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European Journal of Political EconomyŽ .Vol. 17 2001 633–639

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The social cost of monopoly whenconsumers resist

Jung Hoon Keem)

Department of Economics, Howon UniÕersity, Wolha 727, Impi, Kunsan 573-718, South Korea

Received 1 April 2000; received in revised form 1 September 2000; accepted 1 October 2000

Abstract

This note considers the effect of defensive consumer lobbying on the social cost ofmonopoly when firms have asymmetric lobbying abilities. I show that surplus-defendingefforts of consumers can make a firm better-off, and increase firms’ rent-seeking outlaysand the social cost of monopoly. The assumption of symmetric lobbying abilities acrossfirms is the reason for the conclusion in the literature that consumer resistance alwaysmakes all firms worse-off and decreases firms’ rent-seeking outlays. q 2001 ElsevierScience B.V. All rights reserved.

JEL classification: D72; L12Keywords: Social cost of monopoly; Asymmetric lobbying abilities

1. Introduction

When firms compete for a monopolist position, consumers may not passivelyaccept the situation and may lobby against monopolization. The social cost ofmonopoly therefore includes the expected sum of firms’ rent-seeking and rent-de-fending outlays, consumers’ surplus-defending outlays, and the deadweight loss.

An interesting question is how consumers’ surplus-defending efforts affectfirms’ rent-seeking outlays and the social costs of monopoly. This question has

Ž . Ž . Ž .been addressed by Wenders 1987 , Ellingsen 1991 , Schmidt 1992 , Fabella

) Fax: q82-654-450-7344.Ž .E-mail address: [email protected] J.H. Keem .

0176-2680r01r$ - see front matter q 2001 Elsevier Science B.V. All rights reserved.Ž .PII: S0176-2680 01 00049-0

( )J.H. KeemrEuropean Journal of Political Economy 17 2001 633–639634

Ž . Ž .1995 and Baik 1999 . Especially, in Ellingsen’s two-stage model, consumerlobbying always decreases firms’ rent-seeking outlays. This note points out thatthis result is due to the assumption of symmetric lobbying abilities across firms.When the lobbying abilities vary across firms, consumer lobbying can increasefirms’ rent-seeking outlays. 1

2. The two-stage lottery model

The model consists of two stages: a positioning stage is followed by aregulation stage. At the positioning stage, the government decides which firm is tobe the monopolist. Firms lobby for the monopolist position. At the regulationstage, the government decides whether or not to regulate. The monopolist andconsumers lobby for a degree of monopoly regulation. If the monopolist is notregulated at all, then in Fig. 1 the monopoly price is P m with the correspondingquantity Qm. The monopoly profit is then maximal and the consumer surplus isminimal. If the monopolist is regulated at the competitive market price P c withthe corresponding quantity Qc, the monopoly profit is minimal and the consumersurplus is maximal. The monopoly profit is T and the deadweight loss associatedwith monopoly pricing is H. The gain in consumer surplus associated withregulation is TqH. T and H are illustrated in Fig. 1.

The players are firm 1, firm 2 and the consumer lobby. All are risk-neutral. Atthe positioning stage, firm 1 and firm 2 lobby for the monopoly position. Let ei

represent the rent-seeking outlay expended by firm i. I assume that the probabilitythat firm i wins the monopoly position takes the form:

e re1 2 2p s and p s .1 2e qre e qre1 2 1 2

Ž .The parameter r )0 represents firm 2’s lobbying ability relative to firm 1.r)1 indicates that firm 2 has greater lobbying ability than firm 1. Firm i’s payoffat the positioning stage is:

e1)W e ,e sV yeŽ .1 1 2 1 1e qre1 2

andre2

)W e ,e sV ye ,Ž .2 1 2 2 2e qre1 2

where V) denotes firm i’s regulation-stage equilibrium expected payoff wheni

firm i is chosen at the positioning stage.

1 Ž .Baik 1999 considered asymmetries between firms and consumers, but not among firms.2 p is equal to 1r2 if e s e s0.i 1 2

( )J.H. KeemrEuropean Journal of Political Economy 17 2001 633–639 635

Fig. 1. Monopoly profit and deadweight loss.

Ž .At the regulation stage, the monopolist say, firm i lobbies for the monopolyrent and consumers lobby for the consumer surplus. Let x represent the rent-de-i

fending outlay expended by firm i and let y represent the surplus-defendingiŽ .outlay expended by consumers against firm i . I assume that the probability that

the firm i is not regulated is:

u xi i 3q s ,iu x qyi i i

Ž .where the parameter u )0 represents firm i’s lobbying ability relative toi

consumers. u )1 indicates that firm i has greater lobbying ability than con-i

sumers. The regulation-stage payoff of firm i is:

u xi iV x , y sT yx ,Ž .i i i i

u x qyi i i

Ž .and that of consumers contending against firm i is:yi

U x , y s TqH yy .Ž . Ž .i i i iu x qyi i i

3 q is equal to 1r2 if x s y s0. The probability that firm i is regulated at the competitive price isi i i

1yq .i


3. Equilibrium monopoly regulation

Now consider the regulation stage. The subgame between firm i and con-Žsumers; the subgame i, has a unique Nash equilibrium Hillman and Riley, 1989;

.Baik, 1994; Nti, 1999 .

