Cartel Punishment and the Distortive Effects of Fines

Cartels punishment and distortive effects of fines* Emilie Dargaud†, Andrea Mantovani‡ and Carlo Reggiani§ December 2015 Abstract: The fight against cartels is a priority for antitrust authorities worldwide but the goal is pursued in many different ways. Several types of fines can be levied on firms that are caught colluding but one common trait is that fines are usually distortive. In this paper we focus on the economic effects of distortive fines. To this end, we compare a fine based on the cartel profit as opposed to one based on the cartel damage. We study the effects of the two fines and show that a potential trade‐off between ex ante deterrence and ex post consumer surplus may occur. We show that such a trade‐off is of particular relevance when antitrust authorities face exogenous fine caps, as it is often the case in practice. The results are robust to a number of extensions, including the relevant case of fines designed to punish managerial firms involved in cartel activities. Keywords: cartel policy, collusion, deterrence, fines. JEL Classification: K21, L44, K42. 1 Introduction The past decade has witnessed a worldwide increase in price‐fixing, market‐sharing and bid‐rigging cartel behaviour. As a consequence, the fight against cartels has evolved to require unprecedented efforts by the relevant antitrust authorities. These efforts led to a gradual convergence of the corporate leniency programs around the world.1 A similar convergence process did not occur in the sanctioning procedures. The legal and enforcement regimes remain quite heterogeneous in different countries and economic areas. For example, while antitrust guidelines in both the US and EU are founded on the principle that punishments should "fit the crime" (see DOJ, 2010, and EC, 2006), in the US the gravity of the offence is measured by the cartel’s illegal gains, while in the EU it is captured by the cartel * We would like to thank Bruce Lyons, Antonio Nicolo’ and seminar participants at East Anglia for helpful comments and discussion. We also thank Lucy Scioscia for editorial assistance. This manuscript supersedes an unpublished working paper (Dargaud et al., 2013) in which we studied the punishing‐the‐manager or punishing‐the‐firm debate. The usual disclaimer applies. † University of Lyon, F‐69007, Lyon, France; CNRS, GATE Lyon St Etienne, 93, Chemin des Mouilles, F‐69130, Ecully, France. E‐mail: dargaud@gate.cnrs.fr. ‡ Department of Economics, University of Bologna, Strada Maggiore 45, 40125 Bologna Italy and Barcelona Institute of Economics (IEB), C/ J. M. Keynes, 1‐11, 08034 Barcelona, Spain. E‐mail: a.mantovani@unibo.it. § School of Social Sciences ‐ Economics, University of Manchester, Manchester M13 9PL, UK. E‐mail: carlo.reggiani@manchester.ac.uk. 1 The EU, for example, revisited its legislation in 2002, largely on the basis of the US experience. Although some differences still remain, scholars and policy makers agree that the so‐called "leniency revolution" (Spagnolo, 2008) brought forth a very effective tool for uncovering existing cartels. On the evolution of the EU and US penalties and policy structure, see also Caree et al. (2010) and Ghosal and Sokol (2014). 1 overcharge. The situation is even more intricate if focusing on the national level. Most jurisdictions determine the amount of "basic fines" which are then adjusted with aggravating (duration, recidivism) or mitigating (cooperation, limited participation) elements. 2 The overwhelming heterogeneity of the punishment strategies to crack down on cartel behaviour does not allow to provide a holistic comparison across all sanctionatory approaches. The common trait, however, is that the penalties employed around the world are likely to distort the decisions of firms. Another important observation is that most jurisdictions impose a predetermined cap on the amount of the fine that can be imposed by the antitrust authority. The existence of maximum fines is justified on the basis of bankruptcy concerns3 and their ultimate goal is to preserve the highest number of active competitors in the market.4 In general, the presence of such costs implies that the sanctionatory measures taken by the antitrust authority cannot always guarantee the complete deterrence of cartel activity (Buccirossi and Spagnolo, 2007; Wils, 2007; Houba et al., 2013, 2014). In this context of incomplete cartel deterrence, we provide an in‐depth analysis of the economic effects of distortionary fines. In particular, given the complex structure of punishment regimes around the world, we will trade‐off some realism in the interest of better highlighting the effects in operation and we focus on two representative policy instruments, used to punish duopolists interacting in a Cournot market. The first instrument is a typical non‐distortive fine, which we shall call profit‐based fine. This may be represented by a simple fixed fine, like the one considered by several contributions in the literature (Motta and Polo, 2003; Aubert et al., 2006; Rey, 2003) or by a fine proportional to the profit (Katsoulacos and Ulph, 2013). The second instrument is a fine proportional to the damage of collusion or, indirectly, to its price overcharge (Buccirossi and Spagnolo, 2007; Katsoulacos and Ulph, 2013; Houba et al., 2013, 2014). We shall call the latter a damage‐based fine. The main feature that we underline is that the damage‐based fine, and more generally non‐profit based sanctions, are likely to have a distortive effect on the output level. In other words, firms involved in cartel activities have an incentive to produce more in presence of a damage‐based fine than with a profit‐based fine. This is an ex post effect, as it takes place only if collusion can be sustained despite the ex ante deterrence effort exerted by the antitrust authority. We address the consequences of such a distortion for both the deterrence and the overall welfare impact of fines. Output distortions have been widely investigated in the context of public economics and taxation (see Auerbach and Hines, 2002, inter alii). The main contribution of this paper is to show that distortions also play a relevant role in the dynamic context of cartels and cartel 2 The exact determination and computation processes vary from country to country. For instance, the basic administrative fine against cartel members can be computed in relation to the turnover. The turnover, however, can be defined in different ways: it may be the value of sales concerned by the infringement (Germany‐Japan), the value of affected commerce (US‐Canada), the global or worldwide turnover (France‐Serbia) or the national turnover (Brazil). Moreover, both the benefit resulting from the cartel activity and the losses caused to society may be taken into account when determining the amount of the fine: this is the case of Hungary and Austria. Less common sanction procedures can be applied. In Mexico, for example, the fine is computed in relation to the general minimum wage. 3 Besides bankruptcy concerns, Block and Sidak (1980) provide other theoretical arguments against draconian sanctions in cartel deterrence. 