1.1 Motivation and Main Results
Since the time of Adam Smith (if not before), economists have recognized the many virtues of competition. However, it has also been argued that competition may be problematic in some respects (see, e.g., Vives 2008). One such claim is that competition may drive firms to engage in unlawful practices; Shleifer (2004, p. 415), for example, argues this point vividly with regard to corruption: “the keener is the competition, the higher is the pressure to reduce costs, and the more pervasive is corruption”. 1 The intuition is straightforward and compelling: When some firms lower their costs by engaging in unlawful practices and competition is fierce, other firms must follow suit or else risk losing market share and potentially being driven out of the market.
This paper analyzes how the intensity of product market competition influences firms’ incentives to use unlawful practices that reduce production costs. Examples of such practices include the non-adherence to expensive workplace safety regulations and the violation of both minimum-wage laws and mandated environmental standards. Real-world examples of minimum-wage and other workplace violations in the USA have been presented by Bernhardt et al. (2009), among others. 2 Lowering production costs by means of unlawful practices provides both a direct and an indirect benefit for an individual firm: The direct benefit is due to the firm’s savings in production costs when all else is held equal, and the indirect benefit arises from its improved competitive position. 3 With regard to these expected benefits from corporate crime, we identify two effects that emerge from more intense product market competition. First, greater competitive pressure allows a larger gain in market share when a firm reduces its costs by resorting to crime, making crime more attractive. In contrast, more intense competition lowers overall price-cost margins and makes an increase in market share less profitable, reducing the incentives for crime. In our model, which of these two effects dominates is dependent on the net reduction in production costs implied by crime. In addition to the direct and indirect benefits, the use of unlawful practices implies expected costs arising from law enforcement. These expected costs may also be influenced by the intensity of competition. We establish that the overall effect of competitive pressure on incentives for corporate crime crucially depends on the actual fine structure.
In our main analysis, criminal firms are subject to a fine consisting of a fixed component and a component that varies with output, where the criminal act reduces marginal production costs. Our simple representation of fines captures important aspects of the enforcement of the law in real-world situations. For example, in order to enforce the Fair Labor Standards Act, the Wage and Hour Division of the U.S. Department of Labor may subject willful violators to criminal prosecution and fine of up to $10,000, in addition to a civil monetary penalty per violation of up to $1,100. Similarly, the Occupational Safety and Health Administration of the U.S. Department of Labor imposes fixed penalties that vary with the gravity of the employer’s violation. With regard to environmental misconduct, the U.S. Code of Federal Regulations employs fixed sanctions for violations of the Clean Water Act. For even graver misconduct, the Sentencing Guidelines for Organizations provide information on the appropriate fine for the assessed offense. 4 These guidelines set out minimum sanctions, resulting in punishments that are not proportional to social harm (Alexander, Arlen, Cohen 1999). In summary, we believe that the representation of fines in our model is in line with the most important aspects of real-world settings. Nevertheless, in an extension, we consider the scenario in which firms are subject to a fine that is proportional to profits. Our primary motivation for including this fine structure stems from its treatment elsewhere in the literature (see, e.g., Branco and Villa-Boas forthcoming) and the idea that profits may equal the maximum amount of fines that can be levied on a firm, making it an interesting benchmark for comparison. However, the practical applicability of this fine structure will often be limited by the difficulty of assessing true economic profit (e.g., Choi and Gerlach 2012).
Our paper clearly identifies how more intense product market competition may either encourage or discourage firms to engage in crime in order to lower production costs. This mirrors the sometimes contradictory findings in the literature. Whereas Shleifer (2004), for instance, proposes that fiercer competition aggravates problems associated with corruption (see the quote above), Ades and DiTella (1999) suggest the reverse (i.e., that more intense product market competition may result in a lower incidence of corruption). In Section 1.2, we discuss in more detail empirical findings on the relationship between competition and corporate criminal conduct.
The setting we use to derive our findings combines the economic model of crime à la Becker (1968) with a model of oligopolistic competition in the vein of Salop (1979). The Salop setup allows us to measure the intensity of competition in two ways: first, the number of firms in the market, and second, consumers’ willingness to switch between firms as approximated by the transportation cost parameter as an inverse measure of the degree of substitutability between products. Changing the latter parameter allows us to adjust the intensity of competition by altering a firm’s demand elasticity. Our main interest lies in the interactions between product market competition, law enforcement, and corporate crime. Our model considers firms that are ex-ante symmetric and decide whether or not to reduce production costs by resorting to illegal means. In our framework, the criminal behavior of firms entails social harm that does not directly affect consumers, as it is not tied to consuming the product. For example, in the case of illegal waste disposal, the implied environmental harm will disadvantage individuals independent of their status as consumers or non-consumers. 5
In our main analysis, we find that more intense competition due to greater substitutability between products may increase or decrease incentives for crime. This is the result of the two opposing effects on the expected benefits from crime referred to above (i.e., that more intense competition allows criminal firms a larger increase in market share but also makes a greater market share less profitable). The first effect dominates in the event of low to intermediate benefits from crime, while the latter dominates in settings featuring high benefits from crime (i.e., in an environment in which the crime rate is already high). With respect to the number of firms in the industry, our framework yields the prediction that more intense competition will reduce crime, since a firm’s market share decreases relatively more than the total expected sanction it faces. However, when the fine is proportional to profits, higher competitive pressure also has a bearing on the expected costs from crime, as the lower profit levels translate into lower absolute fines. This additional effect turns out to be decisive when assessing the impact of competitive pressure on firms’ incentives for crime, such that higher competitive pressure unambiguously increases corporate crime incentives when fines are proportional to profits.