( )Lemma 1 A . Let Õ represent the prize ratio of the consumer to firm i,( )TqH rT. At the subgame i, the equilibrium total outlay of firm i and ofconsumers is:

2) ) )C 'x qy s 2TqH Õu r Õqu ,Ž . Ž .R , i i i i i

where the subscript ‘R’ denotes the regulation stage.

Ž .The proof of Lemma 1 A is straightforward and omitted. At the equilibrium of) Ž .the subgame i, the winning probability of firm i is q su r Õqu and thei i i

) ) Ž .expected deadweight loss is C 'q HsHu r Õqu .H , i i i i

Next, we consider the positioning stage. The positioning-stage game has aunique Nash equilibrium, which constitutes a unique subgame-perfect equilibriumof the whole game.

( )Lemma 1 B . Let V represent the regulation-stage equilibrium expected payoff) ) (( ) ( ))2ratio of firm 2 to firm 1, V rV s Õu qu u r Õu qu u . The equilib-2 1 2 1 2 1 1 2

rium total outlay of the firms at the positioning stage is:2 2

rV u u1 2) ) )C 'e qe sT q ,P 1 2 2 ž / ž /Õqu Õqu1qrVŽ . 1 2

where the subscript ‘P’ denotes the positioning stage.

Ž .The proof of Lemma 1 B is straightforward and omitted. The equilibrium) Ž . )winning probability of firm 1 is p s1r 1qrV and that of firm 2 is p s1 2

Ž .rVr 1qrV . The equilibrium expected total outlay at the regulation stage is:

C)'p)C) qp)C)

R 1 R ,1 2 R ,2

1 Õu rV Õu1 2s 2TqH q ,Ž . 2 21qrV 1qrVÕqu ÕquŽ . Ž .1 2

and the equilibrium expected deadweight loss, Harberger cost, is:

1 u rV u1 2) ) ) ) )C 'p C qp C sH q .H 1 H ,1 2 H ,2 1qrV Õqu 1qrV Õqu1 2

) ) Ž . ) ) )Hence, C qC is the expected total outlay, Tullock cost, and C qC qCP R P R HŽ .is the expected social cost of monopoly.


Table 1.Ž .The payoffs and the costs normalized with respect to T

Passive-consumer case Active-consumer case22 21 u 11

Payoffs W rT1 ž / ž /ž /1q r Õqu 1q rV12 22

r u rV2W rT2 ž / ž /ž /1q r Õqu 1q rV2

2 22r u u rV1 2

Costs C rT qP 2 2ž / ž /Õqu Õqu1q r 1q rVŽ . Ž .1 2

1 Õu rV Õu1 2Ž .C rT 0 Õq1 qR 2 21q rV 1q rVÕqu ÕquŽ . Ž .1 2

1 u rV u1 2Ž . Ž .C rT Õy1 Õy1 qH 1q rV Õqu 1q rV Õqu1 2

Let us now compare the costs incurred when consumers actively lobby formonopoly regulation with the costs incurred when consumers passively accept themonopoly. Let the superscript ‘O’ denote the case of the passive consumer. The

O O O Ž Ž .2 . OTullock cost is C se qe s2T rr 1qr , the Harberger cost is C sH,P 1 2 H

and the social cost of monopoly is COqCO. The payoffs and the costs areP H

summarized in Table 1.

4. Main results

Ž . ŽWe can find a set of parameter values such that 1r 1qr -1r2 and 1r 1q.rV )1r2 hold. That is, firm 1’s equilibrium winning probability is less than

1r2 when the consumer lobby passively accepts the monopoly, and greater than1r2 when the consumer lobby actively defends the consumer surplus. Our resultscome from recognizing this possibility.

( )Proposition 1. There exists a set of parameter Õalues Õ,r ,u ,u at which the1 2( )following holds: the surplus-defending efforts of the consumer lobby i make one

( ) O ) O) 4 ( )firm better-off and the other one worse-off W )W and W -W , ii raise1 1 2 2

4) O ) O Ž Ž ..2 Ž Ž ..2Ž Ž ..2 Ž ŽClaim. W )W ´W -W . That is, 1r 1q r - u r Õqu 1r 1q rV ´ rr 11 1 2 2 1 1

..2 Ž Ž ..2Ž Ž ..2q r ) u r Õqu rVr 1q rV .2 2

Ž Ž ..2 Ž Ž ..2Ž Ž ..2 Ž Ž .. Ž Ž ..Ž Ž ..Proof. 1r 1q r - u r Õqu 1r 1q rV m 1r 1q r - u r Õqu 1r 1q rV1 1 1 1ŽŽ . Ž .. Ž Ž .. ŽŽ . Ž .. Ž Ž ..m 1q rV r 1q r - u r Õqu . 1q rV r 1q r - u r Õqu -1´V-1.1 1 1 1

