Price Flexing and Chain-Store Competition VI/VI.J... · Price Flexing and Chain-Store Competition beyond using the local stores or outlets.5 In these circumstances, retail markets

Price Flexing and Chain-Store Competition

by

Paul W. Dobson Michael Waterson Loughborough University University of Warwick

March 2005

ABSTRACT Price flexing by chain-store retailers refers to the practice of adjusting prices on a store-by-store basis according to the degree of local competition. In effect, it represents a form of third-degree price discrimination, taking advantage of the fact that consumers tend to be geographically constrained and only willing or able to shop in a limited area. However, it is clear that not all retailers use this practice. Instead some retailers choose to set national prices that apply uniformly across all their stores. This paper considers the strategic motives that may lay behind the choice of setting local prices or national prices that apply across separate local retail markets. The paper shows why different market circumstances may favour one pricing policy over another. The paper also considers how consumers fare from these pricing policy choices, demonstrating that while there may be conflicting interests there may also be situations where firms’ and consumers’ preferences are in accord. Key Words: Price flexing, chain-store retailers, competition, price discrimination, local prices, national prices JEL Codes: L10, L11, L40, L66, L81

Addresses for Correspondence: Paul W. Dobson, Business School, Loughborough University, Loughborough LE11 3TU,

United Kingdom – E-mail: [email protected] Michael Waterson, Department of Economics, University of Warwick, Coventry CV4 7AL,

United Kingdom – E-mail: [email protected]


1. Introduction

It is highly unusual, but not unheard of, for a competition authority to declare a business

practice to be anti-competitive and operate against the public interest but still not prohibit or

limit the practice and/or provide or recommend an alternative remedy to its effects. Just such

an outcome arose in the context of particular grocery retail chains in the UK using “local

price flexing” to adjust prices according to the degree of local competition (with variation not

be related costs). In its investigation of the UK supermarkets sector, the Competition

Commission (2000) concluded that the practice of local price flexing when used by the major

retail chains distorted retail competition and adversely affected the public interest.1 However,

no suitable remedy could be identified and no subsequent action was taken, and so the

practice continues.2

Yet, it is evident that local pricing is common across many retail sectors. In the case of UK

supermarkets, local price differences appear relatively modest in comparison to some other

instances.3 For example, the Federal Trade Commission found that in its investigation of the

Staples/Office Depot merger, average prices for office supply superstores varied by as much

16% depending on the extent of local competition in the US.4

1 In terms of competition effects the Commission concluded that the practice “distorts competition in the retail supply of groceries in the UK in that it tends to focus some elements of price competition into localities where particular lower-priced competitors are present and away from other areas and contributes to the position that a majority of grocery products are not fully exposed to competitive pressure” (2000, paragraph 2.406). In regard to broader welfare concerns, the Commission concluded that this practice adversely affects the public interest as “customers tend to pay more at stores that do not face particular competitors than they would if those competitors were in the area” (2000, paragraph 2.409). However, price flexing was not the only practice found to be anti-competitive and against the public interest and yet no remedy was offered. The same outcome applied to persistent below cost selling when used by the major multiple retailers. 2 The Competition Commission determined that it could not identify a remedy that would be proportionate in effect and in regard to the regulatory cost. In particular, the Competition Commission ruled out recommending the imposition of national pricing (on grounds that this would not allow for differential pricing based on legitimate factors such as regional cost differences). Similarly, it ruled out recommending a requirement than any price differences between stores should be broadly related to costs (on the grounds that this would be impractical to implement and regulate). Other options were considered and also rejected. 3 Individual product prices were found in some retailers to vary considerably (by as much as 100%), but average prices only differed across each chain by up to 3%. Even so, the monetary sums involved can be quite significant given the importance of the sector. For example, the Competition Commission (2000, paragraph 7.124) found that for the largest retailer, Tesco, customers in its lower-price (“Local”) stores saved between £10.5 and £25.9 million a year over the prices charged in higher-price (“National”) stores. 4 Federal Trade Commission v. Staples, Inc. and Office Depot, Inc., Civ. no.97-701 (TFH), 1997. The FTC used evidence on local pricing to argue that a merger between Staples and Office Depot would raise prices by reducing local market competition. See Dalkir and Warren-Boulton (1999) for a summary.

1


Nevertheless, it is clear that not all retailers adjust prices to cater for specific local conditions.

Some chain-store groups adopt uniform pricing. For example, this has for a long time been

the policy of the UK’s largest clothing retailer, Marks & Spencer. Moreover, in some sectors

it is common for all multiple retailers to price identically across their stores, e.g. UK

electrical goods retailers (MMC, 1997a,b). While in other sectors, chain-store pricing

policies vary from retailer to retailer. Indeed, this was found to be the case with UK

supermarkets, where, of the leading fifteen groups, eight priced uniformly while seven priced

according to local conditions (Competition Commission, 2000).

However, a common concern for competition authorities must be that as retail sectors

continue to consolidate, the number of possible instances and forms of market power abuse

are likely to grow. In particular, with consumers tending to be geographically constrained in

their shopping for a wide range of the goods they wish to purchase, it may be envisaged that

consolidation will not just lead to higher concentration at national levels, it will also lead to

higher concentration at the local level – thus restricting choice for consumers from where to

make their purchases. With major retailers then facing less competition at the local level, the

opportunity to exploit geographically constrained consumers may be expected to increase.

Price flexing thus represents a possible effective means by which third-degree price

discrimination could be practiced: pricing low when competition is intense, but pricing high

when competition is weak or absent.

In some instances, price flexing in this manner may not be practical. For example, it may be

the case that local markets overlap each other, creating an effective chain of substitution

across the country. This might well be the case with higher value consumer durable goods –

like expensive electrical goods – where consumers are willing to undertake extensive search

activity before making a purchase. Similarly, price flexing may not be practical when

consumers have access to alternative direct selling routes like the Internet. However, for

most everyday items like groceries, toiletries, and other fast-moving consumer goods

(“FMCGs”), along with petrol, cigarettes and alcohol, there may be few practical alternatives

2


beyond using the local stores or outlets.5 In these circumstances, retail markets may be

highly localised, with consumers only normally travelling short distances in making shopping

trips, and, when local competition is limited, retailers may be well placed to exploit this

situation.

Even so, it may not always be the case that a retailer wishes to be in a position where it can

adjust prices to suit local conditions. There are practical reasons why a retailer may wish to

adopt a national uniform pricing strategy. For example, this may be in keeping with the

image and reputation that it might be seeking for consistency in its pricing and offering “good

value” to all its customers, e.g. a retailer offering “every-day low prices” (“EDLP”), or if the

retailer relies on national advertising campaigns to promote its prices. Equally, it may want

to avoid the menu/ticketing and management costs involved with having to set different

prices at different stores, and make adjustments on a store-by-store basis rather than on a

national basis. Furthermore, and something related to the aspects addressed in this paper, the

retailer may want to commit to uniform prices as a means of avoiding being dragged into

local price wars that are destructive to profits, and instead focus on competition in a national

sense.

Thus, it is not clear cut that one pricing policy – local pricing or uniform pricing – will be

generally favoured over another. The purpose of this paper, though, is to consider how the

nature of oligopolistic competition between chain-store retailers might influence this pricing

policy choice. In particular, we explore here the possible strategic reasons for why firms may

commit themselves to one or other type of pricing policy, examining the importance of

different local market circumstances. We also consider what this might generally mean for

consumers.

In undertaking this analysis, it should be made clear that it is not our intention to re-examine

any specific case decisions, including whether or not in the context of UK supermarkets the

Competition Commission was right to deem price flexing as anti-competitive but still allow it

5 Clearly, improvements in retail technology such as electronic-point-of-sale (“EPOS”) systems make this possibility more practical, given that it can reduce menu and ticketing costs and allow for regular price changes either across different stores as well as over time (e.g. with short-term price promotions).

3


to continue, not least as these are highly complex matters with an array of specific

circumstances that have to be taken into account.6 Rather, it is hoped that this paper adds

further insight into the circumstances and effects of firms using or avoiding competitive price

discrimination, to which there is now a burgeoning literature (e.g. Holmes (1989), Corts

(1998), Armstrong and Vickers (2001), Cooper et al (2005), Stole (2005), inter alia).

