Market Effects of Changes in Consumers' Social Responsibility

Market Effects of Changes in Consumers’

Social Responsibility

AURORA GARCIA-GALLEGO

LEE/Economics DepartmentUniversitat Jaume I, Castellon, Spain, and

University of Cyprus, Nicosia, [email protected]

NIKOLAOS GEORGANTZIS

GLOBE-Economics DepartmentUniversidad de Granada

Granada, [email protected]

In a duopoly model of vertical differentiation, we study market equilibriumand the resulting social welfare following an increase in the consumer’s will-ingness to pay (WTP) for products sold by socially responsible manufacturers.Different types of such changes emerge depending on their effects on consumerheterogeneity. We show that, in most cases, increases in the consumers’ socialconsciousness yield higher profits to socially responsible firms and may leadto higher levels of social welfare, provided that the market structure is leftunchanged. However, when an increase in the consumer’s social consciousnesschanges the market structure, welfare may fall, while the duopolists’ profits rise.The resulting tension between private and social interest calls for a cautiousattitude toward information campaigns aimed at increasing the consumer’ssocial consciousness.

1. Introduction

In modern societies, people are increasingly aware of the impact of theirconsumption choices on the quality of public goods like, for example,the environment. Ostrom (2000) suggests that such an increasing trend

A significant part of the present research was developed while the authors were visitingthe Economics Department at the University of Cyprus, whose hospitality is gratefullyacknowledged. We thank the Spanish Ministry of Education and Science (grants PR2007-0152 and PR2007-0153 and project SEJ 2005-07544/ECON) and Bancaja (project P1 1B2007-14) for financial support in different stages of the research. Comments by a referee andan associate editor of this journal triggered a substantial revision leading to a significantimprovement of the manuscript. All remaining errors are our own responsibility.

C© 2009, The Author(s)Journal Compilation C© 2009 Wiley Periodicals, Inc.Journal of Economics & Management Strategy, Volume 18, Number 1, Spring 2009, 235–262

236 Journal of Economics & Management Strategy

in the consumer’s social awareness can be explained as an evolutionaryprocess leading to the emergence and expansion of social normsfostering prosocial behavior. Benabou and Tirole (2006) illustrate severalcases of interaction between an individual’s self image and the socialnorms prevailing in the economy as a source of motivation for prosocialbehavior. A practical consequence of these analyses is that privateand public decision makers may try to affect the consumer’s socialresponsibility in order to induce the desired market outcomes. Forobvious reasons, economists have been reluctant to study changes inwelfare when preferences change. However, Stigler and Becker (1977)and Becker (1996) assume that, even when individual choices vary,the underlying preferences are stable, while people develop socialand personal capital that changes their consumption decisions overtime. Thus, the aforementioned increases in the consumers’ socialresponsibility can be seen as part of the personal and social capitalformation process.

There are several empirical studies reporting measures of con-sumers’ WTP for green products.1 A look at the most recent of themconfirms two broadly accepted facts, which are central to our analysis.First, there is an increasing trend among consumers worldwide to prefergreen products over their standard substitutes.2 Second, consumers areheterogeneous with respect to their WTP for green products.3 The issueof taste heterogeneity has been captured by most theoretical modelsstudying the role of consumers’ ecological consciousness on marketequilibrium. Approaches adopted by different authors vary in manyways, especially depending on whether consumer heterogeneity con-cerns their WTP for the ecological attribute itself, as in Moraga-Gonzalezand Padron-Fumero (2002), or some other features like their income, asin Arora and Gangopadhyay (1995) and Bansal and Gangopadhyay

1. For example, Camacho et al. (2004) compare revealed and hypothetical/statedmeasures of the consumer’s higher WTP for a recyclable office table as compared withthe standard (nonrecyclable) variety. They find that survey data are a good predictor ofa consumer’s median WTP for an improvement in the environmental performance of amarketed good.

2. Pham and Rambo (2003), Harris (2006), Suzuki et al. (2004), and Tsagarakis andGeorgantzıs (2002) use very different approaches to document the increasing trend ofecological consciousness in four different countries: Vietnam, China, Japan, and Greece,respectively. In fact, the last two explicitly deal with the role of information as a meansof increasing people’s willingness to accept costlier options favoring environmentallyfriendlier market outcomes.

3. Explicit references to the existence and the causes of such heterogeneity can befound, for example, in Blamey (1997) where willingness to pay depends on personalattributes like awareness of environmental need, consequences of and responsibility forpersonal action, and acceptance of policy initiatives. Loureiro and Lotade (2005) identifydifferent factors that may be responsible for heterogeneous valuations of products withan ecolabel. At a theoretical level, Nyborg’s (2000) framework could be used to explaindifferent levels of social consciousness as different combinations of homo oeconomicus andhomo politicus in the consumers’ utility functions.

Market Effects of Changes in Consumers’ Social Responsibility 237

(2003), or their ideal product variety, as in Conrad (2005). Taking thedistribution of consumers’ valuations as given, all of these studies focuson standard policy instruments, like minimum environmental quality,taxes and subsidies.4 To our knowledge, ours is the first normativeapproach to changing consumer attitudes5 in the context of a verticaldifferentiation model with application to markets with a public goodexternality.

