The Maximal Damage Paradigm in Antitrust Regulation: Is it Something New?

Transcription

1 The Maximal Damage Paradigm in Antitrust Regulation: Is it Something New? It is well known that cartels are harmful for consumers. To counteract cartels, cartel formation is by law an economic crime with the antitrust authority (AA) as its crime fighter. Recently, Harrington (2004, 2005) studied a general model of cartel formation and its ricing based uon rofit maximization. In this article, we discuss the novel aroach in Houba et al. (2009), who take the maximal damage for consumers as the key criterion. Some develoments of this aroach are introduced and related to the literature. Introduction Desite a large literature on enforcement against individual illegal behavior, the theory of regulation is still in its infancy when it comes to enforcing market cometition. Illegal anti-cometitive behavior is much more comlicated since it tyically is a concerted illegal action erformed within an ongoing relationshi over time, called a cartel. Any theory of regulation therefore requires a dynamic setting, for examle an infinitely-reeated oligooly model with grim trigger strategies. In this article, we discuss an innovative but unconventional aroach in which we study the maximal-sustainable cartel rice in a reeated oligooly model, i.e., the largest cartel rice for which the equilibrium conditions for sustainability hold. This differs from the standard aroach in which the cartel maximizes rofits. The main reason for doing so is that exerimental economics establishes that economic agents often behave differently from standard microeconomic theory. Also, there is emirical evidence in suort of Baumol s (1958) hyothesis that managers of large cororations seek to maximize sales rather than rofits. Sustainability of cartel behavior offers a more robust criterion that does not deend on the cartel s objective. Then, the characterization of consumers maximal damage can be regarded as a worst-case scenario for consumers. It is therefore natural to aly this new aroach to regulation and comare the main results with those obtained for a rofit-maximizing cartel in Harrington (2004, 2005). This article is organized as follows. Section 2 introduces the maximal-sustainable cartel rice in a benchmark model without regulation. In section 3 we analyze the imact of AA enforcement Harold Houba is associate rofessor at the Deartment of of the VU University. He obtained his Ph.D. from Tilburg University in Houba is affiliated with the VU since His secialization is bargaining theory with alications to labor and environmental economics. Evgenia Motchenkova is assistant rofessor at the Deartment of Economics of the VU University. She obtained her Ph.D. from Tilburg University in Motchenkova is affiliated with the VU since Her secialization is the economics of antitrust regulation, in articular leniency rograms. Quan Wen is rofessor at the Deartment of Economics of the Vanderbilt University in Nashville. He obtained his Ph.D. from the University of Western Ontario in London, in Wen is affiliated with Vanderbilt since His secializations are bargaining theory, reeated games and their alications to economics. on the maximal-sustainable cartel rice. In section 4, we comare, by means of an examle, our aroach to the one in Harrington (2004, 2005). Section 5 concludes the analysis. The Benchmark Model Consider an oligooly market where n 2 symmetric firms comete in rices with either homogenous or heterogeneous roducts over infinitely many eriods. All firms have a common discount factor δ є (0,1) er eriod. Since we deal with symmetric outcomes, we simlify n (,...,) є to є. We adot the following notation: 37

