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Global vs. Local Com petition

∗

Patric k Legros

†

and Konrad Stahl

‡

October 10, 2002

Abstract

We analyze the impact of increased outside opportunities brought

to consumers by improved access to a global market on local mar-

ket performance under monopoly vs. oligopoly. If consumers choose

once where to buy, we show that under all forms of organizing the

local market, increased competition from the global market will lo-

cally crowd out variety. The eﬀect on prices is much less clear. While

increased global competition yields a price reduction under monopoly,

prices may increase under oligopoly. We check the robustness of these

results in various extensions and draw consequences on competition

and industrial policies.

JEL Classiﬁcation Numbers: D83, L12, L13, L81.

Keywords: Global competition, monopoly, oligopoly, search, price vs.

quality competition.

1 Introduction

What are the eﬀects of increasing global competition on local markets? A s

to its eﬀects on local pric es, a comm on view is that in provid in g a utility

increasing outside option to consumers, globalization reduces their partici-

pation in local markets. One might expect that in this situation increasing

∗

We would lik e to thank participants at seminars and workshops at Toulouse, ECARES,

Berlin, Lausanne, Mannheim, University College London, University of Rotterdam for

lively discussions and comments. Both authors beneﬁted from the ﬁnancial support of

EU TMR Network contract n

o

FMRX-CT98-0203. Legros beneﬁted also from the ﬁ-

nancial support of the Communauté française de Belgique (projects ARC 98/03-221 and

AR C00/05-252).

†

ECARES, Université Libre de Bruxelles and CEPR.

‡

University of Mannheim, CEPR, CESifo and ZEW.

1

global competition unequivocally restrains market po we r in local markets,

leading to a price decrease beneﬁting all consumers. There w ould thus be

little scope for competition policy in these markets.

1

Ho wev er, dependen t on

local market structure, even in this simple world an increase in the outside

option may induce self-selection of consumers in a w a y that the demand faced

b y local suppliers becomes more inelastic, and th us increases their mark et

power.

2

Increases in global competition also ch a nge local incen tives to provide

qual ity .Qualitycomesinmanydiﬀerent dimension s; for instance, quality of

the commodity itself, qualit y of service to the customer, quality assurance

through reputation, or matc hing quality as aﬀected by the number of varieties

oﬀered. In this paper’s analysis, w e focus on the last dimen sion, i.e. on the

ev olution of variety oﬀered locally when global competition increases. Our

analysis should ha ve quite natural implications for the other dimensions of

quality.

Local market structure also matters in the provision of that quality: In-

creased local quality increases local market deman d , whic h may beneﬁtall

local traders. Therefore, qualit y is a collective good, and the private incen-

tives to contribute to it vary with local market structure. This introduces a

new dimension in to any comp arison between monopolistic and oligopolistic

behavior, and ev en m ore complicates an evaluation of the disciplining eﬀect

of global competition.

In this paper, we focus on the impact of increased outside competition on

the trade oﬀ between the d isciplining eﬀect of competition from oligopoly and

the in tern aliza tion incen tive from monopoly in th e provision of local qu ality,

and on local prices. Amongst the questions w e ask is whether, in the face of

increasing global competition, competition policy and even m ore, industrial

policy should restrict, or promote the concentration of local mark et po wer.

We conclude that mark e t conditions are not v ery informative when it

comes to w elfar e statements. For instance, we ﬁnd regimes in which pric e-

1

Yet demands on local industrial policy buﬀering the redistribution of economic activity

could substantially increase.

2

This point is made in Legros and Stahl (2002)

2

cost-margins increase when outsid e competition increases.Wealsoobserve

regimes under which prices ar e higher under oligopoly with free entry than

under monopoly. In particular, w e sho w that under a consum er surplus crite-

rion, oligopoly is preferable to monopoly only if outside competition is weak,

and monopoly is preferable when outside competition is strong. These conclu-

sions reﬂect the fact that m on opoly better in ternalizes positive externalities

of the type alluded to above, and thus are quite general. The intensity of

global competition thus matters in the determination of prescriptions for

competition policy and industrial policy incen tives.

Our model is speciﬁed for, and can be most easily interp reted within the

speciﬁc con text of competition between intern et and local traders in a market

for inspection goods. (Its reinterpretation for the other aforementioned situ-

ations is natural.) It incorporates t wo features we consider essentia l in the

interface between global and local competition. The ﬁrst is that consumers

(ﬁrms) incur diﬀerential access costs to the local vs. the global market. The

second is that in many instances consumers (ﬁrm s) must acquire detailed

knowledge about the alternatives available in the market (and the status of

their preferences relativ e to them) before the purch ase decision is taken, and

that the tw o trading channels diﬀer in con veying the relevan t inform a tion .

More speciﬁcally, ow in g to a m uch larger market, internet traders tend to

provide a larger variety of commodities. For instance, almost any textbook

can be found on A m azon.com. Ho wev er, a custo m er who wa nts to discrimi-

nate bet ween these textbooks will hav e only access to the tables of conten ts,

sometim es a few excerpts, and reviews by previous readers. By contrast, a

bookstore usually oﬀers a smaller set of textbooks, but by browsing through

eac h of them our consum er can get a better feel of whic h textbook is most

suited to her tastes.

Here, we are only in ter ested in local market eﬀects, and to simplify we

do not formally model the global (e.g., in tern et) market but rather posit

that it provides an outside opportunity utilit y to consumers. We model the

local (e.g., bookstores) market as a diﬀerentiated goods market, organized

alternatively as an oligopolistic structure involv ing specialized ﬁrms that sell

one v ariety of a diﬀerentiated comm odit y, or as a monopoly selling all varian ts

3

in that mark et.

As customary, comm odit y variants are speciﬁed b y locations on the cir-

cumference of a Salop-circle (Salop, 1979). A s in Salop’s model, consumers

are diﬀerentiated by ideal varieties on this circle, but beyon d this, by their

relativ e costs of accessing the in ternet vs. the local retail market. Another

new feature is that the typical consumer can precisely specify her surplus

only upon the inspection of the commodit y variants, after her access deci-

sion to the trading cha nnel. Ex-ante, that decision is taken on the basis of

an expected (indirect) utility criterion. How ever, ex-post, the consumer is

facedwithverydiﬀerent alternativ es before the purchase decision is tak en.

While many more variants may be sold in the e-commerce channel, she can

perfectly inspect the varian ts on sale only in the local market.

Quite naturally, the consumer’s expected utilit y from patronizing the lo-

cal mark et increases in the n umber of varian ts oﬀered locally, and decreases

in local prices. Thus in a market opened by oligopolistic single variant sell-

ers, unilaterally taken entry and price setting decisions confer externalities on

all other sellers. These externalities can be inter na lized by the monopolist.

Con sistent with m any m arkets, w e assume in our baseline m odel that prices

are not predetermined but are disco vered once consumers visit the market.

This generates an ex-post hold-up problem for consum ers, ev en if consume rs’

price anticipations are me t in equilibrium. Under oligopoly, this is partia lly

alleviated by price competition.

The monopolist may alleviate the hold-up problem b y pre-announcing

lo wer prices, and to credibly comm it to them before consum ers go to the

market. Thisistheﬁrst extension analyzed later, In the second extension,

consum ers are allowed to switc h to the e-commerce trading ch an nel after

having found the suitab le variant in the local market. Thus in this case, the

local monopolist (as w ell as the oligopolists) faces not only ex-ante,butalso

ex-post competition from the global market.

One of the interestin g questions arising here is whic h local market organi-

zation will provide higher utility to the consum er s: the oligopolistic market

in which the externalities are not internalized but competition exercises its

price disciplining force; or the monopolistic market in which the externalities

4

are in ternalized, but monopoly is constrained only by competition from the

global ma rk et. The answer to this question is not only in teresting in its o wn

righ t. It has an obv ious bearing on the relative survival of local mark ets,

since the market providing high er utilit y will do better.

Our results are mainly developed within a comparativ e statics exercise,

determ ining the eﬀects on local market performa nce of an increase in the

expected utilit y consumers obtain from participating in the global mark e t.

We show ﬁrst and surprisingly, that under both forms of organizing the local

market, increased competition from the global mark et will crowd out vari-

et y, thus unequivocally leading to a local qualit y loss. However, the eﬀect

of increased competition on pr ices is muc h less clear. Wh ile increased global

com petition reduces prices under monopoly, prices increase under oligopoly

when global competition is w eak, and decrease only when it is strong! Lo-

cal w elfare eﬀects mimic the eﬀects on prices. Thus with increasing global

com petition, local w e lfare increases under monopoly, but decr eases under

oligopoly! The total w elfare comparison of the performance under the two

market structures is possible only under strong global competition. Yet in

this situation , monopoly welfare dominates oligopoly.