Various studies, Endres (1997) among them, propose the use ofstate campaigns as a means of increasing people’s ecological awareness.However, there seems to be no systematic recognition of the effect thatsuch campaigns may have on consumer heterogeneity and its effectson the economic and overall performance of the market. An exampleof heterogeneity-reducing changes in elicited degrees of environmentalconsciousness is provided by Tsagarakis and Georgantzıs (2002), whopresent results from a survey responded before and after an informativesession on the use of recycled water for irrigation. It is found that theinformative session significantly increases the respondents’ willingnessto use recycled water. Heterogeneity among respondents is reduced,given that the information provided during the session is more effectiveamong those who had initially reported a lower willingness to userecycled water. Suzuki et al. (2004) present evidence for the contraryeffect of information contingent on people’s initial environmentalconsciousness. In their study, the informative session is more effective

4. Due to their focus on environmental quality standards, taxes, and subsidies,these papers are rather weakly related to our main argument concerning the role ofchanges in consumers’ WTP. Nevertheless, due to the similarity between ours and theirunderlying theoretical frameworks, it is worth mentioning the studies by Constantatosand Sartzetakis (1999) on environmental taxes, Motta and Thisse (1999) on environmentalquality standards, and Nadaı and Morel (1999) on ecolabeling. Recently, Innes (2006) useda product differentiation model, which is similar to ours to address the issue of consumerboycotts. Apart from Conrad’s (2005) model, Deltas et al. (2004) also develop a horizontaldifferentiation model with some vertical differentiation flavor, but as stated before bothpapers’ objectives are different to that pursued here. On the standard policy instruments,Lyon and Maxwell (2002) provide a very insightful overview with special emphasis onthe existing empirical findings and Lutz et al. (2000) who use a fairly general verticalproduct differentiation framework to show that if the high-quality firm can commit toa quality level before regulations are promulgated, it induces the regulator to weakenstandards, and welfare falls. This last study highlights the dangers of lengthy delaysbetween legislative mandates for new regulations and their implementation. The keydifference between their model and earlier models of minimum quality standards (likeArora and Gangopadhyay, 1995) is the timing of firm and government actions: now thehigh-quality firm has the leadership role. Finally, Crampes and Hollander (1995) rule outsunk costs and show that a low-quality producer benefits from a mildly restrictive qualitystandard whereas a high-quality producer suffers from it. Consumers’ welfare increases ifthe firm producing the higher quality does not increase its quality significantly in responseto the increase in quality by its rival.

5. Market effects of changes in the distribution of consumer types have been studiedby von der Fehr and Stevik (1998) and Bloch and Manceau (1999). However, these papersstudy persuasive advertising in the context of horizontal differentiation.


among those who were initially more environmentally conscious. Thus,in terms of our framework, their reported information-led change inenvironmental consciousness is of the heterogeneity-enhancing type.Harris (2006) recognizes the effectiveness of environmental awarenesscampaigns in China among university students and the urban popula-tion. However, it is suggested that more satisfactory results would bereached if state campaigns were targeted toward those who have lowerenvironmental knowledge and consciousness, like old people and ruralpopulations.

In all of these studies, the social desirability of increasing a pop-ulation’s environmental consciousness seems to be taken for granted.Our analysis shows that this is not necessarily true without relying onthe argument, used for example by Conrad (2005), that the social valueof products manufactured by socially responsible firms may be over-estimated by the consumer. To deal with socially undesirable increasesin the consumers’ social responsibility we use an argument similar toRodrıguez-Ibeas (2007), paying special attention to discontinuities inequilibrium behavior due to a change in the industry structure.

Following Baron (2001), committing to a socially beneficial invest-ment is a form of strategic corporate social responsibility (CSR). Ourapproach explains a firm’s CSR as a vertical differentiation strategy.Examples include cause-related marketing, eco-labeling, and corporatedonations to “worthy” causes. Although many real-world examples ofsocially responsible behavior concern markets with an environmentalexternality, Bagnoli and Watts (2003) adopt a more broadly applicableframework in which a socially responsible manufacturer links hisproduct to a public good, while in the absence of any prosocial concerns,the manufacturer does not link the product to such a public externality.

Adopting the vertical differentiation framework by Mussa andRosen (1978), we assume that, apart from the standard feel good effectperceived by the buyers of a green seller’s products, firms’ corporatestrategies imply a contribution to a public good, which is not capturedby consumers’ valuations. Our basic assumption is that, all otherbeing equal, consumers have some preference for products sold bysocially responsible manufacturers. Increases in the consumers’ WTPfor a firm’s CSR may increase or decrease consumer heterogeneity.Following the existing literature, there are three meaningful structuresthat should be analyzed in this framework: (1) monopoly with completemarket coverage, (2) duopoly with incomplete market coverage and (3)duopoly with complete market coverage. This framework allows usto consider changes in the consumers’ WTP for green firms’ productsleading to continuous changes in the market outcome or discontinuousshifts across different market structures. This feature of our model


is responsible for a somehow counterintuitive result, which can besummarized as follows.

As preference heterogeneity increases, equilibria progress frommonopoly to duopoly with the full market covered, to duopoly withincomplete coverage. Transitions from monopoly to duopoly with fullmarket coverage do not cause any discontinuous “jumps” in any ofthe equilibrium magnitudes. On the contrary, as already observedby Wauthy (1996), transitions from complete to incomplete marketcoverage in a duopoly entail discontinuous “jumps” in equilibriumqualities, prices, and social welfare. In this case, shifting toward moresocially responsible consumer preferences in the region of the boundarybetween the two duopolistic structures may change the market outcomein a welfare-reducing fashion.

The remaining part of the paper is structured as follows. Section2 presents the theoretical model and discusses the results. Section 3concludes. In an appendix, we compare market equilibrium with thefirst-best solution and discuss the implications of our framework forsocial welfare.

2. The Model

Let a maximum of two potentially socially responsible firms sell aprivate product to a population of consumers. Consumer i’s utility fromthe consumption of up to one product unit from firm j, is given by

Ui j = max{vi s j − p j , 0}, (1)

where j ∈ {1, 2}, while sj denotes firm j’s degree of CSR, vi is consumeri’s valuation of a marginal increase in a firm’s CSR, and pj is seller j’sprice. The standard product is also sold in a market at the competitiveprice, normalized to p = 0, by a competitive fringe of firms, which donot adopt any kind of CSR. Therefore, without loss of generality, weassume that when the market is not covered by the sales of the twofirms, consumers buy the standard product in the competitive marketenjoying the non-CSR-related aspects of it. This implies that the productis perceived as differentiated by the consumers as long as at least oneof the two firms adopts a different level of CSR from its rival and thecompetitive fringe. Therefore, if one of the two firms wants to sell theproduct at a higher price than the competitive one, potentially yieldinga positive profit, it must commit to a positive level of CSR.

