On Market Definition under Price Discrimination

with Imperfect Targeting

by

David Glasner

John Hilke

William Pegram*

October 2004

Preliminary Draft: Not for quotation or attribution without permission of the

authors

_______________________________

* Glasner and Hilke are economists with the Bureau of Economics in the

Federal Trade Commission. Pegram is assistant professor in the Business and

Public Services Division at Northern Virginia Community College. The authors

have participated in a number of cases in which price discrimination played a

prominent part in defining the market and in assessing competitive effects. This

paper was prompted in large part by our participation in the merger between

Donnelley and Meredith/Burda printing operations. Glasner and Pegram were

staff economists working on investigation and subsequent litigation of the

Donnelley matter. Hilke served as the expert witness for Complaint Counsel in

the administrative hearing. We are indebted to Jon Baker, Steve Brenner, Ian

Gale, Debra Holt, and Earl Thompson for their helpful comments and suggestions

on earlier drafts of this paper. We are solely responsible for any remaining errors

or misstatements. The views expressed in this paper are entirely our own and do

not necessarily reflect those of the Federal Trade Commission or individual

Commissioners.

On Market Definition under Price Discrimination

with Imperfect Targeting

I. Introduction

It would not be easy to name a market phenomenon more widely

discussed in the industrial organization literature than price discrimination.

Indeed, the concept of marginal revenue was introduced in the mid-1920s

precisely in order to make a general analysis of price discrimination tractable. It

was largely owing to that success that the concept quickly became, and of course

remained, a staple of economics textbooks (Sraffa 1926, Robinson 1933, Hicks

[1935] 1952).

The critical empirical importance of price discrimination was remarked on

long ago by George Stigler (1968, 13-14) who observed that price discrimination

constitutes the most compelling evidence for the existence and exercise of market

power. Practically any seller with market power, whether stemming from

product differentiation, legal barriers to entry, or coordinated interaction, has a

powerful incentive to price discriminate by raising price (and reducing the

quantity sold) to customers that are relatively insensitive to price changes and

reducing price (and increasing quantity sold) to customers that are relatively

sensitive to price changes. Moreover, economists have identified a broad array

of business conduct and pricing practices as attempts to set prices corresponding

to customers’ valuations rather than to sellers’ costs, i.e., to price discriminate

(e.g., Shapiro and Varian 1998, 19-81).

So it is not surprising that price discrimination figures prominently in

antitrust law.i

Because price discrimination is evidence of the exercise of market power,

showing that price discrimination has occurred may be a critical step in

establishing antitrust liability. It is also possible that a particular anticompetitive

theory may be contingent on the ability of one or more firms to price discriminate.

The Merger Guidelines (section 1.12) recognize the special role of price

discrimination in certain anticompetitive theories by allowing for a relevant

market to be delineated based on an anticompetitive theory in which a merger

would allow a subset of vulnerable customers to be targeted for a discriminatory

price increase.

Textbook treatments of price discrimination assume that the seller can

perfectly distinguish between two classes of customers: those with relatively

inelastic demand, to whom price is raised, and those with relatively elastic

demand, to whom price is reduced. But what if a seller knows that two such

classes exist, but cannot distinguish perfectly between them? Does the inability

to distinguish perfectly between the two groups substantially reduce the

profitability of price discrimination? And if so, is there a minimum level of

targeting accuracy that is necessary for a seller to be able to price discriminate

profitably? Finally, in the context of antitrust enforcement, does imperfect

targeting undermine the relevance or impair the utility of price discrimination as

an anticompetitive theory, thereby precluding or limiting its use as a basis for

defining relevant antitrust markets?ii

There is, in fact, a vintage literature, emerging from the observation of a

linkage between price discrimination and product differentiation, that sheds light

3

on the targeting problem. If a seller can offer differentiated products (for

example, hard-cover and paper-back books or first-class and coach airline tickets)

that appeal to customers with differing elasticities of demand, price discrimination

can be profitable even if sellers have no way to estimate the demand elasticities of

individual customers. Customers with relatively inelastic demand prefer to pay a

high price for the deluxe, first-class, or high-end, option rather than pay a low

price for the no-frills, economy, or low-end option; customers with relatively

elastic demands opt for the low price. In other words, customers self-select.

Unless the availability of a high-price option causes current customers to switch

to a competing product, the targeting problem is solved, or at least mitigated.iii

We therefore begin in the next section by considering how sellers may

cope with imperfect targeting by offering differentiated products that induce

customers to self-select. However, sellers seeking to price discriminate may

sometimes be unable to induce their customers to self-select. We therefore

consider in section III, the implications of imperfect targeting to a seller that

offers a single product. Since targeting, on average, will be at least as accurate as

raising prices to randomly chosen customers, random targeting defines a lower

bound for the profitability of price discrimination. To make our analysis relevant

to the problem of defining a relevant market conditional on price discrimination,

we consider a simple model of a discriminating hypothetical monopolist that

could not profitably raise price by 5 percent to all its customers, but could

profitably raise price by 5 percent to its vulnerable customers. Since a relevant

4

market can be defined under section 1.12 of the Merger Guidelines if and only if

the hypothetical monopolist could price discriminate profitably, the question

arises: how accurate must the hypothetical monopolist be in targeting these

vulnerable customers for the targeted price increase to be profitable? We find

that, under a 5-percent threshold for a price increase, profitable price

discrimination requires only targeting only slightly more accurate than random

selection. We extend the analysis in Section IV to take into account the

incentive, under price discrimination, to reduce price to some customers as while

raising price to others. We conclude in section V.