With regard to enforcement policy, we show that stricter law enforcement has a deterrent effect irrespective of the fine structure. When we consider firms’ decision about market entry, we show that stricter law enforcement can either increase or decrease the number of firms entering the market. This represents an influence of law enforcement that should impact the optimal enforcement policy, as there is excessive entry in the Salop setup. Moreover, we identify a complementarity between law enforcement and a firm’s ability to commit to abstaining from the use of criminal methods to reduce production costs.
The structure of our article is as follows. After discussing the related literature in Section 1.2, we describe the model in Section 2.Section 3 contains our main analysis, where we assume a two-part fine system (comprising a fixed sanction and a sanction proportional to firm-specific output). In Section 4, we briefly consider a fine proportional to profits. Section 5 concludes.
1.2 Related Literature
In addition to the contributions to the literature mentioned in Section 1.1, the present paper is linked to theoretical research investigating corporate crime. Studies on illegal reductions in corporate costs include Danziger (2010) and Basu, Chau, and Kanbur (2010), who examine minimum-wage violations, and Baumann and Friehe (2012), who investigate non-compliance with employment protection legislation. In the realm of environmental economics, a rich literature on law violations focusing on the imperfect enforcement of pollution or technology standards has developed, ranging from Harford (1978) to contributions as recent as Arguedas (2013). However, this research does not touch on our central point of interest, namely the relationship between competition in product markets and corporate crime. Mullin and Snyder (2009) provide a survey on corporate crime; however, they are primarily concerned with principal-agent considerations with regard to the organization of firms and the question of who should optimally be sanctioned (shareholders, the responsible employee, or both). Our paper abstracts from the fact that there must be an individual wrongdoer in the corporation and the important distinction in that context between individual and corporate liability. The contribution closest in focus to ours is Branco and Villas-Boas (forthcoming), who also examine competition and incentives for corporate crime when the latter entails lower production costs. In contrast to our study, Branco and Villas-Boas use a Cournot setup with homogeneous products in their basic model and only consider a sanction equal to profits in the event of detection. The two studies can be seen as complements: Our approach allows additional insights, in that product substitutability is introduced as a measure for competitive pressure in addition to the number of firms. Importantly, we investigate different sanction structures, and our fixed-fine scenario probably more accurately reflects the majority of real-world regimes.
In the empirical literature dealing with the influence of competitive pressure on criminal behavior, many studies have considered the case of corruption, finding mixed results. Some studies establish a negative relationship between more intense competition (mostly due to fewer restrictions on trade) and the extent of corruption (see, e.g., Ades and DiTella 1999; Laffont and N’Guessan 1999; Badinger and Nindl 2014). 6 Suggestive empirical evidence presented by Emerson (2006) points in the same direction. Sahakyan and Stiegert (2012) report that corruption is seen by firms as more favorable if they do not face significant competition. In contrast, Diaby and Sylwester (2015) find that more intense product market competition leads to an increase in bribes paid, and Alexeev and Song (2013) provide evidence whereby more intense competition results in more corruption, allowing cost reductions. Some contributions have also examined how other kinds of law violations depend on the intensity of competition. Datta, Iskandar-Datta and Singh (2013) document a positive relationship between the intensity of competition and corporate earnings management, and Karlinger (2009) presents evidence that increased competition may lead to an expansion of the underground economy. With regard to tax evasion, Tedds (2010) obtains the result that firms with more than three competitors are more likely to under-report profits than firms with fewer than three competitors. However, in contrast, de Mello (2009) reports less VAT tax evasion when market regulation is more pro-competitive. All in all, while many studies point to a positive relationship between competition and illegal behavior, contrary results have been found as well. 7
Another related strand of (empirical) literature uses laboratory experiments to explore individuals’ incentives to employ unethical methods in settings of varying competitive intensity. For example, Harbring and Irlenbusch (2011) document more prevalent sabotaging between contestants in a tournament when wage spreads are higher. Likewise, Charness, Masclet, and Villeval (2014) report a higher likelihood of cheating and sabotage when participants are informed about their relative performance. According to Schwieren and Weichselbaumer (2010), individuals performing poorly in a task use cheating more extensively. Cartwright and Mezes (2014) find a non-linear relationship between the intensity of competition and cheating, with cheating being most likely in medium-intensity competition.
Our research interest – how the intensity of product market competition shapes firms’ incentives to lower production costs by illegal practices – is also related to the literature in antitrust economics that analyzes the practices firms utilize in order to directly lower the competitive pressure in the industry. Predatory pricing, tying the sale of different products, sabotage, and raising rivals’ costs fall into this category. In addition, collusion and mergers can lower competitive pressure, but these require the consent of several firms (see, e.g., Belleflamme and Peitz 2015 or Motta 2004 for excellent coverage). With regard to collusion, for example, there is empirical evidence indicating that higher concentration and lower advertising intensity make collusion more likely (see, e.g., Gual and Mas 2011; Symeonides 2003). However, it is presumably difficult to interpret this as evidence of the relationship between competitive pressure and antitrust offenses in general due to the very specific problems associated with establishing successful collusion.