We normalize the consumers’ population to unity and assume thatthe consumer-specific valuation parameters reflecting their preferencesfor firms’ CSR are uniformly distributed between m and n. By assumingthat the density of the distribution is d = 1/(n – m), we keep the


FIGURE 1. EXAMPLES OF INCREASES IN CONSUMERS’ WTP FORSOCIALLY RESPONSIBLE FIRMS’ PRODUCTS

population of consumers constant in all types of changes in thedistribution of v.

Figure 1 presents the types of changes in the consumers’ socialconsciousness, which can be modeled as increases in one of the twotaste parameters, m (example 1) and n (example 2), or both of them(example 3). We use the term heterogeneity-reducing for the case ofWTP increases depicted in example 1, heterogeneity-enhancing for WTPincreases corresponding to example 2, and heterogeneity-preserving forWTP increases like the one depicted in example 3.

Notice that, we focus on the case of total-mass-preserving changesin the distribution of consumers, which could be due to, say, someprosocial campaign targeting the existing consumer population. Tomodel nonmass-preserving ones would be of some interest, as ananalogue of changes caused by the entry of new, more socially con-scious consumers. However, although this alternative approach wouldproduce qualitatively similar results to those reported here, it wouldnot allow us disentangle the effects of changes in the consumer’s WTPfor quality from the effects of increasing the total consumer population.

Similar to Lutz et al. (2000) and Liao (2008), we assume that thefirm’s degree of CSR implies a fixed cost that is a convex function of thefirm’s level of social responsibility as denoted by


C j (s j ) = 12

k · s2j . (2)

We consider a two-stage game in which firms first choose theirlevel of social responsibility and then their prices. We solve the two-stage decision problem following backward induction. Therefore, in allcases, we solve first for firms’ pricing decisions and then substituteinto firms’ profit functions to obtain the subgame perfect equilibriumdegrees of social responsibility.

Regarding the market structure, there are three relevant config-urations: (1) a monopoly of a socially responsible firm whose sales coverthe whole market (or Monopoly-Complete coverage, for whose magnitudeswe use the subscript MC), (2) a duopoly of two socially responsible firmswhose sales cover only a part of the market (or Duopoly-Incomplete coverage,denoted by DI), and (3) a duopoly of two socially responsible firms whosesales cover the whole market (or Duopoly-Complete coverage, denoted bythe subscript DC). Given that consumers buying the standard productin the competitive market enjoy zero utility and firms supplying themearn zero profits, the part of the market, which is not covered by the twofirms’ sales contributes nothing to the social welfare and is equivalentto the case of zero consumption. Following Liao (2008), we analyze eachcase within the range of taste parameters in which the correspondingstructure emerges in equilibrium. Figure 2 shows firms’ market sharesunder each case.

2.1 Monopoly with Complete Coverage

of the Market (MC)

The monopolist will cover the whole market by fixing the maximumprice that makes all consumers buy a unit of the product. This priceequals the level at which the least socially conscious of all consumersvalues the seller’s degree of social responsibility (the one with theminimum vi):

pMC = msMC . (3)

The firm’s revenue from selling at this price to the whole market isrMC = pMC 1 = msMC. Taking the cost of the firm’s level of social respon-sibility into account, the firm’s profit is given by πMC = rMC − CMC =m · sMC − 1

2 ks2MC , which has a single maximum for

s∗MC = m/k. (4)


FIGURE 2. MARKET PARTITIONS UNDER THE THREE CASES STUD-IED

At this level of social responsibility the firm’s price becomes p∗MC = m2/

k, yielding maximum profits

π∗MC = m2

2k. (5)

We assume that social welfare is the sum of consumers’ utilitydue to the feel good effect from consuming a socially responsible firm’sproduct, plus the public good externality due to a firm’s CSR, minus theassociated fixed cost. More detailed discussion of the consequencesof our assumptions for social welfare is provided in the appendix.It must be noted that assuming a linear relation between a firm’slevel of CSR and its associated contribution to the public good, is asimplifying but certainly restrictive way of modeling the public goodexternality as an increasing function of a firm’s social responsibility.Nevertheless, our main results on assessing the desirability of changesin the consumers’ social responsibility through discontinuous shiftsacross different market structures do not depend on the aforementionedlinearity assumption.

For the monopoly case considered here, given that all consumersbuy a unit of the product, and that the firm has adopted the level ofsocial responsibility in (4), social welfare is


SW∗MC = m + n

2s∗

MC + s∗MC − 1

2ks∗2

MC = m(n + 2)2k

, (6)

which is an increasing function of both extremes of the distribution oftastes m and n, whereas the monopolist’s choice of social responsibleactivity level, price, and associated profits only depend on the minimumamong all valuations of social responsibility in the market. Therefore,the monopolist’s interest is not totally compatible with social welfaremaximization. This is a general property of the market-driven socialresponsibility studied here, as can be shown by comparison betweenequilibrium social welfare and the corresponding first-best choices (seethe appendix).

It would be reasonable to ask now whether the monopolist wouldrather leave a part of the market uncovered by raising the price to po inorder to reach up to a consumer with a valuation of socially responsiblesellers’ product of vo > m. Such a strategy would reduce its demandbelow maximal market coverage, yielding a higher profit margin. Wecan calculate the optimal po = nsMC/.2 for which vo = n/2. In order forvo > m, it must hold that n > 2m. However, as we will see in Section 2.3,where we discuss endogenous market structure, for n > 2m the secondfirm becomes active, giving rise to a full coverage duopoly. Hence, thelist of cases studied here is complete without the case of an incompletecoverage monopoly.

From the derivatives ∂π∗MC/∂n = 0, ∂π∗

MC/∂m = mk , ∂SW∗

MC/

∂n = m/2k and ∂SW∗MC/∂m = (n + 2)/2k, and given that ∂π∗

MC/∂m ≥∂SW∗

MC/∂m ⇔ n ≤ 2(m − 1), we reach the following result:

Proposition 1: Equilibrium monopoly profits and social welfare are in-creasing functions of m. The effect of m on the former dominates its effect onthe latter when m > 1 + (n/.2). Social welfare increases with increases in n,while profits do not depend on n.