II. Targeting under Product Differentiation and Self-Selection

Although we discuss the logic of the targeting problem more formally in

the next section, it may be helpful to begin by explaining why imperfect targeting

reduces the profitability of price discrimination. Under uniform pricing, some

customers are generally more responsive to a price change than others. If a seller

can identify the less price-responsive customers price-responsive (i.e., those with

less elastic demands), it can gain by raising price to these customers and cutting

price to the more price-responsive customers.

The conventional analysis of price discrimination does not concern itself

with how the seller can distinguish between less and more responsive customers.

What if the seller cannot distinguish between customers – at least not perfectly?

Consider, for now, the less responsive customers with relatively inelastic

demands. The seller, seeking to raise price just to them, could err in two ways.

5

One is to fail to identify, and thus fail to raise price to, a price-insensitive

customer; the other is to mistake, and raise price to, a price-sensitive customer for

a price-insensitive customer. The first error reduces the profitability of price

discrimination, but cannot make it unprofitable. The second, if repeated too

often, can make it unprofitable, so our concern here is mainly with the second

type of error.

If mistargeted, price-sensitive customers could respond in two ways. One

is to reduce purchases, the other is to switch to a competing supplier or to a

substitute product. The profitability of price discrimination thus depends on the

size of the price increase, the relative frequency with which price-sensitive

customers are mistargeted, and on the foregone profit when mistargeted

customers reduce or terminate their purchases.

Is a seller that cannot distinguish between price sensitive and

price-insensitive customers precluded from profitable price discrimination? Not

necessarily, because even with no knowledge about individual customers, the

seller can differentiate its product in a way that appeals to the divergent tastes of

its customers. A seller might, for example, offer price-insensitive customers a

product with enhanced features for which they would pay a premium. To retain

price-sensitive customers unwilling to pay a premium for enhanced features, the

seller could offer a low-priced, economy option without the added features. By

offering two options, thereby inducing customers to self-select, the seller avoids

having to target customers individually. Price-insensitive customers, whom the

6

seller would like to target for a price increase, will choose the high-price option

while price-sensitive customers, whom the seller does not want to target for a

price increase, will choose the low-price option. The low-price option avoids the

loss of price-sensitive customers when an enhanced product is offered at a

premium price.iv

A similar point was made in perhaps the earliest economic analysis of

price discrimination, Jules Dupuit’s pioneering 1850 discussion of railway

passage. (See Ekelund 1970.) Dupuit observed that by offering different classes

of passenger transport, railway companies extracted more revenue from

passengers than they could with just one class of service and one rate schedule.

A railroad, Dupuit argued, increases its profit by degrading the quality of its

lowest class of service below the optimal quality under uniform pricing.

Third-class quality is so unattractive that only the most price-sensitive passengers

travel third-class rather than pay a quality premium. At the same time, the

railroad offers a deluxe first-class service by which it extracts the surplus of

passengers with the least elastic demands.

It is not because of the few thousand francs which would have to

be spent to put a roof over the third-class carriages or to upholster the

third-class seats that some company or other has open carriages and wood

benches . . . What the company is trying to do is to prevent the passengers

who can pay the second-class fare from traveling third class; it hits the

poor, not because it wants to hurt them, but to frighten the rich. . . . And it

7

is again for the same reason that the companies, having proved almost

cruel to third-class passengers and mean to second-class ones, become

lavish in dealing with first-class passengers. Having refused the poor

what is necessary, they give the rich what is superfluous.

However, some sellers, unlike Dupuit’s railroad company, may find that

competition from low-end substitutes prevents them from degrading their low-end

option in order to increase high-end demand. Whether because of low-end

substitutes or because of deliberate low-end quality degradation, a

price-discriminating seller typically perceives a highly elastic demand for its

low-end offering. Thus, a seller that adopts a discriminatory pricing strategy, but

does not reduce price to some customers as it raises price to others, must already

be operating under a powerful competitive constraint in serving its most

price-sensitive customers. Although it may seem paradoxical, a seller that, in

adopting a strategy of price discrimination, cuts price to some customers while

raising it to others cannot have been under a severe competitive constraint before

it began to price discriminate.

Although product differentiation can, by inducing self-selection, avoid the

problem of mistargeting price-sensitive customers for a price increase, it is still

possible that some price-insensitive customers, who would pay a high price if

there were no low-price option, will forego the premium option if a low-price

option is available. However, if we bear in mind the distinction between a seller

that sells in a highly competitive market at the low end, but seeks to raise price to

8

vulnerable customers by offering a premium version, and a seller that is not

competitively constrained either at the high or the low-end, it is not difficult to see

why product differentiation will be profitable even if some price-insensitive

customers choose the low-price rather than high-price option.