In particular, this paper seeks to build on Dobson and Waterson (2005), which examines the

strategic motives facing a single chain-store retailer over whether to use local or uniform

pricing. This paper considerably extends this analysis by addressing the more realistic

situation where there is more than one chain-store retailer operating in an economy, and

where multiple retailers compete with each other on a national as well as local basis. As

such, the consideration of chain-store competition in an oligopolistic setting allows for a

richer set of possibilities to consider. It allows us to consider how each retailer views its

position in respect of a rival chain-store retailer, how individual and joint preferences differ,

and whether partial collusion in the form of (tacit) agreement or understanding over pricing

policy alters outcomes in a privately and perhaps socially beneficial way.

What emerges from this paper is that the choice over pricing policy can have a significant

bearing on ensuing price competition, affecting firms’ profits and consumer welfare

considerably. While the analysis reveals market circumstances where firms’ choices will

directly run counter to consumers’ interests, this is not always the case. Furthermore, local

pricing is shown as not always being against the interests of consumers, as uniform pricing

may have competition-dampening effects that are detrimental to consumer interests.

The structure of the paper is as follows. The next section discusses the framework and the

assumptions employed in the modelling. Section 3 shows the outcomes from pricing under

each of the possible pricing policy configurations. Section 4 examines the pricing policy

choices based on firms’ individual preferences. Section 5 then considers choices based on 6 For example, this is apparent from the Competition Commission’s (2000) own careful deliberations on the matter in the context of supermarkets. In this regard, our model abstracts from local cost differences in retail operations and asymmetries in firms’ positions (e.g. regarding store sizes, locations, product ranges, target

4


joint preferences. Section 6 addresses consumers’ interests in regard to the effects on

aggregate consumer welfare. Section 7 offers some concluding remarks.

2. The Set-up

The retail sector under consideration consists of two chain-store retailers, A and B, operating

in a country made up of distinct and economically separate local retail markets. To keep the

analysis as tractable as possible, we represent the country as consisting of just three local

(separate) markets. Both retailers operate in one of these markets – a “high-demand” market

that supports both firms, for example a large/affluent city. While in each of the other two

(“low-demand”) markets, only one of the retailers operates – with retailer A having a (local)

monopoly position in one of these markets, and retailer B a monopoly position in the other.

In this context, the two local monopoly markets might be thought of as smaller, less affluent

towns or rural areas where opportunities for opening stores are greatly restricted either by

tight planning rules or the unlikelihood of being able to recover fixed (start-up) costs if a rival

were already well established. This is in comparison to what might be considered as the

larger, more affluent city where greater store opportunities exist and the larger size of the

potential market offers greater scope for recovering start-up costs, thus allowing for both

retailers to be present.7

This is, of course, a considerable over-simplification of differences in demand and

competition conditions that are likely to exist between real local markets. However, this

bifurcation of markets captures in a very simple manner the notion, as observed in practice,

that local markets differ in respect of both the extent of demand (e.g. where population sizes,

as well as consumer tastes and incomes, vary from one region to another) and the number of

markets, market shares, buyer power, etc.), all of which were found to be significant aspects of the UK supermarket sector and evidently influenced the Competition Commission’s conclusions on price flexing. 7 See Bresnahan and Reiss (1987) for some general empirical support, in the context of US retail markets, for the assumption that entry conditions vary across local markets.

5


players operating, and thereby the possible intensity of local competition.8 In particular, it

captures the general fact that while chain-stores may operate right across a nation or a region,

they do not commonly operate in every local market. In some instances they face each other

as direct competitors, in others they do not.

To ease the exposition, we assume that the two firms are in symmetric positions. Specifically,

it is assumed that while the competing retail services may be different, each chain has no cost

or demand advantage over its rival.9 So, for example, the two “monopoly” markets are

assumed to be identical, while in the “duopoly” market the firms face symmetric demand for

their respective differentiated retail offerings. In addition, though, we allow for the extent of

consumer demand to vary across the two market types. This is captured in the model by

allowing the demand intercept term to be lower in each of the two monopoly markets

compared to the duopoly market (where in addition aggregate demand is increased when

consumers have strong preferences for retailer variety or differentiation).

It is further assumed that there is no demand or cost connection between the markets (so that

profits are separable across the markets).10 In respect of demand, the perspective taken is that

these local markets are sufficiently separated from one another (in geographic terms) that

8 In considering the extent of store choice facing consumers at the local level, competition authorities have tended to examine local markets in respect of drive times between stores or choice in postal areas. For UK supermarkets, the Competition Commission (2000, Appendix 6.3) identified that out of 1,700 stores surveyed, 175 stores were found to have a “monopoly” or “duopoly” status in local catchments (in respect of 10- and 15-minute drive times around each of the stores). However, when restricted to competition between the major “one-stop-shop” grocery retailers and with 10-minute drive times, then 627 out of the 1,700 stores were found to have “monopoly” or “duopoly” status. More recently, it has been reported that out of the 1,452 postal areas of Britain, the leading grocery retailer, Tesco, was found to have “an almost total stranglehold” on the retail food market in 108 areas, while accounting for over 50% of grocery spending in a further 104 areas (see “Tesco profits feed fears of a stranglehold”, Sunday Times, April 18, 2004). 9 It would be possible to extend our framework to consider the firms in asymmetric positions. However, this would be at the cost of making the analysis considerably more complex without adding much further insight beyond adjusting the scope for individual pricing policy preferences, rather than whether they exist or not, which is our key focus. In support of this claim, see Dobson and Waterson (2005) for some illustrations allowing for cost and demand asymmetries in the more simple setting of there being just one chain-store operating (and instead facing independent retailers rather than a rival chain-store group). 10 While it might be reasonable to consider demand not to be linked in the context of distinct local markets the same may not be generally true of costs. Local costs may be independent in regard to hiring labour and renting/purchasing sites but there is likely to be other elements where the chain-store might have economies of scope across its local markets. Notably, this might apply in procurement where the more markets it operates in the more likely it will be able to negotiate greater discounts from suppliers. Additionally, there might be economies from centralising administration. We do not discuss these considerations further in this paper.

6


consumers only purchase goods from their own local market. That is, there no cross-territory

purchasing because, for example, the goods are not easily transported or consumers would

face too much inconvenience and loss of time shopping outside of their own locality – as

might well be the case with, say, buying groceries.11 In regard to costs, we further assume

that operating costs are identical for all retailers and, in addition, that the retailers operate

under constant unit and marginal costs, which without further loss of generality are taken to

be zero.12

Complete information is assumed to apply on all these aspects, so that both firms are fully

aware of each other’s cost and demand positions, as well as their own respective positions.

Armed with this information, firms compete through setting prices in view of their choices of

pricing policy (i.e. whether they have each decided to adopt local or national pricing).

Because our prime interest is in comparing producer and consumer welfare under different

scenarios while aggregating over different markets, using a general demand specification

would not allow for effective comparisons to be made due to the potentially complex trade-

offs that feature in our framework.13 Accordingly, we limit our attention in this paper to a

particularly simple linear demand specification that allows us to compute and compare

outcomes, but one that still affords important flexibility in allowing us to capture in a very

straightforward way differences in demand and the intensity of competition between the local

markets. An added benefit of this approach, especially in view of the complexity of the

equations, is that all the results can be neatly portrayed in a simple diagrammatic form.

11 Accordingly, the kind of retail sector we have in mind is not one involving major shopping goods, like expensive consumer durables where search/transaction costs may be small in comparison to the relatively higher price of the product so that consumers may search more widely than their own locality, or similarly where consumers have particularly strong preferences for a certain retail service meaning that they are prepared to travel long distances (e.g. for designer clothing and other conspicuous consumption goods). Equally, our analysis does not relate to those markets well suited to “distance selling” (e.g. by telephone or through the Internet) where the geographic scope of a market extends to the whole country, or even to whole world. 12 Implicitly, retailing unit costs are viewed as being the same from area to area, which clearly may not be the case in practice. While it is possible to incorporate local cost differences in the model, we abstract from these considerations in this paper for the sake of analytical tractability. 13 This is, for example, borne out by Corts’s (1998) analysis where, in a general demand framework, all that can be shown in “symmetric best response” situations, i.e. that mirror our context, is that uniform pricing would entail price falling in the “strong” market and rising in the “weak” market”, without any further possible insight into the profit and welfare implications. In this regard, our analysis is intended to provide additional insights beyond those of Corts, albeit in a limited way in view of our restricted attention to a linear demand specification.

