TY - JOUR
AU - Baumann, Florian
AB - Abstract This article shows that shifting losses from consumers with heterogeneous harm levels to vertically differentiated duopolists increases product safety levels, while narrowing the degree of product differentiation. Our setup features observable (but possibly nonverifiable) product safety levels and firms subject to strict liability according to a parametric liability specification. Firms’ expected liability payments depend on both product safety and price levels which critically influences the repercussions of shifting losses to firms. From a social standpoint, shifting some losses to firms is always beneficial. 1. Introduction 1.1. Motivation and Main Results Product liability makes manufacturers of defective products liable for harm caused to their consumers, and has gained major importance in the United States and increasingly does so in Europe (e.g., Lovells 2003). Controversies about its use and potential excessiveness receive attention in the media and in academia (Polinsky and Shavell, 2010a, 2010b; Goldberg and Zipursky, 2010). A main insight from the standard model with fully informed, homogeneous consumers is that—absent costs of litigation—product safety levels (and other market outcomes) are independent of whether or not product liability applies (see, e.g., the recent survey by Daughety and Reinganum 2013). We analyze how product liability influences product safety levels (and other market outcomes) in a market in which products with different safety levels are offered to consumers with heterogeneous harm levels. How product liability relates to vertical product differentiation has not been analyzed in the preceding literature. The market for bicycles may serve as an example for a market in which product varieties with different safety levels are sold to consumers who differ in their harm levels. Product defects may cause serious injury to the bicyclist even in solo accidents.1 The harm due to an accident will vary across victims as a result of heterogeneity in terms of wealth or health, for example. While product safety is valuable for all potential victims, the heterogeneity in harm levels implies heterogeneity in the willingness to pay for higher safety. We show that product liability influences product safety levels (and other market outcomes) in a market with vertically differentiated products despite consumers’ full information about product safety. In our setup, two firms sell their products, each with a specific safety level, to consumers with heterogeneous harm levels. In Stage 1 of the two-stage competition, firms commit to observable (but possibly non-verifiable) product safety levels. Price competition takes place in Stage 2 for given safety levels, and always leads to full-market coverage. Like, for example, Daughety and Reinganum (2006), we assume that compensation is determined by the tort system and not by contracting between firms and consumers. Firms are subject to strict liability with incomplete compensation of victims of product-related accidents.2 In the spirit of Daughety and Reinganum (1995), we vary the liability system’s allocation of losses between injurers and victims and trace out the implications for product safety levels, the degree of product differentiation with respect to product safety, the intensity of price competition, and welfare. In equilibrium, one firm offers a risky product at a low price and the other firm produces a high-safety variety at a high price. Shifting losses to firms induces both firms to increase their safety investments in a way that decreases the level of product differentiation. The fact that shifting more losses to firms changes product safety levels stands in a sharp contrast with the irrelevance result from the literature introduced above. The explanation for our finding runs as follows. Firms design the products’ safety characteristics with strategic motives, the marginal consumer, and a firm-specific average consumer in mind. The strategic motive results from the fact that more extensive product differentiation will result in softer price competition. Shifting more losses to firms makes safety less important for consumers, causing a reallocation of consumers to the low-safety firm such that both firms face an average and marginal consumer with a higher harm level (all else equal), and a moderation of the importance of the strategic motives. Both implications cause higher safety by the low-safety firm and in equilibrium also a higher safety level results for the high-safety firm. When assessing the overall effect of shifting more losses from consumers to firms using a utilitarian welfare function, we find that it is socially optimal in most (i.e., not all) scenarios, whereas allocating some losses to firms is always socially optimal. With regard to the impact of different components of welfare, it may be that the increase in welfare results from firms gaining profits and consumers losing utility, that is, counterintuitive distributional consequences may result from a greater reliance on product liability.3 Our article contributes to the literature in the following ways (see the next section for a discussion of the relationship to the literature): in a market with imperfect competition and consumers differing in expected harm, we identify the influence of product liability on the degree of product differentiation as an important area to be included in the discussion of the pros and cons of product liability. We establish that the liability system can be of critical importance to welfare even when consumers perfectly observe the level of safety. 1.2. Related Literature The present analysis responds to Oi (1973), who provides a first discussion of the scenario with heterogeneous consumers when the products’ safety levels may differ. Since our work studies the interaction of product liability and vertical product differentiation, the present article can be related to contributions on product liability and the industrial-organization literature on endogenous product differentiation. There is a vast literature on product liability (see, e.g., the surveys by Daughety and Reinganum, 2013 or Geistfeld, 2009). The standard setup considers perfectly competitive firms, identical risk-neutral consumers, costless trials, and that both care costs and expected harm are proportional to output. It delivers the result that strict liability and no liability are equally efficient when consumers are perfectly informed about care and do not misperceive risk (e.g., Hamada, 1976; Shavell, 1980). In our setup, the extent to which product liability is made use of has important efficiency implications even when we maintain the assumptions regarding consumer information. Besides imperfect consumer information, endogenous fixed costs of care (Daughety and Reinganum, 2006; discussed in more detail below) and cumulative harm (Daughety and Reinganum, 2014) also call the irrelevance result regarding product liability into question, as they lead to profit-maximizing care being dependent on the level of output/consumption. Both aspects are absent in our setting. Daughety and Reinganum (2006) analyze a scenario in which perfectly informed consumers are served by (potentially differentiated) firms engaging in Cournot competition. A key difference between the present article and Daughety and Reinganum (2006) lies in the fact that we consider consumers who are heterogeneous in their expected harm levels in the event of an accident, whereas the heterogeneity between consumers in Daughety and Reinganum (2006) may result only after the accident (if at all). Accordingly, in our setting, consumers differ in their willingness to pay for safety at the time the purchase decision is made. In addition, in Daughety and Reinganum (2006), whether or not goods are close substitutes (horizontally) is controlled via an exogenous parameter, whereas the extent of (vertical) product differentiation is an endogenous outcome in our framework.4 Nevertheless, there are a number of features that the present article and Daughety and Reinganum (2006) share. Firms commit to safety in the first stage and choose a competition parameter in Stage 2 (which is quantity in their setup and price in ours). Moreover, the