4 In the EU, for example, the European Commission may impose fines up to 10% of firms’ overall total annual turnover (EC, 2006; Bos and Schinkel, 2006; Bageri et al., 2012; Fabra and Motta, 2013). Within this limit, fines may reach up to 30% of the company’s annual sales to which the infringement relates. In the US there is no formal legal upper bound on the antitrust fines. The United States Sentencing Guidelines (USSG) indicate a 10% base fine of the affected commerce plus 10% for the damage inflicted on consumers; different aggravating factors can be added, thus raising the total fine. However, in many cases, total fines are reduced due to firms’ inability to pay. In Canada, the limit is set at 10% of total company sales. 2 deterrence. In particular, using a revenue equivalence requirement, we identify situations in which antitrust authorities face a trade‐off between ex ante deterrence, better achieved through a non‐distortive profit‐based instrument, and ex post overall welfare, enhanced through the adoption of a distortive damage‐based fine. We show that the trade‐off is more likely to arise when, as it often happens in reality, competition authorities face statutory ceilings on the amount of fines which can legally be imposed. We then proceed by relaxing some relevant assumptions. First, as the majority of cartel cases involve managerial firms, we evaluate the impact of our two benchmark fines in presence of managers whose decisions are not fully aligned with the owners of the firm. Second, we introduce a third type of fine, proportional to the extra profits generated by cartel activity. This combines the features of the two previous instruments as it is both proportional to the damage caused by the cartel and based on the firms’ profits.5 Third, we consider an adjusted revenue equivalence that takes into account the expectations regarding the interval range in which the cartel is supposed to be supported. All in all, the robustness of our results is confirmed by all the extensions. In particular, both the ex ante and ex post economic effects which we clearly identified in the simple initial scenario are still in operation. The rest of the paper is structured as follows. In Section 2 we review the most closely related literature and precisely locate our contribution. In Section 3, we present the basic model. In Section 4 we introduce the features of the two types of fines and evaluate their comparative performance on cartel deterrence. Section 5 considers the welfare effects of the two fines. Section 6 presents some relevant robustness checks to reinforce the validity of our results and Section 7 provides a brief discussion of the results and concludes. The proofs are in the Appendix. 2 Related literature and contribution Despite the intuitive nature of the possible tension between ex ante deterrence and ex post output distortion, this paper is one of the first to fully explore such a trade‐off, decompose all the relevant economic effects, evaluate the deterring and welfare effects of each instrument and, innovatively, to identify and explore the trade‐off faced by antitrust authorities when choosing the appropriate penalties for cartel behaviour. Since the pioneering work of Becker (1968), economists have developed an extensive literature related to "optimal sanctions".6 Sanctions should not only seek to punish detected cartels ("ex post effectiveness") but also to discourage firms to engage in such illegal practices ("ex ante effectiveness"). Block et al. (1981) provide early evidence of the relation between antritrust deterrence, measured as the effort to both detect and fine cartel activity, and the reduction in the industry markup. The deterrence effect of different antitrust enforcements is investigated in Aubert et al. (2006) and Motta and Polo (2003) in the context of leniency. Souam (2001) considers revenue based fines as opposed to damage based fines in a context of uncertainty about the existence of a cartel. The model highlights the interaction between the antitrust authority and the firms and, in particular, the possibility of Type I (non colluding firms being prosecuted) and Type II 5 6 Fines based on illegal gains are analysed in Harrington (2004, 2005) and Houba et al. (2010, 2012), inter alia. For example, see Besanko and Spulber (1989), and recent contributions by Buccirossi and Spagnolo (2007) and Allain et al. (2011), inter alii. 3 (colluding firms not being fined) errors when punishing firms. In our paper we focus only on the latter type of error. Two recent papers, Bageri et al. (2013) and Katsoulacos and Ulph (2013), consider aspects closely related to our analysis and complement our results: the former mainly focuses on the distortionary effects of revenue based fines, while the latter considers the impact on ex ante deterrence, although across markets that differ in terms of competitiveness level. Our paper differs from both contributions as we thoroughly address the trade‐off between the distortionary impact and the deterrence effect of different sanctionatory approaches. In particular, we formally show the ambiguous effect that distortive fines may have on cartel deterrence and total welfare. The most closely related paper, developed in parallel to ours, is Katsoulacos et al. (2015). The paper uses a similar methodology and compares three types of fines (two similar to the ones we consider and a revenue‐based one). In our paper, we focus for expositional simplicity on the case of duopoly but, given the monotonicity property of Cournot games, our analysis is likely to carry on for any number of firms. Katsoulacos et al. (2015) price‐setting oligopoly is, in a way, more general; however, in their setting a deviation has rather extreme consequences, as the cheated firms obtain no profits. Moreover, the quantity versus price competition assumption may have bearings that go beyond theory: recent experimental evidence by Mermer et al. (2015) shows that cooperative play is more likely in a game of strategic substitutes (like quantity competition) rather than strategic complements (like price competition). Besides the different approaches to competition, our research questions and results also differ. Whereas Katsoulacos et al. (2015) ask the question of what is the best instrument an antitrust authority should adopt, our goal is to highlight and address all the economic effects of distortionary penalties used in a dynamic setting like cartels. Moreover, whereas their results unquestionably call for an overcharge based fine, our conclusions suggest that the picture may be more nuanced. In particular, given the prevalence of consumers’ surplus as a welfare standard, we highlight that in presence of distortionary effects the antitrust authority may face a trade‐off between ex ante and ex‐post deterrence. 