7


In setting out the demand specification for each market, we will denote the duopoly market

by i and the monopoly market controlled by A as j and that by B as k. Consumer preferences

in each of the two market types are represented by a standard quadratic utility function in

respect of purchasing a composite good.14 In the case of the duopoly market, the utility

function for the representative consumer takes the form

Vi(qAi,qBi) = qAi + qBi – (qAi2 + 2γqAiqBi + qBi

2)/2 + zi

where qAi and qBi respectively represent the quantity supplied by each of the chain-stores for

market i, while γ ∈ [0,1) captures the consumer’s perception of the substitutability between

the retailers’ services and product offering (becoming closer substitutes as γ → 1), and zi

represents all other goods and has a price normalised to unity. The consumer’s budget

constraint is taken as mi = pAiqAi + pAiqAi + zi.

In the monopoly market controlled by firm A, with the absence of variety, the utility function

takes the form for market j:

Vj(qAj) = αqAj – (qAj2)/2 + zj α ∈ (0,1]

Here, the consumer’s budget constraint is mj = pAjqAj + zj. Similarly, for the monopoly market

controlled by firm B, the utility function for market k is

Vk(qBk) = αqBk – (qBk2)/2 + zk α ∈ (0,1]

The analogous budget constraint is mk = pBkqBk + zk.

Constrained optimisation of the utility functions reveals indirect demand in each market as

pAi(qAi,qBi) = 1 – qAi – γqBi (1a)

pBi(qBi,qAi) = 1 – qBi – γqAi (1b)

pAj(qAj) = α – qAj (1c)

pBk(qBk) = α – qBk (1d)

Solving for the direct demand functions reveals

qAi(pAi,pBi) = (1 – γ – pAi + γpBi )/( 1 – γ2) (2a)

qBi(pAi,pBi) = (1 – γ – pBi + γpAi )/( 1 – γ2) (2b)

8


qAj(pAj) = α – pAj (2c)

qBk(pBk) = α – pBk (2d)

Thus the two critical parameters of our framework, which turn out to have a considerable

bearing on our results, are α and γ. The former captures in a simple way the notion that in the

“smaller” monopoly markets consumer demand may be less, in respect of both consumers’

willingness to pay and the scale of demand, than in the “larger” duopoly market, with the

difference becoming greater the closer α is to zero. The latter allows for different degrees of

intensity of price competition in the duopoly market with which to compare to the absence of

competition in the monopoly markets, with the difference becoming greater the closer γ is to

unity.

In regard to the nature and form of competition in the industry, equilibrium outcomes for the

retailers are modelled in the form of a two-stage game. In the first stage, each retailer decides

its pricing policy – whether to practice local (L) or uniform (U) pricing. In the second stage,

the firms simultaneously determine their prices being aware of each other’s first-stage

decision. The equilibrium concept is sub-game perfection. The outcomes from the second

stage are considered in the next section, examining in turn each of the four possible pricing

policy configurations that might arise depending on each retailer’s choice over whether to use

local pricing or uniform national pricing. Section 4, then considers the outcomes from the

first stage, where the retailers individually choose (and commit to) their pricing policy. Here,

the symmetry in the model simplifies matters somewhat since the respective profit

comparisons facing both retailers are identical. Section 5 explores joint preferences over

pricing policies and the outcomes that could be expected to emerge if the firms could collude

in their choice of pricing policy but not in respect of the individual prices they set thereafter –

a situation which may be thought of as one of “partial collusion”.

14 This “good” could be thought of as either an individual good with a specific amount of retail service attached or more appropriately in the case of multi-line retailers a composite basket of goods.

9


3. Pricing Outcomes

We begin by outlining the outcomes when both chain-store groups adopt local pricing before

considering the situation where they both adopt uniform pricing, followed by the asymmetric

situation where one adopts local pricing while the other adopts uniform pricing.

3.1. Local pricing by both retailers – (L,L)

When both retailers adopt local pricing, each retailer sets a price for each local market to

maximise profit in that local market. First, consider firm A’s situation. With zero operating

costs, its profit function in each of its monopoly markets is πAj = pAjqAj. Substituting in the

expression for demand, (2c), optimising with respect to pAj and solving yields the monopoly

price as pLA

L j = α/2, quantity as qL

A Lj = α/2 and local market profit as πL

A Lj = α2/4. Identical results

hold for firm B in respect of its monopoly market.

In the contested market, firm A’s profit function is

)3()1/()1(),( 2iBiAiAiBiAiAiAiAi pppppqp ∀γ−γ+−γ−==π

On optimising with respect to pAi, firm A’s best-response function in the contested market is

pAi(pBi) = (1 − γ + γpBi)/2 (4)

Similarly for firm B, we can analogously derive its best-response function in the market as

pBi(pAi) = (1 − γ + γpAi)/2 (5)

Using (4) and (5), we can solve for the pair of local pricing equilibrium prices

)6()2/()1( γ−γ−== LLBi

LLAi pp

Then, from (2a), (2b), (3) and (6), the quantity sold by each retailer and their respective profit

levels in the contested market are:

)7(])2)(1/[()1(;)]2)(1/[(1 2γ−γ+γ−=π=πγ−γ+== LLBi

LLAi

LLBi

LLAi qq

Combined profits for each retailer across both its markets under local pricing are thus

)8()4/(])2)(1/[()1( 22 α+γ−γ+γ−=Π=Π LLB

LLA

10


3.2. Uniform pricing by both retailers - (U,U)

With both retailers adopting uniform pricing, each of them sets a single price to maximise its

combined profits. For firm A, this is

)9()(1

)1()(),( 2 ⎟⎟⎠

⎞⎜⎜⎝

⎛−α+

γ−γ+−γ−

=+=Π ABA

AAjAiABAA ppppqqppp

Rearrangement of the FOC shows that the best-response function for chain A in this case is

(10)2

))1(1)(1()( 221

⎟⎟⎠

⎞⎜⎜⎝

⎛γ−

γ+γ+α+γ−= B

BAppp

The analogous best-response function for chain B is

(11)2

))1(1)(1()( 221

⎟⎟⎠

⎞⎜⎜⎝

⎛

γ−γ+γ+α+γ−

= AAB

ppp

Using (10) and (11) to solve for the pair of equilibrium prices reveals

)12()24(

))1(1)(1(2γ−γ−γ+α+γ−

== UUB

UUA pp

Using (2), the total quantity sold by each firm across all the markets it operates in is

)31()24)(1())1(1)(2(

2

2

γ−γ−γ+γ+α+γ−

== UUB

UUA QQ

Total profits for each retailer are then

)41(]24)[1(

)]1(1)[2)(1(22

22

γ−γ−γ+γ+α+γ−γ−

=Π=Π UUB

UUA

3.3. Uniform pricing by one firm and local pricing by the other – (L,U) and (U,L)

Consider next the situation where firm A, say, sets local prices while firm B sets a uniform

price applicable to both of its stores (observing that these roles can be reversed without

affecting the overall analysis). Here, firm A sets the local monopoly price (α/2) in its

monopoly market while its best-response function in relation to the contested market, where

it faces competition from retailer B, is represented by (4). In contrast, firm B’s best-response

function is given by (11). Solving for the equilibrium prices shows:

11


)a15(58

)])1(2)(1(2)[1(2γ−

αγ+γ−γ++γ+γ−=LU

Aip

)b15(58

)]1(22)[1(2γ−

γ+α+γ+γ−=LU

Bp

)c15(2α

=LUAjp

Using (2), we can derive the individual quantities sold by each firm in each market:

a)16()58)(1(

)))1(2)(1(22γ−γ+

αγ+γ−γ++γ+=LU

Aiq

)b16(2α

=LUAjq

)c16()58)(1(

))2()1)(2(2)(1(22

2

γ−γ+γ−α−γ−γ+γ++γ+

=LUBiq

)d16(58

))2(1)(2()1(22

2

γ−γ−α−γ−γ+−γ−α

=LUBkq

The combined profits for firm A from local pricing across its markets can be expressed as

)17(4)58)(1(

)])1(2)(1(2)[1( 2

22

2 α+

γ−γ+αγ+γ−γ++γ+γ−

=π+π≡Π LUAj

LUAi

LUA

We find that the combined quantity sold by firm B is

)18()58)(1(

)2))(1(22(2

2

γ−γ+γ−γ+α+γ+

=+≡ LUBk

LUBi

LUB qqQ

Thus total profits for firm B from uniform pricing are

)19()58)(1(

)]1(22)[2)(1(22

22

γ−γ+γ+α+γ+γ−γ−

==Π LUB

LUB

LUB Qp

Finally, note that the equilibrium outcomes for the other asymmetric case, i.e. for (U,L)

where firm A sets a uniform price while firm B sets local prices, are directly analogous to the

above expressions.