Suppose the seller is not constrained at the low-end. In that case the

seller prevents price-insensitive customers from buying the low-end product by

degrading the low-end product while reducing its price. The seller profitably

differentiates the products sufficiently to discourage price-insensitive customers

from bargain hunting and purchasing the discount product. This is why Dupuit

observed that the railway company degrades third-class passage “to prevent the

passengers who can pay the second-class fare from traveling third class; it hits the

poor, not because it wants to hurt them, but to frighten the rich.” However, a

seller under competitive constraint cannot degrade quality at the low-end without

driving low-end customers to competing suppliers. And if the low-end market is

already highly competitive, the seller has no incentive to reduce price to increase

sales, because, as a price taker, it is already selling as much as it wants to at the

competitive price. The seller’s only incentive is to introduce a premium high-end

product appealing to price-insensitive customers. Since the seller is not reducing

price at the low-end, the profitability of its price-discrimination strategy does not

depend on preventing potential high-end customers from buying the discount

option instead. Without price discrimination, there is just one option. Adding a

high-end option aimed at price-insensitive buyers is profitable if the rents earned

9

from the sales of the high-end option exceed the fixed costs of developing and

marketing the new high-end product. Only if those fixed costs are high relative

to potential rents, can the second type of mistargeting undermine

self-selection-inducing product differentiation as a price-discrimination strategy.

To better understand how product differentiation facilitates price

discrimination, it may be helpful to mention two examples discussed in an earlier

treatment of imperfect targeting (Hausman, Leonard and Velturro 1996). One

example involved sophisticated applications software (e.g., graphics, architectural

design, mathematical programming), purchasers of which were either highly

knowledgeable professionals with relatively inelastic demands for advanced

features or moderately sophisticated non-professionals with relatively elastic

demands for those features. Because the software application is distributed in

standardized packaging to anyone willing to pay the quoted price, it was

suggested that targeting was unlikely to be precise enough for price

discrimination to be profitable.

However, the earlier discussion of this example did not consider product

differentiation as a way of overcoming the targeting problem. In fact, software

manufacturers routinely offer low-end and high-end versions (Quicken and

Quicken Deluxe or RealOne Player and RealOne SuperPass) calculated to induce

customers voluntarily to disclose the nature of their demands. A classic case of

price discrimination in the computer industry (albeit one involving hardware not

software) involved just such product differentiation. Shortly after introducing its

10

revolutionary 386 microprocessor, Intel introduced a discounted version: the

386SX (which differed from the 386 only in having a disabled math

co-processor). The functional difference between the chips allowed Intel to

extract a premium from buyers with relatively inelastic demands for computing

power. Although Intel actually bore a higher cost to produce the partially

disabled 386SX chip than to produce its fully operational counterpart, Intel priced

the SX chip below the undisabled one to induce inelastic demanders to self-select

and pay a premium price. The SX chip became a textbook example of profitable

price discrimination, highlighted in Shapiro and Varian’s (1998) veritable “how

to” manual for price discrimination in the information age.

The other example was the Donnelley case (FTC v. Donnelley), which

turned on product market consisting of commercial print buyers of rotogravure

printing services for whom the alternative offset printing process was not an

economical alternative could be delineated. The issue, in other words, was

whether a hypothetical monopolist over gravure printing could target gravure

print buyers with a relatively inelastic demand for gravure printing without

mistargeting gravure print buyers with a relatively elastic demand.v In

dismissing its original complaint, the Donnelley commission held that a

hypothetical gravure monopolist could target vulnerable gravure customers with

sufficient accuracy for a discriminatory price increase to be profitable. However,

as the foregoing discussion has shown, targeting is unnecessary for profitable

price discrimination if a seller can induce vulnerable customers to self-select.

11

Since gravure printers have both offset and gravure equipment, a gravure

monopolist could induce self-selection by allowing customers to choose between

a low offset and a high gravure price.vi

We have shown in this section that imperfect targeting may well have no

adverse effect on the profitability of price discrimination if product differentiation

can be used to induce customer self-selection. Our discussion also underscores

the distinction between the relatively elastic demand in the low-end market and

the relatively inelastic demand in the premium market that underlies any

successful attempt to price discriminate. Thus, it should not be surprising that,

under price discrimination, customers with highly elastic demands pay prices at or

near marginal cost. That a seller charges some of its customers prices that are

highly competitive, reflects not the lack, but the enhanced exercise, of market

power. We now consider the profitability of price discrimination when product

differentiation cannot be used profitably to induce customer self-selection.