In the field of industrial organization, our paper is also related to the literature on process innovations and their interdependence with product market competition, as technically both process innovations and unlawful practices involve a trade-off between something akin to investment costs (represented in our setup by sanctions in the event of detection) and a potential reduction in production costs. Boone (2000) provides a very interesting contribution to the R&D literature in this respect, considering different models of product market competition. In our framework, cost reductions imply social harm, which distinguishes our work from the literature on process innovations and raises different welfare implications.
2 The Model
We consider a market that can be characterized by a Salop circle of circumference one. Consumers are evenly and continuously distributed along the circle, where the mass of consumers is normalized to one. Each consumer buys one unit of the good traded in the market.
8 In addition to paying the price for the good, a consumer incurs (quadratic) transportation costs
We concentrate on parameter constellations for which consumers always buy from one of the two firms between which they are located. A consumer located between firm i and firm
The indifferent consumer in the interval is located at distance
Equation  clearly indicates the two main elements determining the intensity of product market competition. The higher the number of firms n, the more intense the competition. In addition, the Salop model allows an easily interpretable second factor that characterizes the intensity of competition between firms: the transportation cost parameter T. The lower the value of T, the more flexible consumers become with respect to switching between firms. Lower values of T thus entail fiercer competition, since even small differences in price can translate into a large shift in demand from one firm to another.
Firms are (ex-ante) symmetric and utilize a production technology with constant returns to scale, implying per-unit production costs of c. However, firms may resort to illegal means to reduce their production costs (e.g., illegal waste disposal, violations of minimum-wage laws, or reductions in workplace safety) that imply harm h per unit of production for society. A firm that takes advantage of the illegal opportunity reduces its production costs per unit by b, where
In order to deter firms, law enforcement consisting of a detection probability and a fine regime is put into effect. We assume that the detection probability Q results from the following audit rule: A firm will be inspected with probability y,
The timing of the main model with a given number of firms is as follows. In stage 1, firms learn the level of cost reduction b associated with illegal production practices. Firms decide whether or not to take advantage of this criminal opportunity in stage 2. This decision cannot be observed by competitors, who must therefore form expectations about the decisions made by their rivals. Next, in stage 3, price setting takes place: All firms simultaneously set their prices and consumers make their purchasing decisions. Finally, random detection occurs and payoffs are realized. 13
3 A Two-Part Fine System
In this section, we derive the equilibrium and the comparative-statics results for the scenario in which the total fine is composed of a variable sanction (proportional to the output produced by illegal means) and a fixed component. For an exogenous number of firms, we first derive the market equilibrium using backward induction and then present comparative-statics results referring to the relationship between competitive pressure and corporate crime incentives. Next, we turn to market entry, welfare and policy considerations, and coordination among firms on a no-crime equilibrium.
3.1 Market Equilibrium
3.1.1 Stage 3: Price Competition
In stage 3, firms determine their prices based on expectations about how competitors choose their product prices (which may depend on whether they resorted to crime at stage 2). The expected profits of a firm i that does not take advantage of the criminal opportunity (referred to as a firm L in the following analysis) is given by
that is, profits per unit times expected demand, where E denotes the expectations operator. The expected profits of a firm i that engages in illegal production (a firm C in the following analysis) amount to
where Q represents the detection probability that will be equal to q when
Our specification of the detection probability implies that a firm C will choose either to price according to marginal costs c (like a firm L) or according to marginal costs
in contrast, for a firm C that prices according to marginal costs
Introducing the parameter
Both prices decrease in the expected share of firms that use illegal practices to reduce production costs and price aggressively, whereas the price difference remains constant. This results from the fact that the lower production costs of criminal competitors that price accordingly lead to more aggressive pricing, forcing all firms to charge lower prices. Furthermore, the price charged by a firm C that prices according to marginal costs
This difference amounts to
The price difference between a firm C that prices according to marginal costs
where we assume that demand is positive for a law-abiding firm even for
which constitutes an upper bound on
Firms of type C that charge
Finally, we obtain the expected profits of a firm L, a firm C that charges
Since equilibrium prices decrease in the share of firms that price according to marginal production costs
From the profit functions, we deduce that a higher share of firms pricing according to
A firm that has chosen to reduce its marginal production costs by resorting to illegal means will charge a price that reflects this cost advantage only if the difference between
where the inequality
3.1.2 Stage 2: Decision on Crime
In stage 2, each firm decides whether or not to take advantage of the illegal opportunity to reduce its marginal costs. The unlawful practice reduces production costs per unit by b but also entails costly expected punishment. Since profit levels depend on the crime and pricing decisions made by other firms, we are searching for a Nash equilibrium in stage 2 of the game. The expected profits of a firm are affected by other firms’ illegal practices only when the latter price aggressively.