12


4. Individual Preferences Over Pricing Policy (1)[(4)EhC Mπγγ γ= ∀+− +−

Having identified the outcomes under each of the four possible pricing policy combinations,

we are now in a position to compare the profits for each firm in order to determine each

firm’s preferences according to the different possible demand and competitive conditions.

Here, it will prove convenient to refer to the local pricing equilibrium price in each monopoly

markets as pm (≡ pLA

L j = pL

B L k = α/2) and the corresponding price in the duopoly market as pd (≡

pLA

L i = pL

B L i = (1–γ)/(2–γ)). In addition, three identities labelled as Z1, Z2 and Z3 (each defined

below) will prove important in establishing propositions relating to comparisons over the

retailers’ profits.

In order to identify each firm’s individual preference over pricing policy, we need to consider

two key profit comparisons. The first is between the firm locally pricing and uniformly

pricing when its rival is locally pricing. The second is between the firm locally pricing and

uniformly pricing when its rival is uniformly pricing. Together, the two profit comparisons

allow us to determine the preference for each firm given the position of its rival, and so

identify the (sub-game perfect) equilibrium choice of pricing policy for a given set of market

conditions (i.e. as determined by the parameter values taken by α and γ).

In what follows, we will focus on the profit comparisons regarding firm A, bearing in mind

that the profit comparisons for firm B are directly analogous.

In respect of the first comparison, taking the difference between the relevant expressions

from (8) and (19) (adapted for retailer A) and rearranging reveals:

09)1(32Y

0)2(16X

where

)20()58()2(4

]Y)2(X)1(2)][2()1(2[

422

421

22211

>γ+γ−≡

>γ−γ−≡

γ−γ−γ−α−γ−γ−α−γ−

=Π−Π ULA

LLA

The denominator in (20) is clearly positive, and thus the sign of the expression hinges on the

sign of the other two terms in square brackets. Here, we can establish that these two terms

13


can be positive or negative and that the signs do not necessarily coincide, and so when its

rival prices locally, each retailer may under particular market conditions (i.e. certain values of

α and γ) have a strict preference for uniform pricing over local pricing. This finding is

formalised in the following proposition:

Proposition 1. For α ∈ (0,1) there exists a zone in (α,γ) space for which a retailer prefers

uniform pricing when its rival is locally pricing. This zone has two boundaries. The first

boundary is given by the condition that the monopoly market price is equal to the duopoly

market price, i.e. pm = pd. The other boundary is pm = pdZ1, where Z1 ≡ X1/Y1, and this lies

above (i.e. outside) the first in (α,γ) space.

Proof. Adapting the method used in Dobson and Waterson (2005), let us take the case of firm

A (noting that firm B’s case is directly analogous). As noted above, the sign of the equation

in (20) rests on two terms. These can be re-expressed to yield two conditions, relating α and

γ, such that when either holds the value of (20) is zero. Specifically ΠLA L = ΠU

A L if α = 2(1–

γ)/(2–γ) or α = [2(1–γ)/(2–γ)]Z1. Note that the first condition amounts to pm = pd while the

second is pm = pdZ1. Next, observe that Z1 takes a value strictly greater than unity as long as

γ ∈ (0,1). This follows since X1 – Y1 = 8γ2(2–γ2) > 0. Thus these two loci divide the profit

space in dimensions (α, γ) into three segments. Expression (20) must take on either a positive

or a negative value in each of these segments. Further, by simple substitution, of (α, γ) values

(0,0) and (1,1), we see that in the lowest and uppermost segments, the expression is positive.

Next note that the expression is strictly convex with respect to α since ∂2(ΠLA L – ΠU

A L )/∂α2 =

Y1/[2(8–5γ2)2] > 0. Hence in the middle section, the expression is negative. Q.E.D.

We can gain some insight into the nature, shape and extent of the zones where uniform

pricing or local pricing might be preferred by the chain-store when its rival prices locally by

observing the form and position of the two boundary lines in (α,γ) space. First, note that the

lower, inner boundary, where pm = pd, is strictly downward sloping and strictly concave to the

origin (α = γ = 0), since dpd/dγ = –2/(2–γ)2 < 0 and d2pd/dγ2 = –4/(2–γ)3 < 0. The upper,

outer boundary is also strictly downward sloping as d(pdZ1)/dγ = – I/[(2–γ)2(32–32γ2+9γ2)2],

14


where the identity labelled I is signed positively since I ≡ 1024–2048γ+1536γ2+1536γ3–

3072γ4+576γ5+944γ6–352γ7–9γ8 = 64(1–γ)(16–16γ+8γ2+32γ3–16γ4–7γ5) + γ6(496–352γ–9γ2)

> 0, so the whole expression is negative. Furthermore, by evaluating at the opposite extreme

values of α and γ, we can observe that these two boundary lines converge in the limit, i.e.

where α 1, γ 0 and α 0, γ 1.

The second relevant profit comparison for each firm is between local and uniform pricing

when its rival is uniform pricing. For firm A, this is the difference between (17) and (14).

Upon rearrangement this yields the following expression:

09)4595)(1(]774864384256[)1(

1652105262208448128256Y

0]15)48)(1(16)[(2()1695192128)(2(X

where

)21()]24)(58(2)[2(

]Y)2(X)1(2)][2()1(2[

75454322

7654322

44226422

22222

>γ+γ+γγ−+γ+γ+γ−γ+γ+γ−=

γ+γ−γ−γ+γ+γ−γ−≡

>γ+γ+γ−γ−γ−=γ−γ+γ−γ−≡

γ−γ−γ−γ−γ−α−γ−γ−α−γ−

=Π−Π UUA

LUA

As with the previous profit comparison, (20), the sign of the expression in (21) hinges on the

sign of the other two numerator terms in square brackets, which can be positive or negative.

As before, preference can exist for uniform pricing over local pricing:

Proposition 2. For α ∈ (0,1) there exists a zone in (α,γ) space for which a retailer prefers

uniform pricing when its rival is uniform pricing. This zone has two boundaries. The first

boundary is given by the condition that the monopoly market price is equal to the duopoly

market price, i.e. pm = pd. The other boundary is pm = pdZ2, where Z2 ≡ X2/Y2, and this lies

above (i.e. outside) the first in (α,γ) space.

Proof. By exactly the same method as the proof to Proposition 1, observing that ΠLA U = ΠU

AU

if pm = pd or pm = pdZ2, where Z2 > 1 for γ ∈ (0,1) since X2 – Y2 = 2γ2(4 – γ – γ2)(8 – 5γ2) > 0,

and that ∂2(ΠLA U – ΠU

AU )/∂α2 = 2(2–γ)Y2/[2(8–5γ2)(4–γ–2γ2)]2 > 0. Q.E.D.

15


Once more, some insight into the shape and extent of the zones where uniform pricing or

local pricing might be preferred can be gained from observing the positions and form of the

two boundary lines. Again, the inner boundary is downward sloping and concave to the

origin in (α,γ) space, while it can also shown that the outer boundary is downward sloping

and that both boundaries again converge in the limit at opposite extremes of α and γ, i.e.

where α 1, γ 0 and α 0, γ 1.

Thus ostensibly, the zones supporting individual preferences for uniform or local pricing

appear very similar. In particular, Propositions 1 and 2 taken together establish that a firm

may have an individual preference for uniform pricing regardless of its rival’s choice for

certain values of α and γ. In addition, though, comparing the boundary conditions from the

two profit comparisons, represented by (20) and (21), allows us to establish the following

important result:

Proposition 3. The scope for (individually) preferring uniform pricing is greater when the

rival chain-store retailer is using local pricing rather than uniform pricing.

Proof. Noting that (20) and (21) each yield two equality conditions and that, in terms of (α,γ)

space, the inner boundary for both is the same, i.e. pm = pd, proof amounts to showing that the

outer boundary for the former lies outside of the latter. This will be the case if Z1 > Z2.

Observing that both identities and their components are signed positive, it follows that if

X1Y2 – X2Y1 > 0 then Z1 – Z2 > 0. This is indeed the case as X1Y2 – X2Y1 = 4γ2(1–γ2)(8–

5γ2)[64–48γ–64γ2+40γ3+17γ4–8γ5] = 4γ2(1–γ2)(8–5γ2)[8(1–γ)(2–γ2)(4+γ–γ2)+γ4] > 0, noting

that all bracketed terms are positive. Q.E.D.