As to an explanation of these results: The monopolist’s market po wer

creates a hold-up problem leading to a relativ ely high price (equal to the

willingne ss to pay of the ”marg in al” consumer), that in equilibrium is antici-

pated b y consumers. A larger n u mber of varieties implies more utilit y for all

consum ers but also a higher price and, b y conca vity of the utility function,

a reduction in the diﬀerence between the inframarginal and the margina l

consumers’ utilities: it follo w s that the ex-ante surplus of a consumer is a

decr easing function of the number of varieties.

Now, in response to an increase in outside utility, the monopolist can

decide either to decrease the n umber of varieties towards slo wing down the

individual variety’s loss of (local) mark et share, or to increase the nu mber of

varieties in order to increase pr oﬁt per consumer. Which strategy is optima l

depends on the trade oﬀ between the speed at which mark et share is lost,

vs. the speed at whic h proﬁt per consumer increases. If the distribution of

consumer ty pes with respect to relative access costs is log-concav e as assumed

5

here, the ﬁrst strategy is proﬁt maximizin g: demand decreases faster than

proﬁt per consumer increases when the n u mber of varieties increases. This

implies a decrease in the number of varieties (i.e. a crowding out eﬀect) as

well as a decrease in prices. It also implies an increase in the w elfa re of

consumers who purchase from the local retail market.

Under oligopoly, the ex-post hold-up problem is wea kened since ﬁrms in

the local market compete for the marginal consumer and will post a price

strictly lo wer than her utility. However, an increase in outside utility implies

lower equilibrium proﬁts for a giv en size of the local market. Hence, in an

equilibrium with free entry, variety will go down. Yet fewer varieties imp lies

less competition ex-post.Thelattereﬀect implies that prices increase under

concavit y of the t ypical consumer’s utility function.

It is tem p tin g to assert that the diﬀerence bet ween outcomes under monopoly

and oligopoly is linked to the diﬀerence in the magnitu de of the hold-up prob-

lem bet ween th e two. How ever, as w e show in the extension, this intuitio n is

incorrect. Allo wing the monopoly to announce and to commit to prices before

consumers decide between local and global markets should giv e maximum

liberty to mon opoly to comm it to low prices while oﬀering more varieties.

Nevertheless, the m on opolist still tends to reduce variet y and prices.

We conclude that it is not so m uc h the hold-up problem that is responsi-

bleforthediﬀerence in behavior under monopoly and oligopoly, but rather

the nature of competition ex-post (onceconsumersareinthelocalmarket).

W ith the global market, the monopolist faces a non-strategic competitor,

and the constraint thus imposed in equilib rium is similar to a participatio n

constrain t. By contrast, under oligopolistic competition ﬁrms face ex-post

strategic competitors and the constraint imposed in equ ilibriu m is similar to

an incentive constraint.

For this reaso n, w e ﬁnally consider ex-post competition in both, the

monopoly and the oligopoly model, by allowing consumers to inspect va-

rieties in the local market before deciding to buy the preferred variety in

the local vs. the global market. The beneﬁt of prior inspection is that the

consumer can order a speciﬁc variet y in the global market while she could

6

not without.

3

Here the reasons for increases in the expected indirect util-

it y in the global market become important. If only prices decrease in the

global market, the crowding out eﬀect is upheld. Ho wev e r, if consumers’ pre-

purchase selection process is improved in the global market, the n umber of

varieties oﬀered b y the local monopoly might increase in the expected utilit y

from purchasing in the global mark et. Such a regime switch in the compara-

tive statics does not arise in the oligopoly case: Local variet y un eq uivocally

decreases in all cases.

The cases discussed are not only inter estin g conceptually. They also

characterize diﬀerent market arrangem ents, and for diﬀerent types of com-

modities. In particular, our baseline model varian ts reﬂect markets for non-

standardized inspection goods such as individually designed fashion goods

that are not sold in the in tern et in identical variants. ex-ante price comm it-

men t should also not be typical in markets for this type of goods, as prices

are not info rm a tive without kn owledge of the goods’ quality c h ara cter ist ics.

By contrast, the extensions rather reﬂect markets for standardized inspe ction

goods (like books and CD s). Only these can be sold with iden tica l charac-

teristics in both market channels, and price announcements tend to be more

inform a tive for this class of commodities.

We ﬁnally surv ey the sparse literature on the subject. The fact that

outside competition aﬀects the performance of a local market is ob v iously

present in discussions on the role of mail order business (e.g., Michael 1994,

Balasubramanian 1998, and Bouckaert 1999) or the impact of electronic com-

merce on conven tio na l retailing (e.g. Ba ye and Morgan 2001, Janssen and

Moraga 2001, and Ulph and Vulkan 2001). None of these papers contains

an analysis of the eﬀect of an increased pressure from outside competition

on the evolution of local market performance, which is the main focus here.

Salop (1979) develops a n um erical m odel without consumer uncertain ty. He

inform a lly perform s comparat ive sta tics that can be reinterpreted in light of

ours, albeit in a much simpler model and only for the oligopoly case. He ob-

3

An alternative extension building on other diﬀerential informational capabilities of the

t wo market channels would be to allow the consumers to ﬁrst shop for information in the

internet and then buy locally. However, this would necessitate a more explicit model of

the informational potential arising in the internet and thus is not considered here.

7

tainsapricereactionoppositetotheonewederivefromourformalanalysis.

At any rate, the gist of our com para tive static analysis is on the compar ison

of eﬀects on oligopoly and mon opoly in diﬀerent variants of a m uch more

complex and general model.

4

Finally, Stahl (1982), Gehrig (1998), and Sc h ulz and Stahl (1996) analyze

price and variant determination in local markets for inspection goods. Sch ulz

and Stahl compare equilibria under diﬀeren t local mark et structures. A ll

ignore th e ro le of outside competition.

As such our model belongs to a small theoretical literature on the ef-

fect of increasing competition on market performance.

5

These papers adress

the disciplining role of competition on incen tive pro visio n in ﬁrms. Com-

petition is usually measured by the number of competitors. W hile cast in

com pletely diﬀerent con texts, these papers show also an ambiguous eﬀect of

increased competition on the variables relevant for performan ce (manageria l

eﬀort, con tractual instruments). However, these models do not feature the

comparison of this eﬀect on diﬀerentmarketstructures.

The rest of the paper is organized as follo w s. Section 2 con tain s the de-

scription of our model. The results for the baseline m o nopoly and oligopoly

cases are derived in section 3. In section 4, we discuss extensions; ﬁrst the

case where the mono polist comm its ex-ante to prices, and second the case

involving ex-post competition from the global market. In our concluding sec-

tion 5, w e draw implications from our analysis on competition and industrial

policies.

2TheModel

Central to our analysis is the ability of diﬀerent local marketeers to substitute

priceandqualityinordertoprovideatlowestcosttoconsumerstheequi-

4

In a paper similarly entitled, Anderson and de Palma (2000) analyse and compare

local competition as competition between neighboring ﬁrms à la Hotelling or Salop, vs.

global competition between brands à la Dixit and Stiglitz. Ghemawat (2001) adresses com-

petition between global ﬁrms (such as McDonald’s) and local ﬁrms (such as neigborhood

restaurants), an aspect that is only tangential to our approach.

5

Early papers are Hart (1983) and Scharfstein (1988). More recent papers are Schmidt

(1997), and Aghion et al. (1997), (1999), Boccard and Legros (2002).

8

librium utilit y called for b y outside competition. The price-qua lity trade oﬀ

is formalized within a generalized v ersion of Salop’s (1979) model of product

diﬀerentiation on the circle. In view of the object of our analysis, the most

important generalizations are that consumers diﬀer in relative access costs

to the global vs. the local markets; that before purc ha sing they ha ve to learn

about the varieties a vailable, and that the t wo markets diﬀer in the learning

options open to consumers. The latter is the central reason for emplo ying a

model in which competition for consumers tak es place in utility space.

6

There is a measure 1 of consumers on a circle of circumference 1.A

consum er is identiﬁed b y a pair (y, θ) , where y ∈ [0, 1] is the consumer’s

ideal variety and θ is her cost of accessing the local market, net of the access

cost to the internet mar ket. Viewed as random variables, y and θ are i.i.d.; y

is uniformly distributed and θ has distribution G. Independence is justiﬁed

b y the fact that there is no natural correlation between access costs and

preferences. Uniform it y of the distribution wrt. y is a natural assumption in

horizon tal product diﬀeren tiation models. We assume that G is log-concave,

a propert y shared b y a large class of distributions (for instance, a normal

cumulativ e distribution is log-conca ve), and has a strictly positive density g

on (−∞, +∞). For example, consum ers living in cen tral cities close to local

retailers, but illiterate in the use of compu ters are char acte rized by large

negative values of θ. Note that log-conca vit y is equivalent to a decr easing

likelihood ratio

g

G

.

