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Microeconomics, 2Microeconomics, 2ndnd Edition Edition

David Besanko and Ronald BraeutigamDavid Besanko and Ronald Braeutigam

Chapter 12: Pricing to Capture Surplus Chapter 12: Pricing to Capture Surplus ValueValue

Prepared by Katharine RockettPrepared by Katharine Rockett

© 2006 John Wiley & Sons, Inc.© 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 SalesRequirements Tie-insPackage Tie-ins (Bundling)

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Prices for UA Flight 815Ticket Price Number of

PassengersAverageAdvancePurchase

$2000 18 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 34 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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Example: Uniform Pricing vs. Price Discrimination

MR

D

MC

Quantity

Price

Uniform Price Monopoly 1st Degree P.D. Monopoly

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Example: Uniform Pricing vs. Price Discrimination

MR

D

MC

Quantity

Price

P1

PU E F

GH

J

KN

L

CS: E+F 0PS: G+H+K+L E+F+G+H+J+K+L+NTS: E+F+G+H+K+L E+G+G+H+J+K+L+NDWL: J+N 0

Uniform Price Monopoly 1st Degree P.D. Monopoly

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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:

MonopolyMC = 2P = 20 - QWhat is producer surplus if uniform pricing is followed?

MR = P + (P/Q)Q = 20 - Q - Q = 20 - 2Q

MR = MC => 20 - 2Q = 2 =>

Q* = 9P* = 11Mc=dvc/dq, 2=dvc/dq, 2=1/dq*dvc (*1/dq), 1/q*vc=2, vc=2qPS= 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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Example: First Degree Price Discrimination

MR (uniform pricing)

D

MC

Quantity

Price

11

2

20

9 18 20

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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 demandP = 100 - QI

MC = AC = 10

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Example: Two-Part Tariff

100

100 Q

P

10

90

4050

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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 dead-weight 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 - QMC = 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

0

P

Q

Demand

Quantity Discrimination

10

40

70

100

30 60 100

450

450

4502700

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Example: Block Pricing

0 0

PP

Q Q

MC

Demand Demand

Quantity Discrimination Single-Price Monopoly

MR

10

55

45 100

100

40

70

100

30 60 100

450

450

4502700 2025

1012.5

1012.5

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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

Q

D - small D - large

MC

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Example: Utility Pricing

P1

P2

Q1s Q1L Q2L Q

D - small D - large

Additional CS

MC

Additional PS

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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 = 20MR2 = 80 - 4Q2 = MC = 20

Q1* = 40

Q2* = 15

P1* = 60

P2* = 50

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Example: Third Degree Price Discrimination

0

100

100

20

60

Q

P

Market 1

Demand 1

MR1

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Example: Third Degree Price Discrimination

0 0

100

100

20

60

80

50

20 40 QQ

P P

Market 1 Market 2

Demand 1Demand 2

MR1 MR2

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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.