To put some colour on these results, it is useful to consider the nature of the averaging effect

that uniform pricing offers in comparison to local pricing. If a firm were a monopolist in

each of its markets, then it would always be preferable to use local pricing to exploit

differences in local demand levels and earn the local monopoly profit in each instance. If

instead the monopolist decided to use a uniform price it would in effect be raising the price in

its low-demand markets while cutting the price in its high-demand markets. By the very fact

16


it would have already been maximising its profits in every possible instance, such a move

could be expected to reduce its profits in each of its markets. This is borne out in the present

setting when γ = 0, as here the retailers’ services are viewed as demand independent in the

duopoly market. Then, as evident from (20) and (21), regardless of the choice made by its

rival, each firm’s profit would always be higher under local pricing so long as there was a

difference in demand levels to exploit (i.e. for α < 1).

In contrast, when the firms’ services are not everywhere demand independent, but compete

with each other when they are present in the same market, then a strategic motive may exist

for adopting uniform pricing. Specifically, a firm may be willing to sacrifice its freedom to

price discriminate and losing some profits in one market if it can be compensated by higher

profits in another market. This becomes possible if a visible, irreversible commitment to

uniform pricing influences the behaviour of a rival in such a way as to dampen the

competition between them when they compete in the same market.15 Thus, if the firm could

commit to a uniform pricing policy that would mean that would necessarily entail it setting a

higher price, it could induce a rival competing in the same market also to raise its price.

However, while the softened competition might raise profits in that market, this could only

come about from a lower price in another market that would likely reduce its profit in that

market. Nevertheless, Propositions 1 and 2 show that circumstances can exist where the net

effect can be to raise the firm’s combined profits by choosing a uniform pricing policy.

So what market conditions are most likely to justify making a commitment to uniform

pricing? The first thing to observe is that uniform pricing would never be profitable if pm <

15 In all of this, for uniform pricing to influence the rival’s pricing behaviour in the desired manner, it must be through a visible, irreversible commitment to avoid a “cheap talk” problem where the rival does not believe that the firm will stick to a uniform pricing policy when it comes to setting individual prices, instead simply reverting to local pricing. This is “cheap talk” aspect is a common problem with pricing commitment strategies designed to soften competition – such as price-matching promises and most-favoured-customer clauses (e.g. Salop (1986), Cooper (1986), and Besanko and Lyon (1993)). In the present context, Dobson and Waterson (2005) discuss examples of the forms of commitment that a chain-store retailer may make to uniform national pricing. These include making an expensive commitment that would render its position worse were it not to adopt uniform pricing than it if did so – such as publishing all prices in a catalogue which then applies across the whole country with no scope for local price deviations, using national advertising to inform consumers about prices, or using of integral price tags standard across a country. In addition, Corts (1998) cites the required commitment of retailers pursuing strategies based on providing “every day low prices”, where price consistency across markets and over time is a critical feature.

17


pd. The reason for this is that the averaging effect of a uniform price would be to raise the

price set in the monopoly market and lower it in the contested duopoly market. Yet, we

know that profit cannot be raised in the monopoly market by raising price, since it is already

maximised by pm. In regard to the duopoly market, a commitment to a uniform pricing

policy, far from dampening competition, would in fact serve to intensify competition as the

firm’s compensating lower price would induce the rival to respond to lower its price as well.

Accordingly, the firm is likely to be faced with the “double whammy” of lower profits from

both its markets if it commits to a uniform pricing policy in these circumstances.

Furthermore, we can note that this condition applies to a wide range of parameter space,

notably when α and γ take on low values, given that, as noted above, the boundary condition

pm = pd is downward sloping and concave to the origin in (α,γ) space, ranging from co-

ordinates (1,0) towards (0,1).

Thus, if there is a prospect of a firm preferring uniform pricing, it must be the case that pm >

pd, as here the averaging effect would mean lowering the monopoly price but raising the

duopoly price. However, the greater the relative gap between the firm’s (higher) monopoly-

market price and its (lower) duopoly-market price when it uses local pricing then the less

inclined the firm will be to make this sacrifice and instead adopt uniform pricing. To see this,

note that such a price gap is particularly pronounced when α and γ both take on high values.

Similarly, the gap in profits made in the two markets will be pronounced. In this case, to

soften competition in the duopoly market, in order to allow it to earn higher profits there, the

firm would need to commit to raising its price considerably to induce its rival to respond by

raising its price significantly. Nevertheless, inducing a correspondingly positive price

response from its rival becomes less likely the higher is the value of γ, since the more

substitutable the services are perceived to be then the less the rival would need to raise its

price in order to increase its own profits as it could simply use the price differential to attract

significantly more demand (at the other retailers’ expense).

In other words, when γ is high, all that a commitment to uniform pricing would do is to

provide its local-pricing rival with a “pricing umbrella” under which it could set a lower price

so as to take custom away from the firm to its own benefit, with little or nothing gained by

18


the firm making the uniform-pricing commitment. Thus, if the firm can earn high profits

from its monopoly market by local pricing, it would be better off not sacrificing these to try

to dampen competition in what is naturally an intensely competitive duopoly market. The

obvious analogy is avoiding the problem of “throwing good money after bad money”.

This tendency for high values of α and γ to limit the scope for a firm being prepared to adopt

uniform pricing applies regardless of whether the rival adopts local or uniform pricing. This

explains the outer boundaries relating to both Proposition 1 and 2. However, these effects are

somewhat tempered if the rival is adopting uniform pricing since here the firm is aware that

its rival is also prepared to commit to a higher price in the duopoly, hence explaining the

finding expressed in Proposition 3. Though, the flip side of this is that the tendency to want

to free ride on a rival’s commitment to uniform will be stronger the greater the monopoly-

profit sacrifice that it would be needed if it were to make a similar commitment.

Accordingly, with independent choices of pricing policy we should expect the scope for

committing to uniform pricing, in the absence of being sure that the rival is likely to match

this commitment, as being a further limiting factor in support of uniform pricing.

All of this suggests that uniform pricing is only likely to arise as an independent commitment

when competition in the duopoly can be suitably softened without too much of a drop in the

monopoly-market price (e.g. when pm is only slightly above pd) and when the tendency to

free ride is small as a consequence of a similar need and ability to dampen competition

suitably (e.g. for mid-high values of both α and γ).

Nevertheless, an important corollary of Propositions 1-3 is that market conditions exist which

separately support all three possible pricing policy configurations, i.e. the two symmetric

configurations where both adopt uniform pricing or both adopt local pricing, along with the

asymmetric configuration where one adopts uniform pricing and the other adopts local

pricing.

The equilibrium pricing policy configurations that emerge from this analysis are perhaps best

illustrated diagrammatically. For this purpose, Figure 1 shows the preferences of the firms in

19


(α,γ) space. Here, as indicated by Propositions 1–3, we have three distinct, non-crossing

boundaries, shown as solid lines, dividing (α,γ) space into four zones. The symmetry

assumption means that the same preference structure holds for both firms, so that the diagram

is identical whether we are considering firm A’s or firm B’s preferences.

The equilibrium pricing-strategy choices follow directly from the position of the three

boundary lines. Both retailers prefer adopting local pricing below the lower boundary, where

pm < pd, and above the upper boundary, where pm > pdZ1, hence the outcome (L,L) in these

two zones. Between these two boundary lines, we have two zones separated by a middle

boundary line, pm = pdZ2. In the lower of these two zones, that is where pm > pd and both pm <

pdZ1 and pm < pdZ2, then both firms would individually prefer to commit to uniform pricing,

irrespective of the rival’s choice, as this offers each of them higher profits than locally

pricing, hence the outcome (U,U). However, in the upper of these two zones, where pm > pd

and pm < pdZ1 but pm > pdZ2, each retailer is better off doing the opposite of its rival. In other

words, we have an asymmetric (sub-game perfect) equilibrium zone where one firm would

prefer committing to uniform pricing if the other firm locally priced, but it would prefer

locally pricing if the other firm committed to uniform pricing, i.e. (U,L) or equivalently (L,U)

applies. Nevertheless, in this “chicken game” situation, each firm would prefer its rival to

adopt uniform pricing while it adopted local pricing, as this offers higher profits as

demonstrated by the following result:

Proposition 4. In the asymmetric pricing policy equilibrium zone, the profits for the chain-

store retailer using local pricing exceed those of the rival retailer adopting uniform pricing.

Proof. The result follows directly from the comparison of profits for a firm under (L,U) as

opposed to (U,L). For either firm, this means comparing expressions (17) and (19). Taking

the case of firm A for illustration, after some rearrangement this profit comparison reveals

02Yand,02Xwhere

)22()58)(2(4

]Y)2(X)1(2)][2()1(2[

33

233

>γ+≡>γ−≡γ−γ−

γ−α−γ−γ−α−γ−=Π−Π UL

ALUA

20


As with the first two profit comparisons, i.e. (20) and (21), the sign of the expression in (22)

hinges on the sign of the other two numerator terms in square brackets, which can be positive

or negative. Again, using the method in the proof to Proposition 1, the two conditions,

relating α and γ, for ΠLA U = ΠU

AL are pm = pd while the second is pm = pdZ3, where Z3 ≡ X3/Y3.