Taking as given that a share
For sufficiently high levels of r, firms choose between being a firm L and being a firm C that charges
Figure 1 illustrates alternative equilibria using
From Figure 1, it is clear that there are numerous cases to be distinguished (that can be characterized by threshold levels of key parameters, as described in detail in Appendix A) and that there are parameter combinations allowing for multiple equilibria. In the remainder of the paper, we assume that
Given the restriction on r, we can describe the equilibrium that emerges as a function of the level of
We obtain the explicit characterization as
where the two critical net benefit levels are given by
It is easy to verify that
an equilibrium with complete deterrence is obtained for any realization of gross benefits from crime b. 17
For low values of the net benefits from crime, no firm has an incentive to employ the illegal means in order to reduce its production costs. Although the first firm to violate the law realizes the largest level of expected demand (should no other firm follow suit), the potential net gain from crime is not high enough to offset the expected fixed sanction. When
Note that since expected profits decrease in the share of firms of type C (which itself increases in
3.2 Comparative-Statics Analysis
Our primary interest in this section is to determine how the intensity of competition and law enforcement influence the prevalence of crime. In our model, an increase in the intensity of competition results either from an increase in the number of firms or from lower transportation costs (and the corresponding higher consumer flexibility). In addressing the influence on the extent of crime in equilibrium, we focus on both the share of firms engaging in criminal acts and the critical net benefit levels.
3.2.1 Intensity of Competition
We start by investigating an exogenous increase in the number of competitors n. The results are summarized by:
Assume a two-part fine system. An increase in the intensity of competition induced by a higher number of firms reduces the prevalence of crime in equilibrium, i.e., the share of criminal firms
The intuition for this first result can be explained as follows. When all else is held equal, an increase in the number of firms reduces the expected market share not only for legal firms but also for criminal firms (as is evident from the equilibrium demand eq.  in combination with eq. ). The higher price-cost margin of criminal firms is thus of lower value as a result, rationalizing the decrease in the prevalence of crime in view of the expected fixed fine. Consequently, for
We now turn to the effect of a change in transportation costs. The results are summarized in:
Assume a two-part fine system. An increase in the intensity of competition induced by a decrease in transportation costs T (weakly) increases
A decrease in transportation costs makes consumers more willing to switch to another firm, and price competition between firms becomes fiercer as a result. The price-cost margins of a firm L and a firm C decrease by the same absolute amount (i.e., the difference between the two types of firms remains unaffected; see eq. ). This effect has a stronger negative impact on the expected profits of a firm C, due to its higher market share in comparison to a firm L. This suggests that corporate crime should be rarer in settings with a lower T. However, at the same time, the expansion of market share obtained by resorting to illegal means of reducing costs increases due to higher consumer flexibility (see eq. ). This effect leads to an increase in the expected profits of a firm C in comparison to those of a law-abiding competitor.
In equilibrium, the sign of the combined effects is ambiguous; as Proposition 2 indicates, it depends on the net benefit per unit of output obtained from crime. For a relatively low value of the net benefit from crime, the difference in market shares between a firm C and a firm L is small, and therefore the first effect described above (i.e., lower price-cost margins) is relatively less important in the comparison of profit levels. As a result, crime becomes more attractive for a given share of criminal firms because the second effect (i.e., the increase in market share) dominates, implying that the share of criminal firms (weakly) increases. In contrast, for a relatively large net benefit from crime, the initial difference in market shares is more pronounced, and the first effect dominates the second, such that the expected profits of a firm C decrease relative to those of a firm L for a given
Because the level of the net benefit from crime has a direct bearing on the share of firms taking advantage of the criminal opportunity, we can explain our findings in another way. By reference to eq. , it is easily established that
Finally, it should be noted that the inclusion of a criminal opportunity in the analysis does not affect the standard prediction that fiercer competition due to lower transportation costs reduces expected profits in equilibrium. 19
3.2.2 Law Enforcement
The parameters at the disposal of a law enforcement agency are represented by the probability of detection q and the two sanction levels s and F.
Assume a two-part fine system. Stricter law enforcement enacted by means of an increase in the variable sanction s, the fixed sanction F, or the detection probability q reduces corporate crime.
With regard to the fixed sanction F, the result can be established by examination of eqs  to . For
The effects of law enforcement are standard. Nevertheless, let us briefly outline the mechanism behind the adjustments. First, consider an increase in the variable sanction s. Such an increase is tantamount to a reduction in the net benefit from crime
In the standard optimal law enforcement framework, an increase in the strictness of law enforcement necessarily decreases potential offenders’ expected payoffs (e.g., Polinsky and Shavell 2007). It is interesting that this outcome may be reversed in the present setting.
Assume a two-part fine system. An increase in the variable sanction s increases expected profits in equilibrium when
The proof follows from eq. . Note that any marginal change in the two critical net benefit levels
Stricter law enforcement affects expected profits through two different channels. First, there is the direct effect whereby higher expected sanctions reduce the expected profits of a firm C while leaving the expected profits of a firm L unchanged. Second, as previously established, the resulting change in the difference in profits between the two types of firms results in a weakly lower share of criminal firms in equilibrium, which increases the expected profits of both a firm L and a firm C. Because these two profit levels are equalized in an equilibrium with
When the net benefits from crime exceed the threshold
In summary, we determine that an increase in the variable sanction always yields (weakly) higher expected profits in equilibrium. For the fixed sanction, this is only the case for intermediate levels of the net benefit from crime, whereas the opposite applies in the event of an all-crime equilibrium. The effect of an increase in the detection probability is again equivalent to a proportional increase in both sanction levels.
