchased (so that the second
block rate will apply between Q1 and Q2) so that p2(Q2) =
100 - Q2
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Then
 = p1(Q1)Q1 + p2(Q2)(Q2-Q1) - TC(Q2)
= (100 - Q1)Q1 + (100 - Q2)(Q2-Q1) - 10Q2
and we must choose Q1 and Q2 to maximize this profit…
MR1 = (100 - Q1) - Q1 - (100 - Q2) = 0
MR2 = (100 - Q2) - Q2 + Q1 = MC = 10
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These are two equations in two unknowns that can be
solved to obtain:
Q1* = 30
Q2* = 60
P1* = 70
P2* = 40 (a quantity discount)
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Example: Block Pricing
Quantity Discrimination
P
100
Demand
450
70
450
40
2700
450
10
0
30
60
100 Q
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Example: Block Pricing
Quantity Discrimination
P
100
Single-Price Monopoly
P
100
Demand
Demand
450
70
1012.5
55
450
40
2700
450
10
0
2025
30
60
100 Q
0
1012.5
45
MR
MC
100
Q
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If the monopolist could set a different block price for each
customer, it would capture the same amount of surplus as a
perfectly price discriminating monopolist.
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Example: Utility Pricing
D - small
D - large
MC
Q
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Example: Utility Pricing
D - small
D - large
Additional CS
P1
Additional PS
P2
MC
Q1s
Q1L Q2L
Q
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Definition: A policy of third degree price
discrimination offers a different price for each segment
of the market (or each consumer group) when
membership in a segment can be observed.
Example: Movie ticket sales to older people or students
at discount
Suppose that marginal costs for the two markets are
the same. How does a monopolist maximize profit with
this type of price discrimination?
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Set the marginal revenue in each market equal to marginal cost.
(i.e., the monopolist maximizes total profits by maximizing
profits from each group individually.)
This implies that MR1 = MC = MR2 at the optimum. Otherwise,
the monopolist could raise revenues by switching sales from the
low MR group to the high MR group.
Example
MC = AC = 20
P1 = 100 - Q1
P2 = 80 - 2Q2
What is the optimal price for each group?
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MR1 = 100 - 2Q1 = MC = 20
MR2 = 80 - 4Q2 = MC = 20
Q1* = 40
Q2* = 15
P1* = 60
P2* = 50
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Example: Third Degree Price Discrimination
Market 1
P
100
Demand 1
60
20
0
100
MR1
Q
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Example: Third Degree Price Discrimination
Market 1
Market 2
P
100
P
Demand 1
80
60
Demand 2
50
20
0
100
MR1
Q
0
20
40
MR2
Q
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Definition: A tie-in sale occurs if customer can buy one
product only if they agree to purchase another product as
well.
1. Requirements tie-in sales occur when a firm
requires customers who buy one product from the firm
to buy another product from the firm.
A requirements tie-in sale may be used in place of price
discrimination when the firm cannot observe the
relative willingness to pay of different customers.
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2. Package tie-in sales (or bundling) occur when
goods are combined so that customers cannot buy either
good separately.
Bundling may be used in place of price discrimination to
increase producer surplus when consumers have different
willingness to pay for the goods sold in the bundle.
But bundling does not always pay…
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Example: Bundling with negatively-correlated
preferences
Reservation Price
Computer
Monitor
Customer 1
$1,200
$600
Customer 2
$1,500
$400
Marginal Cost $1,000
$300
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Optimal Pricing Policy
Without bundling: pc = $1500 pm = $600
Profitcm = $800
With bundling:
pb = $1800
Profitb = $1000
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Example: Bundling with positively-correlated
preferences
Reservation Price
Computer
Monitor
Customer 1
$1,200
$400
Customer 2
$1,500
$600
Marginal Cost $1,000
$300
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Optimal Pricing Policy
Without bundling: pc = $1500 pm = $600
Profitcm = $800
With bundling:
pb = $2100
Profitb = $800
In general, bundling a pair of goods only pays if their
demands are negatively correlated (customers who
are willing to pay relatively more for good A are not
willing to pay as much for good B).
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1. Price discrimination generally allows a
monopolist (or any firm with market power) to
capture more surplus than a uniform pricing policy.
2. First degree (or perfect) price discrimination allows
the monopoly to produce efficiently and capture all
the resulting surplus.
3. Second degree price discrimination may or may
not allow as much surplus to be created and
captured as perfect price discrimination, depending
on the precise form of the discrimination.
4. Third degree price discrimination generally does
not create or allow as much capture of surplus.
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5. In order to capture surplus from any form
of price discrimination, a firm must have
some market power, have some information
on the differential willingness to pay of
customers and must be able to prevent
resale (arbitrage) among customers.
6.Tie-in sales may be used in place of price
discrimination, when price discrimination is
not possible, in order to allow the
monopolist to capture additional surplus.
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