Observe, though, that Z3 < 1 for γ ∈ (0,1). This follows since X3 – Y3 = – 2γ < 0. Thus the

two loci divide the profit space in dimensions (α, γ) into three segments, with pm = pd lying

above pm = pdZ3, with the latter shown as a dotted line in Figure 1. By simple substitution, of

(α,γ) values (0,0) and (1,1), we see that in the lowest and uppermost segments, the expression

is positive. Also, observe that the expression in (22) is a quadratic function in respect of α

and is strictly convex in this respect, i.e. ∂2(ΠLA U – ΠU

AL )/∂α2 > 0, hence the expression must be

negative in the middle section. Finally, note that the expression is positive when pm > pd,

which applies for the asymmetric equilibrium zone, as shown in Figure 1. Q.E.D.

The implication of Proposition 4 is that in the asymmetric equilibrium zone there is likely to

be a co-ordination problem (with each retailer preferring local pricing while its rival

uniformly prices) when the firms simultaneously make their choice over pricing policy. The

only escape from this (at least in pure strategy terms) is for one of the firms to commit both

credibly and visibly to its pricing policy in advance of its rival. In this case there would be a

first-mover advantage from committing to local pricing, leaving the rival to commit to

uniform pricing. In the absence of sequential commitments, though, the co-ordination

problem points to each firm adopting a mixed strategy approach, as usual in such “chicken”

circumstances, when moves are made simultaneously by the players.

5. Joint Preferences Over Pricing Policy

The analysis in the last section shows that there is scope for a firm to commit profitably to

uniform pricing. However, a firm would only be willing to give up the ability to price

discriminate across its local retail markets if the profit sacrifice from its monopoly market

were not too great to dampen competition suitably in the duopoly market. The free-rider

problem associated with independent choices, though, restricts this prospect since a firm

21


making this commitment effectively provides an attractive pricing umbrella for its rival, who

is then able to benefit from this without necessarily having to make the same commitment in

return.

This suggests that it is possible for circumstances to arise where the firms are caught in a

prisoners’ dilemma situation, with each preferring the other to commit to uniform pricing but

each not prepared itself to commit to such a policy, even though both of them could be better

off if they both made such a commitment.

For certain, this is only likely to apply to certain market circumstances. For example, it could

be expected that it would still be the case that local pricing would offer firms higher profits

when this meant that prices were higher in the duopoly market than in the monopoly markets.

This is on the same principle expounded above that the balancing effect of uniform pricing

would be to raise the monopoly-market price to no beneficial effect (as the local monopoly

profit would have already been achieved) while lowering the duopoly-market price, which

would simply serve to intensify competition and destroy profits in that market. Equally, it

could be expected that when the gap between a high monopoly-market price and a low

duopoly-market price was too great, firms would still not find it jointly preferable to sacrifice

their high monopoly profits for the sake of dampening price competition in the duopoly

market. Nevertheless, at the margin, it might be possible for joint preferences to allow for

greater scope in favour of uniform pricing (i.e. as long as α and γ are not “too high”).

The above intuition is supported by a comparison between the firms’ joint profits when they

both use local pricing as opposed to when they both use uniform pricing. Using (8) and (14),

the difference between the combined profits of firms A and B when they both use local

pricing compared to when they both use uniform pricing is:

0)1)(1(3)1(5Y

058X

where

)23()24()2(2

]Y)2(X)1(2)][2()1(2[)()(

324

24

22244

>γ+γ−γ−+γ−≡

>γ−≡

γ−γ−γ−γ−α−γ−γ−α−γ−

=Π+Π−Π+Π UUB

UUA

LLB

LLA

22


Using this comparison, we can then establish the following proposition concerning joint

preferences for both retailers’ adopting uniform pricing as opposed to both adopting local

pricing:

Proposition 5. For α ∈ (0,1), a zone exists in (α,γ) space for which the retailers jointly prefer

both of them adopting uniform pricing over both of them adopting local pricing, as defined

by two non-overlapping boundaries, the inner one in (α,γ) space being pm = pd and the outer

one being pm = pdZ4, where Z4 ≡ X4/Y4. Furthermore, this upper/outer boundary lies above

the two upper boundaries for private preferences towards uniform pricing as established in

Propositions 1 and 2.

Proof. The existence of the zone where uniform pricing is jointly preferred and the nature of

its two boundaries follow directly from the method used as the proof for Proposition 1,

observing that (ΠLA L + ΠL

B L ) = (ΠU

A U = ΠU

BU ) if pm = pd or pm = pdZ4, where Z4 > 1 for γ ∈ (0,1)

since X4 – Y4 = 8γ – 2γ2 – 4γ3 > 0, and that ∂2(ΠLA L +ΠL

B L – ΠU

A U – ΠU

BU )/∂α2 = Y4/[(4–γ2–2γ2)]2

> 0. Next, from Proposition 3 we know that the upper boundary for privately preferring

uniform pricing when the rival is uniform pricing (i.e. pm = pdZ1) lies, in (α,γ) space, strictly

above and outside that corresponding to when the rival adopts local pricing (i.e. pm = pdZ2),

this follows since Z1 > Z2. Accordingly, to conclude the proof we are required to show that

Z4 > Z1. This is the case since X4Y1 – X1Y4 = 4γ(2–γ)(2–γ2)[16–4γ2–10γ2+γ3] > 0. Q.E.D.

The implication of Proposition 5 is that if it were possible for there to be joint agreement on a

common pricing policy, then this would extend the scope for which uniform pricing would be

chosen compared to when firms had to make unilateral commitments. Figure 2 shows this

result in diagrammatic form, where the outer boundary for joint preferences over uniform

pricing, indicated by pm = pdZ4, lies above and to the right of the private preference outer

boundaries, respectively pm = pdZ1 and pm = pdZ2, shown as dashed lines. As the diagram

illustrates, the area where uniform pricing is jointly preferred, labelled (U*,U*), extends

particularly to higher values of α, as well as higher values of γ. Correspondingly, the upper

zone where local pricing is jointly preferred, i.e. the upper (L*,L*) zone in Figure 2, is

23


considerably smaller in size than the equivalent area in Figure 1 where symmetric local

pricing emerges under individual preferences.

Accordingly, we can see that circumstances might arise where it would be in the mutual

interest of the firms to act jointly in determining a common pricing policy of uniform

pricing.16 However, this still begs the question of how in practice they could secure this

outcome and overcome the prisoners’ dilemma nature of the situation.

Indeed, the situation can be considered as one of the firms seeking to undertake “partial

collusion”, in the sense of the firms agreeing over a pricing policy but not individual prices.

In a related context involving collusion over relative prices, Winter (1997) cites situations

where firms have made formal agreements to limit the extent to which they price discriminate

between different groups of consumers (distinguished by their price sensitivity), in relation to

discounts offered through coupons, but not the product prices themselves. He argues that

there may be practical reasons that support this form of partial collusion, since it is likely to

be the case that it is relatively easier to observe and monitor each other’s general pricing

policy clearly more difficult to monitor individual prices when each stocks several thousand

product lines.

However, in the event that legally binding agreements are not permitted for such partial

collusion (and all the agreements that Winter cites have been struck down by the courts on

price-fixing grounds), firms would have to resort to tacit collusion. While beyond the scope

of the present paper and its one-shot game framework, it is clearly possible that, in a dynamic

context, tacit partial collusion may be feasible as it might prove relatively easy to monitor

16 There are, of course, two other profit comparisons we could consider involving comparisons between the asymmetric case and each of the two symmetric cases. Analysis of these – with details available upon request from the authors – shows that profits in the asymmetric case are always dominated by both firms either using uniform pricing or both using local pricing. In particular, the corresponding outer boundaries for (ΠL

A L + ΠL

B L ) =

(ΠLA U + ΠU

B L ) and (ΠL

A U + ΠU

B L ) = (ΠU

A U = ΠU

BU ) lie, respectively, marginally to the left and marginally to the right of

pm = pdZ4, while having the same inner boundary of pm = pd. We should also add, that in respect of practicality, the firms are only likely to be interested in considering their joint preferences towards symmetric choices, given that an asymmetric choice would (as Proposition 4 demonstrated) likely lead to conflict over which retailer would be prepared to adopt uniform while the other adopted local pricing, which in the absence of side-payments can be expected to create an ongoing tension, meaning that it would be difficult to sustain an agreement between the firms on the matter.