III. The Profitability of an Imperfectly Targeted Price Increase When a

Uniform Price Increase Would Not be Profitable

Although product differentiation may allow a seller seeking to price

discriminate to induce vulnerable customers to self-select, there may be

circumstances that deter a seller from introducing differentiated products. As

noted above, introducing differentiated products requires incurring some fixed

costs, which may sometimes be prohibitive. A seller contemplating the

introduction of a line of differentiated products, must compare the expected profit

12

from price discrimination with differentiated products and customer self-selection

with the expected profit from price discrimination with a single product and an

attempt to target vulnerable customers for a price increase. We therefore proceed

with an analysis in which a seller supplies a single product and seeks to target its

vulnerable customers for a price increase.

To make this analysis directly relevant to the antitrust concern that

motivates our analysis, we consider the scenario implicit in section 1.12 of the

Merger Guidelines. In explaining how to delineate a relevant market within

which to assess a proposed merger, the Merger Guidelines (section 1.1) propose a

thought experiment in which a hypothetical monopolist raises price uniformly by

a small but significant amount (usually taken to be 5 percent). If the price

increase is profitable, the set of products over which the hypothetical monopolist

could raise price defines a relevant market. If not, the set of products must be

expanded to include enough substitutes to enable a hypothetical monopolist to

raise price profitably over the expanded set of products.

However, the Guidelines (section 1.12) recognize that some mergers must

be assessed under an anticompetitive theory that asserts that only a subset of

customers of the merging parties (and perhaps of their competitors) are vulnerable

to a price increase. The relevant market is then delineated not just in terms of the

product, but in terms of the class of customers vulnerable to a price increase.

The definition of the relevant market is then conditional on a theory of price

discrimination, because the thought experiment under which the relevant market

13

is defined presumes that the hypothetical monopolist could not profitably raise

price to all customers. In these circumstance, the relevant market may be

defined, on strictly demand-side grounds (inasmuch as price discrimination

encompasses supply-side substitution) as the subset of customers vulnerable to a

price increase (Merger Guidelines, sec. 1.12).

Let us now explain precisely how imperfect targeting might preclude the

delineation of a relevant market conditional on a theory of price discrimination.

Given the merger of two competing firms, suppose that the hypothetical

monopolist could not profitably raise price to all customers, but could profitably

do so by at least 5 percent to some subset of customers. There are two possible

reasons why these vulnerable customers are not already paying the added 5

percent: a) competition between the merging firms has been keeping price close

to the competitive level; b) the merging firms could not distinguish between

vulnerable customers who would pay a premium for the product they sell and

invulnerable customers who would switch to substitute products offered by

non-merging firms rather than absorb a price increase by the merging firms. If

none of the vulnerable customers were paying a premium before the merger

because of a), then vulnerable customers might be adversely affected by the

merger. If, however, the absence of a premium were owing to b), then there is no

reason to assume that the merger would create an added risk of a price increase to

vulnerable customers unless the merger somehow allowed the combined firm to

identify vulnerable customers more easily than was previously the case. To

14

determine whether the absence of any premerger price premium was because of a)

or b), we wish to calculate whether the hypothetical monopolist could profitably

try to target vulnerable customers even though mistargeting might induce some

less vulnerable customers to switch to suppliers of alternative products. This

exercise can, in principle, allow us to calculate the minimum targeting success

rate under which a targeted price increase of a given magnitude (say 5 percent) is

more profitable for the hypothetical monopolist than maintaining the uniform

pre-merger price.

To determine whether a discriminatory price increase would be profitable

for a hypothetical monopolist when it cannot avoid mistargeting invulnerable

customers, we must precisely specify the premerger equilibrium that provides the

profit benchmark. Assume that before the merger there are only two suppliers of

some product G which sells for $1/unit. Some, but not all, purchasers of G prefer

it to the closest substitute, a competitively supplied product, O, (which also sells

for $1) and would be willing to pay at least $1.05/unit for G rather than buy O

instead.vii

The remaining purchasers of G are indifferent (or nearly so) between

the two products and would switch to O before paying even $1.05/unit for G.

Since our hypothetical monopolist cannot identify with certainty which

customers would pay a premium of at least 5 percent for G over what they paid in

the premerger equilibrium, we want to know how much mistargeting would make

the attempt to price discriminate unprofitable. Our calculation requires an

assumption about the marginal cost of the hypothetical monopolist. Although we

15

are free to assume any value for marginal cost, our assumption must be consistent

with profit maximization by the hypothetical monopolist. In particular, marginal

cost must, under profit maximization, equal marginal revenue. If the best that the

hypothetical monopolist can do, without price discriminating, is to maintain the

permerger price, then we can infer the elasticity of demand facing the

hypothetical monopolist directly from the ratio price to marginal cost.

Suppose, then, that the marginal cost of the G-producers is $0.50/unit.

For the G-monopolist to be maximizing its profit (at least without price

discriminating) at the pre-merger price of $1.00, it must perceive an elasticity of

demand equal to 2 (in absolute value). Otherwise, the G-monopolist could gain

by charging a lower (if elasticity is greater than 2) or a higher (if elasticity is less

than 2) price.viii

Thus, under the Guidelines thought experiment for defining a

relevant market conditional on price discrimination, the G-monopolist is charging,

given its marginal cost, the profit-maximizing uniform price to its customers.

