Price
Discrimination
Chapter 13
Slides by Pamela L. Hall
Western Washington University
©2005, Southwestern
Introduction


Price discrimination is legal unless it substantially limits
competition
 Firms will actively price discriminate in an effort to enhance profits
A firm with monopoly power has some control over output
price when it is facing a negatively sloping demand curve
 May be able to increase profits by discriminating among consumers
• For example, a bar may sell drinks at a lower price per unit during happy
hour

Generally, a firm desires to sell additional output if it can find
a way to do so without lowering price on units it is currently
selling
 By separating market into two or more segments
• Called price discrimination (or Ramsey pricing)

Analogous to a multiproduct firm’s supplying products in different markets
2
Introduction


Our aim in this chapter is to illustrate how firms are always probing
market for ways to enhance profits
For a firm’s long-run survival, it must constantly devise novel pricing
techniques for enhancing profits
 Firms who first develop such pricing techniques can earn pure profits


• Firms who do not will, in the long run, fail
We first state underlying market conditions required for price
discrimination
We develop categories of first-, second-, and third-degree price
discrimination
 Evaluate efficiency and welfare effects of each type

First-degree price discrimination includes pricing strategies such as twopart tariffs
 Tie-in-sales and bundling are discussed as an alternative to this type of price
discrimination
3
Introduction

Second-degree price discrimination offers potential social benefits
 If a firm did not price discriminate it might not be able to produce a desired
commodity

Third-degree price discrimination segments the market
 For instance, into a foreign and a domestic market

We discuss quality discrimination
 Generally, same implications associated with price discrimination hold for
quality discrimination as well

In all large companies, applied economists are actively developing
methods for price discrimination
 For example, after deregulation of airline industry in 1978, airline economists
developed price-discriminating techniques for improving profit
• Such as requiring a Saturday night stay or 14-day advance bookings
4
Conditions for Price
Discrimination

In terms of demand elasticities, if elasticities
associated with market segments are the same
 No incentive on part of a firm to price discriminate
• Because profit-maximizing output and price are identical in both
markets

Two necessary conditions for price discrimination
are
 Ability to segment market
• Exists if resales become so difficult that it becomes impossible to
purchase a commodity in one market and sell it in another market

When resale is possible, arbitrage will eliminate any price
discrepancies and Law of One Price will hold
 Existence of different demand elasticities for each market
segment
5
Conditions for Price
Discrimination

A firm may price discriminate across any category
of consumers
 Such as income level, type of business, quantity
purchased, geographic location, time of day, brand name,
or age
• For example, doctors may charge less for treatment of lowincome patients, and a defense contractor may charge military
$500 for a hammer that costs other costumers only $20

Depending on how a market can be segmented,
economists have categorized various types of price
discrimination into
 First-, second-, and third-degree price discrimination
6
First-degree Price Discrimination

Complete price discrimination, perfect price discrimination, or firstdegree price discrimination
 Occurs when it is possible to sell each unit of product for maximum price a
consumer is willing to pay


Table 13.1 lists characteristics and examples of first-, second- and thirddegree price discrimination
First-degree price discrimination involves tapping demand curve
 Illustrated in Figure 13.1

First unit of commodity is sold to a consumer willing to pay highest price,
0A
 Second unit to a consumer willing to pay at a slightly lower price
• And so on until demand curve intersects SMC
• In this case, demand or AR curve becomes MR curve

As firm increases supply, price declines only for additional commodity sold, not for all
commodities supplied
7
Table 13.1 Characteristics of First-, Second-,
and Third-Degree Price Discrimination
8
Figure 13.1 First-degree price
discrimination
9
First-degree Price Discrimination


As shown in figure, firm equates MR to SMC and supplies a
level of output Q1
 Results in TR being represented by area 0ABQ1
 STC by area 0FEQ1
 Pure profit by area FABE
Each consumer who purchases commodity is paying his or
her maximum willingness-to-pay, WTP, for commodity
 Receives zero consumer surplus from purchasing commodity
• Area FABE contains total consumer surplus, for an output level of Q1