3.3 Endogenous Market Entry
In Sections 3.1 and 3.2, we treated the number of firms as an exogenous variable to represent changes in competitive pressure by different levels of either the number of firms or transportation costs. In the following analysis, we incorporate firms’ market entry decision. The influence of transportation costs and law enforcement on the number of firms is interesting in itself and furthermore allows us to test the robustness of our results. To do so, we add a stage 0 to the game in which firms decide about market entry, paying entry costs amounting to K. At this initial stage, firms do not yet know the realization of the benefits b that are obtainable from illegal behavior, but only that they are distributed on
With regard to the comparative-statics analysis of this extended model, a change in parameters now induces an indirect effect due to the accompanying change in the number of firms (in addition to the direct effect described above). This can be expressed by restating the equilibrium share of firms of type C as
to highlight the direct and indirect effects.
For the intensity of competition, one exogenous parameter remains, namely the transportation costs T. 20 We obtain the results summarized in:
Assume a two-part fine system and that the entry condition is guided by eq. . An increase in the intensity of competition induced by a decrease in transportation costs T implies a (weak) decrease in the number of firms n and an ambiguous effect on the prevalence of crime. For
The proof follows from Propositions 1 and 2 in combination with eq. , which implies a (weakly) positive effect of T on n. ■
As was true for the case of an exogenous number of firms n, the total effect of a change in the substitutability of products has an ambiguous effect on the prevalence of crime and depends on the level of the net benefit from crime. As delineated above, the direct effect of more intense product market competition for intermediate levels of net benefit is an increase in the incentives for crime, but a reduction in incentives is found for settings featuring high net benefits. In addition to our previous results, an indirect effect now arises due to the fact that more intense product market competition leads to lower expected profits, reducing the number of firms in the market. The accompanying increase in market share for the remaining firms implies higher expected gains from crime as long as the net benefit from crime is positive. As a result, the effect of more intense product market competition is tilted toward a higher prevalence of crime in equilibrium. However, this indirect effect might not be sufficient to offset the direct effect when there are high net benefits from crime.
With respect to law enforcement, we concentrate on the effects of an increase in either the variable sanction s or the fixed sanction F, since the effects of a higher detection probability can be understood as a proportional increase in the two sanction levels. For market entry, we find:
Assume a two-part fine system and that entry is determined by eq. . An increase in the variable sanction s leads to a (weak) increase in the number of firms n. An increase in the fixed sanction F may decrease or increase n where the introduction of a fixed sanction (weakly) reduces the number of firms. The number of firms is (weakly) lower for
For the variable sanction, the proof follows directly from Proposition 4 in combination with the market entry condition. For the fixed sanction, consider eqs  and . For
As shown in Section 3.2, an increase in the variable sanction s always leads to an increase in firms’ profit levels in equilibrium due to the deterrence of competitors and the tamer price competition among firms of type C. Accordingly, an increase in the variable sanction will be accompanied by an increase in the number of firms. With regard to an increase in the fixed sanction F, firms again benefit from increased deterrence of competitors but are directly negatively impacted by the higher expected fine in the event of an all-crime equilibrium. For originally low levels of the sanction, the all-crime equilibrium is likely to emerge, and the negative effect on expected profits dominates. In contrast, for high sanction levels, the deterrence effect dominates and expected profits increase. In summary, the number of firms in the industry is expected to decrease in response to an increase in F when F is small; however, there is a critical value of F for which a further increase in the fixed sanction entails an increase in the number of firms. Therefore, the relationship between the fixed sanction and the number of firms is expected to be u-shaped.
We now turn to the effects of law enforcement on crime prevalence, which are summarized in the following proposition:
Assume a two-part fine system and that entry is determined by eq. . The deterrent effect of an increase in the variable sanction s is greater when the number of firms is endogenous in comparison to a scenario with an exogenous number of firms. An increase in the fixed sanction F generally decreases the prevalence of crime; however, for a marginal increase in the sanction F that causes that one firm less to enter the market, crime can become more prevalent, as the indirect effect of a lower number of competitors can dominate the (marginal) effect on deterrence.
The statements follow from Propositions 1 and 3 in combination with Lemma 2. ■
For a change in the level of the variable sanction, we find that both the direct and the indirect effect point in the same direction with regard to the impact on crime. Crime becomes less attractive as a direct result of the higher sanction; in addition, the accompanying increase in the number of firms in the market equilibrium reduces individual market shares, diminishing the benefits from crime even further. For the fixed sanction, it is clear that all firms resort to crime when
3.4 Welfare and Policy Considerations
The central feature of our framework is that it links product market behavior with decisions concerning illegal activities that involve social harm. Our results reveal that law enforcement influences product market outcomes (including market entry decisions), a finding that should be considered in enforcement policy. In this section, we briefly discuss how this impact on the product market affects optimal law enforcement policy in comparison to the standard trade-off described by Polinsky and Shavell (2007), among others.