two papers are closely related because, in both frameworks, firms consider a “business stealing” effect when determining safety, the safety choice depends on a firm’s output level, and both firms and harmed consumers always bear some costs resulting from a product-related accident.5 Another related article is Choi and Spier (2014) building on Ordover (1979). In that paper, perfectly competitive firms choose precautions facing consumers with either a high or a low accident probability, where safety is firms’ private information and risk type is consumers’ private information. When contracts comprise a price and stipulated damages to be paid in the event of an accident, firms have an incentive to lower the latter to screen risk types, providing a welfare rationale for mandatory product liability. In the industrial-organization literature, vertical product differentiation is studied in Shaked and Sutton (1982). Firms first choose their quality level before they compete in prices, and offer different levels of quality to mitigate the intensity of price competition.6 In our article, we investigate how product liability influences firms’ product safety choices. The preceding industrial-organization literature on vertical product differentiation has instead focused on minimum-standard requirements as the policy instrument of choice (Ronnen, 1991; Crampes and Hollander, 1995). A robust result in this literature is that the use of a mildly restrictive minimum quality standard leads to an increase in the profits of the low-quality firm whereas the high-quality firm always loses profits when a quality standard is imposed. With respect to consumer surplus, Crampes and Hollander (1995) show for a fully covered market that all consumers gain from the introduction of a minimum-standard requirement if the response of the high-quality firm to the quality choice of its rival is weak. Moreover, the authors show that welfare increases if the introduction of the standard reduces the level of product differentiation despite the lower profits for the high-quality firm and the potential loss in surplus for some consumers. Our analysis highlights the similarities and differences between the results obtained from using either product liability or a minimum-standard requirement. Allocating a greater share of losses to firms reduces the difference in the products’ safety levels which may also result from a stricter minimum-standard requirement. However, due to the rather complex interaction of product liability and product differentiation, the welfare effects of resulting changes in market shares and safety levels are less clear-cut when compared to the case with a minimum quality standard. In addition, there are some important differences between product liability and minimum quality standards. If firms have to compensate a larger share of losses, this reduces their scope for vertical differentiation because consumers perceive products as more similar even when holding the difference in care levels constant. In contrast, the use of or change in the level of a minimum-standard requirement does not influence consumers’ perception of quality differences. In addition, the minimum-standard requirement effectively determines safety of the low-safety firm, whereas product liability does not similarly restrict the firms’ choice set. Finally, a liability regime can be implemented even if safety is only observable but not verifiable, which would preclude the application of a minimum-standard requirement.7 1.3. Plan of the Paper Section 2 presents the model. Section 3 derives the socially optimal allocation as a benchmark for the market outcome established in Section 4. In Section 5, we explain how product liability influences the market equilibrium before we discuss repercussions on welfare in Section 6. Section 7 concludes. 2. The Model We consider a market with the following characteristics:8 Firms. There are two risk-neutral firms competing in prices and safety levels. Firm i offers one variety of the product where the product is characterized by its safety features xi, xi∈[0,1], i=1,2. The safety features are defined in such a way that the probability of a product-related accident is given by 1-xi. Unit production costs amount to axi2/2.9 Both firms simultaneously choose the safety features by committing to a specific product design (specific xi) in Stage 1. Firms’ labels are chosen (without loss of generality) such that Firm 1 is the low-safety firm and Firm 2 the high-safety one (i.e., that x1≤x2). At Stage 2, the products’ safety features are common knowledge and firms simultaneously set prices pi. Consumers. Demand stems from of a continuum of risk-neutral consumers whose mass is normalized to one. Each consumer buys one unit from either one of the two firms. With regard to the consumption features, consumers value both varieties according to the parameter v (assumed to be large enough to ensure full market coverage in equilibrium). Most importantly, consumers differ with respect to the level of (expected) harm h incurred in the event of an accident, where h is uniformly distributed on the interval [1,2] and consumers’ private information.10 Consumers may differ with respect to their level of harm for several reasons. For example, the level of harm could be a function of consumer-specific characteristics such as wealth, professional status, or health. Firms cannot observe the specific level of harm when selling the product to a consumer and we do not consider contract schemes that allow firms to screen consumer types.11 This assumption is reasonable in mass markets, for example, where products are distributed through retailers. A consumer’s net expected utility after purchase of a good is given by the valuation v less the price paid and less uncompensated expected harm. Liability scheme. Product liability is strict but the expected level of damages fall short of consumer harm for at least one of two possible reasons. First, the injurer escapes suit with probability 1-β, β∈(0,1) (as in, e.g., Shavell, 1984 and Schmitz, 2000). Injurers may escape liability, for example, because victims do not choose to bring suit fearing that their evidence fails the causality test. The level of β is common knowledge.12 In addition, in the event of a trial, it may be that the level of compensation is set below the level of harm, a potential discrepancy that we consider as the policy variable. For most practical scenarios, when part of the accident loss is due to property damage, arriving at a more or less accurate estimate of the property value is often difficult and can be guided by policy decisions about what kinds of references may be used and what kinds of evidence are admissible before court to inform about the level of the loss (e.g., Kaplow and Shavell, 1996). Difficulties in assessing harm are even more pronounced in the context of temporary or permanent physical harm and lost earnings. The generosity of different legal regimes with respect to pain and suffering is a case-in-point (e.g., Shavell, 2004). To take this into account, we explore the implications of varying the allocation of compensable losses between firms and consumers by using a policy variable γ, 0≤γ≤1. In other words, the level of compensation transferred from the liable firm to the harmed consumer in the event of trial is γh, such that setting γ=1 implies that all compensable losses on the part of consumers are actually compensated by firms. In summary, for the agents in our model, the firms’ expected damages payment from a consumer with harm level h is given by κh, with κ=βγ, whereas the expected harm that remains with the consumer is (1-κ)h. Timing. The timing of events is as follows: In Stage 0, the policy maker decides about the policy parameter γ. In Stage 1, firms simultaneously choose levels of product safety. In Stage 2, firms simultaneously set prices and then consumers decide from which firm to buy. Finally, accidents occur according to the accident risks of firms 1 and 2, and compensatory payments mandated by the liability regime are transferred. Equilibrium. We focus on a pure-strategy equilibrium with interior solutions for the safety levels. We thus impose a parameter restriction that, first, ensures safety levels between