Which firm captures
 Since all of consumer surplus is captured by firm, all consumers are
indifferent between buying commodity or not
Lowest price offered by firm is p1 = SMC(Q1)
 Because additional revenue generated by selling an additional unit of
output is less than additional cost SMC
10
First-degree Price Discrimination



Last consumer willing to purchase commodity pays this lowest price, p1
Consumers who are not willing to pay p1 do not purchase the commodity
All other consumers who do purchase commodity pay a price higher
than p1 equivalent to their maximum WTP
 Thus, at p1 and Q1, what consumers (society) are willing to pay for an
additional unit of commodity is equivalent to what it costs society to produce
this additional unit, SMC(Q1)
• Represents a Pareto-efficient allocation



With first-degree price discrimination there is no deadweight loss (inefficiency)
However, distribution of wealth between consumers and owners of firms may be
questionable for maximizing social welfare
First-degree price discrimination is difficult to attain
 One example is a roadside produce stand
• Prices vary depending on type of automobile consumer is driving and where he is
from

Person driving a Lincoln with New York plates will probably pay a premium for boiled
peanuts at a roadside stand in Georgia
11
Intertemporal Price
Discrimination

Type of first-degree price discrimination
 Product’s price is based on different points in
time

Price is initially set high
 To capture consumer surplus from those
consumers willing to pay high price rather than
wait

Price is lowered over time
 To capture further consumer surplus from those
consumers unwilling to pay high price and willing
to wait
12
Two-Part Tariffs

Consumers pay for ability to purchase a commodity and
possibly again for actual commodity
 E.g., pay a membership fee for joining a country club in addition to
any greens fee
 E.g., pay an entrance fee to get into a bar and then pay for drinks


Firm will price discriminate on entrance fees to extract as
much of a consumer’s WTP as possible
Commodity being sold is priced so it will maximize
admission
 Subject to constraint that additional output cannot be sold below cost
• At p = SMC

Will expand number of consumers paying entrance fees compared with no
price discrimination condition of MR = SMC
13
Two-Part Tariffs

Price discrimination on entrance fees is achieved
through coupons and discounts by age or for
membership in certain organizations
 For example, in 1955 Disneyland opened in rural
Anaheim, California
• In 1950s and 1960s, Disneyland employed a two-part tariff


Admission price was charged along with a cost for each attraction
Cost of tickets for attractions varied
 Rides like Dumbo cost the least (an A ticket) and rides like
Pirates of the Caribbean cost the most (an E ticket)
14
Two-Part Tariffs

A two-part tariff assuming only one consumer is also illustrated in Figure
13.1
 Firm sets an entrance fee that takes all consumer surplus
• Where p = SMC at p1, area p1AB

Sets a price of p1 that results in output Q1
 Firm’s profit is same as first-degree price discrimination, FABE
• No deadweight loss exists
 However, may be social-welfare implications from transfer of surplus from
consumers to firms

Firms will also use a two-part tariff in pricing tie-in sales
 Firm with monopoly power will require consumers to purchase two or more
commodities that are complementary goods
• For example, up until late 1960s, IBM required consumers who purchased an IBM
computer to also purchase their punch cards


Priced computer at a perfectly competitive price
Employed monopoly pricing for punch cards, where MR = SMC < p
15
Bundling



In many cases firms are unable to practice first-degree price
discrimination
 Because consumer preferences are not completely revealed
 Cost of revealing these preferences may be prohibitive
In such cases, difference in consumers’ willingness- to-pay
for commodities and marginal cost of producing
commodities can be exploited
 By selling commodities in bundles
Bundling exists when a firm requires consumers to
purchase a package or set of different commodities rather
than some subset of commodities
 For example, many portrait studios will sell a package of photos in
different sizes and poses rather than each photo separately
16
Bundling