24


each other’s general pricing policy, and in particular to see whether appropriate commitments

to uniform pricing have been undertaken and are being maintained. For example, it may be

possible that such tacit collusion could be engineered through trigger or stick-carrot type

strategies.

An alternative means of achieving the same outcome would be for the firms to be jointly

obliged to set uniform prices by an outside body.17 For instance, a competition authority

which required the retailers not to price discriminate and instead to offer uniform national

prices could, perhaps unwittingly, allow the firms to achieve this outcome when the firms

could not achieve this by themselves. Indeed, it is possible that even a signal (or veiled

threat) from a competition authority, that it was unhappy with third-degree price

discrimination being practiced against geographically constrained consumers, might provide

the necessary impetus for firms collectively to adopt uniform pricing.18

6. Consumer Welfare

Thus far we have only considered the preferences of the firms competing in the market.

Clearly, the choice of pricing policy, which can alter the balance of prices in the markets,

may have an impact on consumers and thereby social welfare. To consider the welfare

effects of the chain-stores’ choices over pricing policy, we focus here on consumers’

interests, assessing the effects on (aggregate) consumer surplus and commenting briefly on

the impact on net economic welfare.

17 Producers supplying the retailers are unlikely to be able to achieve this (even they wanted to and had the power over retailers to make them comply) since such a move would likely be regarded as an attempt to set or influence resale prices, which in most countries might be regarded as illegal if were viewed as amounting to resale price maintenance. See Chen (1999) for a full analysis. 18 In this context, as remarked in the Introduction, the requirement for the major UK supermarket retailers to set uniform national prices was considered but rejected by the Competition Commission in 2000. However, by designating local price flexing as anticompetitive and against the public interest, there has been a subsequent change in the stance by those retailers using the practice, either through a shift to national pricing for stores catering for the one-stop-shop grocery market or a lessening on the extent of the goods price flexed as became evident in the submissions made to the Competition Commission (2003) inquiry on the contemplated mergers involving Safeway.

25


Given that choice is fixed, consumers would naturally prefer the lowest possible prices in

their respective markets. In the present setting, consumers in the different markets may be

expected to have divergent interests in respect of the pricing policies used by the two chain-

store retailers. As pm rises above pd, the uniform price charged by a retailer becomes lower

than the monopoly market price but higher than the duopoly market price. Thus, in its

smaller, less affluent “town” market, consumers are worse off with local pricing, whereas in

the large/affluent “city market they are better off with local pricing. Clearly, whichever

policy each retailer ultimately decides on, consumers in those markets where price is lowered

(compared to what would emerge under an alternative pricing regime) would benefit, while

the other consumers would lose out. Accordingly, there is unlikely to be unanimity of

preferences amongst consumers.19

To consider the overall impact on consumers we examine the respective levels of aggregate

consumer surplus under each pricing regime, recognising that different consumer groups will

likely have different preferences but looking at the net difference as an unweighted

aggregation of the different consumer utility functions. Specifically, aggregate consumer

surplus, S, is taken as the sum of the (constrained) representative consumer utility functions

over the three markets (i.e. respectively over Vi(qAi,qBi), Vj(qAj) and Vk(qBk)):

)24(])([])([

]))(2)(([2

212

21

2221

BkBkkBkBkAjAjjAjAj

BiBiAiAiiBiBiAiAiBiAi

qpmqqqpmqq

qpqpmqqqqqqS

−+−α+−+−α+

−−++γ+−+=

Evaluating the terms with respect to the different equilibrium values when both firms adopt

local pricing and when they both adopt uniform pricing, the aggregate consumer surplus in

each respective case, i.e. SLL and SUU, while abstracting from any income effects, is:

)25(4/])2)(1/[(1 22 α+γ−γ+=LLS

)26(])24)(1[(

)]36710)(1()36)(1(241310[22

432222432

γ−γ−γ+÷

γ+γ+γ−γ−γ+α+γ−γ−γ−α+γ+γ+γ−γ−=UUS

19 This finding fits with Corts’ analysis, principally his Proposition 3 (1998, p. 315).

26


Taking the difference between the two levels and rearranging reveals:

0892024Y

04111224X

where

)27()24()2(4

]Y)2(X)1(2)][2()1(2[

32

32

222

>γ+γ−γ−≡

>γ+γ−γ−≡

γ−γ−γ−γ−α−γ−γ−α−γ−

−=−

S

S

SSUULL SS

As with the profit comparisons, the sign of the above expression rests on the sign of the term

in square brackets on the numerator in the first part of the equation and the square bracketed

term in the second part of the equation. The following proposition establishes the market

conditions where aggregate consumer surplus is higher depending on the choice by both

firms of local pricing or uniform pricing:

Proposition 6. For α ∈ (0,1) there exists a zone in (α,γ) space for which aggregate consumer

surplus is greater under local pricing. This zone has an inner boundary where pm = pd while

the other boundary, pm = pdZS, where ZS ≡ XS/YS, lies strictly above (i.e. outside) the first. On

the other side of these boundaries, uniform pricing by both firms offers higher aggregate

consumer surplus.

Proof. The proof is on the same basis as that to Proposition 1. Specifically, we find that SLL

= SUU if α = 2(1–γ)/(2–γ) or α = 2(1–γ)XS/[(2–γ)YS], with the former condition amounting to

pm = pd and the latter to pm = pdZS. Then, observe that ZS > 1 for γ ∈ (0,1), since XS – YS = 8γ

– 2γ2 – 4γ3 > 0. Thus, the second condition requires higher values of α for it to hold when

compared to the first condition. Next, evaluate the surplus comparison with the extreme

values of α and γ and observe that ∂2(SLL–SUU)/∂α2 = – YS/[2(4–γ2–2γ2)2] < 0, hence the

expression is strictly concave with respect to α. It then follows that the zone which supports

SLL > SUU applies where α,γ ∈ (0,1) with pm = pd operating as the lower boundary and pm =

pdZS as the upper boundary. Q.E.D.

27


As with the profit comparisons, conditions on the nature and shape of these boundaries can be

readily identified. The inner boundary is, of course, the same as before where pm = pd, i.e.

strictly downward sloping and concave in (α,γ) space. The outer boundary can be shown to

be strictly downward sloping and concave. Furthermore, the two boundaries converge at

opposite extremes of the parameter space, i.e. as α 1, γ 0 and α 0, γ 1.

It might be considered that firms’ preferences might be directly at odds with consumers’

preferences, at least as measured in respect of aggregate consumer surplus. However, this is

not the case as the following proposition establishes:

Proposition 7. (a) For pm < pd then firms’ individual and joint preferences over pricing policy

are directly at odds with those of consumers. (b) For pm > pd, firms’ individual choice of

pricing policy leading to (U,U) or (U,L) is always at odds with consumers’ aggregate

preference, but for (L,L) some market conditions exist where there is a shared preference. (c)

For pm > pd, firms’ joint/coordinated choice of pricing policy leading to (L*,L*) is always at

odds with consumers’ aggregate preference, but for (U*,U*) some market conditions exist

where there is a shared preference.

Proof. (a) By direct reference to Propositions 1, 2, 5 and 6. (b) By reference to Propositions

1, 2, 3 and 6, taking note that ZS > Z1 so that the boundary pm = pdZS lies above the boundary

pm = pdZ1 in (α,γ) space. (c) By reference to Propositions 5 and 6, taking note that ZS < Z4 so

that the boundary pm = pdZS lies below the boundary pm = pdZ1. Q.E.D.

Proposition 7(a) makes immediate sense in view of the effect that uniform pricing has in

these circumstances as by comparison with local pricing, the averaging effect intensifies

competition in the duopoly market, resulting in lower prices to the benefit of consumers,

while raising prices in the monopoly markets but where consumer surplus is low anyway.