As an inverse measure of social welfare, we use the sum of social costs resulting from the production of the goods, including the social harm resulting from any law violations and the costs of law enforcement. This measure of total social costs is plausible, since the assumption that all consumers buy one unit of the product implies that consumers’ gross utility from consumption is independent of the market equilibrium, such that the sum of payoffs is maximized for minimized costs. Ex-ante expected social costs amount to
The first two terms represent market entry costs nK and the costs of law enforcement, where
where we use
When stricter law enforcement increases deterrence (i.e., reduces the share or output of firms of type C), the standard comparison between the reduced net harm from crime (
Against the background of the discussion presented in Section 3.2, these additional considerations affecting social welfare primarily concern the optimal combination of the two sanctions s and F. When
3.5 Coordination on the No-Crime Equilibrium
In our preceding analysis, we have considered law enforcement as a measure to curtail illegal behavior. However, our analysis in Section 3.1 has shown that the possibility to employ illegal practices to reduce one’s production costs and price aggressively can be understood as a prisoners’ dilemma for firms. Expected profits decrease in the share of firms that take advantage of the criminal opportunity and price aggressively. Firms may therefore try to coordinate on the equilibrium in which no firm resorts to illegal practices (denoted the no-crime equilibrium hereafter) when their market interaction is repeated. Here, we briefly report the findings generated by such an extension (for more details, see Appendix E). 22
To investigate the possibility of coordination on the no-crime equilibrium in the model with an exogenous number of firms, we consider an indefinitely repeated version of the one-shot game used in our main analysis and derive the critical discount factor from the incentive-compatibility constraint, relying on grim-trigger strategies.
We can establish the following results (proved in Appendix E):
Assume that the total fine has a fixed and a variable component and that net benefits from crime fulfill
- (i)An increase in the fixed fine F makes coordination on the no-crime equilibrium more likely.
- (ii)An increase in the net benefits from crime
makes coordination on the no-crime equilibrium less likely.
- (iii)An increase in the number of firms n makes coordination on the no-crime equilibrium less (more) likely when
- (iv)An increase in transportation costs T makes coordination on the no-crime equilibrium more likely.
The results indicate the complementarity between public law enforcement and private coordination efforts with regard to the possibility of attaining the no-crime equilibrium. A higher fixed fine eases coordination on a no-crime equilibrium because it diminishes deviation profits. Continuation profits decrease as well for
4 A Fine Proportional to Profits
In this extension, we assume that instead of the two-part fine system (consisting of a variable and a fixed part), the fine is defined as a share
The expected profits for a firm C amount to
With regard to the equilibrium crime rate, we again establish two critical values for the variable net benefit from crime:
With regard to equilibrium selection, Harsanyi and Selten (1988) introduce two selection criteria: payoff dominance and risk dominance. The risk-dominance selection concept is typically applied in the context of two-player simultaneous-move games and – according to Harsanyi and Selten (1988) – is not necessarily the first criterion to be applied when payoff dominance and risk dominance produce conflicting recommendations. Evidence such as that presented by Rankin, Van Huyck, and Battalio (2000) indicates that payoff dominance is indeed empirically important in repeated contexts. In this respect, the outcome in our game may also be viewed as a long-term stable outcome. As a result, we use the refinement of payoff-dominance to choose between equilibria, such that the no-crime equilibrium
Accordingly, we obtain
which implies expected profits of
Turning to our comparative-statics analysis, we first address our key research interest – that is, the relationship between competitive pressure and corporate crime incentives.
Assume that the fine is proportional to expected profits. More intense product market competition induced by either a decrease in transportation costs or an increase in the number of firms (weakly) increases the expected crime rate by (weakly) reducing the critical value
In contrast to the two-part fine system, more intense competition in the product market always increases the incentives for criminal behavior in the scenario with a fine proportional to profits. This result can be explained by the additional mechanism that was absent in the scenario with the fixed sanction. This additional effect stems from the fact that an increase in the intensity of product market competition reduces expected profits in equilibrium. If the sanction imposed on the firm is proportional to this profit level, this implies that expected sanctions decrease while the effects on benefits from crime remain unchanged. It is this decline in expected sanctions that is responsible for the unambiguous increase in the expected crime rate in this setting. The above analysis establishes that a fine proportional to expected profits clearly leads to a positive relationship between the intensity of competition and the incentives for crime. Branco and Villas-Boas (forthcoming) assume that
With respect to the comparative-statics results for law-enforcement parameters, both scenarios yield the same prediction: namely, that stricter law enforcement diminishes the prevalence of crime.
Assume that the fine is proportional to expected profits. Stricter law enforcement induced by an increase in f or q (weakly) reduces the expected crime rate by (weakly) increasing the critical value
Competition is often blamed when firms utilize unlawful practices to lower their production costs. In light of the fact that such crime can cause considerable social harm, this paper explores the interaction between the intensity of product market competition, incentives for corporate crime, and law enforcement. In our oligopolistic model with horizontally differentiated products, we establish that an increase in the number of firms decreases the prevalence of corporate crime. In contrast, greater substitutability between different products may or may not increase corporate crime. This ambiguity is due to the presence of two countervailing effects. On the one hand, more intense competition induced by greater substitutability makes crime more attractive due to the relatively larger increase in market share that a firm can achieve by engaging in criminal behavior. On the other hand, more intense competition reduces price-cost margins, making any increase in market share less profitable. In our setting, which of these two effects ultimately dominates depends on how strongly the production costs of criminal firms are reduced by the illegal practices. Crime increases in the intensity of competition for intermediate gains – that is, when the equilibrium before the change was characterized by a relatively low crime rate. In contrast, for settings featuring high benefits from crime and therefore an initially high crime rate, more intense competition may instead reduce incentives for crime.