Consu m ers wish to consum e at most one unit of the commodit y. If a con-

sumer with ideal variety y consumes variety by where |y − by| =: x, his utilit y

gross of the price p paid is giv en b y h (x) , where h is a strictly decreasing

and strictly concav e function with h

0

(0) = 0.

There are two types of ﬁrm s activ e in the local mar ket, that are consider ed

in two diﬀerentvariantsofthemodel. Intheﬁrst variant, a mon opolist oﬀers

m varian ts. In the second, there are m specialized producers oﬀering one

variant each.

The timing of ev ents is as follows:

7

6

A recent example of this type of model is provided by Armstrong and Vickers (2001).

7

We will modify the timing in the extensions to allow for prices to be set ex-ante, or

9

• The n um ber m ofvarietiesissetinthelocalmarket(bythemonopolist

or, via entry, by the oligopolists).

• Consumers learn their relativ e cost θ of going to the local market.

• Consumers anticipate that the expected utility from purchasing from

theglobalmarketisu; w e assume that u has range (−∞,h(0)) . Hence,

if u = −∞, the global market is not attractiv e for any consumer, while

if u = h (0) , the local market will cease to exist since all consumers

strictly prefer the global market for an y pair (m, p) on the local mark et.

• Consumers observe the number m of varieties in the local market. For

convenience m is treated as a con tinuous variable.

• Consumers decide whether to go to the local market or to buy from

the global m arket.

• Prices p aresetinthelocalmarket.

• Nature draws y and consumers who go local learn, by trying diﬀeren t

varieties and comparin g prices, the variety-price pair that maxim izes

their utility.

The assumption that consum ers learn about their best variet y only after

they hav e committed to buy from one market place captures the idea that

consumers can discriminate among varieties only by inspection; comparative

inspection is only possible in the local ma rket (e.g., by going into stores and

trying on clothing, or perusing books). In the last section, we allo w for the

possibility for a consum er to ﬁrst inspect varieties in the local market and

then buy the preferred variety in the global mark et.

The ex-ante utilit y of a consumer who purchases from the global market

is exogenously given by u = h

− q, where h is the expected gross utility and

q is the expected price in the global mar ket. As we assume that there is no

to allow consumers to purchase in the global market after having searched in the local

mark et.

10

strategic response of the global market to local changes in the local mark et,

the precise speciﬁcation of the global mark et is not crucial.

In the local market, there is a ﬁxed cost F ≥ 0 to in troduce a new

variety and a marginal cost c ≥ 0 per unit sold. F ma y refer to the cost of

leasing shopp ing spac e.

8

We make the standard assum ption that varieties are

alw ays symmetrically located on the circumference of the circle.

9

Consumers

choose their mode of shopping in an ticipa ting the equilibriu m prices in the

local market. Because the consum ers learn their ideal variet y after ha ving

decided where to shop, each consumer has the same ex-ante expected utility

(before the access cost and prices) from shopping in the local mark et. Thus,

there exists in equilibrium a trigger value

˜

θ (m) suc h that all consum ers with

cost less than this value shop in the local market, and consumers with cost

greater than this v alue shop in the global mark et.

10

Since by assumptio n θ and y are i.i.d. and the marginal cost of production

is constan t, the strategic beha vio r of ﬁrms (net of entry decisions) is indepen-

dent of the mass of consumers. It is therefore enough to ﬁnd the con tinuation

equilibria for a mass one of consumers, i.e., to ﬁnd the sym m etric equilibrium

price p (m) and the symmetric maximal acceptable distance x (m) between

the ideal point of a consumer and a given variety. Tw o regimes are a-priori

possibleinequilibrium. Intheﬁrst regime, the price is large enough that

some consumers decide not to consum e after having learned their ideal vari-

ety. We will say that the market is not c overed. In the second regime, the

price is low enough so that all consumers ﬁnd it optimal to consume some

variety. We will sa y that the ma rket is covered.

To simplify, w e assume that it is not possible to co ver the mar ket with

8

Thus, when introducing m variants, the monopolist incurs a ﬁxed cost mF .Inorder

to facilitate the comparison with the oligopolistic outcome, we ignore economies of scale

in ﬁxed costs the monopolist undoubtedly enjo ys. As we will see later, the introduction

of economies of scope will only reinforce our main welfare result that under stiﬀ global

competition, local monopoly yields higher consumer utility than oligopoly.

9

Our assumptions on consumer learning their utility ex-post implies that this assump-

tion is without m uch loss of generality.

10

Note that a necessary condition for the retail market to attract a positive mass of

consumers is that if price is equal to marginal cost and if all varieties are sold, i.e., if

θ

∞

=lim

m→∞

˜

θ (m)=h (0)−

R

1

0

h (x) dx − c + q, we have G (θ

∞

) > 0. Stronger conditions

are in fact necessary in order for the retail market to break even.

11

only one variet y; if only one variety is oﬀered in the market, the consumer

whose ideal variety is farthest awa y, i.e. at a distance of 1/2, has utility h

¡

1

2

¢

from purc hasing that variety. Since the price mu st be at least equal to c for

the ﬁrm to break even, the mark et is not covered whenever

h

µ

1

2

¶

<c. (1)

As men tioned before, we consider two organizational structures for the

local market: a multiproduct monopoly and an oligopoly with free entry in-

volving single product ﬁrm s. We will be inter ested in comparin g the perfor-

mance of each structure as the global market becomes a stronger competitor,

i.e., as u increases.

3 M arket Responses to Global Competition

3.1 Properties of the ProﬁtFunction

The residual demand facing the local market depends on the lev el of surplus

that it oﬀers customers. This ex-ante surplus is a function of the n umber m

of v a rieties oﬀered which can be thought as an indicator of quality, and of

the price p that consumers will pay. In the baseline version of our model, the

mon opoly chooses m to maximize ex-ante proﬁts, while it sets p to maximize

proﬁts ex-post, i.e., once custom ers are in the shop. The oligopoly with free

en try introduces competition both ex-ante and ex-post: ex-p ost, the symmet-

ric price p is the non-cooperativ e equilibrium of a diﬀerentiated oligopoly

while the number of variables m, i.e., ﬁrms, is set ex-ante so as to make

en try and exit unproﬁtable. These diﬀerences in commitm ent between the

t wo market structures are apparen t in the reduced form proﬁt functions of

the industry.

In this section w e deriv e general properties of a proﬁt function assum-

ing full commitment on varieties and prices; properties that will be k ey in

deriving the comparativ e static results for the equilibria under each market

structure.

Given a pair (m, p), a con sumer has an ex pected utility of 2m

R

1

2m

0

h (x) dx−

12

p − θ of shopping locally, relative to an expected utilit y of u = h − q of shop-

ping globally. Thus, the demand the local mark et will attract is the measure

of consumers whose relativ e cost of shopping locally is less than

˜

θ (m, p)=2m

Z

1

2m

0

h (x) dx − p − u. (2)

We say that the market is covered if p ≤ h

¡

1

2m

¢

, i.e. th e price char g ed is

less than the w orst alternativ e hit b y the typical consum er. Let us restrict

attention to pairs (m, p) forwhichthemarketiscovered;wewillverifylater

that the covering condition is alw ays satisﬁed. When the co vering condition

is just satisﬁed, i.e., wh en p = h

¡

1

2m

¢

, the expected utility to local consum ers

is

H (m)=2m

Z

1

2m

0

h (x) dx − h

µ

1

2m

¶

. (3)

This surplus H will pla y a centra l role in the ensuing analysis. Wh ile

it is diﬃcu lt to sign the ﬁrst derivativ e of H, wecanshowbyanindirect

argument that H is a strictly decreasing and con vex function .

Lemma 1 H is a strictly decreasing and convex function.

The expected proﬁt of the local industry is then π (m, p)=G

³

˜

θ (m, p)

´

(p − c)−

mF. It is conven ient to make a c h an ge of variable. Let v =2m

R

1

2m

0

h (x) dx−

p − u be the expected surplus of local consumers net of θ.Thenp =

H (m)+h

¡

1

2m

¢

− v − u, and the proﬁt can be rewritten as

π (m, v)=G (v)

µ

H (m)+h

µ

1

2m

¶

− v − u − c

¶

− mF (4)

while the co vering cond ition p ≤ h

¡

1

2m

¢

canbewrittenas

m ≥ H

−1

(v + u) .

Lemma 2 (i) π (m, v) is concave in m.

(ii) For each m, π is single-peaked in v, i.e., has a un iqu e extremum that

is a maximum .