Otherwise, we would not be concerned with defining a narrow market in which

the G-monopolist could profitably increase price to only some of its customers.ix

Since our assumption about marginal cost allows us to determine the

elasticity of demand perceived by the G-monopolist in the initial

non-discrimination equilibrium, we can use that knowledge to determine the

proportion of that demand accounted for by the two distinct categories of

customers that, we have assumed, are now purchasing from the G-monopolist. In

one category (let us call them LV-customers) are those that would switch from G

16

to O if the price of G rose by as much as 5 percent. If their demand is linear, the

implied elasticity of LV-demand at the initial price is 20.x The other category

includes those customers (let us call them HV-customers) that would continue to

buy as before even if the price of G rose by at least 5 percent. The elasticity of

HV-demand at the initial price is 0.

If we know the overall elasticity of demand perceived by the

G-monopolist, the characteristics of the two types of demanders that constitute

that demand, the relative proportions of these two types of demanders follows

immediately. If the LV-elasticity is 20 and the HV-elasticity is 0, an overall

elasticity of 2 requires that the HV-customers account for 90 percent of G-sales

and LV-customers for 10 percent.xi

Knowing the relative proportions of the two subgroups in the overall

market also lets us infer the probability that a customer chosen at random belongs

to either group. The probability that a randomly chosen customer is a

HV-customer (LV-customer) is 90 (10) percent. Thus, the G-monopolist could,

by random selection, expect to achieve success in targeting customers for a

5-percent price increase 90 percent of the time.

Having determined the random targeting success rate, we must now

calculate the minimum targeting success rate required for a discriminatory

5-percent price increase to be profitable for the G-monopolist.xii

Suppose the

G-monopolist successfully targets one HV-customer for a price increase to $1.05.

The associated increase in profit is then $0.05 as the profit margin for this

17

customer would increase from $0.50 to $0.55, corresponding to a 10-percent

increase in the profit margin, twice the increase in price since price is twice

marginal cost. On the other hand, if the G-monopolist mistakenly targets one

LV-customer for a price increase, that customer switches to an O-supplier and the

G-monopolist loses the entire profit margin ($0.50) generated by that customer.

Thus, the G-monopolist gains $0.05 for every correctly targeted HV-customer and

loses $0.50 for every mistargeted LV-customer. The profit loss from

mistargeting is, therefore, ten times greater than the profit gain from successful

targeting. This means that the G-monopolist will not profit from a discriminatory

price increase, unless it targets successfully 10 times more frequently than it

mistargets. This might seem, at first sight, to be a demanding requirement. But

recall that the G-monopolist could expect, simply by random selection, to target

correctly 90 percent of the time, or nine times more often than it mistargets. The

improvement in targeting accuracy over random targeting necessary for price

discrimination to be profitable, i.e., to raise the expected targeting success rate

from 90 to 91 percent, does not seem overly demanding.

We found earlier that the random targeting success rate for the

G-monopolist follows directly from an assumption about marginal cost, and we

have now just seen that the relation between price and marginal cost determines

the minimum targeting success rate for the G-monopolist. We, therefore, present

in Table I calculations for alternative assumptions about the ratio of price to

marginal cost of the implied random targeting success rates (equal to one minus

18

the share of the percentage of invulnerable customers required for an overall

elasticity of demand equal to that implied by the price-cost ratio) and the

corresponding minimum targeting success rates required for price discrimination

to be profitable.xiii

The calculations show that when the ratio of price to marginal

cost is low, and the G-monopolist does not lose much from mistargeting a

LV-customer, the minimum targeting success rate tends to be relatively low.

However, given the assumed underlying elasticities, the implied overall elasticity

is possible with a relatively high ratio of LV-customers, so that the difference

between the random targeting success and the minimum targeting success rate

falls as the ratio of price to marginal cost rises. Thus, contrary to what one might

infer from considering the minimum targeting success rate in isolation, successful

targeting may become more difficult as the ratio of price to marginal cost falls.

TABLE I

P/MC

Implied

Elasticity of

Demand

Implied

Share of

purchases by

LV-customer

s

Random

Targeting

Success Rate

Minimum

Targeting

Success Rate

1.0526

20

100.00%

0.00%

50.00%

1.1

11

55.00%

45.00%

64.52%

1.25

5

25.00%

75.00%

80.00%

1.5

3

15.00%

85.00%

86.96%

19

1.75 2.33 11.67% 88.33% 89.55%

2

2

10.00%

90.00%

90.91%

3

1.5

7.50%

92.50%

93.02%

4

1.33

6.67%

93.33%

93.74%

5

1.25

6.25%

93.75%

94.11%

However, this result is subject to significant qualification on two grounds.

