1 Capturing Surplus Chapter 12. 2 Chapter Twelve Overview 1.Introduction: Airline Tickets 2.Price Discrimination First Degree Second Degree Third Degree

1

CapturingSurplus

Chapter 12

2

Chapter Twelve Overview

1. Introduction: Airline Tickets

2. Price Discrimination• First Degree• Second Degree• Third Degree

3. Tie-in Sales• Requirements Tie-ins• Package Tie-ins (Bundling)

1. Introduction: Airline Tickets

2. Price Discrimination• First Degree• Second Degree• Third Degree

3. Tie-in Sales• Requirements Tie-ins• Package Tie-ins (Bundling)

Chapter Twelve

3Chapter Twelve

Uniform Price Vs. Price Discrimination

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 the same good or service.

4Chapter Twelve

Forms of Price Discrimination

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: A policy of second degree price discrimination allows the monopolist to offer consumers a quantity discount.

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.


Definition: A policy of second degree price discrimination allows the monopolist to offer consumers a quantity discount.


5Chapter Twelve

“Willingness to Pay” Curve

Definition: The consumer's maximum willingness to pay is called the consumer's reservation price.

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.

Definition: The consumer's maximum willingness to pay is called the consumer's reservation price.

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.

6Chapter Twelve

Forms of Price Discrimination



7

D

MCP1

PU E F

GH

J

K N

L

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

Chapter Twelve

MR

Quantity

Uniform Price Monopoly 1st Degree P.D. Monopoly

Uniform Price Vs. Price Discrimination

Price

8Chapter Twelve

Is it Reasonable?

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.

9Chapter Twelve

Pricing Surplus – Monopoly

MC = 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* = 11

PS= Revenue-TVC = PQ-2Q = 11(9)-2(9) = 81

10Chapter Twelve

Pricing Surplus – Monopoly

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!

11

MR (uniform pricing)

D

MC

Quantity

Price

11

2

20

9 18 20

Chapter Twelve

First Degree Price Discrimination

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.)

12Chapter Twelve

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.

Second Degree Price Discrimination

13Chapter Twelve

Two Part Tariff

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, or the like.

14

100

100 Q

P

10

90

4050

Chapter Twelve

Example:

All customers are identical and have demand

• P = 100 - Q• MC = AC = 10

Example:

All customers are identical and have demand

• P = 100 - Q• MC = AC = 10

Two Part Tariff

15Chapter Twelve

Two Part Tariff

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.

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.

16Chapter Twelve

Two Part Tariff

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.

17Chapter Twelve

Block Tariff

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

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

18Chapter Twelve

Block Tariff

• 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

19Chapter Twelve

Block Tariff

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

20Chapter Twelve

Key Equations

These are two equations in two unknowns that can be solved to obtain:

• Q1* = 30• Q2* = 60

• P1* = 70• P2* = 40 (a quantity discount)

These are two equations in two unknowns that can be solved to obtain:

• Q1* = 30• Q2* = 60

• P1* = 70• P2* = 40 (a quantity discount)

21

0 0

PP

Q Q

MC

Demand Demand

MR

10

55

45 100

100

40

70

100

30 60 100

450

450

4502700 2025

1012.5

1012.5

Chapter Twelve

Block Pricing

22Chapter Twelve

Block Pricing

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.

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.

23 Q

D - small D - large

MC

Chapter Twelve

Utility Pricing

24

P1

P2

Q1s Q1L Q2L Q

Additional CS

MC

Additional PS

Chapter Twelve

D - small D - large

Utility Pricing

25Chapter Twelve

Third Degree Price Discrimination


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?


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?

26Chapter Twelve

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.

MC = AC = 20

P1 = 100 - Q1

P2 = 80 - 2Q2

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.

MC = AC = 20

P1 = 100 - Q1

P2 = 80 - 2Q2

Optimal Pricing

ExampleExample

27Chapter Twelve

MR1 = 100 - 2Q1 = MC = 20MR2 = 80 - 4Q2 = MC = 20

Q1* = 40Q2* = 15

P1* = 60P2* = 50

MR1 = 100 - 2Q1 = MC = 20MR2 = 80 - 4Q2 = MC = 20

Q1* = 40Q2* = 15

P1* = 60P2* = 50

Optimal Pricing

ExampleExample

28

0

80

50

20 40 Q

P

Demand 2

MR2Chapter Twelve

0

100

100

20

60

P

Demand 1

MR1

Third Degree Price Discrimination

Q

Market 1Market 1 Market 2Market 2

29Chapter Twelve

Tie-in Sales – Requirements

Definition: A tie-in sale occurs if customer can buy one product only if they agree to purchase another product as well.

• 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.

30Chapter Twelve

Tie-in Sales – Bundling

• 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…

31Chapter Twelve


32Chapter Twelve


Optimal Pricing Policy

Without bundling: pc = $1500 pm = $600

• Profit cm = $800

With bundling: pb = $1800

• Profit b = $1000





• Profit b = $1000

33Chapter Twelve


34Chapter Twelve






• Profit b = $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).





• Profit b = $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).

35Chapter Twelve

Reservation Price

The reason is that the price is determined by the purchaser with the lowest reservation price.

If reservation prices for the two goods are negatively correlated, bundling reduces the dispersion of reservation prices and so raises the price at which additional units can be sold.

The reason is that the price is determined by the purchaser with the lowest reservation price.

If reservation prices for the two goods are negatively correlated, bundling reduces the dispersion of reservation prices and so raises the price at which additional units can be sold.

36Chapter Twelve

Advertising

The firm can capture surplus using nonprice strategies such as advertising.

The firm can capture surplus using nonprice strategies such as advertising.

Documents

1 Capturing Surplus Chapter 12. 2 Chapter Twelve Overview 1.Introduction: Airline Tickets 2.Price Discrimination First Degree Second Degree Third Degree