Effective method for enhancing profit when
consumers have heterogeneous demands
 But firm is unable to effectively separate consumers by
their preferences and then price discriminate

Specifically, bundling is an alternative when firms
are unable to perfectly price discriminate
 For example, automobile dealers often offer a package
containing a number of options, such as leather seats
and antilock brakes
• Consumers can purchase package containing leather seats and
antilock brakes

Cannot purchase leather seats or antilock brakes separately
17
Bundling

Suppose Robinson is willing to pay more for leather seats than Friday
 Friday is willing to pay more for antilock brakes than Robinson
• As shown in Table 13.2, if options were sold separately, maximum price that could
be charged is $1300 for leather seats and $1000 for antilock brakes


Revenue would be $2300 from each consumer, with TR = $4600
If dealer could perfectly price discriminate and charge each consumer
their maximum WTP for each option
 First-degree price discrimination would yield TR = 2000 + 1000 + 1300 +
2500 = $6800
• However, since dealer cannot do this, it bundles leather seats with antilock brakes

Robinson is willing to pay $3000 and Friday $3800
• By charging each consumer $3000, TR = $6000

Greater than revenue derived from not bundling but lower than revenue from perfect
price discrimination
18
Table 13.2 Bundling
19
Bundling


Bundling is most effective when demands of two
consumers are highly negatively correlated
 See Table 13.3
Local governments have recently adopted bundling
in an effort to entice voters to pass local-option tax
measures
 Targeting tax revenue to a bundle of specific projects
• Such as school improvements, a retirement center, a sports
complex, and a transit facility improves likelihood of tax passing

Negative correlation of these projects makes bundling a very
attractive method for funding
 If voters had to consider each project separately, probability of
all projects receiving majority support would decrease
20
Table 13.3 Bundling with
Positively Correlated Demands
21
Second-degree Price
Discrimination

Cost of a 1-ounce letter is 22.2¢ using Standard Class (bulk mail)
 Compared with 37¢ for regular First Class mail

Bulk rate discount is an example of second-degree price discrimination
 Commonly used by public utilities
• For example, per-unit price of electricity often depends on how much is used

Second-degree price discrimination (also known as nonlinear pricing)
occurs
 Where a firm with monopoly power sells different units of output for different per-unit
prices
• Every consumer who buys same unit amount of commodity pays same per-unit price
• Price differs across commodity units and not across consumers
• Same price schedule is offered to all consumers and consumers self-select which price per
unit they will pay

Mixed bundling is an alternative type of bundling associated with second-degree
price discrimination
 Firm will offer commodities both separately and as a bundle
• With bundled price below sum of individual prices
22
Second-degree Price
Discrimination

In some cases it may be possible for a firm with
monopoly power to earn a pure profit only if it price
discriminates
 Consider second-degree price discrimination where a
monopoly establishes two prices for a commodity
• A higher per-unit price for the commodity offered in a smaller size
and a lower per-unit price for a larger size
• As illustrated in Figure 13.2, monopoly would be operating at a
loss if it offers a single (linear) per-unit price for commodity

SATC curve does not cross AR curve at any output level
 No single price will yield a positive pure profit
• If firm price discriminates, it will earn a pure profit by selling Q1
units of commodity in smaller unit size at a price of p1 and Q2 - Q1
units of commodity in larger unit size at a price of p2
23
Figure 13.2 Second-degree price
discrimination yielding a pure profit
24
Second-degree Price
Discrimination

Pure profit from selling smaller unit size is represented by
area (SATC2)p1AB
 Greater than loss (negative pure profit) from selling larger unit size,
area EBCD


Consumers can now consume a commodity that would not
be available if firm did not price discriminate
 Firm can earn a pure profit
Both consumers and firm are better off by price
discrimination
 Implies a Pareto improvement and an associated increase in social
welfare
• One justification for allowing a regulated monopoly to practice price
discrimination
25
Second-degree Price
Discrimination