3 Benchmark model In order to make our analysis as clear and as simple as possible, we consider a standard duopoly model in which firms compete à la Cournot in the final product market. The inverse demand is linear, and given by p = a  Q , where Q = q1  q2 . The marginal cost is constant and equal to c for both firms. The resulting profit function is:  i = p(Q)qi  cqi , i = 1,2, (1) For simplicity of notation and without loss of generality, we set A = a  c , so the firms’ objective function can be rewritten as follows:  i = ( A  Q)qi , i = 1,2, and A is high enough to guarantee that all quantities and profits are non‐negative. 4 (2) The basic stage game is repeated infinitely over time. In each stage, firms decide whether to play non‐cooperatively, or to produce the collusive output. As a result, the payoffs for each firm are denoted respectively as  iN ,  iC , and  iD , where N indicates the Cournot‐Nash equilibrium, C the collusive equilibrium, and D the deviation from collusion, when the rival sticks to its cartel output level. To simplify notation, by using symmetry, we remove subscript i . In the absence of fines, it is immediate to verify that  N = A2 /9 ,  C = A2 /8 and  D = 9 A2 /64 . Collusion is sustained through a grim trigger strategy (Friedman, 1971): if one firm deviates from the collusive agreement, it is punished by reverting to Cournot competition forever. Let  i  [0,1] define firm i ’s individual discount factor. We assume players’ intertemporal preferences are pairwise symmetric, hence 1 =  2 =  . Standard derivations show that firms form a sustainable cartel when their discount factor is sufficiently high, i.e.   ( D   C )/( D   N ). In the present setting, this implies:  9  17 (3) This represents our benchmark case. For future reference, the collusive per‐firm output is q C = A/4 , and the Cournot‐Nash one is q N = A/3 . 4 The fight against cartels: two types of fines We start by focusing on two types of fines that try to deter cartel formation. The first type directly targets the firms’ profits and we shall call it profit‐based fine. The second one is based on the damage caused by the illegal cartel activity. It should be noted that such a fine is proportional to the price overcharge and we shall call it damage‐based fine. We suppose that a cartel agreement requires some communication between the firms’ management, therefore generating tangible evidence. However, consistently with the literature (Rey, 2003; Motta and Polo, 2003; Aubert et al., 2006; Avramovich, 2010), we assume that the evidence disappears at the end of each period and therefore firms are not sanctioned in case of deviation. 4.1 The profit‐based fine The antitrust authority is assumed to detect the collusive behaviour between managers with probability  . 7 When this happens, it launches an investigation leading to a successful prosecution of the cartel. A total fine F is imposed implying that each firm pays F/2 . Type I errors (firms which do not collude but are still prosecuted) are assumed not to occur, whereas Type II errors (colluding firms are not fined) do. Under these assumptions, the colluding firms jointly maximise:  = ( A  Q)Q  F . 7 (4) The exogeneity of the parameter  eliminates several potential effects of the antitrust policy. If  depended on the firms’ prices (or quantities), then the cartel would adopt complex price patterns (Harrington, 2004 and 2005; Harrington and Chen, 2006; Houba et al., 2013). 5 Taking the first‐order condition and imposing symmetry, it is straightforward to find that each firm still produces A/4, as the expected fine F is fixed and as such does not distort firms’ choices. It follows that q PC = q C = A/4 , where subscript P identifies the equilibrium for the profit‐based fine. This implies that the strategic response by the cheating firm also remains the same, and so does its final payoff, as we assumed that firms are not punished in case of deviation. Therefore,  PD =  D = 9 A2 /64. Clearly, the Cournot‐Nash profits do not depend on the fine and hence are unchanged. The only difference with respect to the benchmark case is represented by the expected payoff in case of collusion, which results in  PC = A2 /8  F/2 . As the incentive to form a cartel appears in presence of a prisoners’ dilemma (i.e. the individual collusive payoff must be higher than the Cournot payoff), we assume that:  PC   N  F  T = A2 , 36 (5) with T being the maximum level of the profit‐based fine.8 Under condition (5), firms can sustain the collusive agreement over time if and only if their discount factor satisfies the following condition:  9  32 F  1  P. A2  17  (6) The above expression showcases the most important features of the profit‐based fine. Straightforwardly, the higher the expected fine, the more difficult it is to sustain collusion. Obviously, in absence of the antitrust policy ( F = 0 ),  P would coincide with the threshold value   = 9/17 . In the opposite scenario,  P = 1 when F = T , and the collusive agreement is not an option for firms and deterrence is complete. Finally, it is important to underline that we choose to focus on a lump‐sum fine to keep matters as simple as possible and to be in line with a number of contributions in the cartel deterrence literature (Motta and Polo, 2003; Aubert et al., 2006; Rey, 2003). However, it is straightforward to show that a proportional profit‐based fine has exactly identical effects provided that F = f C .9 8 This, a fortiori, also guarantees that cartel expected payoffs are non‐negative. In other words and in line with the extant literature, the antitrust authority attempts to deter cartels by making them less stable. Notice that our assumption is also consistent with the implicit or explicit ceilings on fines imposed in most legal systems to avoid jeopardising the financial stability of convicted firms (Bageri et al., 2013; Houba et al., 2013), as it was previously introduced. 9 The proportional fine is non‐distortionary as the cartel maximises (1 f )  C , a parallel downwards shift of the profit curve: hence, the maximum cartel profit is still reached at of collusion is obtained for   (  D C qC P = q = A /4  (1   f )  C C . Each firm’s cartel profit is  P )/(  D   N ) = ( 6 D 2 2 = (1   f ) A /8 = A /8   F /2 C D N   P )/(    )   P . and, hence, sustainability 4.2 The damage‐based fine The antitrust authority may not punish cartels by directly targeting profits: fines are often computed on the basis of some other proxy of the damage caused by the illegal activity. We consider a damage‐based fine that is levied on the output gap implied by the formation of a cartel. In our setting, such an instrument is almost equivalent to a fine on the price overcharge, as in Houba et al., (2013, 2014), inter alia. This implies that, when collusion is detected, a fine  is levied proportionally to the damage in term of foregone output compared to the Cournot‐Nash equilibrium. The probability  is assumed to be unchanged compared to the profit‐based case, implying that the expected revenue for the antitrust authority is now  (Q N  QDC ) , where the additional superscript D indicates variables referring to the damage‐based fine case. The latter discussion implies that firms now jointly maximise:  = ( A  