2 - N and M denote the cometitive (Nash) equilibrium rice, resectively, the maximal collusive rice. - π() is the rofit function of an individual firm in any eriod. π() is continuous and strictly increasing for є [ N, M ]. - π ot () is a firm s rofit from unilateral deviation against the cartel when all the other cartel members set their rices at. π ot () is continuous and π ot ()>π()>0 for є [ N, M ]. - λ() is the degree of cartel stability and it is defined as ot π( ) / π ( ), for (, ], λ( ) N 1, for. λ()<λ( N ) 1 for all є ( N, M ] is decreasing for all є ( N, M ]. The degree of cartel stability is a new concet. Standard intuition imlies that a higher λ() means less incentives for cartel members to deviate and a stabler cartel. Furthermore, a higher cartel rice imlies a higher incentive for each cartel member to deviate. Since the function λ might be discontinuous at = N, as Examle 2 illustrates, we introduce N M λ lim λ( ) 1 and λ λ( ). 0 The above oligooly model without regulation is a standard infinitely-reeated game. Throughout this article, we focus on grimtrigger strategies to sustain cartel rice > N in which any deviation leads to the reetition of the cometitive (Nash) rice in every eriod thereafter. The underlying rationale is that cartels are based uon trust and, by the recirocal nature of humans, all trust is gone after someone cheats. The equilibrium concet is a subgame erfect equilibrium. In the absence of regulation, the necessary and sufficient condition to sustain є ( N, M ] as a cartel rice is ot δ ot N 1 π ( ) π ( ) π( ) 1 δ 1 δ (1) δ 1 λ( ). The socially worst outcome is the maximalsustainable cartel rice that is defined C max, s.t. (1). (2) [, ] Due to the monotonicity of π()/(1 δ), the maximal-sustainable cartel rice C also maximizes the cartel s rofit. A direct aroach would solve (1) for as a function of all arameters, which requires the inverse function λ -1 (1 δ). Later, however, this aroach is not alicable. Instead, we analyze the roerties of the threshold level for δ as a function of є ( N, M ] and, then, translate these roerties into the maximal-sustainable cartel rice as a function of δ in the (δ,)-lane. This indirect aroach allows for an easier interretation. Proosition 1 In the absence of regulation, the maximalsustainable cartel rice C is non-decreasing in δ є (0,1), and C = N, for δ є (0, 1 λ), C є [ N, M ), for δ є [1 λ ; 1 λ ), C = M, for δ є [1 λ, 1), We conclude this section with a well-known examle. Examle 2 Consider a homogeneous Bertrand oligooly model with linear demand 2 and 0 marginal costs. Note that N =0 and M =1. For all є ( N, M ], each of the n firms may deviate by slightly undercutting the others to obtain the full cartel rofit, i.e., λ()=1 for all є ( N, M ]. Consequently, λ= λ =1/n. Proosition 1 imlies < = Antitrust Enforcement In this section, we examine the imact of regulation. Given є [ N, M ], the robability that the AA investigates the market outcome in a eriod and finds the firms guilty of collusion is β() є [0,1), where β() is increasing in and β( N )=0. Uon being caught, violators will be fined by the amount k()π(), where k() is increasing and continuous such that k( N )=0 and k()>0 for all є ( N, M ]. The function β( ) reflects that a higher cartel rice attracts susicions and makes detection more likely. Any cartel takes this negative effect into account when deciding uon the rice, see Harrington (2004, 2005). The AA is a assive layer in this model, while firms are the active layers. The detection robability β( ) is limited by the resources of the authority, and the fine schedule k( ) is limited by legislation. The OECD (2002) reorts detection robabilities 1/7 β() 1/6 and enalty schemes 2 k() 3. These facts imly 2/7 β() k() 1/2, or an exected enalty roughly between 30% to 50% of the illegal cartel rofits. Therefore, the AA may not be able to deter violations. Here, we assume 0<β()k()<1 for all є ( N, M ] meaning any cartel is temted to set its rice above the cometitive rice. Another asect is how cartel members react to detection. In some cases, being caught once is sufficient to deter cartel activity in the future. In other cases, the economic sector is notorious for cartel activities desite many convictions (meaning members ay the fines and continue 38