zero and one and, second, rules out so-called leapfrogging incentives (first discussed in Motta, 1993). Leapfrogging incentives in a candidate equilibrium would be present when either the high-safety firm would be better off from producing a product variety with a safety level below the one of the low-safety firm or the low-safety firm would profit from producing a product safer than the product of the high-safety firm. Whereas leapfrogging is a dominated strategy in Motta (1993), the cost asymmetry imposed by the different levels of average compensable consumer harm may make leapfrogging profitable in our setup. We find that an upper bound on the probability of trial excludes leapfrogging incentives for the high-safety firm (see Appendix A). This constraint may also be stated in terms of an upper bound for the cost parameter a, a≤5/6+1/β. A lower bound for the cost parameter a is implied by our focus on interior solutions for the safety levels, a≥9/4+β/4(4-3β). Combining the two constraints, we assume that: Assumption 1 It holds that a∈[9/4+β/4(4-3β),5/6+1/β]. In Appendix A, we demonstrate that Assumption 1 also ensures (1) no leapfrogging incentives for the low-safety firm, (2) the second-order conditions for firms’ profit maximization, and (3) that both firms are active.13 3. Benchmark: First-best Safety Levels and Split of Consumers We start our analysis by deriving the first-best levels of product safety and the socially optimal split of consumers as a benchmark. Given a fully covered market and the uniform gross benefit from products v, the maximization of social welfare is tantamount to minimizing total social costs SC, consisting of production costs and expected harm. If a social planner finds it optimal that firms 1 and 2 differentiate their products by choosing different safety levels ( x1<x2), it is clear that the products of the low-safety firm should be allocated to consumers with low levels of harm and vice versa. Denote by ĥ the harm level of the consumer who separates the population such that consumers with h≤ĥ obtain the product from Firm 1 and consumers with h>ĥ receive the product of Firm 2. Social costs can be stated as   SC=(h^−1)(ax122+(1−x1)1+h^2)+(2−h^)(ax222+(1−x2)h^+22), (1) where (1+ĥ)/2 and (ĥ+2)/2 represent the average expected harm of consumers served by Firm 1 and Firm 2, respectively. Our findings for the first-best allocation are summarized in the following lemma (see Appendix B): Lemma 1 The socially optimal safety levels are x1*=5/4a and x2*=7/4a, implying the socially optimal degree of product differentiation Δx*=x2*-x1*=1/2a. The market is segmented such that consumers with harm level h≤(>)ĥ*=3/2 obtain the product from Firm 1 (Firm 2). The social planner uses product differentiation to account for consumers’ heterogeneity regarding the level of harm in a product-related accident. In the social optimum, each firm serves half of the market and safety levels are chosen to minimize the sum of production costs and average harm of consumers served. Optimal safety levels decrease in the costs of safety a. For the marginal consumer with expected harm 3/2, the saving in production costs from a reallocation from Firm 2 to Firm 1 (i.e., ax22/2-ax12/2) is equal to the increase in expected accident costs (i.e., (x2-x1)ĥ). 4. The Market Equilibrium In this section, we derive the market equilibrium using backward induction. 4.1. Stage 2: Price Competition We start by analyzing price competition between firms 1 and 2 for given product safety levels. A consumer with harm h receives an expected damage payment κh from his supplier in the event of an accident. All consumers with h weakly below (strictly above) ĥ will buy from the low-safety Firm 1 (high-safety Firm 2), where the harm level of the consumer indifferent between buying from Firm 1 and buying from Firm 2 denoted ĥ follows from14  p1+(1−x1)h^(1−κ)=p2+(1−x2)h^(1−κ), where pi denotes the price set by firm i, such that   h^(x1,x2,p1,p2)=p2−p1(1−κ)Δx (2) when Δx=x2-x1>0. In that case, Firm 1 serves consumers with h∈[1,ĥ] and Firm 2 serves those with h∈(ĥ,2], such that q1=ĥ-1 and q2=2-ĥ refer to the demand of Firm 1 and Firm 2, respectively. Equation (2) highlights that the responsiveness of the firms’ market shares to changes in price levels is critically determined by the difference in product safety levels (i.e., the extent of product differentiation) and the specifics of the liability regime (represented by the level of κ). When Δx=0, all consumers would buy the cheaper product. When Δx=0 and p1=p2, all consumers are indifferent between the two products and we assume that, in this case, they are randomly allocated to firms. Firm i’s profit equation can be written as   πi=(pi−axi22−(1−xi)κℓi(x1,x2,p1,p2))⏟=:δiqi(x1,x2,p1,p2),i=1,2, where ℓ1=(1+ĥ)/2 and ℓ2=(ĥ+2)/2 represent expected average harm in the event of a product-related accident for consumers of Firm 1 and Firm 2, respectively. The term δi corresponds to the mark-up δi charged by firm i. Profit maximization with respect to prices yields the first-order conditions   ∂πi∂pi=qi+δi∂qi∂pi−(1−xi)κ∂ℓi∂piqi=0,i=1,2 (3) which highlight a particularity of the relationship between vertical product differentiation and product liability. The first two effects are well-known: charging a higher price increases the firm’s profits due to the higher profit margin for all units sold but induces some consumers to change their supplier. The third term is a novel aspect resulting from firms’ liability. It measures the impact of a marginal increase in the price level on the firm’s expected liability (due to the implied change in the firm’s clientele). Whereas the loss of firm-specific demand due to an increase in the own price level is the same for firms 1 and 2, the change in the firm’s expected liability due to an increase in the own price level is asymmetric such that ∂ℓ1/∂p1<0<∂ℓ2/∂p2 obtains. This is important for our analysis such that we take note of it in: Lemma 2 The marginal effect on the firm’s expected liability stemming from a higher price represents a marginal benefit (cost) for Firm 1 (2). The intuition for this result is as follows: whereas Firm 1 loses consumers with the highest expected harm when raising its price—thereby depressing the average harm of the consumers served—Firm 2 loses consumers with the lowest expected harm after increasing its price. Solving for equilibrium prices, we obtain the equilibrium mark-ups   δ1(x1,x2)=q1(x1,x2)(Δx(1−κ)+κ(1−x1)2)δ2(x1,x2)=q2(x1,x2)(Δx(1−κ)−κ(1−x2)2). Both firms charge a mark-up on their average costs per unit produced.15 For both firms, the mark-up is positively related to the own market share (i.e., qi) and the degree of effective product differentiation (i.e., Δx weighted by the share of noncompensated harm). However, the additional influence of liability (the second term in parentheses) is asymmetric, increasing Firm 1’s mark-up and decreasing Firm 2’s mark-up. The intuition lies with the additional effect of price increases on profits described in Lemma 2 which leads Firm 1 to charge relatively higher prices. With price levels given by the sum of production costs, expected liability payments, and the mark-up, the harm level of the indifferent consumer results as   h^(x1,x2)=6(1−κ)+a(x1+x2)2(3−2κ) (4) and the (reduced) profit equation as a function of safety levels only is given by   πi=δi(x1,x2)qi(x1,x2),i=1,2. (5) 4.2. Stage 1: Product Safety Solving the first-order conditions for the equilibrium product safety levels resulting from the maximization of expression (5) for Firm 1 and 2, we find   x1M=34a+κ8a−74a(4−3κ)−κ26a−54a(4−3κ) (6) and   x2M=94a+κ8a−174a(4−3κ)−κ26a−134a(4−3κ), (7) where the superscript M denotes market equilibrium outcomes.16 From firms’ safety choices, the degree of product differentiation results as   ΔxM=32a−κ(5−4κ)2a(4−3κ). (8) The use of expressions (6) and (7) allows us to give a complete description of the market equilibrium where Assumption 1 guarantees that no profitable deviation strategy exists and x2M<1. We start with how consumers are allocated to firms 1 and 2 and arrive at the indifferent consumer’s harm level:   h^M=32+κ2a−34(3−2κ) (9) which implies q1M=ĥM-1≥1/2 and q2M=2-ĥM≤1/2. Firm 1 achieves a market share higher than (equal to) one half for κ>0 ( κ=0). For the equilibrium mark-ups, we obtain   δiM=(qiM)2(2−κ)(3−2κ)2a (10) such that δ1M/δ2M≥1. This establishes that Firm 1’s mark-up exceeds that of Firm 2 when product liability plays a role (i.e., when κ>0). This pattern, favoring Firm 1, also shows with respect to profits which are given by   πiM=(qiM)3(2−κ)(3−2κ)2a (11) for i=1,2, such that π1M/π2M≥1. We summarize the results from this section regarding the market equilibrium in the following proposition. Proposition 1 Suppose Assumption 1 holds. The market equilibrium is described by safety levels x1M and x2M given by expressions (6) and (7), the indifferent consumer’s harm level ĥM given by expression (9), and mark-ups δ1M and δ2M given by expression (10). We now move on to our main research interest, that is, how incentives for product differentiation are shaped by product liability in our framework. 