If consumers who are willing to pay for larger size units pay a price in
excess of marginal cost
 Firm could lower p2 by some amount to induce consumers to buy more
• Price is still greater than marginal cost


Firm will still make a profit on these sales
 Profit occurs because, given price discrimination, such a policy would not affect
profits from any other consumers
As indicated in Figure 13.2, we determine optimal price for larger size
units, p2, and total quantity sold of both small and large sizes, Q2
 By setting p = SMC

Determine optimal quantity of smaller size units, Q1, and associated
price, p1
 By maximizing revenue from smaller size units minus lost revenue from not
quantity at bulk price per unit, p2
26
Second-degree Price
Discrimination
F.O.C. is
 MR1(Q1) – p2 = 0
 Solving for Q1 yields optimal quantity for firm
to supply in smaller units
 Firm can sell this level of output at p1
 In Figure 13.2, maximization problem results
in additional revenue above bulk price p2 of
[(p1 - p2)Q1], represented by area p2p1AE

27
Self-Selection Constraint

One problem with a firm maximizing smaller-unit revenue
 Consumers rather than firm determine who will purchase smaller
versus larger sizes of commodity



Nothing to prevent a consumer who usually purchases
commodity in bulk from purchasing smaller size unit
If firm’s price/quantity solution of p1 and Q1 yields
unintended result of consumers shifting from purchasing
larger size units to smaller size units
 Will not be profit-maximizing solution
Firm instead must determine optimal price and quantity that
will provide incentive for consumers to purchase unit size
that maximizes firm’s profit
28
Self-Selection Constraint



If consumer surplus for consumers purchasing larger size
unit is greater than their surplus from purchasing smaller
size unit
 Consumers will self-select and purchase larger size unit
Otherwise, self-selection will not occur and bulk purchasers
will switch to purchasing smaller size unit
Considering self-selection constraint on determining profitmaximizing price and quantity
 Maximization problem is
• Where CS1 and CS2 are bulk consumers’ surplus from instead
purchasing smaller size unit and their surplus from purchasing in bulk,
respectively
29
Self-Selection Constraint



If at unconstrained optimal solution, where MR1(Q1)
- p2 = 0, self-selection constraint holds
 Firm will maximize profits by setting MR1 = p2
If CS1 > CS2 at MR1(Q1) - p2 = 0, firm would further
increase price of smaller size unit until CS1 = CS2
For a linear demand curve the condition of CS1 =
CS2 corresponds to revenue-maximizing condition
MR1(Q1) = p2 = 0
30
Self-Selection Constraint

Can demonstrate this condition with Figure 13.2
 Let p = a - bq be inverse linear demand function faced by firm

Then CS1 = CS2
 (a – p1)Q1 ÷ 2 = (p1 – p2)(Q2 – Q1) ÷ 2
• Multiplying both sides by 2 and substituting linear demand function for p1 and p2
yields

Q1 = Q2/2
 Result is equivalent to F.O.C. for maximizing revenue MR1(Q1) - p2 = 0

Solving for Q1 yields this equivalence
 a – 2bQ1 – (a – bQ2) = 0
• Illustrated in Figure 13.2


Q1 = Q2/2
Area p1aA representing CS1 is equivalent to area EAD representing CS2 at MR1(Q1) - p2
=0
Thus, for a linear demand curve, self-selection constraint is always
satisfied
31
Third-degree Price
Discrimination

Some managers believe only reason a firm would sell its product at a lower price
in its foreign market
 To drive competing firms out of business and then exercise monopoly power by
increasing price
• However, in many cases, reason is that firm is practicing third-degree price discrimination


Common form of price discrimination
 Examples include senior-citizen discounts, lower prices in foreign versus domestic markets, and
happy hours at bars
Whenever markets have different demand elasticities and arbitrage among
markets is impossible
 Firm can engage in third-degree price discrimination
• Occurs when a firm with monopoly power sells output to different consumers for different
prices