First, it follows from an overly restricted view of the targeting problem. The

forgoing analytical exercise focused solely on the profitability of a price increase

to HV-customers, which, in general, is just one side of the problem of profitable

price discrimination. The other side of the problem is whether to reduce the price

to LV-customers. The logic of price discrimination is symmetric, so that, in

general, if it is profitable to raise price to some customers it will be profitable to

reduce price to others. In our example, if the LV-elasticity of demand is 20 in

the pre-merger non-discrimination equilibrium, then the profit gain from reducing

price to LV-customers far exceeds that from raising price to HV-customers. An

LV-elasticity of 20 implies that the marginal revenue from LV-customers is $.95

a unit. With linear demand and perfect targeting, the G-monopolist would

maximize profit by cutting price to LV-customers to $.7725, which would elicit a

455 percent increase in LV-unit sales. While the G-monopolist’s profits from

HV-sales would rise by just 10 percent after a 5 percent price increase, its profits

20

from LV-sales would rise by over 200 percent. HV-customers generate 90

percent of profit before price discrimination and 76.4 percent of profit after price

discrimination. We provide a more general treatment of the targeting question in

the next section to take account of the possibility that price reductions to

LV-customers can generate increased profit for the G-monopolist.

IV. Price Discrimination under Imperfect Targeting when it is Profitable to

Reduce Price to Some Customers

Under our assumptions about the initial non-discrimination equilibrium

and the opportunity for price discrimination, the profit opportunity from reducing

price and increasing sales to LV customers greatly exceeds the profit opportunity

from raising price and restricting sales of HV customers. How does the incentive

to reduce price to LV customers affect the targeting analysis of the previous

section? The answer, of course, depends on what happens when price is

mistakenly raised to LV-customers to whom the G-monopolist would prefer to

reduce price.

Before we can determine what happens when price is mistakenly raised to

LV-customers we must first consider an ambiguity in our simple targeting

analysis. What accounts for the increase in sales to LV-customers in the event of

a price reduction? Are current LV-customers increasing purchases or does the

reduced price induce switching by new LV-customers that had formerly been

buying the close substitute O? If the increase in sales is accounted for by current

LV-customers, then not cutting (much less raising) price to current LV-customers

is very costly to the G-monopolist. However, if the increase in sales stems from

21

new LV-customers that switch from O-suppliers because of the reduced price of

G, then the mistargeting of current LV-customers is not so costly, because

mistargeted LV-customers can be replaced by offering a low price to

LV-customers that switch from O-suppliers. Although either explanation for the

increase in LV-sales is logically tenable, it does seem that if the responsiveness of

quantity sold to a price increase reflects switching by customers from G to O, the

responsiveness of quantity sold to a price decrease would reflect switching by

customers in the opposite direction.xiv

Let us now assume that the perceived LV-demand curve reflects both

switching by LV-customers back and forth between G and O at their particular

point of indifference between G and O. At the initial price of $1, all

LV-customers whose point of indifference between G and O was between $1 and

$1.05 are purchasing G, but all of them would switch back to O if the price rose to

$1.05. As the price falls below $1, additional LV-customers will switch from O

to G and LV-customers already purchasing G will increase their purchases of G in

response to the reduced price of G. Let k represent the fraction of the increase in

quantity demanded from any price reduction for G below the current price of $1

that is attributable to increased purchases by existing LV customers. The fraction

of the increased quantity demanded resulting from switching by LV-customers

switching from O is then represented by 1-k.

Under our assumptions about the pre-merger equilibrium, and for any

values of θ and k, we can compute the profitability of a 5 percent price increase

22

targeted at HV-customers combined with the optimal price reduction offered to all

LV-customers except those mistakenly targeted for a price increase. The

profitability of this pricing strategy can be compared with one in which no

HV-customers are targeted for a price increase, but the price is reduced optimally

to all LV customers. This comparison allows us to derive the set of values of θ

and k for which a price increase to HV-customers will be optimal. For example,

given θ = .95, a 5 percent price increase to HV-customers will be profitable

provided that k is less than .56. (See mathematical appendix for details of

derivation.)

Thus, even with a moderately high replacement rate for mistargeted

LV-customers, it is more than likely that a price increase imperfectly targeted at

HV customers will be the most profitable pricing strategy for a hypothetical

G-monopolist.

V. Conclusion

Despite a long tradition of concern about price discrimination as an

antitrust problem, it has been argued that profitable price discrimination will turn

out to be unprofitable if targeting is imperfect. The implication of this concern is

that anticompetitive theories contingent on price discrimination provide an uneasy

basis for antitrust enforcement. We focus on two aspects of targeting of price

discrimination that ease this concern. First we review the long-standing

understanding that customer self-selection in the presence of product

differentiation greatly improves the odds that price discrimination is profitable.

23

Second, we find that changes in the relationship between the price-cost ratio and

the minimum targeting success are closely related to the mutual interdependence

of price, marginal cost, elasticity of demand, the minimum targeting success rate,

and the mix between those customers that are vulnerable and those that are not

vulnerable to a discriminatory price increase. Taking these interrelationships into

account, we find that for price discrimination to serve as a basis for market

delineation under the Guidelines, targeting need be only modestly more accurate

than the random selection of customers for a 5-percent price increase. Moreover,

if sellers can replace mistargeted customers by offering new customers moderate

discounts, the likelihood that imperfect targeting could cause an otherwise

profitable price-discrimination strategy to be unprofitable seems remote indeed.

