©2005, Southwestern Slides by Pamela L. Hall Western Washington University Price Discrimination...

©2005, Southwestern

Slides by Pamela L. Hall

Western Washington University

Price Discrimination

Chapter 13

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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

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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 two-part tariffs Tie-in-sales and bundling are discussed as an alternative to this type of price

discrimination

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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

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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

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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 low-income 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

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First-degree Price Discrimination Complete price discrimination, perfect price discrimination, or first-

degree 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 third-

degree 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

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Table 13.1 Characteristics of First-, Second-, and Third-Degree Price Discrimination

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Figure 13.1 First-degree price discrimination

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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

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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

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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

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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

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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)

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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

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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

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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

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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

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Table 13.2 Bundling

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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

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Table 13.3 Bundling with Positively Correlated Demands

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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

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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

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Figure 13.2 Second-degree price discrimination yielding a pure profit

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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

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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

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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

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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

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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 profit-maximizing 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

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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

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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 Q1 = Q2/2

• Illustrated in Figure 13.2 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

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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

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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

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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

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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

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Figure 13.3 Third-degree price discrimination for two markets

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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

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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/D

j)]• Where D

j = (∂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

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Relationship indicates that prices in any two markets are equivalent if own-price elasticities of demand are equal If D

2 > D (demand is more elastic in foreign market, market 1), then • 1 + (1/D

2) < 1 + (1/D1)

Which implies p1/p2 < 1 or p2 > p1

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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

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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

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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

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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

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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

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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

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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

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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

©2005, Southwestern Slides by Pamela L. Hall Western Washington University Price Discrimination...

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