Q )Q   (Q N  Q ). (7) Taking the first order conditions and using symmetry, the individual collusive outcome is given by q DC = A/4  /4 . Hence: Remark 1 The collusive output is affected by the damage‐based fine. In particular, one can immediately notice that q C < qDC . The expected fine is now taken into account by the colluding firms in their maximization process, and it induces an increase in the output level. This will have important consequences in terms of social welfare, as we will discuss in the next section. The corresponding payoff of a firm participating in the cartel can be easily obtained, and it is given by  DC = A2 /8   2 A  3 /24 . Interestingly, following Remark 1, the strategic response of the deviating player now includes the expected fine rate. This in turn affects the deviation payoff, which amounts to  DD = 3 A   2 /64 . As a consequence: Remark 2 The damage‐based fine decreases the incentive to deviate from the collusive outcome, as  PD >  DD . A complete evaluation of the respective effectiveness of the two policy instruments will be performed in the next section and it involves also the comparison between collusive payoffs  PC and  DC . However, Remark 2 already unveils one of the possible strengths of the profit‐based vis à vis the damage‐based fine: if a damage‐based fine is imposed, deviating from a collusive agreement becomes less profitable for firms. As Cournot‐Nash payoffs are not affected by the fine, we can now compute the threshold value of the discount factor which sustains collusion under the damage‐based fine. We need to ensure that the individual collusive payoff is still higher than the Cournot one. This requires:  DC   N    t = 7 A . 3 (8) Assuming (8) holds, firms can sustain the collusive agreement over time if and only if:  9 A  21  D. 17 A  3 (9) Similarly to the previous case, the higher the expected fine, the more difficult it is to collude. Finally, it is immediate to verify that  D    when the expected fine rate tends towards zero, and that  D = 1 when  = t . 4.3 Profit‐based versus damage‐based fine: which one better deters cartel formation? The two types of fines can be compared and precise conditions can be found for which one is more effective than the other in deterring collusion. The following holds: Proposition 1 Suppose F  T and   t , then the profit‐based fine is more effective in deterring collusion if and only if: 4 A 2 ~ F > T (  ) = . 51A  9  ~ ~ The opposite holds for 0 < F < T (  ). Moreover, T (  ) is increasing in  . Proof See the Appendix. Proposition 1 conveys two main messages. The first one has an intuitive appeal: the instrument that prevails in deterring cartels depends on the relative intensity of the profit‐based fine as compared to the damage‐based. Second, the higher the expected damage‐based fine, the higher the profit‐based needs to be in order to deter collusion more effectively. Finally, ~ notice that the threshold T depends on the probability of detection  . This happens despite such a probability is identical under both types of fines: the reason is that the damage‐based fine is distortionary and affects the firms’ choices ( q DC ), implying that not only the actual fines’ intensity (  or F ) affects the comparison but also their common probability  . Revenue equivalence The results in Proposition 1 are strongly affected by the possibility that the antitrust authority charges two different levels of sanctions, depending on whether it opts for the profit‐based or for the damage‐based instrument. However, it is more relevant to the policy maker to find out which of the two instruments performs better for a given value of the expected revenue. In this context, a revenue equivalence requirement implies: F =  (Q N  QDC ). 8 (10) Following (10), condition (5) can be re‐written as:  ( A  3 ) 6 A2 < . 36 (11) By comparing (11) with (8), we find that the binding condition is t . Indeed, it is relatively easy to verify that (11) holds when   t = A/3 . This indicates that a damage‐based fine is more effective in eradicating collusion when the antitrust authority is allowed to impose very high fines. Moreover, under (10) the threshold discount factor  P that appears in (6) can be re‐expressed as:  Pre  9  16  ( A  3 )  1 , 17  3 A2  (12) where the superscript re indicates revenue equivalence. We can therefore compare the two instruments to find that: Proposition 2 Under (10),  Pre   D if 0 <   t1  (3  2 2 ) A and  Pre <  D if t1 <   t . Proof See the Appendix. The main message of Proposition 2 is that the comparison between the two types of fines in terms of deterrence capability depends on the level of the fine. If the expected fine rates are relatively low (   t1 ), the profit‐based instrument is more effective in destabilizing collusion than the damage‐based one. On the other hand, if the expected fine rates are relatively high (  > t1 ), the damage‐based fine is to be preferred over the profit‐based one. This is consistent with the previous remark that the damage‐based instrument performs better when fines are intended to completely deter cartels, i.e. in the limit case of  = t . This result can be interpreted by focusing on two opposite effects. On the one hand, we know that, unlike the lump‐sum fine, the damage‐based fine makes the deviation payoffs less appealing (Remark 2), thus increasing the incentives to stick to the collusive outcome. The "cheated" opponent, sticking to the collusive agreement, expects to be fined proportionally to the non‐produced output. For this reason it increases its output, and therefore the best‐response output of the deviating firm decreases. On the other hand, the damage‐based fine, being distortive (Remark 1), has a stronger impact on firms’ collusive payoffs than the profit‐based one. Indeed, under revenue equivalence: ( PC ) re = A2  ( A  3 ) .  8 12 (13) It is then immediate to demonstrate that  DC  ( PC ) re < 0 . Ceteris paribus, this makes collusion easier to sustain in presence of a profit‐based fine. 9 The relative strength of these two conflicting forces determines which tool is better suited to deterring cartel activity. If the fines are relatively low, then the first effect dominates, making collusion less stable under a profit‐based fine. On the contrary, if the fines are relatively high, the second effect dominates and the value of the minimum discount factor that sustains collusion results higher under the distortive damage‐based fine. As antitrust authorities are often under some pressure to prevent cartel formation by imposing fines that are not prohibitively high, our results suggest that a profit‐based tool may be preferred. However, when missing the mark, the profit‐based fine generates additional losses to consumers. The distortive damage‐based instrument, as we know from Lemma 1, guarantees a higher level of collusive output than the profit‐based fine. These considerations suggest to look more in depth at the welfare effects of these different types of fines. 