Proposition 1 shows that a monopolist would only benefit fromincreases in the least social responsible consumer’s WTP, while socialwelfare would be enhanced by increases in any of the two taste pa-rameters. Furthermore, for sufficiently low (high) degrees of consumerheterogeneity the firm may benefit more (less) from an increase in mthan the society as a whole. This is our first result concerning possibleincompatibilities between private profitability and social desirability ofincreases in the consumers’ social consciousness.


2.2 Duopoly with Incomplete Coverage

of the Market (DI)

Most of the analysis in this case closely follows Motta (1993). For thepurposes of our analysis, we restate the main results in terms of theparameters m and n. Without loss of generality, we consider that one ofthe two firms chooses a higher degree of CSR than the other: s1DI > s2DI.6

Given prices p1DI > p2DI, there are two marginal consumers. One, withvaluation x1DI = (p1DI − p2DI )/(s1DI − s2DI ), who is indifferent betweenthe two sellers, and another, with valuation x2DI = p2DI /.s2DI , whois indifferent between buying from the less socially responsible firmand buying from the competitive market. The two firms’ demands areexpressed as

q1DI =(

n − p1DI − p2DI

s1DI − s2DI

)(1

n − m

), (7)

q2DI =(

p1DI − p2DI

s1DI − s2DI− p2DI

s2DI

) (1

n − m

). (8)

Then, the revenues from the price-setting stage are

r1DI = p1DI ·(

n − p1DI − p2DI

s1DI − s2DI

)(1

n − m

), (9)

r2DI = p2DI

(p1DI − p2DI

s1DI − s2DI− p2DI

s2DI

)(1

n − m

)(10)

whose derivatives must be equal to zero for the first order conditionsof the Bertrand equilibrium to be satisfied, giving us the equilibrium ofthe price-setting stage

p1DI = 2ns1DI (s1DI − s2DI )4s1DI − s2DI

, (11)

p2DI = ns2DI (s1DI − s2DI )4s1DI − s2DI

(12)

yielding revenues

r1DI = 4n2s21DI (s1DI − s2DI )

(n − m)(4s1DI − s2DI )2 , (13)

r2DI = n2s1DI s2DI (s1DI − s2DI )(n − m)(4s1DI − s2DI )2 . (14)

6. Arora and Gangopadhyay (1995) give a detailed proof why firms will never chooses1 = s2, which also holds in our case.


It is straightforward to apply the result shown by Arora andGangopadhyay (1995) to show that, for each firm, these revenuefunctions are concave in own levels of engagement with the sociallybeneficial activity. In addition, the positive cross derivatives of equilib-rium revenues with respect to the involvement of the rival firm with asocially beneficial activity indicate that social responsibility levels arestrategic complements.

Equilibrium in the first stage of the game requires

∂π1DI

∂s1DI= 0 ⇒ ∂r1DI

∂s1DI= ∂C1DI

∂s1DI

⇒ 4n2s1DI(4s2

1DI − 3s1DI s2DI + 2s22DI

)(n − m)(4s1DI − s2DI )3 = ks1DI , (15)

∂π2DI

∂s2DI= 0 ⇒ ∂r2DI

∂s2DI= ∂C2DI

∂s2DI⇒ n2s2

1DI (4s1DI − 7s2DI )(n − m)(4s1DI − s2DI )3 = ks2DI (16)

whose simultaneous solution gives the equilibrium choices of firms inthe first stage of the game. As the aforementioned authors observe, theequilibrium characterized by the solution of the system equations (15)–(16) is guaranteed by the concavity of the revenue functions and theconvexity of the cost function. We use equations (15) and (16) in orderto obtain an analytical solution for the subgame perfect equilibrium,where the ratio of marginal revenues must be equal to the ratio ofmarginal costs

∂r1DI /∂s1DI

∂r2DI /∂s2DI= 4

(4s2

1DI − 3s1DI s2DI + 2s22DI

)s1DI (4s1DI − 7s2DI )

= s1DI

s2DI. (17)

Concerning this equation, Motta (1993) pointed out that it has a singlereal root7 given by

s1DI = λ · s2DI , (18)

where λ = 5.2512. Once this relation is used in the solution of theequation in expression (16), we obtain the subgame perfect equilibriumlevels of social responsibility

s∗1DI = λ3n2(4λ − 7)

k(n − m)(4λ − 1)3 , (19)

s∗2DI = λ2n2(4λ − 7)

k(n − m)(4λ − 1)3 . (20)

7. And two imaginary ones given by s1DI = 0.249383 ± 0.564509i .


With these levels of social responsibility chosen in the subgame perfectequilibrium of the game, equilibrium prices become

p∗1DI = 2λ3n3(4λ − 7)(λ − 1)

k(n − m)(4λ − 1)4 , (21)

p∗2DI = λ2n3(4λ − 7)(λ − 1)

k(n − m)(4λ − 1)4 . (22)

For these social responsibility levels and prices, firms’ shares aredefined by the two marginal consumers’ conditions on the [m, n] interval

x∗1DI = (2λ − 1)n

4λ − 1, (23)

x∗2DI = (λ − 1)n

4λ − 1, (24)

which guarantees that, for all positive values of n and nonnegativevalues of m, the former is higher than the latter and that the higherboundary never exceeds n. The other restriction for this structure toemerge is satisfied if x∗

2DI > m ⇒ n > 4.7056m.In the subgame perfect equilibrium characterized here, both firms’

profits are positive and those earned by the more socially responsiblefirm are higher than the profits of the less socially responsible one asindicated by

π∗1DI = λ4n4 (4λ − 7) · [

8 · (λ − 1) · (4λ − 1) − λ2 · (4λ − 7)]