13

The relevant ﬁrst order conditions for π (m, v) are

π

m

=0:G (v)

H (m)

m

− F =0 (5)

π

v

=0:g (v)

µ

H (m)+h

µ

1

2m

¶

− v − u − c

¶

− G (v)=0. (6)

If we represen t their graphs in (v, m) space, both of these graphs are increas-

ing. Indeed, since

H(m)

m

is a decreasing functio n of m, it is necessary that v

increases with m in order to satisfy (5). Since H (m)+h

¡

1

2m

¢

is increasing in

m, it is necessary that v increases in ord er to satisfy (6). We can sho w that

for a given u these graphs in tersect only once and moreover that the graph

of π

v

=0intersects the graph of π

m

=0from belo w .

Lemma 3 (i) if π

m

(m, v)=0then (ˆm − m) π

m

(ˆm, v) < 0 and (ˆv − v) π

m

(m, ˆv) >

0;

(ii) if π

v

(m, v)=0then (ˆm − m) π

v

(ˆm, v) > 0 and (ˆv − v) π

v

(m, ˆv) < 0;

(iii) The graph of π

v

=0intersects the graph of π

m

=0only once and

“fr om b elow”: if (m, v) satisﬁes π

m

= π

v

=0, then when ˆv<v,π

v

(ˆm, ˆv)=

0 ⇒ π

m

(ˆm, ˆv) > 0 and when ˆv>v,π

v

(ˆm, ˆv)=0⇒ π

m

(ˆm, ˆv) < 0.

These properties are represen ted in Figure 1 where the arrow s indicate

the direction of increasing industry proﬁts. (The bracketed part of the curve

m = H

−1

(v + u) willplayarolelaterinthepaper.)

3.2 Mon opoly

Once m is ﬁxed, the problem of the monopolist is to choose ex-post the price

that maximizes his proﬁt; since the mass of customers shopping locally is set

at this poin t, this is equivalen t to choosing the segment of the market that

he wan ts to serve. By symm etry, the monopoly chooses x ≤

1

2m

to maximize

x (h (x) − c) . Let x

∗

be the unconstrained optimum

h (x

∗

) − c + xh

0

(x

∗

)=0, (7)

and let m

∗

=

1

2x

∗

. We assume that ﬁxed costs are small enough so that

when a measure one of consumers buys from the local mark et and when

14

0=

m

π

0=

v

π

v

m

()

uvHm +=

−1

}

Figure 1: Directions of increasin g industry proﬁts

15

m = m

∗

, the monopoly makes positive pr o ﬁts, i.e.,

x

∗

(h (x

∗

) − c) >

F

2

. (8)

If m<m

∗

, the monopoly w ould ﬁnd it optimal to set ex-post p =

h

¡

1

2m

∗

¢

>h

¡

1

2m

¢

(remember that h is decreasing). In this case the θ =0

consumer has an expected utility of u

L

=2m

R

1/2m

∗

0

£

h (x) − h

¡

1

2m

∗

¢¤

dx.

Ex-ante all types θ ≤ u

L

− u prefer to go to the local market, and the ex-ante

proﬁt of the monopoly is

π (m)=G

¡

u

L

− u

¢

µ

h

µ

1

2m

∗

¶

− c

¶

m

m

∗

− mF.

As long as m<m

∗

,πis the proﬁt function in a neighborhood of m. Assuming

that π (m) ≥ 0, the marginal proﬁtis

π

0

(m)=

Ã

2

Z

1/2m

∗

0

·

h (x) − h

µ

1

2m

∗

¶¸

dx

!

g

¡

u

L

− u

¢

µ

h

µ

1

2m

∗

¶

− c

¶

m

m

∗

+

π (m)

m

.

Since h (x) >h

¡

1

2m

∗

¢

when x<

1

2m

∗

,π

0

(m) > 0 and the monopoly wants

to increase the segment of the mark et that he serv es. This proves that the

market is co vered.

Lemma 4 Ther e exists m

∗

such that if the mon opoly enters the local sector,

it chooses a number of varieties gr eater than m

∗

and the market is covered.

Therefore, a monopoly will c h oose m ex-ante in order to co ver its market

ex-post,i.e.,m ≥ m

∗

and p = h

¡

1

2m

¢

. This implies that the (symmet-

ric) price increases in the n umber of varian ts as it is determined from the

total utility of the ”marginal” consumer. T he expected consumer surplus

(net of θ ) from purchasing from the local market is then giv en by (3), or

H (m) ≡ 2m

R

1

2m

0

£

h (x) − h

¡

1

2m

¢¤

dx. Hence, from Lemm a 1, the surplus of

consumers is decreasing in the n umber of varieties. W h ile consumers value

more varieties, the reservation price of the marginal consum er is also increas-

ing in the number of varieties. Since the monopoly w ill set a price equal to the

reservation price of the marginal consumer, and since this reservation price is

16

increasing and concav e in the number of varieties, infra-m a rginal consumers

have less surplu s w hen the value to the marginal consu m er increases.

The hold-up problem preven ts the monopoly from separating the price

decision fr om the variety decision and therefore creates a one-to-one rela-

tionship bet ween the decision to give more surplus to the consumers and the

decision to decrease varieties. Whether or not the mon opoly will eﬀectiv ely

decide to giv e more surplus to the consumers in response to an increase in

their outside op tion u depends on the relative eﬀects on the demand and on

the proﬁt per consu m er.

The monopoly c hooses m to solv e

max

m

G (H (m) − u)

µ

h

µ

1

2m

¶

− c

¶

− mF (P0)

m ≥ m

∗

.

We are in terested b y the comp ara tive statics of a solution m

M

(u) with

respect to u. Ignoring the constrain t m ≥ m

∗

, the ﬁrst order condition yields

H

0

(m) g (H (m) − u)

µ

h

µ

1

2m

¶

− c

¶

−G (H (m) − u)

h

0

¡

1

2m

¢

2m

2

−F =0. (9)

Foraninteriorsolutionm>m

∗

, the second order condition is satisﬁed

and the implicit fu nction theorem implies that the sign of

dm

M

(u)

du

is

dm

M

(u)

du

∝ −H

0

(m) g

0

(H (m) − u)

µ

h

µ

1

2m

¶

− c

¶

+g (H (m) − u)

h

0

¡

1

2m

¢

2m

2

.

Using (9),

h

0

¡

1

2m

¢

2m

2

= H

0

(m)

g (H (m) − u)

G (H (m) − u)

µ

h

µ

1

2m

¶

− c

¶

−

F

G (H (m) − u)

,

which upon subs titutio n in the previous exp ress io n yields

dm

M

(u)

du

∝ −H

0

(h − c)

·

g

0

−

g

2

G

¸

−

g

G

F.

By log-conca vit y of G, g

0

−

g

2

G

< 0. From Le m m a 1, the ﬁrst term in the

sum is negative and therefore

dm

M

(u)

du

is negative. Since the price is an increas-

ing function of the n umber of varieties, the unconstrained maximum n u mber

17

of varieties m

M

(u) is strictly decreasing in u. No w, as long as m

M

(u) ≥ m

∗

,

m

M

(u) is the solution to P0, otherwise the solution is to set m = m

∗

. If

theconstraintbindsatsomeu, it binds for all ˆu>uand therefore the

monopoly does not adjust his prices or the varieties oﬀered when u is large

enough. Whether or not the constraint is binding depends on the value of

m

M

(h (0)) . Our reasoning so far is local; a “global” proof that varieties de-

crease as u increases is provided in the Appendix. The preceding argument

is sum m arize d in

Proposition 5 As u increases, the monopolist oﬀe rs less varieties and the

local price decreases.

(i) If m

M

(h (0)) ≥ m

∗

, the monopoly optimizes by choosing for any u a

number of varieties m

M

(u) , strictly decr easing with u.

(ii) If m

M

(h (0)) <m

∗

, there exists u

∗

∈ (−∞,h(0)) such that for all

u<u

∗

the solutio n is m

M

(u) , and for all u ≥ u

∗

the solution is m

∗

.

The surplus of consum ers is decreasing in the nu mber of varieties oﬀered.

Hence, if the monopolist wants to give more utilit y to his consumers, he

needs to decr ease the n u mber of varieties. Faced with stronger competition

in the form of a larger u, the monopolist will tra de oﬀ the compensating

demand eﬀect needed not to lose consume rs, which is equal to the variation

of u, with the resulting loss in proﬁts when these consumers sho w up in his

shops. The proposition sho w s that the demand eﬀect domina tes, i.e., that

the monopoly will oﬀer a larger surplus to his consume rs and thus decrease

varieties and increase prices. Once again, the seemingly perv erse result that

the monopolist moves to increase local demand y et increases local prices is

due to his inability to comm it to (lo w ) prices. We will see later that allowing

for full price com mitment will chang e his attitu de only if global competition

is suﬃciently strong.