In our setting, product market incentives are important drivers of decisions concerning illegal practices, and crime deterrence likewise influences the product market. In this regard, our model produces an interesting finding related to the effects of stricter law enforcement on expected profits that may alter entry decisions. At first glance, higher expected sanctions reduce profits, as they must be borne by firms that choose to engage in illegal practices. However, the deterrence effect of higher sanctions reduces the fierceness of price competition in the market, resulting in higher expected profits. As a result, the effects of different kinds of sanctions may vary. While sanctions proportional to output and therefore to social harm have a positive impact on expected profits, a fixed sanction has a non-monotone effect on profits. Consequently, the relationship between the number of firms and law enforcement resulting from a fixed sanction may be u-shaped. More generally, the fact that law enforcement implies repercussions on product market competition indicates that policy-makers should take these effects into consideration in their attempts to optimize law enforcement. In addition, our finding that corporate crime reduces expected profits in equilibrium may help to explain certain real-world occurrences, such as the emergence of voluntary agreements among firms on standards addressing bribery (see, e.g., the Rules of Conduct set out by the International Chamber of Commerce). Our analysis has pointed out that law enforcement can support private efforts to coordinate on a no-crime outcome.
Our analysis suggests that blaming competition exclusively for inducing the illegal conduct of firms may sometimes be unjustified, opening up many avenues for future research. For instance, it may be interesting to consider scenarios in which the benefits of unlawful practices can vary across firms, as well as settings in which these benefits are so great that law-abiding firms are driven out of the market. If consumers’ preferences could be shifted to encourage purchasing from law-abiding firms, we would obtain deterrent market incentives via reputation effects in a dynamic setting. Moreover, our analysis has shown that the specifics of the sanctions applied have an impact on the relationship between competition, law enforcement, and crime. This is an important insight that might generalize to other areas of non-compliance, and it underscores the importance of aligning the scholarly representation of sanctions with real-world sanction schemes.
A Proof of Lemma 1
No crime: There will be no crime in equilibrium and
All firms are of type C and charge
Some firms are of type C and charge
This must fall on the unit interval and thus imposes constraints on the parameters that may allow for this outcome to occur. Specifically, we obtain
Firms benefit equally from being a firm L and charging
All firms are of type C but charge
as this ensures that
All firms are of type C and some charge
a critical level that must fall on the unit interval and thus imposes constraints on the parameters that potentially allow for this outcome to occur. Specifically, we obtain
The level of the fixed fine that causes a strict preference relative to being a firm L is given by
B Proof of Proposition 1
The sign follows from
which is fulfilled for
With regard to the first critical net benefit level
With respect to the second critical net benefit level
C Proof of Proposition 2
which is larger (smaller) than zero when
where the inequality follows from
Turning to the second critical benefit level
where the inequality follows from
D Calculation of Expected Transportation Costs
Total expected transportation costs result from
which after some manipulations simplifies to eq. .
E Coordination among Firms
To investigate the possibility of coordination on the no-crime equilibrium, we follow the standard approach involving a grim-trigger strategy. That is, we consider an indefinitely repeated version of the one-shot game used in our main analysis and derive the critical discount factor from the incentive-compatibility constraint. We assume that the net benefit from crime is the same in every period. All firms maintain no-crime as long as no firm chooses to reduce its production costs by illegal practices and price aggressively. Should any firm deviate, the equilibrium of the one-shot game results forever.
When one firm deviates, it captures the full benefits (as
The continuation profits that result should the cooperation break down are specified in eq.  and are a function of the net benefits from crime
Denoting the common discount factor by
We are interested in whether and how law enforcement policy, net benefits from crime, and the characteristics of product market competition (i.e., n and T) influence the likelihood of successful coordination on the no-crime equilibrium (the critical discount factor). Our findings in this regard are summarized in Proposition 7 presented in Section 3.5, the proof of which is expelled below.
From eq. , the derivatives of the critical discount factor
We thank Talia Bar, Helmut Bester, Dennis Gärtner, J.J.A. Kamphorst, Eric Langlais, Tim Reuter, Urs Schweizer, and conference participants at the Annual Meetings in 2014 of the American Law and Economics Association, the European Association of Law and Economics, the German Economic Association in Hamburg, and the Royal Economic Society in Manchester, as well as workshop participants at the Humboldt University Berlin, the University of Düsseldorf, the University of Connecticut, and the University of Bonn for their much-appreciated comments on earlier versions of this paper. In addition, we are very grateful for the suggestions made by the editor in charge Till Requate and two anonymous referees.
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A similar argument has been proposed with regard to earnings manipulation (Datta, Iskandar-Datta, Singh 2013; Bagnoli and Watts 2010) and tax evasion (Goerke and Runkel 2011), among other issues. In addition, although their contribution is not concerned with criminal acts, Hellmann, Murdock, and Stiglitz (2000) point out that more intense competition in the banking sector may lead to less prudent risk-taking behavior among bankers.