2k (4λ − 1)6 (n − m)2

= n4 · 0.0244386

k (n − m)2 , (25)

π∗2DI = λ3n4 (4λ − 7) · [2 · (λ − 1) · (4λ − 1) − λ · (4λ − 7)]

2k (4λ − 1)6 (n − m)2

= n4 · 0.00152741

k (n − m)2 .(26)

Finally, the social welfare corresponding to equilibrium behaviorunder this market structure is given by


SW∗DI =

∫ n

x1

v · s∗1DI · dv +

∫ x1

x2

v · s∗2DI ·dv + s∗

1DI + s∗2DI − 1

2k(s∗2

1DI + s∗22DI

)

= n2

(n − m) k

(0.0691 · n2

n − m+ 0.3015

). (27)

From inspection of expressions equations (25)–(27), we reach thefollowing straightforward result:

Proposition 2: In the case of an incomplete coverage duopoly, both firms’profits and social welfare are strictly increasing functions of the term n2

n−m .

Proposition 2 implies that each one of the taste parameters affectsboth firms’ profits and social welfare in similar ways. An increase inany of the two parameters increases profits and welfare. Furthermore,the denominator (n − m) of the term mentioned in Proposition 2implies a negative effect of consumer heterogeneity on profits and socialwelfare.

2.3 Duopoly with Complete Coverage

of the Market (DC)

In this case, both firms are active in the market with strictly positiveoutputs whose sum is equal to unity. Although previous studies byRonnen (1991), Arora and Gangopadhyay (1995), and Lehmann-Grube(1997) have presented similar models, we restate the main features ofthe setup in terms of the taste parameters m and n, and discuss recentfindings by Liao (2008).

For any pair of prices p1DC > p2DC leading to full coverage ofthe market, there will be a consumer whose valuation of his supplier’slevel of social responsibility will make him indifferent between the moreresponsible firm, which charges a higher price and the less responsiblefirm charging a lower price. This marginal consumer’s valuation isx1DC = (p1DC − p2DC )/(s1DC − s2DC ). We can write the two firms’ quotason the [m, n] segment as d1DC = n − x1DC and d2DC = x1DC − m,which, when multiplied by the consumer density d = 1/(n – m) giveus, respectively, the two firms’ demands

q1DC =(

n − p1DC − p2DC

s1DC − s2DC

)(1

n − m

), (28)

q2DC =(

p1DC − p2DC

s1DC − s2DC− m

) (1

n − m

). (29)


We use expressions equations (28) and (29) to write the two firms’revenue functions that are relevant for the decisions of firms in the pricesetting stage of the game

r1DC = p1DC

(n − p1DC − p2DC

s1DC − s2DC

)(1

n − m

), (30)

r2DC = p2DC

(p1DC − p2DC

s1DC − s2DC− m

) (1

n − m

). (31)

Regarding the pricing equilibrium in this configuration, it has beenshown that there are two different situations that should be analyzedcorresponding to an interior and a corner pricing solution. Assumingthat the market is fully covered by the two firms’ sales, Tirole (1988)obtained an interior pricing equilibrium, defined as the solution tothe system ∂r1DC/∂ p1DC = 0, ∂r2DC/∂ p2DC = 0. Later, Wauthy (1996)characterized a corner solution of the pricing game in which the low-quality firm’s price equals the lowest valuation of its product’s quality inthe market. He then examined the quality choice stage, assuming thatquality improvements are costless. However, assuming a fixed cost,which is a convex function of quality, and accounting for the fact that anequilibrium must be robust to deviations, which may alter the industryconfiguration, Liao’s (2008) proposition 1 states that a covered marketoutcome with an interior solution in the price stage is not an equilibrium.Thus, the only meaningful configuration that has to be analyzed underfull coverage duopoly is one in which the low-quality firm’s price isgiven by

p2DC = ms2DC . (32)

A second major finding in Liao’s (2008) analysis concerns the con-ditions under which a complete or an incomplete coverage duopoly willemerge in equilibrium. As the author observes, a given configurationis an equilibrium only if it is robust to individual deviations, whichmay shift the industry from one structure to another. Thus, ratherthan assuming a given market structure, Liao’s (2008) analysis obtainsequilibria that account for both “continuous” and “discontinuous”individual deviations from a given strategic profile. Thus, the inequalityx∗

2DI > m ⇒ n > 4.7056m, mentioned in the previous section and inMotta (1993) as the condition for an incomplete coverage monopoly toemerge, does not account for discontinuous deviations. Following thisobservation, Liao (2008) establishes a more restrictive condition givenby n ≥ 4.7226 m. Furthermore, for the interval of n ∈ [ 4.7125m, 4.7226m],both incomplete and complete coverage duopolies can be sustained in


FIGURE 3. BOUNDARY CONDITIONS FOR n > m and n − m = 1

equilibrium, but the former is shown to Pareto-dominate the latter.Thus, for the remaining analysis, we will consider that an incompletecoverage duopoly will also emerge in this interval.

Finally, Liao (2008) obtains the other boundary condition for acomplete coverage duopoly to emerge, given by n > 2m. As we saw inSection 2.1, this condition implies that this case emerges under the sameconditions as those under which a potential monopolist would havefound it profitable to leave part of the market uncovered. SummarizingLiao’s (2008) findings on the boundary conditions, a complete coverageduopoly with a corner pricing equilibrium will be observed whenever4.7125m > n > 2m. A graphical representation of these boundariesin the bidimensional space of parameters m and n is provided inFigure 3. Also, the unit-density assumption adopted by Liao (2008) andearlier by Boom (1995) and Shaked and Sutton (1982), among others,leads to a uniparametric specification of the aforementioned boundariesusing n – m = 1. The resulting condition for the emergence of a completecoverage duopoly becomes 0.26926 < m < 1. For a comparison betweenthis and the more general biparametric specification of the model, referto Figure 3.