5. Product Liability and Market Equilibrium: Comparative-Statics Results In this section, we assess the implications of product liability for the market equilibrium. Specifically, we investigate the repercussions of product liability by describing the effects of an increase in the firms’ share of compensable harm γ. As a first step, we suppose that firms are not subject to strict product liability (by setting γ=κ=0) and compare the market equilibrium with the first-best benchmark derived in Section 3. Lemma 3 Suppose Assumption 1 holds. Without product liability, the market equilibrium displays an excessive degree of product differentiation with a suboptimal product safety level by Firm 1 and a supraoptimal product safety level by Firm 2. Both firms serve one half of the market, charge symmetric mark-ups, and earn the same level of profits. Proof. The proof follows from Lemma 1 and Proposition 1. From expressions (6) and (7), equilibrium care levels amount to x1M=3/4a=x1*-1/2a and x2M=9/4a=x2*+1/2a, highlighting the divergence of equilibrium safety and first-best safety levels. □ The fact that the market equilibrium displays an excessive degree of product differentiation has been established before (e.g., Crampes and Hollander, 1995) and can be explained as follows. In addition to trading off the cost of a higher safety level with the higher price made possible by a safer product (due to the higher willingness to pay), a marginal change in safety levels influences profits via the intensity of the ensuing price competition. From a social point of view, softer price competition in itself is an irrelevant, purely redistributive aspect, whereas the distorted firm safety levels imply that safety is no longer social cost minimizing for the respective average consumer types served by firms. To soften price competition, the low-safety firm offers a variety with lower than first-best safety and the high-safety firm offers a variety with higher than first-best safety. Otherwise the market equilibrium without liability is symmetric; both firms charge the same mark-up (equal to δ1=δ2=3/4a) and earn profits amounting to π1=π2=3/8a. Our contribution to the literature lies in the consideration of product liability. Accordingly, the novelty of our analysis shows when product liability is introduced (i.e., γ and therefore κ become positive). First, we consider the influence on product safety levels, the degree of product differentiation, and the {allocation of consumers to firms}: Proposition 2 Suppose Assumption 1 holds. An increase in the firms’ share of accident losses (1) increases both firms’ product safety levels, (2) decreases the degree of product differentiation, and (3) increases the equilibrium market share of Firm 1, such that Firm 1 serves more than half of the market when κ>0. Proof. The proof of parts (1) and (2) follows from Equations (6) to (8) (see Appendix C). Part (3) follows from the expression for the indifferent consumer (9). □ For given safety levels, an increase in the firms’ share of losses has a direct impact on how consumers are split between firms (as described by expression (4)). Consumers are less concerned about the accident risk, implying that some consumers switch from Firm 2 to Firm 1, that is, the firm-specific expected average harm levels ℓ1 and ℓ2 increase, providing an argument for higher safety levels. In addition, the fact that consumers care less about the difference in product safety levels means that product differentiation has less potential to soften price competition. In other words, there are two effects resulting from an increase in the firms’ share of losses (higher expected harm levels of consumers served and lower incentives for product differentiation). Whereas both point toward a higher level of x1, the effects are mixed when it comes to the choice of x2. To understand this reasoning formally, we scrutinize firms’ decision-making in Stage 1. Firms’ first-order conditions for product safety in Stage 1 can be rearranged as best-response functions, that is, functions that yield the profit-maximizing level of product safety of firm i for a given safety level of firm j. Specifically, we obtain   x1BR=2κ(2+a−κ)+a(2−3κ)x23a(2−κ)x2BR=12+2κ(a+κ−5)+a(2−3κ)x13a(2−κ). Under Assumption 1, the best-response functions have a positive slope, indicating strategic complementarity between firms’ product safety levels. Shifting more losses to firms decreases the slope of the best-response functions, indicating that strategic motives become less important. Matching our preceding informal arguments, an increase in the level of κ via a higher γ shifts x1BR outwards, that is, makes it privately optimal for Firm 1 to choose a higher product safety level for any x2.17 The shift of Firm 2’s best-response function prescribes higher or lower x2 depending on the level of x1.18 However, the shift of Firm 1’s reaction function implies that Firm 2’s safety level will move into the direction of higher safety on Firm 2’s new reaction function; the new equilibrium will display higher safety levels for both firms. Figure 1 illustrates the best-response functions for the extreme scenarios in which the firm’s share of compensable losses is either equal to zero or equal to one, that is, γ=0 and γ=1, respectively, assuming a=9/2 and β=1/4. The figure clearly illustrates the outward shift of x1BR and the fact that the shift of x2BR depends on the level of x1. Holding firms responsible for compensable accident losses results in a higher equilibrium safety level for firms 1 and 2 and a diminished degree of product differentiation ΔxM. Figure 1. View largeDownload slide Firms’ Product Safety Best-response Functions Under No Compensation ( κ=0) and Full Compensation ( κ=β) for a=9/2 and β=1/4. Figure 1. View largeDownload slide Firms’ Product Safety Best-response Functions Under No Compensation ( κ=0) and Full Compensation ( κ=β) for a=9/2 and β=1/4. We note that—despite perfect information—product liability has a direct bearing on firms’ safety levels. This contrasts sharply with the result that equilibrium care is independent of the liability regime obtained for markets in which consumers share the same level of (expected) harm (see, e.g., Shavell, 1980). In the present framework, shifting losses to firms lowers firms’ incentives to aim at product differentiation because its pacifying influence on price competition becomes weaker. Instead, firms’ safety levels are increasingly shaped by how they relate to total expected costs (including their production costs and expected consumer harm). At this point, let us briefly highlight an important difference between product liability and minimum quality standards. Under the latter, a low-quality firm must increase its quality level to abide by the higher minimum quality standard. In contrast, under product liability with a higher compensatory mandate, the low-safety firm is free to consider balancing the higher liability payments by shifting its focus more on low-harm consumers (through an even lower safety level). Our findings show that this is not optimal for the low-safety firm. In our analysis, we find a positive relationship between the firms’ share of losses and safety choices, respectively. In other words, the pattern we find for equilibrium safety levels under product liability bears some resemblance with that obtained for a minimum-quality standard. Nevertheless, the