5 Welfare implications The main message of the previous section is that if low fines are appealing to antitrust authorities then a profit‐based instrument should be selected when considering ex ante cartel deterrence. This may be the case as antitrust authorities often face caps or other pressures to keep sanctions within certain limits. However, if the cartel takes place, profit‐based fines induce an ex post negative effect on consumer surplus. The quantity produced under collusion in the damage‐based case is in fact higher than that produced under collusion when adopting the profit‐based tool. The aim of this section is to explore this possible trade‐off. In so doing, we focus on the expected welfare generated by each instrument. In our setting, the success of cartel deterrence crucially depends on the patience of firms. For analytical convenience we assume that from the antitrust authority perspective there is a uniform distribution of the firms’ discount factor, i.e.  ~ U [0,1].10 The expected welfare can then be written as: EW =  jW N  (1   j )W C , (14) where  i is the threshold discount factor in regime j , W N is a generic measure of welfare generated under Cournot‐Nash competition, and W C is the one associated to the cartel. This allows us to compare the impact of the two fines on both consumer surplus and total welfare. 5.1 Consumer surplus The top priority of antitrust authorities in many countries is to protect consumers’ interests.11 Hence, it is worth evaluating the impact on consumer surplus of the two instruments that we consider. As the demand function is linear, and given that we consider a symmetric duopoly, 10 This may be the case if the antitrust authority has no prior information about the time preferences of the firms that operate in the market. As a consequence, any discount factor is equally likely to occur. 11 The dispute on the appropriate standard for antitrust enforcement seems still unsettled. For example, see Salop (2010) for arguments in favour of consumer surplus as a standard and Sidak (1981) and Carlton (2007) for arguments in favour of a total welfare standard. See also Pittman (2007) for a thorough discussion. 10 consumer surplus can be written as: CS = Q 2 /2  2q 2 . (15) In the benchmark case, in which no penalty is implemented, collusion is sustainable for  >   = 9/17 . Following (14), the expected consumer surplus is: ECS * =  [2(q N ) 2 ]  (1    )[2(q C ) 2 ] = 3 2 A. 17 (16) When the profit‐based fine is adopted, the expected consumer surplus amounts to: ECS P =  P [2( q N ) 2 ]  (1   P )[2(qPC ) 2 ] = 3 A2 28 F  , 17 17 (17) which is obviously higher than in the benchmark case. The relevant output levels q N and q C  qPC are unaffected by the fine, that however increases the interval region where collusion is successfully deterred (  P >   ). This, in turn, reduces the probability that firms’ discount factors are sufficient to support the collusive behaviour. Turning to the damage‐based fine, the expected consumer surplus is: ECS D =  D [ 2( q N ) 2 ]  (1   D )[2( q DC ) 2 ] = 3 A 2  [ 214 A 2  255 A  153(  ) 2 ] . (18)  17 51(17 A  3 ) When comparing ECS D with ECS  , we have that not only collusion is less likely to occur, as  D >   , but also that q DC > q Cp , as already acknowledged in Remark 1. If the cartel persists, the effect of the damage‐based instrument is to raise the cartel quantity as compared to the standard case. Under revenue equivalence, it is also possible to evaluate which one is better from a consumer’s standpoint. Proposition 3 0 <   t 2  A(167  24913 )/186 , Under (10), ECS Pre  ECS D if and ECSPre < ECSD if t 2 <   t . Moreover, we find that t 2 < t1. Proof See the Appendix. The following decomposition helps to explain why this occurs: ECS Pre  ECS D  ( Pre   D )[2( q N ) 2  2(q PC ) 2 ]  (1   D )[2(q DC ) 2  2(q PC ) 2 ] Š0 0 0 Deterrence differential 11 0 Expected ex post loss (19) We clearly identify two effects: a "deterrence differential" and an "expected ex post loss". The former captures the different deterrence effects associated to the profit‐based fine vis à vis the damage‐based fine. Both instruments increase the interval region where collusion cannot be supported. However, as we know from Proposition 2, when fines are relatively low (i.e.  < t1 ), the profit‐based fine is more effective (  Pre >  D ) and the deterrence differential is therefore positive. The second effect captures the absence of a positive output distortion under the profit‐based fine. As only the damage‐based instrument induces cartel members to increase the collusive output, the second term of (19) represents the ex post loss induced by the profit‐based instrument. Hence, when expected fines are relatively low (i.e.  < t1 ), it is the balance between these the two effects that indicates which fine is more likely to enhance consumer surplus. In particular, such effects compensate each other at rate  = t 2 < t1 . On the other hand, if the fines are relatively high, then both effects go in the same direction and  Pre <  D . In that case, the damage‐based fine is clearly dominating from the expected consumer surplus viewpoint. Importantly, a trade‐off is identified in the interval region where t2 <   t1 . For such intermediate values of the fine rate, the deterrence differential is still positive as  Pre >  D . However, this effect is dominated by the expected ex post loss, implying that a damage‐based fine is to be preferred from an expected consumer surplus perspective. The previous discussion is summarized in Figure 1. Figure 1 : Deterrence Effect and Expected Consumer Surplus  t t1 ECS  ECS D re P  Pre   D ECS Pre  ECS D t2  Pre   D  Pre   D ECS Pre  ECS D A 12 The trade‐off identified for intermediate values of the fine rates ( t2 <   t1 ) can be particularly relevant for antitrust authorities when they face different constraints in the level of punishment. Figure 2 illustrates the EU case in which firms participating in a cartel cannot pay fines higher than 10% of their total annual revenue (Houba et al., 2013, 2014; Bageri et al., 2013). Figure 2 : Fine caps  t FC P t1 FC D t2 A0 A For a given level of A , which represents a proxy of the market size, the antitrust authority would like to increase the punishment as high as possible, as that would increase the likelihood of deterrence. However, as illustrated by the functions FCi , a fine cap based on the revenue translates in an increasing convex function of A . This implies a maximum fine being represented by the curves FCi . More precisely, in the case of a profit‐based fine, the cap FCP is proportional to the revenue of the cartel, whereas a damage‐based fine would shift out the fine cap to FCD .12 Indeed, due to the output distortion, the revenue is lower for any value of A . As a consequence, there are values of A for which an antitrust authority may face the trade‐off 12 The revenue of the cartel clearly also depends on the marginal cost: in presence of the profit‐based fine, the revenue is ( A 2  2 Ac ) /4. The FC i constraint is binding if the percentage of the cap and/or the marginal cost are not too high. For intermediate values of the percentage of the cap and/or the marginal cost, the FC i curves shift up and the curves lie above trade‐off also for low values of A . 