3 illegal business). γ є [0,1] is the cartel culture arameter that reflects the robability that the firms will behave cometitively (i.e. sto illegal business) after each conviction. Notorious imlies γ=0, while γ=1 means the sector becomes cometitive after the first detection. All models in the literature assume either γ=0 or γ=1. Let V() be the resent value of a cartel member s exected rofit if the cartel sets rice є [ N, M ] in every eriod. This value consists of the current illegal gains π(), the exected fine β()k()π(), the exected continuation ayoff where suerscrit R refers to regulation. Program (5) is a well-defined rogram since є [ N, M ], which can be deducted as follows. Since the monotonicity roerties of Λ() (increasing) and λ() (decreasing) are oosite, the intersection λ()=λ () is unique and coincides with R. Furthermore, any R can also be sustained by the cartel. So, the range of rices in (4) is a closed subinterval of [ N, M ]. Comaring (2) and (5), we observe that N R C M meaning that regulation may reduce the maximal-sustainable cartel rice in general. Similar to Proosition 1, we derive the "Current regulation is ineffective" of a renewed cartel after detection β()(1 γ) δv(), and the exected continuation ayoff of not being detected (1 β())δv(), from which we obtain 1 β( k ) ( ) π( ) V( ) π( ), 1 δ[1 γβ( )] 1 δ (3) (, ]. So, introduction of regulation reduces the cartel s rofitability. Does it also affect sustainability? The cartel has its own destabilizing forces working from within, because individual cartel members have an incentive to cheat on the cartel. Here, cartel members adot modified grimtrigger strategies to sustain > N : 1 Firms continue to set a rice >0 with robability 1 γ after each conviction (and with robability γ set the cometitive rice N ever after). 2 Any deviation by some cartel members leads to the cometitive rice N in every eriod ever after. Then, the rofit from a unilateral deviation is equal to the short term gain of π ot () in the current eriod, followed by the cometitive equilibrium with π( N )=0 forever after. Consequently, the necessary and sufficient condition to sustain cartel rice є ( N, M ] is V() π ot (), or 1 δ[1 γβ( )] λ( ) Λ( ) (4) 1 β( k ) ( ) Under regulation the maximal-sustainable cartel rice is given by R max, s.t. (4). (5) [, ] thresholds on the discount factor δ. Doing so, (4) can be rewritten as 1 λ( )[1 β( k ) ( )] δ Δ( ) 1 λ( ) [1 γβ( )] (6) The function Δ() is continuous and increasing in, k() and β(). Proosition 3 Under regulation, the maximal-sustainable cartel rice R is non-decreasing in δ є (0,1) and decreasing in γ є [0,1]. Furthermore, we have R = N, for δ є (0, 1 λ), R є [ N, ), for δ є [1 λ, Δ( M )), R = M, for δ є [Δ( M ), 1), An overall increase in β() or k() shifts Δ( M ) and the entire curve to the right. Clearly, inequality (6) is more restrictive than (1) imlying that introduction of regulation restricts the set of discount factors for which collusion can be sustained for every ossible rice є ( N, ]. This imlies that cartel stability is reduced comared to the benchmark case. Moreover, the fact that Δ() is increasing in imlies that the regulation is more effective against collusion on higher rices. When Δ( M ) δ<1, the regulation is not effective to deter the cartel from setting its monooly rice. It is interesting to investigate whether regulation can eradicate the monooly rice for all cartel cultures. Solving Δ( M )<1 for γ yields γ < {λ( M )[1 k( M )β( M )]}/β( M ), where the right-hand side remains ositive under 0<β()k()<1. Hence, industries that are notorious for cartel behavior cannot be eradica- 39

4 ted by regulation unless one is willing to adot regulation that fully takes away the illegal gains (i.e. β()k()>1 for all є ( N, ]). Another imlication is related to the effect of the degree of cartel stability λ() on sustainability of the monooly rice. Since Δ/ λ<0, sectors where the degree of cartel stability is higher (λ() closer to 1) have less restrictive conditions for sustaining consumers worst rice M. This makes regulation less effective in these sectors. The main message is a mixed blessing for regulation. On the one hand, roosition 3 identifies non-emty sets of arameter values for which regulation is effective in reducing the maximalsustainable cartel rice, i.e., R < C. On the other hand, as long as regulation obeys β() k()<1, there will remain a large non-emty set of arameter values for which R = M, meaning the regulation is ineffective. We conclude this section with an examle. Examle 4 Reconsider Examle 2 and let β()=β and k()=k, where k<1. Then, (5) becomes 1 1 δ γδβ ( δγ, ) max, s.t.. [0,1] n 1 kβ Note that =0 is feasible in the quadratic constraint if and only if δ 1 1/n. The constraint can be rewritten as [1 n(1 δ)]/[(nγδ+k)β], which is the solution to the roblem if it is