The mutual preference for local pricing expressed in Proposition 7(b) is explained by the

prisoners’ dilemma situation that the firms face, jointly wishing to coordinate on uniform

pricing but not prepared to commit unilaterally to such a policy, thereby leading to lower

prices in the duopoly market for the benefit of consumers overall. In contrast, the mutual

28


preference for uniform pricing expressed in Proposition 7(c) relates to the sizeable gains in

surplus that consumers in the monopoly market make through the averaging effect of uniform

prices, which more than offsets the reduced surplus that consumers in the duopoly market

suffer.20

Figure 3 illustrates the results from Propositions 6 and 7 with (α,γ) space divided into three

zones by the two solid line boundaries pm = pd and pm = pdZS . Here consumers collectively

prefer uniform pricing if α and γ both take low to moderate values or very high values,

represented by zones U1 and U2. Aggregate consumer preferences for local pricing are

restricted to a small zone L for other values of α and γ. The relevant profit boundaries are

marked with dotted lines, to show those areas where mutual preferences arise and those areas

where firms and consumers are likely to have conflicting preferences, as demonstrated by

Proposition 7.

Clearly, we could go on from here to identify the sum effect on social welfare, measured for

example as the sum of aggregate consumer surplus and profits, without regard to distribution.

However, since the functional forms used are clearly special, not much purpose will be

served by doing so. We have identified certain market circumstances where there may be

mutual preferences, so that social welfare will be in line with firms’ decisions. Equally, we

have shown there will be opposing effects for a range of other market circumstances, so the

sum impact will depend upon the details of the model, rather than there being any general

implications. It is very likely that areas where there is a conflict between the firms’ pricing

policy preferences and societal preferences will exist, principally when aggregate consumer

surplus is considerably disadvantaged.

20 See Winter (1997) for further analysis and insights on why firms’ joint preferences for limiting or removing third-degree price discrimination across markets may be in line with total welfare.

29


7. Conclusion

Even with the simple scenario examined in this paper, it is clear that price flexing, as a form

of third-degree price discrimination over geographically constrained consumers, is a complex

issue. Unlike pure monopoly situations where local pricing would always be the preferred

pricing policy for separate retail markets, in oligopoly situations a strategic motive may exist

to sacrifice profits in a “strong” (non-competitive) market to increase them in a “weak”

(competitive) market. However, as shown in this paper, the incentive is limited when the

private cost to a firm doing this on its own is that it is providing a pricing umbrella for its

rival to exploit. Accordingly, the market conditions where both firms would independently

use uniform pricing are shown to be very limited. Yet, it is possible that the incentive for

undertaking this could still be sufficiently strong to encourage one firm on its own to make

this commitment while the other adopted local pricing. Thus it is possible for symmetric and

asymmetric equilibrium configuration to arise involving both firms or just one firm adopting

uniform pricing.

However, these dampened incentives and co-ordination problems that limit uniform pricing

would be alleviated if the firms could collude over the pricing policy. Here our model shows

that the scope for jointly choosing uniform pricing would increase significantly. This could

be viewed as a form of “partial collusion”, whereby firms (tacitly) agree to the same pricing

policy (i.e. local pricing or uniform pricing) but then independently set individual prices. The

problem for any investigating authority would then, in the absence of an overt agreement, be

to determine whether the choice of pricing policy was made on an individual or joint basis –

something that may prove difficult in practice given the different positions on the matter from

one retail sector to another.

Yet, in regard to welfare, even though a strategic motive to dampen competition may lie

behind the choice of uniform pricing or equally the ability to exploit geographically

constrained consumers with local pricing, it does not mean that the preferences of firms and

consumers are always out of line. Indeed, with unilateral choices of pricing policy it is

possible for both firms and consumers to benefit from local pricing for some parameter

30


values shown in our model. Equally, for joint choices of pricing policy (i.e. partial collusion)

it is possible for the choice of uniform pricing to be in both firms’ and consumers’ interests.

What does this mean for competition policy? First, our analysis indicates that it cannot

necessarily be assumed that price flexing is an anti-competitive practice in an oligopoly

setting. Secondly, forcing firms to set uniform prices may be worse for consumers than

leaving firms to set prices on a local basis. However, going beyond this to draw policy

conclusions regarding particular market circumstances represented by our model is clearly

not appropriate. While our model provides some indication of the circumstances where

firms’ choices and social welfare are likely to be in or out of line, there are important

limitations of our analysis that should be borne in mind. In particular, our analysis does not

take account of the kinds of cost and retailer preference asymmetries that tend to govern most

real markets, for example allowing for the possibility that price flexing may simply be down

to local cost and consumer preference differences, with prices tailored to suit better local

conditions and needs. Equally, though, our model does not take account of price flexing

serving a predatory motive when used against small firms to undermine their competitive

position, especially when linked with persistent below cost selling. Such aspects are worthy

of more attention and offer interesting avenues for future research.

31


REFERENCES Armstrong, M. and Vickers, J. (2001), “Competitive Price Discrimination”, RAND Journal of Economics, Vol. 32(4), pp. 579-605. Besanko, D. and Lyon, T.P. (1993), “Equilibrium Incentives for Most-Favoured Customer Clauses in an Oligopolistic Industry”, International Journal of Industrial Organization, Vol. 11(3), pp. 347-367. Bresnahan, T.F. and Reiss, P. (1987), “Do entry conditions differ across markets?” Brookings Papers on Economic Activity, 1977:3, pp. 833-81. Chen, Y. (1999), “Oligopoly Price Discrimination and Resale Price Maintenance”, RAND Journal of Economics, Vol. 30 (3), pp. 441-455. Competition Commission (2000), Supermarkets: A report on the supply of groceries from multiple stores in the United Kingdom, Cm 4842, TSO: London. Competition Commission (2003), Safeway plc and Asda Group Limited (owned by Wal-Mart Stores Inc); Wm Morrison Supermarkets PLC; J Sainsbury plc; and Tesco plc: A Report on the Mergers in Contemplation, Cm 5950, TSO: London. Cooper, J.C., Froeb, L., O’Brien, D.P., and Tschantz, S. (2005), “Does Price Discrimination Intensify Competition? Implications for Antitrust”, Antitrust Law Journal, Vol. 75 (2), pp. 327-373. Cooper, T.E. (1986), “Most-Favored-Customer Pricing and Tacit Collusion”, RAND Journal of Economics, Vol. 17, pp. 377-388. Corts, K.S. (1998), “Third-Degree Price Discrimination in Oligopoly: All-Out Competition and Strategic Commitment”, RAND Journal of Economics, Vol. 29, pp. 306-323. Dalkir, S. and Warren-Boulton, F.R. (1999), “Prices, Market Definition, and the Effects of Merger: Staples-Office Depot (1997)”, in J.E. Kwoka and L. White (eds.), The Antirust Revolution: Economics, Competition and Policy, 3rd Edition, Oxford University Press: Oxford. Dobson, P.W., and Waterson, M. (2005), “Chain-store pricing across local markets”, Journal of Economics and Management Strategy, Vol. 14 (1), pp 93-119. Holmes, T.J. (1989), “The Effects of Third-Degree Price Discrimination in Oligopoly”, American Economic Review, Vol. 79, pp. 244-250. MMC (1997a), Domestic Electrical Goods I: a report on the supply in the UK of television, video cassette recorders, hi-fi systems and camcorders, Monopolies and Mergers Commission, Cm 3675, TSO: London.

32


MMC (1997b), Domestic Electrical Goods II: a report on the supply in the UK of washing machines, tumble dryers, dishwashers and cold food storage equipment, Monopolies and Mergers Commission, Cm 3676, TSO: London. Salop, S. (1986), “Practices that (credibly) facilitate oligopoly coordination”, in J. Stiglitz and G. Mathewson (eds), New Development in the Analysis of Market Structure, MIT Press: Cambridge, MA. Stole, L.A. (2005), “Price Discrimination and Imperfect Competition”, in M. Armstrong and R. Porters (eds.) Handbook of Industrial Organization Vol. 3, Elsevier: Amsterdam. Winter, R.A. (1997), “Colluding on relative prices”, RAND Journal of Economics, Vol. 28(2), pp. 359-371.

33


Figure 1 – Equilibrium pricing policy configurations

α

0

1

(L

pm=pdZ2
(L,L)
m d

{(U,L),(L,U)} (U,U)

pm=pdZ3

1

γ

pm=pd,L)

p =p Z1

34


Figure 2 – Configurations under joint preferences

α

0

1 * *

pm=pdZ

(L

pm=pdZ1

γ

2 (U

*,L*)

3

pm=pdZ4

1

pm=pd

(L ,L )

*,U*)

5


Figure 3 – Aggregate consumer preferences over pricing policy

α

0

1

pm=pdZ

(U

pm=pdZ1

γ

2

1)

(

3

pm=pdZ4

pm=pd

(U2)

L)

6

pm=pdZS

1

Documents

Price Flexing and Chain-Store Competition VI/VI.J... · Price Flexing and Chain-Store Competition beyond using the local stores or outlets.5 In these circumstances, retail markets