Every unit of output sold to a given category of consumers sells for same price
 For example, nonprofit rate for Standard Class (bulk) mail is 12.7¢ compared to 22.2¢ charged
to for-profit consumers
In contrast to second-degree price discrimination, where price differs across
commodity unit and not across consumers
 In third-degree price discrimination price differs across consumers and not across
commodity unit
32
Third-degree Price
Discrimination

Consider two markets each with different demand
elasticities
 Assume demand curves are independent, so no leakage exists
among markets
• Thus, consumers in market with a lower price cannot resell product in
another market with a higher price

For determining optimal selling prices and outputs, let pj(qj)
be inverse demand function in jth market segment and
express revenue in jth market segment by
 TRj(qj) = pj(qj)qj, j = 1, 2,
• Where qj is quantity sold in jth market segment
 Total revenue is
• TR(Q) = TR1(q1) + TR2(q2)

Where total quantity sold, Q is
 Q = q1 + q2
33
Third-degree Price
Discrimination

Letting STC(Q) be short-run total cost function, firm
maximizes profits by

Partial differentiation yields F.O.C.s

If MR1 > MR2, total revenue and profit can be
increased by shifting output from market 2 to
market 1
 Enhancement in total revenue can continue until
marginal revenues in both markets are equal
34
Third-degree Price
Discrimination

In general, for k markets MRj(qj*) = SMC(Q*) for all k
markets
 If a monopoly can divide its market into k independent submarkets
• It should divide overall output among k markets in such a way that it
equalizes marginal revenue obtained in all markets

MR1(q1*) = MR2(q2*) = … = MRk(qk*)
• This common marginal revenue should be equal to marginal cost of
overall output

MR1(q1*) = MR2(q2*) = … MRk(qk*) = SMC(Q*)
• Price charged in each market is determined by substituting qj* into
market’s average revenue function, pj* = ARj(qj*)

A graphical illustration for two markets (say, foreign and
domestic) is provided in Figure 13.3
35
Figure 13.3 Third-degree price
discrimination for two markets
36
Third-degree Price
Discrimination

Consider a level of MR = MR*
 This value of marginal revenue is attained in both markets only if
quantities sold in two market segments are q1* and q2*

Remaining F.O.C. requires that this common MR in two
market segments be equated to SMC
 Determines optimal (Q, MR) combination
 By summing horizontally MR curves in each of two markets, we
determine total output for a given level of MR, qj|MR
• Equating qj|MR with SMC determines optimal level of total output, Q*

Optimal quantities and prices in the two markets are q1*, q2*,
p1*, and p2*
 Determined by demand curve in each market given optimal output
levels
37
Third-degree Price
Discrimination


Price is highest in market segment with more steeply sloped
demand function
 Domestic market with more inelastic demand
Can investigate relationship of prices in separate markets
and elasticity by recalling that
 MRj(qj) = pj[1 + (1/Dj)]
• Where Dj = (∂qj/∂pj)(pj/qj) is own-price elasticity of demand in market j

Can relate prices charged in separate markets to own-price
elasticities of demand in each of these markets
 Given that condition for the two markets is
38
Third-degree Price
Discrimination

Relationship indicates that prices in any two
markets are equivalent if own-price
elasticities of demand are equal
 If D2 > D (demand is more elastic in foreign
market, market 1), then
• 1 + (1/D2) < 1 + (1/D1)

Which implies
 p1/p2 < 1 or p2 > p1
39
Third-degree Price
Discrimination

Foreign market is charged lower price
 More price sensitive due to a greater degree of competition from
other firms (more elastic demand)

Prices will be lower in market where demand is more elastic
and arbitrage is not possible
 For example, elasticity of demand for movie matinees is more elastic
than evening movies
• Matinee prices are lower because opportunity cost of going to a matinee
is higher

Working and going to school coincide with matinee time
• Similarly, senior citizens and college students are groups with relatively
lower incomes