3.3 O lig o poly with Free Entry

As usual, w e iden tify a v ariety with a ﬁrm (think of many independent shop

o w n ers). Relative to the monopoly situation, there is now an ex-post com-

18

petitive eﬀect.Thisneweﬀect prevents the local oligopolists from extracting

too muc h ren t from the consum ers.

We focus on the symmetric free-entry equilibrium. With m is ﬁxed, the

ex-post price is determined b y standard competition à la Hotelling on the

circle. Let p (m) be the ex-post equilibrium price corresponding to m ﬁrms.

Replicating argumen ts for the monopoly case, w e can sho w that m is alwa y s

c h osen suc h that the mar ket is co vered.

Lemma 6 In a free-entry equilibrium, the equilibrium number of ﬁrms m is

such that the ex-post equilibrium price is p (m) ≤ h

¡

1

2m

¢

, i.e., the ma rke t is

covered.

>From now on w e can assum e that m ≥ m

∗

.Letp (m) ≤ h

¡

1

2m

¢

be

a candidate symmetric price equilibrium when there are m symmetrically

located ﬁrm s. If i and j are two adjacent ﬁrms on the circle, a necessary and

suﬃcient condition for equilibrium is that ﬁrm i does not gain b y deviating

to price p 6= p (m) . M easu ring distances with respect to ﬁrm j, the marginal

consum er is at a distance x where

h (x) − p = h

µ

1

m

− x

¶

− p (m) .

Firm i

0

s ex-post payoﬀ is

¡

h (x) − h

¡

1

m

− x

¢

+ p (m) − c

¢

x. Simple com-

putatio ns sho w that this function is locally concave in p at p = p (m) ,

11

and

the ﬁrst order condition for p = p(m) to maximize this function is

p (m)=c −

x

dx/dp

(10)

= c −

h

0

¡

1

2m

¢

m

.

Note that the equilibrium price is a de cre asing function of the n umber of

11

Indeed, π

00

(p)=2

dz

dp

+(p − c)

d

2

z

dp

2

. Now,

d

2

z

dp

2

∝−

dz

dp

©

h

00

(z) − h

00

¡

1

m

− z

¢ª

where

the right hand side equal to zero at p = p (m) since z (p (m) ,p(m)) =

1

2m

. The implicit

function theorem implies that

dz

dp

=

1

h

0

(z)+h

0

(

1

m

−z

)

< 0 and it follows that proﬁts are locally

concave at p = p (m) .

19

varieties:

dp

O

(m)

dm

∝

h

00

¡

1

2m

¢

2m

+ h

0

µ

1

2m

¶

(11)

< 0.

Hence, decreasing the number of varieties will increase the equilibrium

price, as long as the equilibrium price is give n by (10): while the total utilit y

of each consumer decreases, the competition for marginal consum ers is less

in tense. Here the price is related to the marginal utilit y of the ”marginal”

consumer, and by strict concavit y this marginal utility decreases in the n um-

ber of varieties. By contr ast, in the mon opoly case the price-cost margin

was related to the total utility of the “margina l” consum er and this utilit y

is increasing in the num ber of varieties.

Since the market must be covered, we still need to verify that the cov er ing

cond ition is satisﬁed at this price, i.e., that h

¡

1

2m

¢

≥ c −

h

0

(

1

2m

)

m

. Let m be

the unique solution of the equation

h

µ

1

2m

¶

= c −

h

0

³

1

2m

´

m

. (12)

Observe that by (7), m

>m

∗

. It follows that when m is in the interval

[m

∗

,m], the oligopolistic ﬁrms will set the monopoly price, and th us the

oligopoly will beha ve as a zero-proﬁt monopoly.

Th us, the equilibrium price, and the surplus given to consumers depend

on the number of varieties pr esent on the m arket. Equilibr ium prices are

p

O

(m)=

(

h

¡

1

2m

¢

if m ∈ [m

∗

,m]

c −

h

0

(

1

2m

)

m

if m ≥ m.

The expected utility of a consumer en tering the local market when m ≥ m

is then

ˆ

H (m)=2m

Z

1

2m

0

h (x) dx +

h

0

¡

1

2m

¢

m

− c

= H (m)+

h

0

¡

1

2m

¢

m

+ h

µ

1

2m

¶

− c

20

Simple computations show that

ˆ

H (m) is incr easin g in m.

12

This is in sharp

con tra st with the mon opoly case since it suggests that in order to give more

utility to the consum ers at equilibrium prices, the local market should in-

cre ase the n umber of varieties sold. From

ˆ

H (m

)=H(m) it follows that

ˆ

H (m) >H(m) for all m>m

. Hence, because of ex-post compet ition

when m ≥ m

the oligopoly can, for the same number of varieties, pro vide a

larger surplus to the consumers than the monopoly, since the ex-post price

is smaller. However, what ultimately determines consumers’ surplus is the

equilibrium n umber of varieties that the oligopoly w ill eventually coordinate

on relative to the monopoly. A s we will see, it can happen that the o verall

surplus oﬀered un der oligopoly is sm aller than under monopoly.

Given m and the anticipated value of p

O

(m) , the dem and falling on the

local market is G (θ (m; u)) , where θ (m; u)=

ˆ

H (m) − u when m ≥ m

and

θ (m; u)=H (m) − u when m ∈ [m

∗

,m]. Finally the ex-ante equilibrium

proﬁt of an olig opolistic ﬁrm gross of the entry cost F is

π

O

(m; u)=

G (θ (m; u))

m

¡

p

O

(m) − c

¢

.

An oligopoly equilibrium is then deﬁned by a n umber of ﬁrms m

O

such that

π

O

¡

m

O

; u

¢

= F and π

O

m

¡

m

O

; u

¢

≤ 0,

i.e., ﬁrmsmakenonnegativeproﬁts and no additional ﬁrm wants to enter.

An equilibrium can exist only if max

m

π

O

(m; u) ≥ F. This conditio n is

also suﬃcient for existence. Indeed, if max

m

π

O

(m; u) <F,no ﬁrm wants

to enter. Suppose now that max

m

π

O

(m; u) ≥ F. Since π is con tinuous

in m, π

O

(0; u)=0and lim

m→∞

π

O

(m; u)=0, there exists m such that

π

O

(m; u)=F and π

O

m

(m; u) < 0. If max

m

π

O

(m; u)=F, ch oose the largest

value of m suc h that π

O

(m; u)=¯π

O

(u) .

Lemma 7 A n equilibrium exists in the oligopoly model if, and only if max

m

π

O

(m; u) ≥

F.

12

Indeed,

ˆ

H

0

(m)=

½

2

R

1

2m

0

h (x) dx −

h

(

1

2m

)

m

¾

−

h

00

(

1

2m

)

2m

+h

0

(

1

2m

)

2m

2

, the term in brackets

is positive since h

0

< 0 and the last term is negative since h

0

< 0 and h

00

< 0.

21

Intuitively, the equilib r iu m condition π

O

m

(m) ≤ 0 states that the per-ﬁrm

demand (i.e., the mass

G(θ(m;u))

m

) elasticity is less than the (absolute value)

of the price-cost m argin elasticity. The price-cost ma rgin elasticity captu res

the direct strategic eﬀect of entry while the demand elasticity captures the

consum ers’ response to en try an ticipating this strategic eﬀect. As w e have

shown, the demand elasticit y is positive (more varieties and lo wer prices

make the local mark et more attractive) while the price-cost margin elasticit y

is negative (more com petition decreases prices ex-post).

Assume for the moment that the equilib rium n u mber of varieties is m

O

>

m

. The follow ing conditions must hold

13

G

¡

θ

¡

m

O

; u

¢¢

µ

−h

0

µ

1

2m

O

¶¶

=(m

O

)

2

F (13)

θ

m

g

¡

θ

¡

m

O

; u

¢¢

µ

−h

0

µ

1

2m

O

¶¶

+ G

¡

θ

¡

m

O

; u

¢¢

Ã

h

00

¡

1

2m

O

¢

2(m

O

)

2

+

2h

0

¡

1

2m

O

¢

m

O

!

≤ 0

(14)

m

O

≥ m. (15)

(13) is the zero proﬁt condition, (14) is the free entr y condition π

O

m

(m; u) ≤

0

14

and (15) is the bound deﬁned in (12) insuring that the mark et is cov ered.

The implicit function theorem applied to (13) implies that at the equilib-

rium value m

O

(u) ,

dm

O

(u)

du

= −

π

O

u

¡

m

O

; u

¢

π

O

m

(m

O

; u)

.

>From (14), the denom ina tor is non-positive. Hen ce, since π

O

u

(m; u)=

−g (θ (m; u))

¡

−h

0

¡

1

2m

¢¢

< 0, it follows that

dm

O

(u)

du

< 0. (16)

Now,

dp

O

(u)

du

=

dm

O

(u)

du

dp

O

(m)

dm

.