mechanism at work is quite different. Next, we turn attention to equilibrium mark-ups and profit levels. Proposition 3 Suppose Assumption 1 holds. An increase in the firms’ share of accident losses (i) decreases Firm 2’s mark-up, whereas the mark-up of Firm 1 may increase or decrease, and (ii) increases the relative mark-up of Firm 1. Proof. The proof follows from Equation (10) in combination with Proposition 2. □ The fact that safety becomes less important for consumers shifts demand toward the low-safety firm. This makes Firm 1 want to increase its price (see the first term in (3)). In addition, Firm 1 tolerates consumers switching to Firm 2 to a greater extent due to its effect on the firm’s expected liability (see Lemma 2). Firm 2’s lower demand and higher expected liability makes a lower mark-up optimal for Firm 2, for the same reasons. In addition, both firms consider that demand is more elastic when κ is raised. In addition to the effects just described, it is clear that the smaller degree of product differentiation makes price competition fiercer, again resulting in downward pressure on mark-ups. In summary, the high-safety firm will lower its mark-up in response to an increase of the firms’ share of accident losses, whereas the low-safety firm may even increase its mark-up (but only if the overall gain in demand of the firm dominates the direct and indirect effects of the lower level of product differentiation). The above considerations have a direct impact on the firms’ expected profit levels which is summarized in the following proposition: Proposition 4 Suppose Assumption 1 holds. An increase in the firms’ share of accident losses (i) decreases Firm 2’s profits, whereas Firm 1’s profit level may increase or decrease, and (ii) increases the relative profit of Firm 1. Proof. The proof follows from expressions (11) together with Proposition 2. □ The results described in Propositions 3 and 4 make clear that allocating more accident losses to firms harms the high-safety firm and has an ambiguous impact on the low-safety firm’s profits.19 This asymmetry parallels the repercussions of an increase in the minimum quality standard.20 As is true for firms, the implication of an increase in the firms’ share of losses on a consumer’s payoff depends on type, that is, the individual level of harm. For example, marginally introducing product liability may harm or benefit consumers with a low level of harm, whereas it always benefits consumers with a high level of harm. At the group level, consumers are always better off from a marginal introduction of product liability, as consumer surplus defined by   CS=v−∫1h^M(p1M+(1−x1M)(1−κ)h)dh−∫h^M2(p2M+(1−x2M)(1−κ)h)dh (12) increases with the firms’ share of losses at γ=0. In contrast, firms as a group are always worse off from a marginal introduction of product liability. The more detailed analysis of these issues is delegated to Appendix D. The analysis in this section has established that allocating a greater share of accident losses to firms lowers the accident risk associated with consuming either variety of the good and influences firms’ profit levels and consumers’ utility in an intricate way. Whether or not these changes are welfare-improving will be discussed in the next section. 6. Product Liability and Welfare In many circumstances, it is realistic to assume that policy makers take how competition unfolds as a given and seek welfare improvements by influencing the circumstances under which firms compete. In the present setting, it is thus interesting to explore how welfare responds to changes in the level of κ induced by changes in γ. In practice, legislators can determine what kinds of harm have to be compensated in principle and what references may be used to measure the value of the compensable harm. When the policy maker influences the outcome indirectly with only one instrument—the liability system’s allocation of losses—the first-best level of welfare will not be attainable. The variables that are relevant to welfare are the safety levels implemented by firms 1 and 2, and the segmentation of consumers (since our focus on a fully covered market implies that the volume of trade is not affected). The benevolent policy maker chooses the level of his only policy instrument—the liability system’s allocation of losses—to minimize the level of social costs defined by   SCM=(h^M−1)(a(x1M)22+(1−x1M)1+h^M2)+(2−h^M)(a(x2M)22+(1−x2M)2+h^M2), (13) taking into account how privately optimal decisions by firms and consumers depend on the level of κ. It is clear from (13) that the allocation of accident losses between firms and consumers bears no direct implication for the level of social costs such that its only role is in guiding private decisions. The marginal change in the level of social costs in response to an increase in γ is given by   dSCMdγ=dh^Mdγ(h^M(x2M−x1M)−a((x2M)2−(x1M)2)2)⏟=:A+dx1Mdγ(h^M−1)(ax1M−1+h^M2)⏟=:B+dx2Mdγ(2−h^M)(ax2M−2+h^M2)⏟=:C, (14) where xiM and ĥM are increasing in γ (see Proposition 2). The total marginal effect in expression (14) is composed of three different terms: term A indicates the change in social costs due to the reallocation of consumers from Firm 2 to Firm 1, terms B and C describe the changes in social costs that result from the change in care levels for given firm-specific demand levels. These implications will be discussed in turn.21 When κ>0, the market is not split equally between firms 1 and 2 which, however, is a characteristic of the first-best allocation. Instead, more consumers buy from Firm 1. However, given that equilibrium product safety levels differ from socially optimal care levels, the first-best split of consumers may not be second best. Indeed, the second-best level for the harm level of the indifferent consumer ĥSB (given the market levels of safety x1M and x2M)   h^SB=h^∗+κ2a−34 exceeds the first-best level when κ>0. Note that as   h^M−h^SB=−κ(1−κ)(2a−3)2(3−2κ)≤0, the benevolent policy maker would like to allocate even more consumers to Firm 1, given the safety levels that result in the market equilibrium. In equilibrium, the relatively higher mark-up of the low-safety firm prevents the second-best allocation of consumers for given safety levels. In other words, the influence that the liability system’s allocation of losses bears on how consumers are split up between firms suggests raising the share γ to one.22 The terms B and C indicate whether the privately optimal safety levels fall short of or exceed what the policy maker would implement given the market equilibrium split of consumers ĥM. From expression (13), setting either B=0 or C=0, we obtain the second-best levels of care xiSB for the given split of consumers ĥM as   xiSB=xi∗+κ(2a−3)8a(3−2κ), where ΔxSB=1/2a=Δx*. For κ>0, the second-best safety levels exceed the first-best care levels, because both firms serve consumers with higher expected harm levels (due to ĥM>ĥ*). Comparing the product safety levels in the market equilibrium with the ones in the second-best allocation, we arrive at x1M-x1SB<0 and x2M-x2SB>0, where the signs follow from Assumption 1. The equilibrium degree of product differentiation exceeds the second-best level for all levels of κ. This is intuitive because firms’ decision-making is still influenced by the desire to soften price competition. Firm 1’s safety choice falls short of the second-best safety level. Accordingly, term B in expression (14) is negative since an increase in Firm 1’s safety level is cost justified in that it reduces the expected harm of Firm 1’s consumers by more than it increases production costs. In other terms, the influence that the liability system’s allocation of losses bears on Firm 1’s safety level also suggests raising γ to one. At the same time, Firm 2’s safety level is excessive compared to the second-best safety level x2SB. Term C is positive since a decrease in Firm 2’s safety expenditures would result in a decrease in precaution costs that more than offsets the increase in expected harm given the allocation of consumers to firms. This argues against a high liability parameter γ. In summary, we have argued that, from increasing the share of losses borne by firms, the policy maker obtains two kinds of marginal benefits—the influence on ĥM