13 t 2 for all values of the fines, giving rise to the highlighted above. Consider market size A0 . The maximum fine that can be imposed lies in t2 <   t1 . The profit‐based fine is ex ante more effective in deterring cartel formation, while the damage‐based fine entails a higher expected consumer surplus. 5.2 Aggregate surplus Suppose now that the antitrust authority does not limit its attention to consumer’s protection, but it considers instead the total social welfare. The revenue collected by the antitrust authority does not affect total welfare, as it constitutes a mere transfer between the firms and the authority. Total welfare can therefore be written as:13 TW = 2  2q 2 . (20) Following the same reasoning as in (14), the expected welfare in the benchmark case amounts to: 7 2 (21) ETW  =   [2 N  2(q N ) 2 ]  (1    )[2 C  2(q C ) 2 ] = A . 17 In the presence of the profit‐based fine, we find: ETWP =  P [2 N  2(q N ) 2 ]  (1   P )[2 C  2(q PC ) 2 ] = 7 A2 20 F  . 17 17 (22) Notice that ETWP  ETW  . The profit‐based raises the expected welfare. The result is very intuitive: the redistributive effect that takes place when using a lump‐sum transfer does not change total welfare in the two scenarios. However, it increases the probability to achieve the welfare‐enhancing Cournot‐Nash outcome, as the fine shifts the threshold discount factor from   to  P . Turning to the damage‐based fine, the expected welfare is: ETW D =  D [ 2 N  2( q N ) 2 ]  (1   D )[ 2 DC  2( q DC ) 2 ] = 7 2  [182 A 2  357  A  153  A  17 51(17 A  3  ) 2 ] . (23) As in the case of the damage‐based fine, the threshold discount factor increases compared to the benchmark from   to  D ; but now also the collusive welfare component W C is affected by the positive output distortion implied by a damage‐based fine. Such a distortion has two effects. First, as known from the consumer surplus analysis, the collusive quantity increases compared to the benchmark case. Second, the collusive profits are now reduced as, from a 13 The complete expression for total welfare is: TW = i2=1 i  CS  AA , where AA is the revenue cashed by the antitrust authority. Following the previous discussion, it is immediate to prove that this boils down to TW = 2   2 q 2 . Notice that the latter expression applies to all regimes, including both a profit‐based fine and a damage‐based fine, assuming that  represents the firms’ profits in presence of a cartel gross of the expected fine, i.e.  = ( p  c ) qi . 14 private viewpoint, too much output is produced. Both the change in the threshold discount factor and the first output effect improve expected welfare, whereas the second output effect on collusive profits moves in the opposite direction. Simple algebraic calculations reveal that the two positive effects always dominate the negative one: intuitively, the negative effect of more output on profits is more than compensated by the positive effect on consumers that also includes a reduction of the deadweight loss. Also the damage‐based fine is therefore superior to the benchmark case in terms of welfare. We can now proceed to compare the effects of the two types of fines under the assumption of revenue equivalence. The following results hold: Proposition 4 Under (10) a damage‐based fine always increases total welfare compared to a profit‐based fine. Proof See the Appendix. Differently from the expected consumer surplus, there is now a policy instrument, the damage‐based fine, that is always preferred by antitrust authority. To understand the intuition behind the result, we can decompose the difference between the total welfare of the profit‐based fine and that of the damage‐based as follows: ETW Pre  ETW D  ( Pre   D ){[ 2( q N ) 2  2( q PC ) 2 ]  ( 2 N  2 PC )} 0 0 Deterrence differential  (1   D )[ 2( q DC ) 2  2( q PC ) 2  ( 2 DC  2 C )]. (24) 0 0 Expected ex post loss By comparing (19) and (24) it is possible to understand the reason why the damage‐based fine is preferred in terms of total welfare. The "deterrence differential" effect, which remains positive for relatively low values of the fine rates (i.e.  < t1 ), is unambiguously reduced by the negative component 2 N  2 C , which indicates the loss in the profit surplus when the cartel is successfully deterred. The "expected ex post loss", which was a clear loss in the case of the consumer surplus, remains negative but, given that 2 DC  2 C < 0 , it decreases in absolute value. Algebraic calculations, however, confirm that the reduction in the "deterrence differential" dominates the change in the "expected ex post loss". Clearly, for relatively high values of the fines (i.e.  > t1 ) both the deterrence and the distortionary effect go in the same direction. 15 Similarly to the case of consumer surplus, there are values of the market size, such as A0 in Figure 2, for which the antitrust authority may be particularly keen on a profit‐based fine on the ground of deterrence. Such a preference, however, is at odds with the maximization of expected overall welfare, that is better served by a damage‐based fine. 6 Extensions and robustness The analysis conducted in the previous sections was deliberately based on a number of simplifying assumptions that allowed us to clearly identify the main effects in operation when considering deterrence and distortive fines. In what follows, we show how our basic setting could be extended in a number of different ways. Some of the extensions, however, involve an increased algebraic complexity. For this reason, we will omit lengthy mathematical expressions from the following discussion.14 Notwithstanding the presence of technical difficulties, we largely confirm the validity of our main results and add some further interesting insights to it. Managerial firms and cartel punishment The majority of firms involved in cartel activity are characterized by a clear separation between management and ownership. The literature on managerial firms underlines how managerial objectives may not be in line with profit maximization. The misalignment may happen for a number of reasons: as far as this paper is concerned, however, it is interesting to ask how the effects of cartel punishment apply when managers’ objectives are not aligned with the firms’ profits. To this goal, we adopt a model à la Vickers (1985) and Fershtman and Judd (1987), who dealt with issues of strategic delegation in oligopoly, as a device to effectively capture the fact that the firms’ decision makers do not necessarily target profits.15 Suppose the firms’ managers aim to maximise a combination of the profits and output as follows: mi =  i  qi = ( A  Q   )qi , i = 1,2, (25) where  represents the relevance of the output for the manager. As output can proxy the size of the firm, the manager may be interested in increasing it beyond the optimal size (Baumol, 1958, inter alia). The parameter  can also be interpreted as the powers delegated from the firms’ shareholders to the appointed manager. Notice that the economic effect of (25) is similar to a reduction of the marginal cost of production. The managers objective functions in presence of collusion, in absence or in presence of punishment, can be obtained similarly. Under these assumptions, the non‐distorted output produced by a firm participating in the C = ( A   )/4 = qMC for each firm, while the Nash quantity is qMN = ( A   )/3 . The cartel is: qPM C = ( A     )/4 . The positively distorted collusive output under a damage‐based fine is: qDM additional subscript M stands for managerial firm. The effect of the managerial delegation 14 All derivations and omitted proofs are available upon request. In an unpublished companion working paper (Dargaud et al., 2013) we used a similar approach to model in a stylized way the "punish‐the‐firm" versus "punish‐the‐person" controversy and analyse its economic consequences. 