24

References

Areeda, P. A. and H. J. Hovenkamp. 2004. Antitrust Law.

Dupuit, J. 1850. “On Tolls and Transport Charges.”

Ekelund, R. B. Jr. 1970. “Price Discrimination and Product Differentiation in

Economic Theory: An Early Analysis.” Quarterly Journal of

Economics 84:268-78.

Glasner, D. 1997. “The Capacity-Diversion Defense in Owens-Illinois and

Donnelley.” Antitrust Law Bulletin 42(1): 5-27

Glasner, D. 2001. “The Logic of Market Definition.” Manuscript. Bureau of

Economics, FTC.

Glasner, D., J. Hilke, and B. Pegram. 2001. “The Donnelley Case: A Study in

the Law and Economics of Price Discrimination.” Manuscript. Bureau

of Economics, FTC.

Hausman, J. A., G. K. Leonard, and C. K. Vellturo. 1996. “Market Definition

Under Price Discrimination.” Antitrust Law Journal 64:367-86.

Hicks, J. R. [1935] 1952. “Annual Survey of Economic Theory: The Theory

of Monopoly.” Econometrica 3(1): 1-20. Reprinted in Readings in

Price Theory, edited by K. E. Boulding and G. J. Stigler, pp. 361-83.

Chicago: Irwin.

Robinson, J. 1933. The Economics of Imperfect Competition. London:

Macmillan.

Samuelson, P. A. 1947. The Foundations of Economic Analysis. New York:

Athenaeum

Samuelson, P. A. 1964. Economics. 6th

edition. New York: McGraw-Hill.

Shapiro, C. and H. Varian. 1998. Information Rules. Cambridge: Harvard

Business School Press.

Sraffa, P. 1926. “The Laws of Returns under Competitive Conditions.”

Economic Journal 36:535-50.

Stigler, G. J. 1968. The Organization of Industry. Homewood, Ill.: Irwin.

25

Viner, J. [1931] 1952. “Cost Curves and Supply Curves.” Zeitschrift für

Nationalökonomie 3(1): 23-46. Reprinted in Readings in Price Theory,

edited by K. E. Boulding and G. J. Stigler, pp. 198-232. Chicago: Irwin.

26

Footnotes

i. Areeda and Hovenkamp in their influential treatise draw an entirely different

lesson from the existence of price discrimination. Since price discrimination is

so pervasive in a dynamic market, the mere existence of price discrimination in

most circumstances does not provide evidence of the sort of market power that the

antitrust laws were meant to curtail. Areeda and Hovenkamp, Antitrust Law

¶ 517c. We certainly agree that price discrimination per se should by no means

constitute evidence of antitcompetitive conduct. However, in the context of

analyzing a merger, the ability to price discriminate certainly suggests that a

merger between two competitors could enhance or entrench already existing

market power and therefore should, at least, be subject to careful scrutiny before

being approved. Moreover, their assumption that price differences associated

with differentiated products is wholly innocent of any undue exercise of market

power is subject to some qualification as our discussion below will make clear.

ii. Hausman et al. argue that, in failing to reckon with imperfect targeting, the

Horizontal Merger Guidelines discussion (section 1.12) of price-discrimination

markets is incomplete and even misleading. In arguing that imperfect targeting

can easily undermine price discrimination, they assume that a hypothetical

monopolist targets a subset of its customers for a 5-percent price increase, and

then deduce the minimum targeting success rate necessary for the price increase

27

to be profitable. See below sections 3 and 4.

iii. Besides solving the targeting problem identified by Hausman et al.,

self-selection-inducing product differentiation also solves the arbitrage problem

that is usually taken to be the most difficult obstacle to price discrimination. We

are indebted to Jonathan Baker for drawing our attention to the fact that

self-selection solves the targeting as well as the arbitrage problems. We also

gratefully acknowledge very helpful discussions with Ian Gale about this issue.

iv. Customers are unlikely to defect from the initial single-prdcut equilibrium

unless there is a very large gap between the premium and the economy options.

The seller might then have to moderate the price increase at the high end in order

not to drive too many customers toward the low price option, or risk losing

low-end customers for whom even the low-end price is too high. In such a

situation, the seller might be willing to incur the added fixed costs of introducing

a third intermediate option (e.g., business class on longer airline flights). See

discussion in the next four paragraphs of text.

v. Hausman et al. mischaracterize the price discrimination theory advanced by

the FTC staff as being predicated on a supposed preference of some print buyers

for gravure over offset. While the FTC staff asserted that some customers did

prefer gravure to offset for quality reasons, their anticompetitive theory of price

discrimination was actually predicated on a gravure cost advantage over offset for