In the analysis that follows, we adopt the assumption of a unit-density distribution of consumers’ tastes, that is d = 1/(n − m) =1 ⇒ n − m = 1. Thus, we confine our focus on the heterogeneity-preserving type of WTP increases shown in example 3 of Figure 1. Under


this assumption, we use equation (32) and the first-order condition∂r1DC/∂p1DC = 0 in order to obtain firm 1’s optimal price

p1DC = s1DC − s2DC + ms1DC

2. (33)

Substituting the equilibrium prices obtained above, we obtain therevenues of the two firms from the price-setting stage of the game

r1DC = (s1DC − s2DC + ms1DC )2

4(s1DC − s2DC ), (34)

r2DC = ms2DC [(1 − m)s1DC − s2DC ]2(s1DC − s2DC )

. (35)

Differentiating equations (34) and (35) with respect to s1DC ands2DC, respectively, and setting k = 1, we obtain the following first-orderconditions that have to be satisfied by equilibrium quality choices

∂r1DC

∂s1DC= s1DC ⇒ (s1DC − s2DC + ms1DC )[s1DC − s2DC + m(s1DC − 2s2DC )]

4(s1DC − s2DC )2

= s1DC , (36)

∂r2DC

∂s2DC= s2DC ⇒

[(s1DC − s2DC )2 − ms2

1DC

]2m2(s1DC − s2DC )2 = s2DC . (37)

Although Liao (2008) provides some discussion on the equilibriumqualities obtained from the solution of the system equations (36)–(37),the complexity of the analytical expressions obtained did not leave anyspace for a meaningful interpretation and further discussion on the con-sequences for profitability and welfare. We have used numerical meth-ods to calculate and plot equilibrium qualities, prices, profits, and socialwelfare resulting from the equilibrium described by equations (36)and (37).

Table I summarizes the results obtained from the calculation of thelimits of all equilibrium magnitudes in the three market structures as mtends to each one of the two boundary values 0.26926 and 1. The resultsshow that transitions from complete to incomplete coverage duopolyare not smooth except for the firms’ profits. The lack of discontinuousjumps in the two firms’ equilibrium profits is a consequence of the factthat Liao’s (2008) boundary conditions are derived under the require-ment that, in equilibrium, firms do not have incentives to unilaterallycause discontinuous jumps of the industry from one structure to theother. If a discontinuous jump were there between one structure and


Table I.

Limit Equilibrium Magnitudes as m Tends to the

Values 0.26926 and 1

EquilibriumMagnitude (X) limm→0.26926− X∗

DI limm→0.26926+ X∗DC limm→1− X∗

DC limm→1+ X∗MC

s1 0.4081 0.4017 1 1s2 0.0777 0.0786 0 –p1 0.2202 0.2156 1 1p2 0.0209 0.0211 0 –x1 0.6029 0.6019 1 –x2 0.2697 – – –q 1 0.6664 0.6674 1 1q 2 0.3332 0.3326 0 –π1 0.0633 0.0633 0.5 0.5π2 0.0039 0.0039 0 –SW 0.6654 0.6588 2 2

another, then a firm shifting from a less to a more profitable structurewould be observed in the region of the discontinuity point.

The most important implication of the results reported in Table Iconcerns the discontinuity of equilibrium social welfare on m = 0.26926.Specifically, in the region of this boundary condition, an infinitesimalincrease in m causes the market to shift from incomplete to completecoverage duopoly and equilibrium welfare to drop from 0.6654 to0.6588. Therefore,

Proposition 3: An increase in consumers’ social responsibility may bewelfare-reducing, if it causes the market to shift from incomplete to completecoverage duopoly.

For a complete view of the behavior of equilibrium magnitudesalong the whole range of values of m, a series of plots is providedin Figures 4–7. On Figures 4 and 5, it is shown that, as observedby Wauthy (1996), the transition from incomplete to complete marketcoverage in duopoly is not smooth. Both plots of equilibrium pricesand qualities exhibit discontinuous “jumps” on the value of m, whichdefines the boundary between the two cases. Figures 6 and 7 revealan important difference between equilibrium profits and social welfare.Namely, while the former exhibits no discontinuities as we move fromone duopolistic structure to the other, the latter does.

Figure 6 reveals that in the case of a duopoly whose salescompletely cover the market, the low-quality firm is harmed by in-creases in the consumers’ social responsibility. This relates to a rather


FIGURE 4. EQUILIBRIUM QUALITIES AS A FUNCTION OF m

FIGURE 5. EQUILIBRIUM PRICES AS A FUNCTION OF m

counterintuitive phenomenon. In complete coverage duopoly, the low-quality firm chooses lower levels of CSR when selling to a populationof more socially responsible consumers (Figure 4), while its equilibriumprice is a nonmonotonic function of m (Figure 5), increasing for lower


FIGURE 6. EQUILIBRIUM PROFITS AS A FUNCTION OF m

FIGURE 7. EQUILIBRIUM SOCIAL WELFARE AS A FUNCTION OF m

and decreasing for higher values. Therefore, when the market is fullycovered and competition between firms becomes a war for market share,the low-quality firm’s level of CSR and profits become a decreasingfunction of consumers’ social responsibility. This contrasts with the


case of a duopoly with incomplete market coverage in which increasingthe consumers’ social responsibility leads to higher levels of CSR andbenefits both firms and the society as a whole (see Proposition 2).

As observed by Wauthy (1996), larger degrees of consumer hetero-geneity favor the emergence of the incomplete coverage duopoly struc-ture. Of course, Wauthy’s (1996) concept of consumer heterogeneity,defined as the difference n − m, is not functional under the assumptionthat n − m = 1. Nevertheless, if we define consumer heterogeneity asthe ratio n/m, which for all positive values of m and n is a monotonictransformation of n – m, our results confirm all predictions in Wauthy’s(1996) conclusions. Namely, as we can see on Figure 4, in a fully coveredduopolistic market, when m decreases, which in the n − m = 1 case corre-sponds to an increase in the population dispersion, the quality differen-tial decreases too. However, note that this incompatibility between thelow-quality firm’s profitability and social welfare maximization is dif-ferent from a rather moderate incompatibility reported in Proposition 1,according to which monopoly profits depend only on increases in m,while social welfare relates positively to both taste parameters.