Resulting in a more elastic demand for commodities
If a firm is able to segment its market based on these
demographics
 It can price discriminate and potentially enhance its profits
40
No Price Discrimination


Figure 13.3 illustrates relationship between ordinary monopoly (no price
discrimination, where full arbitrage exists among consumers) and price
discrimination
A horizontal summation of individual market demand curves, qj|AR
 Is market demand curve facing firm if no price discrimination exists
• Note discontinuity of MR curve associated with this market demand curve


Due to kink in market demand curve
Optimal output is where SMC = MR at output Q' associated with
common price p'
 Common price is between prices charged in the two market segments when
price discrimination is practiced
• At this common price, firm sells q1' in market 1 and q2' in market 2
• MR1 > MR2

Firm could increase profits by practicing price discrimination
41
No Price Discrimination

Effect of third-degree price discrimination on social welfare is ambiguous
 Social welfare could be enhanced or reduced
• Depending on consumers’ preferences and wedge between price and marginal
costs

Sufficient condition for social welfare to decline is
 If total output from price discrimination does not increase

Sufficient condition for a social-welfare gain is
 If third-degree price discrimination results in satisfying demand in a market
where zero output would be supplied with no price discrimination

For example, prior to airline deregulation, airlines could not compete in
terms of price and were required to service certain routes
 Resulted in many empty seats on flights and airlines competing for

passengers in terms of service and meals
Since deregulation, airlines compete in terms of price
• They generally fill every seat
• Resulted in greatly expanded airline travel

Satisfying markets (particularly vacation traveling) that were small or nonexistent before
42
Combination of Discrimination
Techniques

In an effort to earn short-run pure profits, firms will employ
combinations of these three price discrimination techniques
 Will constantly be devising new methods for price discrimination
• For example U.S. Post Office uses both second- and third-degree price
discrimination in pricing mail delivery


In long-run, costs will adjust to any short-run profits from
price discrimination
 Leading to long-run equilibrium with associated normal profits
Firms failing to engage in price discrimination will
experience declining revenue
 Be forced out of business
43
Combination of Discrimination
Techniques

Individual consumer can increase her utility by shifting
consumption patterns and capturing lower price per unit
offered by price-discriminating firms
 By doing so consumer is able to recoup some of surplus
appropriated by firms
• Unfortunately, firms constantly change their prices or quantity as market
conditions change


For example, candy manufacturers will alter number of ounces in different
sizes of candy bars
 Changes per-unit price for each size but keeps prices the same
Changes in price discrimination have resulted in a whole
industry developing for assisting consumers
 For example, travel agents will assist consumers in finding lowest
fares for particular destinations
44
Quality Discrimination

There is a difference in consumers’ willingness-to-pay for a
given quality rather than quantity of a commodity
 For example, manufacturer of DVD players is practicing quality
discrimination
• By offering a range of different physical components and different
warranties for its DVDs

Fundamentally, price discrimination and quality
discrimination are identical models
 Same implications associated with various degrees of price
discrimination hold for quality discrimination

Actual commodity may be the same with a difference only in
service
 Or commodity itself may be altered
45
Quality Discrimination

Product quality can also take form of determining
level of its durability
 A highly durable product, such as a new consumer
appliance designed to last a lifetime, may result in market
saturation
• Once most consumers have purchased product there remains
only limited product demand
 A firm may also face competition from resale of durable
goods it produced previously
• For example, if product (such as aluminum) can be recycled at a
competitive price

Monopoly power of firm could be eroded away
46
Quality Discrimination

Number of strategies firms can use to
counter product durability problem
 Build in planned obsolescence of product by
• Marketing an improved version of product
• Changing its physical appearance

For example, automobile manufactures generally change
their vehicle models’ appearance and market models’
improvements on an annual basis
 Lease their products instead of selling them
• Maintains a firm’s market power by giving it control
over new market and market for resales
47