15 16 parameter is to make firms more aggressive and increase their production. A very similar effect is also obtained on managers’ payoff. For example, the Nash payoff is mMN = ( A   ) 2 /9 , whereas the collusive payoffs are, respectively, C mMC = ( A   ) 2 /8 , mPM = ( A   ) 2 /8  F/2 C = [3 A2  2A  3( ) 2   6 A  2  3 ]/24 . The latter payoff expression shows and mDM how the positive distortion of the damage‐based fine interacts with the powers delegated to the managers. The condition   ( A   )/3 = t M guarantees that the game is a prisoner’s dilemma. Interestingly, the mere presence of a manager does not affect the stability of collusion and, as shown by Lambertini and Trombetta (2002), the threshold discount factor is unaffected:   9 / 17 =   . Under our assumptions, collusive behaviour is stable if and only if: 9 288 F    PM , 17 17( A   ) 2 (26) 9 384     DM , 17 1717 A     3  (27)  under a profit‐based fine and:  under the damage‐based fine. It is worth noticing that, unlike the case of managerial firms and no cartel policy, the effectiveness of both fines in deterring collusion interacts with the measure of the powers delegated to the manager,  . In particular, the higher is  , the lower the increment of the thresholds  PM and  DM are compared to the no fine benchmark. Appointing a manager may have negative effects on static profits, as firms are more aggressive, but it has the advantage of making firms more resilient to the deterring pressure of the antitrust authorities. The effectiveness and welfare effects of the profit‐based fine can be compared with those of the damage‐based by using revenue equivalence: C F =  (QMN  QDM ). (28) Under the previous assumptions, we can state the following results: Proposition 5 Under (28): re re re >  DM , ECSPM > ECSDM and ETWPM < ETWDM if (a)  PM re re re < ETWDM if t2M <   t1M ; (c) < ECSDM and ETWPM >  DM , ECSPM 0 <   t2M ; (b)  PM re re re  EP <  DM , ECSPM < ECSDM and ETWPM < ETWDM if t1M <   t M . Our main results are qualitatively confirmed in case the antitrust authority punishes firms whose decision makers have objectives not fully aligned with profits. In particular, for intermediate values of the punishment ( t2M <   t1M ) the trade‐off between ex ante deterrence and welfare continues to arise. It is interesting, however, to analyse how the relative effectiveness of each fine is affected by the misalignment of the managers’ incentives,  . If the fine rates are relatively low ( 0 <   t2M ), the deterrence superiority of a profit‐based fine is not 17 uniformly affected by  . The misalignment first affects negatively the relative deterrence superiority of the profit‐based; for intermediate values of the fines, instead, the parameter  re tends to increase the positive difference between  PM and  DM : as the ex ante deterrence effect becomes more relevant, the intensity of the trade‐off may be enhanced by the presence of managerial firms. For relatively high values of the fine ( t1M <   t M ), the superiority of the damage‐based is reduced by the extent of the misalignment of managerial incentives. A similar pattern applies to the expected consumer surplus. In particular, in the region where the trade‐off takes place ( t2M <   t1M ), the effect of  is to initially decrease the relative welfare superiority of a damage‐based fine but then, for slightly higher levels of the fines,  enhances the preference for the damage‐based fine. Finally, the positive total welfare effect of a damage‐based fine mostly decreases in  . Overall, our results appear robust to the presence of managerial firms and the relevance of the trade‐off we highlighted might be further enhanced. Extra profit based fine The profit‐based fine considered in the main part of the paper is a lump‐sum or an equivalent proportional fine based on the overall profits of the firm. This fine was compared to a damage based fine, computed on the quantity reduction/price overcharge of collusion. An interesting related question is to evaluate how the results change if, instead, a fine based on the collusive extra profits is imposed. In other words, also the profit‐based fine is designed to be somewhat proportional to the damage caused by the cartel. This new fine, with rate  , changes the colluding firms problem as follows:  = ( A  Q)Q   [( A  Q)Q  ( A  Q N )Q N ]. (29) As the objective function (29) can be re‐written as:  = ( A  Q)Q1      ( A  Q N )Q N . (30) The output produced by a firm participating in the cartel is not distorted and turns out to be C qEP = A/4 = qC for each firm. The additional subscript EP stands for extra profit fine. The C = A2 (9   )/72 , while the deviation Cournot‐Nash payoff accruing to the collusive firm is  EP payoffs are also unaffected compared to the no punishment benchmark. The condition   1 C   N and that the game is a prisoner’s dilemma. Under our assumptions, guarantees that  EP collusive behaviour is stable if and only if:  9 8     EP . 17 17 (31) The relative deterrence and welfare effectiveness of the extra‐profit fine as compared to the damage‐based fine can be evaluated using revenue equivalence:  (Q N  QDC ) =  [( A  Q)Q  ( A  Q N )Q N ]. 