Therefo re, (16) and (11) yield

dp

O

(u)

du

> 0.

13

Note that Π

m

(m; u):=π (m; u) − F + mπ

m

(m; u) and therefore Π

m

(m; u) ≤ 0 is

equivalent to π

m

(m; u) ≤ 0 when π (m; u)=F.

14

After making use of (13) to substitute for mF .

22

Assume now that the equilibrium nu mber of varieties is m

O

∈ [m

∗

,m].

Then proﬁts are equal to zero at the m ono poly price

G

¡

H

¡

m

O

¢

− u

¢

(h

µ

1

2m

o

¶

− c)=m

O

F.

The left hand side is decreasing in u; hence, since the marginal oligopoly

proﬁt must be negativ e, the eq uilibr ium nu mber of varieties decreases when

u increases. Because the monopoly price is increasing in m, the equilibrium

price also decreases when u increases.

Proposition 8 In a free entry oligopolistic equilibriu m, as u increases, the

num ber of varieties decreases. T here exists a cutoﬀ global market utility u

such that for all u<ulocal pric es increase, and for all u>uprices decre ase

in u. In the latter case the oligopoly behave s like a zero-proﬁt monopoly.

3.4 Welfare

We are interested in comparin g welfare under the t wo market structures. If

the expected utility of local consume rs is S when the outside option is u, the

expected consum er surplus is

CS (S, u)=G (S − u) S +(1− G (S − u)) u

= u + G (S − u)(S − u) .

Under monopoly, local consu m er plus producer surplus is W

¡

H(m

M

(u)),u

¢

=

CS(S, u)+π

M

(u) where m

M

(u) and π

M

(u) are the optimal number of local

varieties and local monopolistic proﬁts, respective ly, when the outside op-

tion is u. Under oligopoly, as oligopolistic proﬁts are zero under free entry,

local w elfa re is W

³

ˆ

H(m

O

),u

´

when u<u, and W

¡

H(m

O

),u

¢

when u>u,

where m

O

is the corresponding oligopolistic equilibr ium n umber of varieties.

In this relativ ely general model, we can giv e t wo welfare statements. The

ﬁrst one is on the change in local consumer surplus resulting from increasing

global com petition. It follows imm ed iately from the resu lts alrea dy deriv ed ,

that with an increase in u,localex-ante consum ers surplus unequivocally

increases under monopoly, and decreases under oligopoly.

23

The second w elfare statemen t is more general as it amoun ts to directly

comparing the outcome from diﬀerent ma rket structures. But it can only be

taken if u is suﬃciently large. Recall that if u>u

, the oligopoly behaves

lik e a zero-proﬁt monopoly and oligopolistic ﬁrms set a price equal to the

value of the marg ina l con sum er. Since in this regim e the no-entry condition

implies that the marginal proﬁtisdecreasingatm

O

, the monopoly oﬀers less

variety than the oligopoly. It follows from Lemma 1 that the local consumer

surplus is decreasing in the number of varieties when the monopoly price is

charged ex-post. Therefore the monopoly proﬁtably oﬀers higher local con-

sumer surplus and also has a larger market share than the local mark et under

oligopoly. We deduct that total consumer surplus is higher with monopoly.

Proposition 9 There is a u

M

<usuch that for all u ≥ u

M

the monopoly

generates larger welfare than the oligopoly.

This result is surprising especially in view of the fact that, in the baseline

v ersion of our m odel used here, consumers are caugh t in a hold-up situation

under monopoly more than under oligopoly (as for an y giv en m the monopo-

list sets high er prices ex-p ost than the olig opolists do.) We will also see that

the welfare results are uph eld in the extensions discussed below .

4 Extensions

4.1 M onopoly : The Value of Pre-A nnoun cing Prices

Assuming that the monopoly cannot commit to prices is an extreme as-

sump tion; coupons, folders, genera l advertisemen t suggest that some level of

ex-ante commitment is feasible. Here w e tak e the other extreme assumption

that the monopoly can perfectly commit ex-ante (i.e. before consum ers de-

cide to visit the local vs. the global mark et) to a pair (m, p) , where p is the

price at whic h an y of the m v a rieties sells in the local market. The analysis

of section 3.1 applies and the consumer indiﬀerent between shopping locally

and globally is given b y (2)

˜

θ (m, p)=2m

Z

1

2m

0

h (x) dx − p − u.

24

Note that

˜

θ is linear in p (in fact

˜

θ

p

= −1)andthat

˜

θ

m

(m, p)=2

Z

1

2m

0

h (x) dx −

h

¡

1

2m

¢

m

=

H (m)

m

is positive and decr easing in m (since H is decreasing in m).

Here also the monopoly c hooses optimally to co ver the ma rket.

Lemma 10 If the monopoly enters the lo cal market, the market is cover ed.

Hence p ≤ h

¡

1

2m

¢

, and after making the c ha nge of variable suggested in

Section 3.1, the problem of the monopoly reduces to

15

max

m,v

π (m, v)=G (v)

µ

H (m)+h

µ

1

2m

¶

− v − u − c

¶

− mF (P’)

m ≥ H

−1

(v + u) .

Thesolutioncanbeinoneoftworegimes:eithertheconstraintisbind-

ing, in which case the solution coincides with that of the mono poly model

consider ed before; or the constraint is not binding in which case the two ﬁrst

order conditions π

m

=0and π

v

=0are satisﬁed.

As long as w e are in the ﬁrst regime, our previous comparativ e statics

results app ly, that is as u increases, varieties and price decrease.

Consider now the non binding regime. Recall that the relevant ﬁrst order

conditions are (5) and (6), respectively. As u increases, the grap h of π

m

=0

does not change, while the graph of π

v

=0moves to the left. H ence, if w e

are in a regime in which the co v ering constrain t is not binding, v and m will

decrease, and we recover locally the earlier results.

No w a potential diﬃculty arises when there is a regime c han ge , i.e., when

w e go from a situation in which the constraint binds to a situation in which

the constra int does not bind. When the constraint binds we are back to the

15

Since H is decreasing and convex, H

−1

is also decreasing and convex. Hence, the

constraint can be writ ten H (m) ≤ v + u or m ≥ H

−1

(v + u) . Note that the “covering”

constrain t m ≥ H

−1

(v + u) do es not impose that m ≥ m

∗

since the monopoly can adjust

the price in order to satisfy the constraint.

25

earlier monopoly problem and by Lemma 3 w e deduct that this optim um

must be in the region π

v

≤ 0 and π

m

≤ 0, as represented b y the bracketed

part of the curv e m = H

−1

(v + u) in Figure 1. In fact, the optimum is in

the regim e of binding constra int if, and only if the graph of m = H

−1

(v + u)

in tersects the area deﬁned by π

v

≤ 0 and π

m

≤ 0. As u increases, the

graph of m = H

−1

(v + u) moves to the left and locally the property is

preserved; w e therefore retain the same compa rative statics. If the graph of

m = H

−1

(v + u) moves to the left “faster” than the graph of π

v

=0then

we enter the second regime where the covering constrain t is not bind ing.

It is simple to sho w that as u is small (u →−∞), there is no value for

the monopoly to pre-announce prices, i.e., to reduce the hold-up problem,

wh ile for u large (u → h (0)) there is value to pre-announcing prices.

Proposition 11 For u suﬃciently large (small) there is (no) value to pre-

announcing pric es.

Clearly the incen tive to commit ex-ante to lo wer prices is vastly reduced

under oligopoly, as the individual ﬁrm can internalize the increase in local

market demand generated from setting a lower price only at the order of mag-

nitude of 1/m. Obser ve ﬁnally that our earlier welfare comparison of local

mon opoly vs. oligopoly is naturally upheld unde r the presen t generaliza tion.

4.2 Ex-P ost Competition from the global mark et

The initial comparativ e static results could ha ve suggested that the diﬀer -

ence in monopolistic and oligopolistic responses w ere due to the fact that

consumers are caught in a severe hold-up problem under monopoly, while

less so under oligopoly. Ho wever, as we ha ve show n in the previous section,

we obtain qualitatively the same comparativ e statics ev en if the monopoly

can eliminate the hold-up problem . The diﬀerence bet ween the two organi-

zational forms is therefore due to the nature of competition rather than to

the magnitude of the hold-up problem.

For both monopoly cases considered, the nature of outside competition

w as similar to an individu al rationality constraint. For the oligopoly, there

26

was also this (ex-ante) individual rationality constraint but also an (ex-

post ) incentive compatibility constraint, since neigh boring ﬁrms com pete for

”marginal” consumers.