between 0 and 1. The right hand side is increasing in δ. To summarize, we have < = < + Note that R < M =1 for all δ є (0,1) if and only if (nγ+k)β>1. Since βk<1, this condition can hold only when nγ is sufficiently large. For sectors with small numbers of firms and γ sufficiently close to 0, the monooly rice will not be eradicated by regulation. Both ossible cases, (nγ+k)β 1, resectively, (nγ+k)β>1, are illustrated by figure 1, where the vertical dotted line at δ=1 1/n reresents the discontinuous jum in C of Examle 2 from N =0 to M =1. The rofit-maximizing cartel rice In this section, we comare our aroach to Harrington (2004, 2005). He defines the endogenous cartel rice as the rofit-maximizing sustainable cartel rice π : π arg max V ( ), s.t. (4). (7) [, ] For exlanatory reasons, we restrict attention to numerical values β()=/2 and k()=3 and γ=2/3 in Examle 4. Then, = + Standard arguments imly V() fails both monotonicity and concavity on [ N, M ]=[0,1], but this function is single eaked on [ N, M ]. Checking the second-order conditions can be avoided, because V() is monotonically increasing from N to its eak and monotonically decreasing from its eak to M. So, alication of the first-order conditions suffices. In contrast, (5) is a well-defined convex rogram. Harrington shows that, in general, (4) is nonbinding for δ sufficiently close to 1 and we may solve the first-order condition V()/ =0. In our case, MAPLE returns Figure

5 the rofit-maximizing cartel rice underestimates the maximal damage to consumers; a bias that might be huge. Since economic agents often behave differently from standard microeconomic theory, the criterion of sustainability of cartel behavior offers a more robust framework that does not deend on the cartel s objective function. In this ersective, our aroach is a worst-case scenario. References Baumol, W. (1958). On the theory of oligooly, Economica, 25, Figure 2 for all δ є [0,1]. Taking also (4) into account imlies that the rofit-maximizing cartel rice π is the minimum of and R. These two rice curves intersect at δ So, on the interval [0,0.955], the rofit-maximizing cartel rice π = R, while for the interval (0.955,1] we have π = < R and the equilibrium condition is nonbinding. Figure 2 illustrates π =min{, R }. This examle offers imortant insights. Whenever constraint (4) in (7) is binding, the maximal-sustainable cartel rice R and the rofit-maximizing cartel rice π coincide and our aroach is comlementary to the analysis in Harrington (2004,2005). Otherwise, i.e., (4) in (7) is nonbinding, these two cartel rices systematically differ. As the figure shows, for δ close to 1, the rofit-maximizing cartel rice π is close to the cometitive rice N and, therefore, seriously underestimates the otential maximal damage to consumers. Our aroach offers a worst case scenario of sustainable cartel behavior. Harrington, J. (2004). Cartel ricing dynamics in the resence of an antitrust authority, The Rand Journal of Economics, 35, Harrington, J. (2005). Otimal cartel ricing in the resence of an antitrust authority, International Economic Review, 46, Houba, H., Motchenkova, E., and Wen, Q. (2009). Leniency rograms in antitrust regulation with an endogenous detection robability, TI discussion aer, (in rearation). OECD (2002). Fighting hard-core cartels: Harm, effective sanctions and leniency rograms. OECD Reort 2002, OECD, Paris, France, htt:// Conclusion In this article, we exlore a general infinitelyreeated oligooly model for the analysis of violations of cometition law under regulation. A novel concet is the maximal-sustainable cartel rice that reflects consumers worst cartel rice among those cartel rices that are sustainable, which endogenizes the cartel formation decision and its ricing strategy. This cartel rice is related to the discount rate and the novel concets of tye and structure of the industry (λ) and cartel culture arameter (γ). Regulation is less effective in sectors where the degree of cartel stability is higher or where the sector s cartel culture to continue business as usual is more rominent. Stylized facts from OECD countries imly that current regulation is ineffective. Finally, our aroach is comlementary to Harrington (2004, 2005) in case equilibrium conditions are binding. Otherwise, 41