and x1M—and one marginal cost—the implication for x2M. From a policy standpoint, it is important to know whether the optimal level of γ is positive and, if so, if it is equal to or lower than one. Proposition 5 Suppose Assumption 1 holds. The firms’ share of compensable accident losses that minimizes social costs (i) is positive and (ii) may be less than one. Proof. Part (i): For γ=0 the term A in expression (13) is equal to zero, term B amounts to -1/2, term C is equal to 1/2 and demand is split equally between firms. Due to dx1M/dγ=β(8a-7)/16a>dx2M/dγ=β(8a-17)/16a, it holds that dSCM/dγ<0 at γ=0. It can be established that d2SCM/dγ2>0 under Assumption 1, such that we can establish part (ii) by reference to two examples. For a=9/2, β=1/4, we obtain dSCM/dγ<0 at γ=1, whereas for a=9 and β=1/10, it holds that dSCM/dγ>0 at γ=1. □ We find that the cost-minimizing level of γ is strictly positive. The beneficial effect of product liability on the lower safety level dominates its adverse effect on the higher safety level. In fact, it may be argued that the introduction of product liability is socially desirable because it dampens firms’ excessive incentives for product differentiation. When γ>0, further increases in the firms’ share of losses may still be worthwhile but the optimal value of γ may be lower than one for certain parameter constellations. This finding is interesting since there is noncompensated harm due to the injurer’s escaping trial with probability 1-β even when γ=1.23 From our discussion of the different marginal effects, it is clear that scenarios featuring a cost-minimizing level of γ less than one must be such that Firm 2’s deviation from the second best regarding the safety choice bears heavily on the level of social costs. This is more likely when the marginal safety cost parameter a is high. Indeed, under Assumption 1, an increase in firms’ share of losses is less effective in reducing social costs the higher the marginal costs of safety are (i.e., d2SCM/dγda>0) and therefore the optimal liability share is weakly decreasing in marginal safety costs. When an interior solution exists for the optimal liability share, an increase in the probability that the firm will be found liable (i.e., β) results in a corresponding decrease in the optimal liability share, such that βγ remains constant. However, the fact that the inappropriate safety choice of Firm 2 is relevant only to a relatively small set of consumers at high levels of γ, shifting all of the compensable losses to firms minimizes social costs in the bulk of scenarios. For example, it can be shown that an optimal liability share lower than one requires that a>6.24 We conclude this section by presenting a numerical example to convey an idea of possible outcomes of shifting losses to firms in our setup. The example is based on a=9/2, β=1/4, and v=3. In this example, Firm 1 always benefits from shifting more losses to firms (Figure 2). Starting from relatively high levels of γ, a further marginal increase in the firm’s share of losses raises the sum of profits and decreases consumer surplus (Figures 2 and 3). Shifting more losses to firms is always decreasing the level of social costs in our example (Figure 4). Figure 2. View largeDownload slide Individual Firms’ Profits and Total Profits for a=9/2 and β=1/4 Figure 2. View largeDownload slide Individual Firms’ Profits and Total Profits for a=9/2 and β=1/4 Figure 3. View largeDownload slide Consumer Surplus for a=9/2, β=1/4, and v=3. Figure 3. View largeDownload slide Consumer Surplus for a=9/2, β=1/4, and v=3. Figure 4. View largeDownload slide Social Costs for a=9/2 and β=1/4. Figure 4. View largeDownload slide Social Costs for a=9/2 and β=1/4. 7. Discussion and Conclusion Firms’ incentives for product safety are shaped by both market forces and anticipated implications regarding product liability. When a product-related accident is more detrimental for some consumers than for others, varieties of the good with different risk attributes will evolve from the firms’ strategic market interaction. This article provides an analysis of the interaction between product liability and vertical product differentiation in a duopoly in which firms first commit to product safety and then compete in prices. Starting from an equilibrium in which firms have no legal obligation to compensate product-related losses and at which product differentiation is excessive, we trace out the implications of raising the firms’ shares of compensable accident losses for accident risk, product differentiation with respect to product safety, the intensity of price competition, and welfare. We establish that since firms’ actions bear not only on their mark-ups and demand levels but also on their expected liability, an intricate relationship between product liability and product differentiation exists. Our results show that allocating more losses to firms entails that both product varieties become safer but less differentiated. Moreover, in our framework in which consumers are perfectly informed about the level of harm and the level of product safety, there are, nevertheless, real consequences from changing the allocation of losses between consumers and firms. These changes increase welfare defined as the sum of consumer and producer surplus in most but, interestingly, not in all cases. Shifting losses to firms benefits consumers with high levels of harm, while possibly lowering the well-being of low-harm consumers. Similarly, shifting responsibility for losses incurred in the event of an accident to firms has asymmetric repercussions for the firm serving the high-safety variant and the firm serving the low-safety good. The intricate effects on firms’ and consumers’ payoffs have important implications when the political economy of product liability is considered. The present analysis studies the influence of product liability on vertical product differentiation when consumers differ in ex-ante expected harm, an important aspect that was neglected in the literature heretofore. We hope that our analysis stimulates further investigations. In some models of vertical product differentiation, market coverage is incomplete. We conjecture that this will bring about additional effects of product liability because we have shown that it is high-harm consumers who benefit from shifting more losses to firms. As a result, in such a setting, allocating more losses to firms is likely to increase the volume of sales. Furthermore, one may consider the scenario in which the quality costs (at least partly) represent fixed costs (e.g., product design). Also, product quality could affect the probability that the firm is found liable in the event of an accident (which is taken as symmetric and exogenous in our model). Other interesting avenues for further research concern consumer information. One natural extension is the scenario in which some or all consumers are not fully informed about their expected harm levels at the time of purchase or may differ in their incentives to sue according to the realized level of harm. Moreover, consumers may not be able to perfectly judge the safety features of the products they buy. In the latter scenario, firms’ incentives for signaling or costly disclosure would be possible avenues of future research. Acknowledgement We are grateful for comments received from Benjamin Edelman, Christian Gollier, Jurjen Kamphorst, Xingyi Liu, Eric Rasmusen, Tobias Wenzel, Abrahman Wickelgren, and participants at the IIOC 2015 (Boston) and workshops in Amsterdam, Bergen, Mannheim, Munich, Paris-Nanterre, and Rotterdam. Moreover, we gratefully acknowledge the helpful suggestions received from two anonymous reviewers. Appendix A. Sufficiency of Assumption 1 for Pure-strategy Equilibrium with Interior Product Safety Levels We focus on pure-strategy equilibria with interior product safety levels. In this Appendix, we show that Assumption 1 results from these restrictions. In addition, we demonstrate that Assumption 1 is sufficient to ensure that firms’ second-order conditions are fulfilled and that both firms actually serve some consumers. [1] No leapfrogging. Denote by q1(x1,x2) and by q2(x1,x2) the demand for the firm offering the low-safety variety of the good and the demand for the firm