This suggests that the main diﬀerence in comparative statics bet ween the

t wo market forms is due to the nature of ex-post competition. We there-

fore introduce ex-post com petition b y allowing consum er s to leave the local

market after inspection, and to purchase the selected comm odit y variant in

the global market. For instance, while it is diﬃcu lt to describe ex-ante the

c haracteristics of a running shoe, it is possible after having tried on diﬀer -

en t shoes in a store to iden tify the exact model and size that is best; it is

then easy to order such an item from the global mark et. Observe, ho wever,

that this arbitrage option is open only for comp letely standard ized inspection

commodities(booksandCDsareotherexamples)..

In this analysis, it is necessary to distinguish between the cost α of ac-

cessing the local market and the cost β of accessing the global one.

16

We

assum e that α has distribution G (log-concave) and, for simplicity, that β is

a constant.

The new timin g is as follow s.

• Consumers learn α and observe the n umber of varieties in the local

market;

• If the consum e r shops on the global market his expected utility is u =

h

− q − β;

• If the consumer goes to the local ma rket, he lear ns by sampling the m

varieties which variety gives him the “best ﬁt” h (x);

— he can th en buy this variety on the local market and his utility is

h (x) − p − α, or

— he can buy this variety from the global mark et and his utilit y is

h (x) − q − α − β.

16

Hence α − β corresponds to the opportunity cost θ of shopping locally in the previous

sections of the paper.

27

There are no w three options open to consumers:

1. Buy from the global market immed iately: surplus is u − β;

2. Sta y in the local market: ex-post surplus is h (x) − p − α;

3. Inspect in the local mark et but buy from the global market: if the best

ﬁtish (x) , her ex-post surplus is h (x) − q − β − α since the consumer

has to pay access costs to both markets.

Theshareofthelocalmarketisthemassofconsumerschoosingthe

second option. Note that the choice between the second and the third option

depends on whether β is larger or smaller than p − q:ifβ<p− q, all

consumers purch ase from the global market. H en ce for consum ers to shop

locally at all, w e need

β ≥ p − q.

17

(17)

This is a simple representation of ex-post price competition from the

global market. Clearly in an equilibrium w ith positive en try this constraint

must be satisﬁed. From an ex-ante perspective, the consumers who decide

togotothelocalmarketarethosewhosetypeis

α − β ≤

˜

θ (m, p(m),u)=2m

Z

1/2m

0

h (x) dx − p (m) − u,

where p (m) isthepricethatconsumersanticipateinthelocalmarket.

In the monopoly c ase without commitment, consumers should an ticip ate

in equilibrium a price

p (m)=min

½

β + q, h

µ

1

2m

¶¾

.

Once the customers sho w up in the local market, the monopolist chooses the

price. The problem is then

17

In this case, no consumers will buy ex-post from the global market; this is due to the

assumption that the cost β is common to all consumers. A non-degenerate distribution

of the cost β would tend to induce the self-selection of consumers: the high β consumers

would remain in the local market whence the low β consumers would move on purchasing

in the global one.

28

max

m

G

³³

˜

θ (m, p (m) ,u)

´´

(p (m) − c) − mF.

Ifthesolutionisintheregion

©

m : β + q>h

¡

1

2m

¢ª

, the solution is iden-

tical to that before, and so the comparativ e static results remain also un-

c h anged. If the solution is in the region

©

m : β + q ≤ h

¡

1

2m

¢ª

, note that

˜

θ (m, β + q, u)=H (m)+h

¡

1

2m

¢

− h

. Hence, the ﬁrst order condition is

H (m)

m

g

³

˜

θ (m, β + q,u)

´

(β + q − c)=F.

Here w e must distinguish between the two diﬀerent sources for the in-

crease in u: either the global m arket allows for better search and inspection

and th us h

increases; or the expected total price (β + q) decreases. If the

improvem ent is due to the latter, w e get

dm

d (β + q)

∝

H (m)

m

g

µ

H (m)+h

µ

1

2m

¶

− h

¶

which is strictly positive. Hence, varieties unambiguously decrea se as β + q

decreases. Hence the previous result of crowding out of local varieties is

upheld.

How ever, if there is an improv e m ent in inspection on the global market,

then

dm

dh

∝ −g

0

³

˜

θ (m, β + q, u)

´

can be positive if g

0

< 0, which typically happens when

˜

θ is large, that is

when u is large.

InthissubcaseonlywehaveaninvertedU-shapedpatternofthemo-

nopolist’s reaction in providing variety to an increase in the outside option:

if the global market oﬀer s low utility to consumers, the mono poly responds

to its increase by decreasing varieties and prices, whilst if the global mark et

oﬀers high utility, the local monopoly will shift to variety competition and

will oﬀer more varieties.

Note that for the oligopolistically structured local mark et the logic is the

same as before: allow in g consumers to inspect varieties in the local market

before arbitraging between the local and the global mark et will create ev en

29

more ex-post competition and th u s decrease oligopoly proﬁt s. There will be

less varieties in response to a stronger global mark et, as ﬁrm s will be pressed

to exit.

All of this lea v es unchanged our earlier w elfare result.

5 Concluding Rem arks

In the analysis of our baseline model we ha v e sho wn that, independently

of the mark et structure, an intensiﬁcation of global competition will cro w d

out varieties in the local market. Comp aring the eﬀects of a stronger global

mark et on monopoly and oligopoly prices, w e hav e found that while prices

will decrease under mono poly, they will increase under oligopoly when global

com petition is weak, and decrease only when global competition is strong.

The main intuition is that the oligopoly can partially comm it to low prices

because there is ex-post competition bet ween ﬁrm s. However, this commit-

ment is w eakened with increasing global competition, as it leads ﬁrms to exit

under oligopoly. How ever, few er varieties decrease competition ex-p o st and

therefo re yield to higher prices.

When we allo w the monopolist to pre-announce prices we ﬁnd that he

will not use the option of committing when the global market is a weak

competitor but will use the option otherwise; y et comparative statics on

prices and varieties are similar to the case where the monopoly cannot pre-

announce prices.

We ﬁnally allow consumers to take advan tage from the inspection services

oﬀered in the local market before eventually shopping in the global market.

In this case, the local market is subject to ex-post price competition. We

show that our resu lts on variety are upheld in general. In particular, variety

decreases under oligopoly and for most of the monopoly case. Only if the

global market becomes a strong competitor due to an improvem e nt in inspec-

tion qualit y, the optimal response of the monopoly migh t be to increase the

n u mber of varieties. Clearly, prices will decrease in either case under direct

price competition.

18

18

While our model appears to be too stylized to be used as the basis for a structural

30

We conclud e that prices are generally poor indicato rs of local mar ket per-

forman ce. The local market substitutes price and quality in order to provide

consumers with giv e n lev els of utilit y. Diﬀerent market structures face dif-

ferent constraints, in particular commitm e nt to prices and ability to limit

the number of varieties, and therefore substitute price-quality in diﬀeren t

ways. When quality becomes the relevant competitive variable — sa y because

price competition is already tight — welfare maximization should fa vor the

market structure that is most able to compete on the quality dimension . In

partic ula r, in our model, the monopolist is better able to compete in vari-

eties which leads to the result that m on opoly is welfare preferab le when the

outside option is v ery valuable.

This has consequ ence s for merger control and for industrial policy. Wel-

fare as generated in our mark et situation may be considered to depend on

thedegreeofconcentration,callitconc, in the local m arket and the magni-

tude of poten tial competition, call it comp. In our model, we can think of

comp = u, where u, asbefore,isthevalueoftheoutsideoption.

In competition policy, it is usually assum ed th a t the equilibriu m w elfare

W (conc, comp) is decreasing in conc and is increasing in comp:highercon-

centration yields price distortions that decrea se welfare while larger potential

competition creates competitive pr essure and leads to an increase in welfare.

This idea is applied in typical mer ger guid elin es that ﬁrst, ask for an evalu-

ation of the local market power, and second, if there is little market power

authorize the merger, otherw ise evaluate more carefully the eﬀects of increas-

ing concen tration. Supported b y formal analyses of imperfect competition

models with homogeno us goods the assumptio n implicit in this evaluation

is that, absent eﬃciency gains, increased concentration generates a welfare

loss. More speciﬁcally, the rule presumes that the equilibrium w elfare func-

econometric model, all the conclusions can be put to a direct empirical test under the

rather mild assumption that due to improved information services and/or more competitive

prices, the typical consumer’s expected utility from shopping in the internet increases over

time.