The collapse of a garment factory building in Dhaka, Bangladesh, on April 24, 2013 (see CBCnews, http://www.cbc.ca/news/world/story/2013/05/06/bangladesh-collapse-possible-murder-charges.html), and the illegal dumping of hazardous chemical waste in Yorkshire, Lancashire, and Shropshire (see Environment Agency, http://www.environment-agency.gov.uk/news/138898.aspx?month=4& year=2012&coverage=National&persona=Prosecution) provide further sad evidence that firms indeed make extensive use of such practices.
Our contribution is thus complementary to the antitrust literature in which firms resort to illegal means with the intention of directly lowering competitive pressure in the industry. However, in our paper, we are primarily concerned about how variations in the intensity of product market competition influence the attractiveness of illegal practices that enhance the competitive position of the firm under consideration. For a more extensive discussion, see Section 1.2.
These Guidelines state that “The base fine is the greatest of: (1) the amount from the table in subsection (d) below corresponding to the offense level determined under
This focus distinguishes our contribution from analyses in which firms deceive consumers in order to increase revenues or offer services to consumers that are deemed unlawful (for the latter, see, for example, Bennett et al. 2013). Moreover, we do not consider the possibility that individuals internalize social harm and its implications for others. For a recent approach of that kind in environmental economics, see Dasgupta et al. (forthcoming).
Openness may affect not only the intensity of competition but also the quality of institutions (see Badinger and Nindl 2014).
Less related to the study at hand are the empirical studies by Bennett et al. (2013) and Garmaise and Moskowitz (2006). Bennett et al. (2013) provide evidence that in a more competitive environment, firms in charge of monitoring vehicle emission standards become more lenient toward their customers. In our model, consumers do not directly benefit from firms’ illegal practices (only indirectly via the adjustment in prices). Garmaise and Moskowitz (2006) conclude that bank mergers that reduce competition in the financial sector may result in a higher rate of property crime in subsequent years. In contrast to our analysis, this indicates an indirect effect of competition in one sector on incentives for crime in some other area.
The results about to be presented also obtain in a setup where demand is a function of the output produced by illegal means (i.e., where the mass of consumers decreases in the extent of firms’ criminal activity). The decrease in demand could result from consumers responding to information about misbehavior within the industry and/or adverse effects on consumers from such practices, without consumers being able to distinguish firms according to their behavior. The analysis is available upon request from the authors.
After describing the equilibrium at the price-setting stage, we will explain the parameter configurations for which this condition holds in equilibrium (see inequality (14)).
We abstract from the possibility of congestion of enforcement resources, which is addressed elsewhere in the literature (see, e.g., Ferrer 2010).
We thereby follow up on the recent discussion about relative audit mechanisms in Bayer and Cowell (2009), Gilpatric, Vossler, and McKee (2011), and Oestreich (forthcoming), among others. Relatedly, in a dynamic setting, Harrington (2005) investigates the optimal price adjustment of a cartel that understands that price changes may trigger the antitrust authority’s suspicion about the cartel’s existence. As in the literature on relative audit mechanisms and in our approach, Harrington (2005) abstains from explicitly modeling the enforcer’s optimization problem.
Firms may have incentives to misrepresent or manipulate their ability to pay. For example, in the literature on the economics of liability law, scholars have discussed the possibility that firms may change their organizational structure (for instance, by contracting out risky activities) in order to restrict their ability to pay (e.g., Ringleb and Wiggins 1990, Wiggins and Ringleb 1992). However, other contributions argue that “piercing the veil”, additional legal instruments, and the moral hazard problems that result from delegation act as limits on such activities (e.g., Brooks 2002, Muir 2014, and White 1998). Within the realm of criminal law, Polinsky (2006) analyzes the scenario in which convicts may argue that they have insufficient funds to pay their fines but will be made to pay a higher fine should their claims be proven false, taking into account the fact that there are court staff positions tasked with determining a defendant’s ability to pay. In reality, some firms indeed argue that they cannot pay the entire fine imposed (e.g., Arlen 2012). If such problems exist, this can be interpreted as an upper limit on the actual level of fines, such that the actual fine imposed on a firm may fall short of the nominal one prescribed by the law.
With endogenous market entry, we introduce an additional stage 0 in which firms decide about market entry facing fixed costs of entry (see Section 3.3).
In most circumstances, especially when increases in the detection probability are costly, underdeterrence is a feature of the optimal enforcement policy chosen by a benevolent policy-maker (see, e.g., Polinsky and Shavell 2007).
Assuming quadratic transportation costs precludes the existence of profitable discrete deviations in price levels, implying that our approach that uses the first-order conditions is exhaustive.
As a result of our restriction on r, we can simplify our notation regarding firms of type C, as there is no longer ambiguity with respect to their pricing decision. We thus denote the profits of firms of type C simply as
Equation (25) below indicates that
This statement follows from equation (25).
An increase in market entry costs K has the same effects as the lower number of firms n described in Section 3.
We thank one of the anonymous referees for this suggestion.
We maintain the notation using
The equilibrium share of firms C in the mixed-strategy equilibrium is given by
We assume that being a criminal firm and pricing according to marginal costs c is dominated by being a law-abiding firm. Note that firms are concerned about any other firm’s criminality only when the other prices aggressively.