Ž Ž ..2 Ž Ž ..2Ž Ž ..2 Ž Ž ..Suppose on the contrary that rr 1q r F u r Õqu rVr 1q rV . Then rr 1q r F2 2Ž Ž ..Ž Ž ..2 Ž . Ž . Ž Ž .. Ž . Ž .u r Õqu rVr 1q rV m 1rVq r r 1q r F u r Õqu . 1- 1rVq r r 1q r F2 2 2 2Ž Ž .. Ž .u r Õqu -1, since 1rV )1. A contradiction.2 2

I


( ) O) ( ) (the total outlay at the positioning stage C )C , and iii increase the ex-P P) ( ) ) ) O O ) 5pected social cost of monopoly C qC qC )C qC .P R H P H

Since the winning firm confronts additional competition, it is tempting toconclude that both firms cannot be better-off. Likewise, since the efforts of theconsumer lobby reduce the regulation-stage payoffs of both firms, it is alsotempting to conclude that the total outlay at the positioning stage cannot begreater. However, given Õs3r2, rs40, u s6 and u s1r2, W OrTf1 2 1

0.000595, W)rTf0.026588; W OrTf0.951814, W)rTf0.039619; COrTf1 2 2 P) w ) ) ) x w O O x0.047951, C rTf0.114001; C qC qC rTf0.749789, C qC rTfP P R H P H

Ž . ) O ) O Ž . ) O Ž . ) )0.547591. We have i W )W and W -W , ii C )C and iii C qC1 1 2 2 P P P R

qC))COqCO.6 The intuition is as follows: in the absence of surplus-defend-H P H

ing efforts of the consumer, firm 2 could have such a large advantage in lobbyingability that firm 1 would not find it worthwhile to spend much at all. Hence, firm 2can secure a large probability of winning with a small expenditure. Once theconsumer lobby defends the consumer surplus, the prize of winning the monopolybecomes smaller for both firms. But it becomes far smaller for firm 2. Thus, at thepositioning stage, firm 2’s advantage in lobbying ability is tempered by its prizedisadvantage. Given that firm 2 spends less, firm 1 might start to spend more. Sofirm 1 can secure a larger probability of winning and the total effect of theconsumer efforts on the positioning-stage outlay can be positive.7 In the nextProposition, we show how strong is the assumption that u su .1 2

Proposition 2. When the firms haÕe equal lobbying abilities at the regulation( )stage, the surplus-defending efforts of consumers always i make both firms

( )worse-off and ii reduce the total outlay at the positioning stage. That is, if( ) ) O ( ) ) Ou su , then i W -W for is1,2 and ii C -C .1 2 i i P P

The proof is simple, since u su implies Vs1. Furthermore, if both the1 2Ž .firms and consumers have equal lobbying abilities rs1 and u su s1 , then1 2

C)qC))CO.8P R P

5. Conclusion

By introducing asymmetric lobbying abilities between two firms, I have shownthat there are circumstances where the surplus-defending efforts of consumers are

5 This proposition does not imply that consumers should not resist monopolization.6 Ž .For any linear demand curve, Õs TqH rT is 3r2. This value satisfies the restriction of

Ž .Ellingsen’s Proposition 4 ii .7 I owe this clear explanation to one of the referees.8

) ) ) O O'Ž .Given rs1 and u su s1, Õ) 17 q1 r4´C qC qC -C qC , which is Ellingsen’s1 1 P R H P HŽ .Proposition 4 ii .


to the advantage of one of the firms, raise the total outlay at the positioning stage,Ž .and increase the expected social cost of monopoly. An example can be con-

structed with more than two firms, in which a number of firms greater than three isŽ .not sufficient for a consumer lobby to be socially beneficial. Ellingsen 1991 ,

Ž . Ž .Fabella 1995 and Baik 1999 all chose symmetric lobbying abilities across firmsin order to consider the effects of the number of firms on the social cost ofmonopoly. The case of asymmetric lobbying ability complements this earlierliterature.

Acknowledgements

I thank anonymous referees, Professor Hillman, Professor Baik, and ProfessorNti. This note is supported by Howon University Research Fund.

References

Baik, K.H., 1994. Effort levels in contests with two asymmetric players. Southern Economic Journal61, 367–378.

Baik, K.H., 1999. Rent seeking firms, consumer groups, and the social costs of monopoly. EconomicInquiry 37, 541–553.

Ellingsen, T., 1991. Strategic buyers and the social cost of monopoly. American Economic Review 81,648–657.

Fabella, R.V., 1995. The social cost of rent seeking under countervailing opposition to distortionarytransfers. Journal of Public Economics 57, 235–247.

Hillman, A.L., Riley, J.G., 1989. Politically contestable rents and transfers. Economics and Politics 1,17–39.

Nti, K.O., 1999. Rent-seeking with asymmetric valuations. Public Choice 98, 415–430.Schmidt, T., 1992. Rent-seeking firms and consumers: an equilibrium analysis. Economics and Politics

4, 137–149.Wenders, J.T., 1987. On perfect rent dissipation. American Economic Review 77, 456–459.