31

tion W (conc, comp) satisﬁes a decreasing diﬀerence condition

[conc > conc

0

]& [comp > comp

0

] ⇒

W (conc

0

,comp) − W (conc, comp) <W(conc

0

,comp

0

) − W(conc, comp

0

),

i.e., that w elfar e loss from increase d concen tra tion is smaller if (potential)

competition is stronger. We can support this rule by our analysis, but also

demonstrate that W (conc, comp) is not necessa rily decreasing in conc:thisis

true only for low values of comp; forlargervaluesofcomp, welfare is actually

gre ater with more concen tration (monopoly) than with less concen tration

(oligopoly). By pointing out a beneﬁt from larger concentration when comp

is small, w e reaﬃrm the general rule of authorizing mergers when poten tial

com petition is important. A t the same time w e underline an absolute beneﬁt

to concen trat ion, namely the ab ility to better internalize extern alities of the

t y pe discussed in this paper. When price competition is dam pened, this

eﬀect is lik e ly to be signiﬁcant and should therefore be part of an eﬃciency

defense.

Finally, our analysis has direct implicatio ns for indus trial policy, i.e., for

the active support of small v ersus large ﬁrm s. In our model, when global

competition is weak, supporting sm all ﬁrms m ig ht be a good idea, while w h en

global competition is strong, supporting small ﬁrms and therefore slo wing

concentration in the local mark et migh t lead to welfare losses.

References

[1] Aghion , Ph .; M. Dewatripont and P. R ey (1997): Corporate Govern ance ,

Com petition P olicy and Industrial P olicy, Europ ean Ec onomic R eview,

41, 797-805

[2] Aghion , Ph.; M. Dewatripon t and P. Rey (1999): Com petition, Finan-

cial Discipline and Growth, Review of Economic Studies, 66, 825-52

[3] Anderson, S. and A, de P alma (2000): From Local to Global Competi-

tion, Europ ean Economic Review, 44, 423-48

32

[4] Arm strong , M. and J. Vickers (2001): Competitiv e Price Discrimination ,

RAN D Journal of Economics, 32, 579-605

[5] Balasubramanian S.(1998): Mail versus Mall: A Strategic Analysis

of Competition bet ween Direct Marketers and Con ven tional Retailers,

Marketing Science, 17, 181-95

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net and the Competitiveness of Homogeneous Product Markets, Amer-

ican Economic Review, 91, 3, 454-74

[7] Boccard, N. and P. Legros (2002): Audit Competition in Insurance

Oligopolies, mime o, ECAR E S.

[8] Bouc kaert, J. (1999): Monopolistic Competition with a Mail Order Busi-

ness, Economics Letters, 66, 303-10

[9] Gehrig, Th. (1998): Competing Markets, Eur ope an Ec onomic R eview,

42, 277-310

[10] Ghema wat, p. (2001): Global vs. Local Products: A Case Study and a

Model, Boston, MA : Ha rvard Business School, mimeo

[11] Hart, O. (1983): The Mark et Mechanism as an Incen tive Sch eme, Bell

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[12] Janssen, J. and A. Moraga (2001): Pricing, Consumer Search and Ma-

turit y of Internet M arkets, Rotterdam: Erasmus Univ ersiteit, mimeo

[13] Legros, P. and K. Stahl (2002): Outsid e Options and their Eﬀect on

Local Markets: A Note on Salop’s Model, Univ ersité Libre de Bruxelles

and Univ ersity of Mannheim, mimeo

[14] Mazo n, C. and P. P ereira (2001): Electronic Com m erce, Consumer

Search and Retailing Cost Reduction, Madrid: Universidad Com-

plutense, mimeo

33

[15] Mic hael, S. (1994): Competition in Organizational Form: Mail Order

v ersus Retail Stores, 1910-1940, Journal of Economic Behavior and Or-

ganization, 23, 269-286

[16] Salop, S. (1979): Mon opolistic Competition with Outside Goods, Bell

Journal of Economics, 10, 141-56

[17] Sc harfstein, D. (1988): Product-Market Competition and Managerial

Slack, Rand Journal of Economics, 19, 147-55

[18] Sc hm idt, K. (1997): M an agerial Incen tives and Product Mark et Com-

petition, Review of Economic Studies, 64, 191-213

[19] Sc hulz, N. and K. Stahl (1996): Do Consumers Search for the High-

est Price? Oligopoly Equilibrium and Mon opolistic Optimum in

Diﬀerentiated-Products Markets, Rand Journal of Ec o nomics, 27, 542-

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[20] Stahl, K. (1982): Diﬀerentiated Products, Con sum er Search, and Loca-

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Price Discrim ina tion , Univ e rsity Colle ge London , m im e o.

6Appendix

6.1 Proof of Lemma 1

Simp le computations lead to

H (m) > 0, 1 <m<∞ (18)

lim

m→∞

H (m)=0 (19)

H

0

(m)=2

Z

1

2m

0

h (x) dx −

1

m

h

µ

1

2m

¶

+

1

2m

2

h

0

µ

1

2m

¶

(20)

H

00

(m)=−

1

2m

3

µ

h

0

µ

1

2m

¶

+

1

2m

h

00

µ

1

2m

¶¶

. (21)

34

Since h is decreasing, h (x) >h

¡

1

2m

¢

when x ∈

¡

0,

1

2m

¢

, hence (18) follows.

Since h is decreasing and concave, H

00

> 0 in (21) and H is strictly con vex.

Since H>0, (19) and (20) are compatible with H con vex only if H

0

(m) < 0.

6.2 Proof of Lemma 2

(i) π

mm

∝ G (v) h

0

(1/2m) < 0.

(ii) From (6) follows

π

v

(m, v)=g (v)

½

H (m)+h

µ

1

2m

¶

− u − c −

·

G (v)

g (v)

+ v

¸¾

. (22)

By log-co ncavity the term in brack ets is increasin g in v. Hence, if there is v

such that π

v

(m, v)=0, this value is unique and furthermore π

v

is positive

forsmallervaluesandnegativeforlargervalues.Thisprovestheresult.

6.3 Proof of Lemma 3

(i) and (ii) follow directly from the discussion in the text. For instance, since

π

m

= G (v)

H(m)

m

− F, if π

m

(m, v)=0, then for ˆm>m,

H(ˆm)

ˆm

<

H(m)

m

and

π

m

(ˆm, v) < 0 and ˆv>v,G(ˆv) >G(v) and π (m, ˆv) > 0.

We prove (iii) in a series of step s.

Step 1: We sho w that at a local maximum the graph of π

v

=0

intersects the graph of π

m

=0from belo w . Since the function

H(m)

m

is

strictly d ecreasin g, it has an inverse fun ction Φ th at is also strictly decreasing.

The ﬁrst order condition π

m

=0can be then written as

m = Φ

µ

F

G (v)

¶

.

Since this is a necessary condition for an in terior solution, w e can sub-

stitute this expression for m in the pr oﬁt function and w e have the new

problem

max

v

ˆπ (v)=G (v)

h

1

2Φ

³

F

G(v)

´

− v − u − c

,

35

where ˆπ is a function of v only while π is a function of m and v.

It follows that

ˆπ

v

(v)=g (v)

h

1

2Φ

³

F

G(v)

´

− v − u − c

+G (v)

Fg(v)

2G

2

(v)

Φ

0

³

F

G(v)

´

Φ

2

³

F

G(v)

´

h

0

1

2Φ

³

F

G(v)

´

− 1

.

If the mono poly makes positiv e proﬁts, the ﬁrstterminthesumispos-

itive. The second term is positive or negative.

19

Assum ing an in terior local

optimum, ˆπ

vv

< 0, and diﬀerentiating the ﬁrst order condition ˆπ

v

(v)=0

yields

dv

du

=

g(v)

ˆπ

vv

(v)

< 0. Hence locally if u increases the optima l value of v

decreases.

Now, by construction, a solution to ˆπ

v

=0solves π

m

= π

v

=0, i.e., the

optimal v is found at the intersection of the graphs of π

m

=0and π

v

=0.

Assume that the graph of π

v

=0in tersects the graph of π

m

=0from

abo v e. Since when u increases the graph of π

v

=0mov es to the left, the

in tersection shifts to the right, that is the optim a l v increases as u increases

which con trad icts the previous observation. Hence at an interior optimum

the graph of π

v

must intersect the graph of π

m

from below .

Step 2: We show that there is no local minim um.

>From Lemm a 10, whenev er the graphs of π

m

=0and π

v

=0intersect,

the poin t (m, v) is a m ax imum.

Step 3: We show tha t there is a unique local maximum.

>From the previous two steps, the graph of π

v

=0cannot intersect the

graph of π

m

=0fro m abo ve. Hen ce, the graph of π

v

=0can “cut” the

graph of π

m

=0only once, and possibly be tangent to the graph of π

m

=0

at other points, e.g., we could have a situati o n like in Figure 1 whe re there are

t wo local maxima . However, this case is not possible because by increasing

19

A solution–i.e., where π

v

≤ 0–exists. Indeed, we cannot have π

v

> 0 everywhere

for then v = h (0) would be the solution, and this is possible only if u =0,m= ∞ and

p =0, which is incompatible with positive proﬁts.

36

u