28

long press runs. The FTC argued that pricing for printing jobs with long press

runs were constrained by low-cost gravure printers not by higher-cost offset

printers. The ability to target vulnerable gravure customers did not require,

under the FTC theory, knowledge about preferences, just knowledge about the

relative costs of the two processes, knowledge readily available to gravure

printers that all had offset as well as gravure capacity. See Donnelley, slip. op.,

fn. 68 at 31. For a full discussion of these issues see Glasner, Hilke and Pegram

(2004). For a discussion of capacity diversion, another supposed obstacle to

profitable price discrimination cited in both Owens-Illinois and Donnelley, see

Glasner (1997).

vi. The targeting analysis of Hausman et al. was also cited by counsel for Oracle

in their court papers in support of Oracle’s position that it would not be possible

for Oracle to target vulnerable customers who viewed Oracle and PeopleSoft as

their best alternatives for high-function enterprise software for a price increase

after the merger. Because even a hypothetical monopolist over the relevant

applications could not be sure whether a customer was truly vulnerable, counsel

for Oracle argued that price discrimination could not be profitable and a relevant

market conditional on price discrimination could not be defined. DOJ,

apparently unwilling to challenge Oracle’s position that a price discrimination

market was untenable, insisted that its proposed product market was defined in

terms of objective product characteristics and required no specific ability to target

29

customers. See

Defendant Oracle Corporation’s Trial Memorandum, section II. “Price

Discrimination Theory Could Not Sustain The Alleged Relevant Markets.”

vii. In this case with the only two suppliers proposing to merger analysis of the

relevant market and of competitive effects collapse into one.

viii. Assuming that the G-monopolist is earning zero profit (i.e., its average cost

is $1 a unit) does not suffice as an equilibrium condition from which to determine

whether the hypothetical monopolist could increase profit through price

discrimination. The excess of price over marginal cost must still be reconciled

with profit maximization in the premerger equilibrium. The irrelevance of the

zero-profit condition to the characterization of the initial non-discrimination

equilibrium can be seen by supposing that postmerger the G-monopolist would

not raise above its average cost of $1 a unit because doing so would invite entry.

That assumption explains why price is not above $1 a unit, but not why, with a

marginal cost of only $.50 a unit, it would not be profitable to reduce price

uniformly and increase output. Unless the marginal revenue of the G-monopolist

is only half a dollar, i.e., it perceives an overall elasticity of demand equal to 2 (in

absolute value), the G-monopolist would increase profit by cutting price. Since,

by assumption, entry would be unprofitable at a price below $1, entry could not

erode the profit resulting from a price cut.

30

ix. The threat of entry obviously constrains a uniform price increase by the

G-monopolist and not a price increase targeted at HV-customers. But the entire

exercise of defining a price-discrimination market was predicated on the

assumption that the G-monopolist could not profitably raise price to all its

customers. It is that assumption which implies that the LV-demand facing the

G-monopolist must, with or without the threat of entry, be highly elastic.

x. The elasticity of demand can be written as follows:

E = (dq/dp)(p/q),

where E is the elasticity of demand (dq/dp) is the inverse of the slope of the

demand curve, i.e., the change in quantity sold, q, resulting from a small change

in price, p. If demand is linear, then (dq/dp) is a constant. Without loss of

generality, we have normalized price and quantity so that q and p are both equal

to 1. Thus, elasticity is equal to the inverse of the slope of the demand curve.

Since an increase in price equal to $0.05 causes a reduction in quantity sold of 1,

the elasticity must equal 20 (in absolute value).

xi. Hausman et al. actually recognize this point, but not its implications.

Describing the effect of a uniform 5-percent price increase when the overall

elasticity of demand is two, they write (p. 368):

[S]uppose that the demand for the product is relatively elastic, e.g., a 5

percent price increase will result in a 10 percent decrease in the quantity

sold. For a 5 percent price increase, 10 percent of the original demand is

from marginal customers who switch in response to the price increase.

The other 90 percent of the original demand is from inframarginal

31

customers who continue to purchase at the higher price. Even though the

inframarginal customers outnumber the marginal customers nine to one,

the number of marginal customers may be sufficiently large to make the 5

percent price increase unprofitable for the hypothetical monopolist.

xii. We observe in passing that imperfect, but better-than-random, targeting does

not make price discrimination unprofitable, but rather tends to diminish both the

optimal price increase to vulnerable customers and the optimal price reduction to

invulnerable customers. The logic is simple, since the imperfectly targeted group

of vulnerable customers is disproportionately made up of truly vulnerable

customers, the average elasticity of the targeted group will be less than the

average elasticity of all customers, but greater than the elasticity of the truly

vulnerable customers. But as long as the average elasticity of the imperfectly

targeted group is less than that of the average elasticity of all customers, it will be

raise price to that group by an amount corresponding to the average elasticity

reflecting the presence of incorrectly targeted price-sensitive customers.

xiii. The table thus extends and clarifies a similar table presented by Hausman

et al. in their paper (p. 375).

xiv. If the G-monopolist is a competitive supplier of O, it could raise the price of

G and retain its LV-customers by offering O at the competitive price to customers

will raising the price for G. This would return us to the self-selection model

discussed above in section II.