offering the high-safety variety, respectively. From (5), given Firm 1 chooses x1M, Firm 2’s profit level obtained from leapfrogging (i.e., choosing x2<x1M) is given by   π2LF=[x1M−x2+κ(1+x2−2x1M)2]q12(x2,x1M) which is maximized for   x2LF=1a[4−3κ]+κ6a+13a[4−3κ]−κ26a+34a[4−3κ]. Profits from deviating to x2LF<x1M amount to   π2LF=[2−κ][6+κ(6a−13)]33456a[3−2κ]2. From a comparison to (5) for i=2 and j=1, leapfrogging is a profitable strategy for   κ≥6(6a−5). Since the maximum value of γ is one, leapfrogging is not profitable for Firm 2 for any feasible γ as long as the share of compensable harm does not exceed a threshold or, more precisely, when   β≤66a−5. This constraint may be formulated as an upper bound for the cost parameter a ( a≤5/6+1/β, as used in Assumption 1). Analogously, when Firm 2 chooses x2M, the profits from leapfrogging by Firm 1 ( x1>x2M) can be deduced from (5) and are given by   π1LF=[x1−x2M−κ(1+x1−2x2M)2]q22(x2M,x1) which is maximized by   x1LF=11a[4−3κ]−κ46−6a3a[4−3κ]+κ221−6a4a[4−3κ]. The profits from choosing x1LF>x2M amount to   π1LF=[2−κ][6−κ(6a−5)]33456a[3−2κ]2. A comparison with profits stated in (11) for i=1 and j=2 yields that leapfrogging would be profitable when   6+κ(6a−13)≤0. Consequently, Firm 1 has no incentive to leapfrog when Assumption 1 holds because a≥9/2 is implied by the lower bound. [2] Interior safety levels 0≤x1M≤x2M≤1. From (6), we deduce that x1M≥0 for any level of γ. From the expression for the degree of product differentiation (8), it follows that x1M<x2M. The constraint x2M≤1 must be evaluated at γ=1 because x2M is a function increasing with γ. Accordingly, we have   94a+β8a−174a(4−3β)−β26a−134a(4−3β)≤1⇔94+β4(4−3β)≤a which is the lower bound on the cost parameter a in Assumption 1. [3] Second-order conditions for a profit maximum. Inserting x1M and x2M into the second-order conditions at the second stage, we obtain   ∂2π1∂p12=a(4−3κ)[6+κ(2a−7)]4(3−2κ)2(1−κ)2(−2+κ) and   ∂2π2∂p22=a(4−3κ)[6−κ(2a+1)]⏞=:X4(3−2κ)2(1−κ)2(−2+κ). The first expression is unambiguously negative, the second one for X>0 which holds according to Assumption 1. Inserting x1M and x2M into the second-order conditions at the first stage, we obtain   ∂2π1∂x12=3a(−2+κ)[6+κ(2a−7)]16(3−2κ)2 and   ∂2π2∂x22=3a(−2+κ)[6−κ(2a+1)]⏞=X16(3−2κ)2. The first expression is unambiguously negative, the second one is negative due to X>0 as argued above. [4] Interior solution for the indifferent consumer 1≤ĥM≤2. From (9), ĥM>1 obviously holds and ĥM≤2 translates into   κ≤62a+1. Since 6/(2a+1)>6/(6a-5) for 4a>6 this restriction is fulfilled due to Assumptions 1. B. Proof of Lemma 1 The first-order conditions for x1 and x2 of the minimization problem according to (1) result in x1=(1+ĥ)/2a and x2=(ĥ+2)/2a. Inserting these values into the first-order condition for ĥ, we obtain after collecting terms   −3+2h^8a=0 which leads to the results stated in Lemma 1. C. Proof of Proposition 2 Differentiating (6) with respect to γ and collecting terms, we obtain   ∂x1M∂γ=β8(a−1)+(6a−5)[4−8κ+3κ2]4a(4−3κ)2=β8(a−1)+(6a−5)[4(1−κ)2−κ2]4a(4−3κ)2=β6(a−1)(1−κ2)+(2(a−1)−κ2)+(6a−5)4(1−κ)24a(4−3κ)2, where all terms are positive due to Assumption 1, 1>β>0, and 1>κ≥0. Next, differentiating (7) with respect to γ and collecting terms, we obtain   ∂x2M∂γ=β8(a−2)+(6a−13)[4−8κ+3κ2]4a(4−3κ)2=β8(a−2)+(6a−13)[4(1−κ)2−κ2]4a(4−3κ)2=β(2a−3)+(6a−13)[4(1−κ)2+(1−κ2)]4a(4−3κ)2, where all terms are positive due to Assumption 1, 1>β>0, and 1>κ≥0. Finally, differentiating (8) and collecting terms, we obtain   ∂Δx∂γ=2βa(4−3κ)2[−5+8κ−3κ2]=−2βa(4−3κ)2[4(1−κ)2+(1−κ2)] which is negative due to Assumption 1, 1>β>0, and 1>κ≥0. D. Implications of Increasing the Firms’ Share of Losses for Consumer Surplus and Total Profits An individual consumer (with expected harm h) who purchases the good from firm i enjoys (expected) utility equal to   U=v−(piM+(1−xiM)h(1−κ)), where it clearly shows that the level of harm is relevant to the consumer’s well-being in the event of an accident only to the extent that the harm is not compensated (measured by 1-κ). A marginal increase in the firms’ share of losses from product-related accidents influences the utility of a consumer who does not switch suppliers as follows:   dUdγ=−dpiMdγ+βh(1−xiM)+dxiMdγh(1−κ)=(1−xiM)(β(h−ℓi)−κdh^Mdγ12)+((1−κ)h+κℓi−axiM)dxiMdγ−dδiMdγ. (D.1) In expression (D.1), a higher level of expected harm makes it more likely that the consumer benefits from a change in the liability system’s allocation of losses because a higher level of h magnifies the marginal benefits resulting from an increase in the level of γ without similar implications for the marginal costs therefrom. This also implies that a consumer of firm i with harm level h+ϵ, ϵ>0, will always benefit from the change in the allocation of losses when the consumer of firm i with harm level h does so. For concreteness, we consider the utility implications of introducing product liability (i.e., the value of expression (D.1) at γ=κ=0) for the consumers at both ends of the harm interval h=1 and h=2. We obtain   dUh=1dγ|γ=0=β109−40a64a⋚0anddUh=2dγ|γ=0=β40a−1164a>0. In other words, starting to shift some of the compensable accident losses to firms is necessarily increasing the utility of individuals with very high levels of harm. High-risk consumers benefit from a cross-subsidization by low-risk consumers of the same firm, dampening potential price increases. In contrast, individuals with low levels of harm will benefit from introducing product liability only when a is sufficiently small (implying that the additional care costs are small).25 This leads to: Proposition D.1 Suppose Assumption 1 holds. The marginal introduction of product liability (i) benefits consumers with a very high harm level (i.e., h≈2) and (ii) may harm or benefit consumers with lower harm levels. Figure D.1 exemplifies the potentially asymmetric implications for consumers of the policy maker’s reliance on product liability. It illustrates expected utility levels for all consumers in the two extreme scenarios in which there is either no product liability (i.e., γ=0) or product liability mandates compensation of all compensable losses (i.e., γ=1), assuming a=9/2, β=1/4, and v=3. The kink identifies the indifferent consumer’s harm level at which the slope changes from -(1-κ)(1-x1M) to -(1-κ)(1-x2M). Figure D.1. View largeDownload slide Utility of Consumers Under No Compensation ( γ=0) and Full Compensation ( γ=1) for a=9/2, β=1/4 and v=3. Figure D.1. View largeDownload slide Utility of Consumers Under No Compensation ( γ=0) and Full Compensation ( γ=1) for a=9/2, β=1/4 and v=3. Next, we turn to the population of consumers. Consumer surplus is given by (12), introduced at the end of Section 5. The marginal effect of increasing firms’ share of losses on the level of consumer surplus thus represents the sum of the implications for the different types of consumers discussed above. Since some consumers may very well be worse off after a marginal increase in γ as argued above, dCS/dγ may sum over positive and negative terms. Proposition D.2 Suppose Assumption 1 holds. An increase in the firms’ share of accident losses γ (i) increases consumer surplus and decreases total profits at γ=0 and (ii) may increase or decrease consumer surplus and total profits when γ>0. Proof. The first part follows from the evaluation of the derivative of CS with respect to the firms’ share of accident losses at γ=0 (which gives 33β/32a) and the evaluation of the derivative of π1M+π2M with respect to the firms’ share of accident losses at γ=0 (which gives -7β/8a). Part (ii) is established by reference to an example at the end Section 6. □ Proposition 5 established that the marginal introduction of product liability is socially desirable. Proposition D.2 explains that this is due to the increase in consumer surplus dominating the decrease in total profits. This gain for consumers follows from the fact that the excessive degree of product differentiation is attenuated by the introduction of product liability, bringing about fiercer price competition. 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Google Scholar CrossRef Search ADS   Shavell, Steven. 1980. “Strict Liability Versus Negligence,” 19 Journal of Legal Studies  1– 25. Shavell, Steven. 