As we have already pointed out in Proposition 3, equilibriumsocial welfare exhibits a discontinuous jump downward as we shiftfrom incomplete to complete coverage duopoly. The main source of thisinteresting and somehow counterintuitive welfare-reducing effect ofWTP increases in the region of the boundary condition between incom-plete and complete coverage duopoly can be explained by referring toFigure 4. It can be observed that the shift from incomplete to completemarket coverage causes the duopolists’ qualities move in differentdirections. Firm 1 decreases its level of CSR and firm 2 increases it.However, as we can see both on Table I and Figure 4, the former of thetwo changes is much larger than the latter, producing a decrease in theoverall social welfare. Of course, a potential source of welfare gains aswe shift from incomplete to complete market coverage could be dueto an increase in the number of buyers served. These buyers are thosewith 0.2697 > m > 0.26926 as indicated by the value of x2 on Table I andthe boundary between the two duopolistic structures. Nevertheless,from the decrease in social welfare caused by a discontinuous shiftfrom incomplete to complete coverage duopoly implies that the welfareeffects of a lower overall CSR adopted in the market is not compensatedby the increase in the number of buyers served due to complete marketcoverage.

We summarize and discuss now the findings reported so far. Twotypes of results have been reported: results on the effects of increases inthe consumers’ social responsibility under a fixed market structure andresults on increases in the consumers’ social responsibility, which yielddiscontinuous jumps across adjacent industry configurations.


When the market structure is not affected, increasing the con-sumer’s WTP for a socially responsible manufacturer’s products isbeneficial for both socially responsible sellers and the society as a wholeonly in the case of an incomplete coverage duopoly. In this case, bothfirms and the economy as a whole benefit more from heterogeneity-reducing increases in the consumers’ social responsibility. In the othertwo cases, we identify several types and sources of incompatibilitiesbetween the private and the public interest. In the monopoly case,the firm only benefits from increases in the WTP of the least so-cially responsible consumer, while social welfare is enhanced by bothheterogeneity-reducing and heterogeneity-increasing changes. In thecomplete coverage case, increases in consumers’ social responsibilityharm the low-quality firm, whereas they increase the high-quality firm’sprofit and social welfare.

When an increase in consumers’ social responsibility affects themarket structure, equilibrium social welfare may present discontinuousjumps. This happens in the region of the boundary condition betweenthe two duopolistic structures. That is, while the transition from a com-plete coverage duopoly to a monopoly does not exhibit discontinuities,the transition from incomplete to complete coverage duopoly is notsmooth. In that case, an increase in consumers’ social responsibility iswelfare-reducing, while firms gain from it. To explain this finding, weobserve that in the region of the corresponding boundary condition, thetwo firms’ quality choices also present discontinuous jumps; downwardfor the high-quality firm and upward for the low-quality one withthe former dominating the latter. The different sizes of these twoopposite reaction of firms to the change in the industry structure areresponsible for the overall welfare loss caused by this jump. This isdespite the increase in the number of buyers served due to shiftingfrom incomplete to complete market coverage.

3. Conclusions

Our theoretical framework explains corporate social responsibility asa costly differentiation strategy. Consumers are heterogeneous in theirreservation prices for a marginal increase in their supplier’s commit-ment to a socially beneficial action, like the protection of the naturalenvironment. We pay special attention to the impact of changes inconsumers’ social responsibility on consumer heterogeneity and on themarket outcome. We find that, the most socially responsible producerin the market benefits from selling to a market with more responsibleconsumers. Interestingly, we find that when a market is partially served


by a duopoly, the firm with a lower degree of social responsibility mayalso benefit from selling to a market with more socially responsibleconsumers. However, this result is reversed in the case of a duopolywhose sales cover the whole market.

Despite its similarity with income increases, raising the con-sumer’s WTP for the products of socially responsible firms is far froma trivial equivalent to “throwing money into the market.” This is espe-cially true when an increase in consumers’ social consciousness causes aduopoly to shift from incomplete to complete market coverage. In thatcase, selling to a population of more socially responsible consumersleads to lower levels of social welfare because it reduces the moreresponsible firm’s incentives to invest in socially beneficial activities.This result holds despite the fact that the shift from incomplete tocomplete market coverage causes the less responsible firm’s CSR to riseand increases the number of consumers served in the market. The mainmessage of our analysis is that increasing the consumer’s WTP for theproducts of socially responsible firms is not monotonically beneficial,neither to the society nor to socially responsible entrepreneurs.

Our analysis is appropriate for assessing the private profitabilityand social welfare effects of exogenous factors, which are perceived indifferent ways by consumers with different attitudes toward social is-sues. A rather generic result concerns the fact that, in most cases, changesin consumers’ WTP that are privately profitable are not necessarilythe most desirable in terms of social welfare. In fact, it is neither easyto obtain interest compatibility between competing manufacturers norcompatibility between private profitability and social welfare, unless weremain within a duopolistic structure with incomplete market coverage.

A straightforward policy implication of our results is that, whileprivately profitable campaigns should not be generally considered tobe socially undesirable, the opposite cannot be guaranteed either. Inother words, only campaigns carefully designed as welfare-enhancingdevices should be trusted by the society as a whole. Otherwise,the existence of privately profitable but potentially welfare-reducingconsumer-awareness messages seems to be a nonnegligible threat formodern markets.

Although we would not like to exaggerate the possibilities of stateintervention in such detailed qualitative aspects of social trends andtargeted awareness campaigns, it should be clear that firms’ attemptsof providing the consumer with more information on the quality oftheir products and their corporate strategies regarding socially desirableobjectives should be challenged against our main finding concerning theincompatibility of private and social interests.