18 (32) Under the previous assumptions, we can state the following results: re re re >  D , ECSEP > ECSD and ETWEP > ETWD if 0 <   t5 ; Proposition 6 Under (32): (a)  EP re re >  D , ECSEP > ECSD and (b)  EP re ETWEP < ETWD if t5 <   t4 ; (c) re  EP > D , re re re re ECSEP < ECSD and ETWEP < ETWD if t4 <   t3 ; (d)  EP <  D , ECSEP < ECSD and re ETWEP < ETWD if t3 <   t. The analysis confirms the robustness of most of our results to considering a profit fine that is also based on damage and not on the overall profits. Like other profit based fines, the extra‐profit fine is also non‐distortive. As such the economic effects in operation in comparing the two fines also carry on from our previous analysis in Sections 3 and 4. The trade‐off between ex ante deterrence and expected welfare continues to arise for intermediate values of the fines. In particular, for lower intermediate values of the fine rates ( t5 <   t4 ), ex‐ante deterrence is in contrast with expected total welfare, whereas for upper intermediate values ( t4 <   t3 ) deterrence contrasts with both welfare standards. Differently from the previous case, now the extra profit fine can be welfare enhancing compared to the damage based quantity one: this happens for very low values of the fines ( 0 <   t5 ). The intuition can be understood comparing a profit‐based fine with the extra‐profit one. Under revenue equivalence, a extra‐profit fine of the same intensity hits only the extra gains of collusion and it is not spread on all the profits, as the profit‐based discussed previously. Ceteris paribus, the former is therefore likely to be more effective than the latter. For very high values ( t3 <   t ), instead, the damage‐based fine is to be preferred, consistently with the results of our initial analysis. Adjusted revenue equivalence In our base model we compared two different approaches to cartel punishment under the assumption of identical expected revenue collected by the antitrust authority. Here we show that our results are valid also when including the ex ante expectations regarding the firms’ discount factor. In other words, we consider the case in which the antitrust authority adjusts the expected fines for the interval range in which cartel formation is supposed to take place. In our setting, this new assumption implies that revenue equivalence writes: (1   P ) F = (1   D )  (Q N  QDC ). (33) The analysis follows the same steps as in Sections 3.3 and 4, although it becomes algebraically more complicated. First, we obtain , the value of the profit‐based fine for which the expected revenue equivalence in (33) holds: A(17 A 2  3 A  (17 A  3 )   ) 72(17 A  3 ) (34) where  = 17 A3  411A2   2448A(  ) 2  3672( )3 . It is also relatively easy to prove that 19 A2 if (8) holds, i.e.:   t = A/3. 36 Then, we rewrite the discount factor  Pare and the welfare expressions ECSPare and ρF < ETWPare that characterize the profit‐based in presence of adjusted revenue equivalence. The main results of our base model are unaffected. In particular, Proposition 2 holds in the same interval region of  , as under (33)  Pare >  D exactly in 0 <  < t1 , while  Pare <  D if t1 <  < t . As for the welfare analysis, we replicate the results of Propositions 3 and 4. In more detail, ECSPare > ECSD when in 0 <  < t2ere , and the opposite in t 2ere <  < t , with t2ere < t1 in the relevant parametric region. The trade‐off between ex ante deterrence and ex post output provision is therefore holding also in this scenario. Finally, we obtain that ETWPare < ETWD , thus completing the validation of the results reported in the main text. 7 Concluding remarks Although the fight against collusive behaviour is based on similar principles around the world, substantial differences can still be seen: this applies especially to the instruments adopted to carry out cartel deterrence. Such differences appear even within the same economic area, as the heterogeneous approach to punishment between EU member states shows. Fines are not always applied to the profits of the firm but often they are levied on the damage caused by the cartel, on the revenue or other relevant definitions of the cartel turnover. The common characteristic of most of the employed fines, however, is to potentially distort firms’ choices. In our analysis we focused on two types of fines, one distorting firms’ output choices and one not. In particular, we highlighted the relevant economic effects that appear in presence of a profit based fine vis‐à‐vis a damage based one. These are two simple but commonly discussed instruments in the literature. In our analysis, the damage based fine is computed on the reduction of the output of collusion compared to a competitive outcome: as such, the fine has the effect of positively distorting the quantity produced by colluding firms. This distortive effect is particularly important in case the antitrust authority does not achieve full ex ante deterrence, as suggested by the prevalence of cartel activity despite the efforts of the authorities. Our results indicate that the comparative effectiveness of the two instruments (profit‐based vs damage‐based fines) is closely related to the intensity of the punishment. A profit‐based instrument is more effective for relatively low levels of the fines. This feature is particularly attractive as antitrust authorities are often under more or less explicit pressures to keep fines low. The advantage of a profit‐based fine, however, may vanish when ex post effects are taken into account. As firms may be sufficiently patient, collusion can take place despite the ex ante deterrence of fines. In that case, a damage‐based fine induces a positive distortionary effect that is beneficial for consumer surplus and the overall social welfare. We showed that for intermediate values of the punishment, the authorities may face a trade‐off between the strength of the ex ante deterrence effect and the expected consumer surplus and total welfare. This is particularly evident in case the law imposes an explicit cap on the fines applied by the authority, as for example in the EU. 20 The identification of such a trade‐off is the most important contribution of the paper. 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The European commission’s 2006 guidelines on antitrust fines: A legal and economic analysis, in World Competition 30(2). 23 Appendix Proof of Proposition 1 Assume that conditions (5) and (8) hold. We compare the two threshold discount factors to obtain  =  D   P . Simple algebraic derivations reveal that: ~  > 0  F > T = 4 A 2 , 51A  9  ~ where we maintain that  < t . Moreover, T < T , as it can be easily ascertained. Under ~ condition (8), it is immediate to verify that T is increasing in both the expected fine  : ~ 68 A 3 T > 0. =  3(17 A  3 ) 2 Proof of Proposition 2 Remember that the comparison between (12) and (9) takes place under the restriction  < t = A/3. The differential can be written as:  re =  Pre   D = 432  [ A 2  6 A  (  ) 2 ] 17 A 2 (17 A  3 ) The sign of  re coincides with the sign of the term in square brackets, A 2  6 A  (  ) 2 . This expression has two real and positive zeros but only one is relevant, as it satisfies  < t ; this is  = t1 = (3  2 2 ) A . This clearly implies that  re > 0 for all values 0 <  < t1 and vice‐versa for t1 <  < t. Proof of Proposition 3 Consider revenue equivalence as expressed in (10). The expected producer surplus resulting from the profit‐based fine re‐writes as follows: ECS Pre  3 A2 14  ( A  3 ) .  17 51 24 (35) It is relatively simple to verify that:  [8 A2  167 A  93(  ) 2 ] . ECS  ECS D = 289  51 re P Given the condition   t = A/3 , the sign depends on the numerator. Hence: ECS Pre  ECS D    t 2 = (167  24913) A. 186 Moreover, it is also immediate to find that t 2 < t1 < t . Proof of Proposition 4 The comparison is performed for 0 <  < t. The welfare differential can be written as: ETWP  ETWDre =   [4 A 2  61A  21 2 ] . 289 A  51 The sign of this expression depends on the term: 4 A 2  61A  21(  ) 2 . It is immediate to verify that it is always positive on our domain, implying that ETWP  ETWDre < 0 always holds. 25