1984. “A Model of the Optimal Use of Liability and Safety Regulation,” 15 RAND Journal of Economics  271– 80. Google Scholar CrossRef Search ADS   Shavell, Steven. 2004. Foundations of Economic Analysis of Law . Cambridge, MA, USA: Harvard University Press. Visscher, Louis. 2009. “Tort Damages” in Michael Faure, ed., Tort Law and Economics . Cheltenham UK, Northampton, MA, USA: Edward Elgar. Footnotes 1. The Australian Competition & Consumer Commission writes at href="http://www.productsafety.gov.au/ content/index.phtml/itemId/973470: “Cyclists can suffer: broken bones, head injuries or death if aspects of the bicycle fail, such as the braking system, steering or pedal cranks; serious injury or death if the bicycle’s head stem cracks or fails, causing the rider to have no steering control; ...”. 2. With regard to defective products, strict liability is the basic principle of the European Directive on Product Liability (85/374/EEC), for example, and assumed in most contributions to the literature such as Daughety and Reinganum (1995, 2006, 2008). The assumption about the liability rule and the one about the level of compensation are separable because from a legal standpoint, one set of norms describes the requirements for liability and another set of norms details the level of compensation due (e.g., Visscher, 2009; Schäfer and Müller-Langer, 2009). 3. With respect to individual instead of group-level payoffs, shifting more losses from consumers to firms changes asymmetrically not only the profits of the high-safety firm and the low-safety one but also the surplus of consumers with different levels of harm. 4. Their model also permits vertical differentiation by different levels of safety investments, but they ultimately focus on symmetric equilibria in which firms choose the same level of safety. Symmetric safety levels can never result as an equilibrium outcome in our setting. The model of Daughety and Reinganum is also used to consider third-party victims, something we abstract from in the present contribution. 5. Chen and Hua (2017) provide another recent study analyzing the impact of product liability on the competition among horizontally differentiated firms. 6. Motta (1993) shows that this also holds when firms compete in quantities instead of prices. 7. We thank an anonymous reviewer for pointing out this distinction to us. 8. A similar framework with a monopolist has been used in (Baumann et al., 2016). 9. This cost function is widely used in the context of competition in quality (see, e.g., Motta, 1993). 10. It is standard to assume that the heterogeneity is due to a parameter with a uniform distribution on an interval with unit length (see, e.g., Kuhn, 2007). 11. For an analysis along these lines, see Choi and Spier (2014). 12. Punitive damages are a means discussed to overcome a probability of suit below one. However, they are very rare outside the United States and even there require “outrageous” misconduct (e.g., Chu and Huang, 2004). 13. The lower bound in Assumption 1 ensures an interior solution for the higher safety level x2. An interior solution for the lower safety level x1 is implied by the lower bound for the interval for expected harm levels. Note that Assumption 1 implies β≤2/3. 14. Without loss of generality, we assume that the indifferent consumer chooses the low-safety variant of the product.} 15. If Δx=0, given the constant production costs per unit and consumers being randomly allocated to firms, the only possible equilibrium is the Bertrand outcome p1=p2=ax12/2+κ(1-x1)3/2, where κ(1-x1)3/2 is the expected compensated harm per consumer who select randomly between firms. The mark-up is equal to zero. 16. The firms’ first-order conditions for safety at Stage 1 display a discontinuity when x1→x2 and x2→x1, respectively, due to the way demand allocates when Δx=0. However, since zero mark-ups result for Δx=0, there is no equilibrium featuring equal safety levels.} 17. After due simplification, the derivative of x1BR with respect to γ follows as 2β(2a(1-x2)+(2-κ)2)/3a(2-κ)2)>0. 18. More specifically, we obtain 2β(2a(1-x1)-(2-κ)2)/3a(2-κ)2) as change of x2BR with γ. 19. Most contributions in the industrial-organization literature dealing with vertical product differentiation consider two active firms and find excessive product differentiation which may be counteracted by regulation (for an exemption, see see Scarpa, 1998, to which we refer in Footnote 24). To check whether our results continue to hold with more than two firms, we performed numerical simulations for the case of three firms in the market. Our results from this exercise are similar in that safety levels for all firms increase with product liability, and in that the low-safety firm may gain in terms of market share and profits when more losses are shifted from consumers to firms, whereas the high-safety firm definitely loses in these regards.} 20. It is a robust result in the literature that the high-quality firm suffers from a tightening of the minimum quality standard (Ronnen, 1991; Crampes and Hollander, 1995). The intuition is that the stricter minimum quality standard serves as a commitment device for the low-quality firm not to lower its quality and induces the high-quality firm to set an even higher quality to differentiate itself from the low-quality firm. This lowers the market share of the high-quality firm, meaning that the low-quality firm enjoys some sort of first-mover advantage. This commitment aspect is not present in our analysis. However, given that the low-safety firm has an incentive to increase its safety level, the implication for the high-safety firm is the same: it makes a lower profit. As is the case for a higher share of accident losses borne by firms in our setup, the picture is less clear with respect to the profit implications of a stricter minimum quality standard for the low-quality firm because it may or may not benefit from a stricter standard (Ronnen, 1991; Crampes and Hollander, 1995). 21. Cremer and Thisse (1994) present a related discussion of three marginal effects when they elaborate on how ad-valorem taxes influence welfare in a vertical product differentiation setup. 22. However, note that term A is equal to zero when γ=0 because the market equilibrium segmentation of consumers is second best in that scenario, meaning that this effect cannot rationalize the marginal introduction of product liability. 23. Baumann et al. (2011) describe a dynamic context in which consumers cannot observe the current product safety levels. In that setup, it also need not be optimal to get as close to full compensation as possible. A related result is established in Chen and Hua (2017). 24. Simulations for the case of three firms show that the welfare-enhancing effect of product liability need not apply. This is mainly due to the fact that the extent of product differentiation is not as excessive when there are three instead of two firms. This result for the case of product liability parallels what was established for minimum quality standards before. Scarpa (1998) considers a scenario with three firms and a market not fully covered, and finds that the welfare-improving effects of introducing a minimum quality standard established for the duopoly case may not carry over. 25. This finding may be compared to the related result from the scenario in which a minimum-safety requirement is introduced. In that case, the combination of both a minimum-standard requirement only slightly above the level chosen by the low-safety firm in the unregulated equilibrium and a modest response of the high-safety firm can assure that all consumers benefit from the policy (see Crampes and Hollander, 1995). In our setting, a similar result is possible for the introduction of product liability. © The Author 2017. Published by Oxford University Press on behalf of the American Law and Economics Association. All rights reserved. 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TI - Product Liability in Markets for Vertically Differentiated Products
JO - American Law and Economics Review
DO - 10.1093/aler/ahx013
DA - 2018-04-01
UR - https://www.deepdyve.com/lp/oxford-university-press/product-liability-in-markets-for-vertically-differentiated-products-DHZPBa3Ken
SP - 46
EP - 81
VL - 20
IS - 1
DP - DeepDyve
ER -