As Comanor and Wilson (1979) have already pointed out, ad-vertising undertaken by firms may increase the consumers’ WTP for amore expensive product and relax price competition. This unambiguousresult concerning the relation between changes in WTP and marketpower becomes less easy to apply by policy makers in the real world,if the effect of those changes on consumer preferences and the resultingutility is taken into account.8 That is, more information about a firm’ssocial objectives may result in higher prices, but people paying higherprices for those products may be happier because this informationmakes them like the products they consume more. Then, the comparisonof pre- and postinformation prices under the assumption that pre- andpostinformation products are essentially the same may yield misleadingconclusions. It would seem that, when markets have an externality ona public good like the environment, which can be objectively evaluatedin terms of social welfare, the effects of changes in the consumers’ WTPbecome easier to assess. Contrary to this conjecture, we find that thesame factors that increase the consumer’s WTP for the product of asocially responsible manufacturer may change the industry structureand reduce social welfare.

Different approaches to the aspects of CSR omitted here arediscussed in Windsor (2006) and Baron (2007). The robustness ofour results with respect to further generalizations, like nontotal-mass-preserving changes in the distribution of consumer tastes, and thenumerous applications of this very simple framework to study otherissues related with changing the consumers’ attitude toward quality,leave considerable space for future research.

Appendix: Social Welfare Analysis: First Best

versus Market Equilibrium

We briefly discuss the implications of our framework regarding socialwelfare in the first-best and second-best solutions. Technical detailsconcerning the derivation of these results are available upon request.

The First-Best Solution: Consider a regulator who is facing the followingproblem: A maximum of two suppliers, 1 and 2, may provide a publicgood by committing to a provision level si , i ∈ {1, 2}, yielding costsgiven by the convex function in (2). Following our assumptions, thereare three components in the expression giving us the level of socialwelfare achieved in each structure: (1) A market-based one related

8. Becker and Murphy (1993) analyze advertising as a product jointly sold togetherwith other conventional products, suggesting that a changing tastes framework is notnecessary in order to explain changes in consumers’ attitudes toward advertised products.


with the feel good effect experienced by the buyers of the private goodwhen purchasing it from a producer who is committed to some levelof socially beneficial activities, (2) the level of public good generatedby the producers whose quantity is a one-to-one transformation of thesupplier’s effort and involvement in a socially beneficial activity, and(3) the producers’ costs from their prosocial behavior. We pay attentionto the case in which the regulator must choose between a single- anda two-supplier provision structure and fix the optimal level of si =s0

i to be provided. The two suppliers also sell a private good, whoseconsumers enjoy some extra utility from buying the product from asocially responsible firm. All assumptions concerning such a sociallyresponsible consumers’ utility and the distribution of valuations of asocially responsible firm are kept as outlined in the main text. Notationfor two-supplier (TWO) and one-supplier (ONE) first-best solutions isintroduced in order to distinguish them from equilibrium structures.

While the comparison of total and individual optimal contribu-tions in the one- and two-supplier first-best solutions can be ranked ina straightforward way (s0

TWO ≥ s0ONE ≥ s0

iTWO), the condition for the two-supplier provision structure to be socially preferable over the single-supplier one is

SW0TWO = (4 + m + n)2

16k≥ SW0

ONE = (2 + m + n)2

8k⇒

√2 ≥ m + n

2.

(A1)

Given the decreasing returns to scale in the production of thepublic good favoring provision by many small plants rather than byfewer larger ones, the result in equation (A1) may be considered arather counterintuitive implication of our setup. However, we mustnot forget that the consumption-related utility of the public good isconstant and equal to the average valuation of social responsibilityin the market. Therefore, parallel to the decreasing returns of theproduction technology, we have “decreasing returns to plant number”in the generation of the consumption-related feel good effect experiencedby the consumer who buys from a socially responsible seller. This is why,we get that if the market-related value of social responsibility exceedsthe threshold given by equation (A1), the decreasing returns to plantproperty dominates the production-related decreasing returns to scaleand thus, the single-supplier structure is preferred by the regulator.

Comparing the Market and the First-Best Solutions: One important ques-tion to ask is whether market equilibrium could reach the first-bestlevel of social welfare. We compare the first-best solution above withthe equilibrium market structures emerging for different combinations


FIGURE A1. COMPARISON OF MARKET EQUILIBRIUM AND SO-CIALLY OPTIMAL STRUCTURES

of the consumers’ taste parameters. Figure A1 plots four straight lines.Three of them, the upward sloping ones, correspond to the boundaryconditions between pairs of equilibrium market structures, whereas thefourth, which is downward sloping, is the condition that determineswhether the single- or the two-supplier structure will be preferred bythe regulator.

We see that in some regions of parameter combinations the firstbest and equilibrium provision structures may coincide. Of course, thiscoincidence does not imply that the first-best outcome will be achievedby market equilibrium. On the contrary, in general, this will not be thecase. However, the mapping of equilibrium market structures againstthe first-best solution is a necessary step when assessing the sources ofdivergence between market equilibrium and socially optimal provisionstructures.

When comparing the actual choices in market equilibrium withthose corresponding to the first-best solution, we find that the mo-nopolist will always adopt a less socially responsible profile thanis socially optimal. When we compare the more responsible firm’schoices with the corresponding first best, we find that, in general,firm 1 (the socially responsible one) may both under- or overprovidethe public good externality entailed in its socially beneficial behavior,depending on the magnitude of the taste parameters. Combinations ofhigh values for m and n lead to the overprovision result, implying that


the consumers’ high valuation of a firm’s social responsibility may leadfirm 1 to the adoption of an excessively high level of CSR. However, thesecond firm always adopts a much lower level of CSR than is sociallyoptimal.

Another interesting result is that due to the differentiation motiveof socially responsible behavior shown to exist for both the incompleteand the complete coverage cases, the two firms will systematically avoidthe social welfare-maximizing adoption of equal levels of engagementwith socially beneficial activities. This is a persistent and robust source ofdivergence between the asymmetric social responsibility levels chosenby firms and the symmetric choice required in the corresponding first-best solution.

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Documents

Market Effects of Changes in Consumers' Social Responsibility