Probing the case for manufacturer liability for harms caused by judgment-proof consumers to others

Friehe, Tim; Rössler, Christoph; Schulte, Elisabeth Article — Published Version Probing the case for manufacturer liability for harms caused by judgment-proof consumers to others European Journal of Law and Economics Provided in Cooperation with: Springer Nature Suggested Citation: Friehe, Tim; Rössler, Christoph; Schulte, Elisabeth (2023) : Probing the case for manufacturer liability for harms caused by judgment-proof consumers to others, European Journal of Law and Economics, ISSN 1572-9990, Springer US, New York, NY, Vol. 56, Iss. 3, pp. 443-460, https://doi.org/10.1007/s10657-023-09786-5 This Version is available at: https://hdl.handle.net/10419/306393 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in EconStor may be saved and copied for your personal and scholarly purposes. You are not to copy documents for public or commercial purposes, to exhibit the documents publicly, to make them publicly available on the internet, or to distribute or otherwise use the documents in public. If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by/4.0/ Vol.:(0123456789) European Journal of Law and Economics (2023) 56:443–460 https://doi.org/10.1007/s10657-023-09786-5 1 3 Probing thecase formanufacturer liability forharms caused byjudgment‑proof consumers toothers TimFriehe1,2 · ChristophRössler3· ElisabethSchulte4 Accepted: 2 November 2023 / Published online: 18 November 2023 © The Author(s) 2023 Abstract We study whether it is socially desirable to hold a monopolistic firm liable for the harm its potentially judgment-proof consumers inflict on third parties. Consumers’ judgment-proofness limits potential product differentiation by pooling different consumer types with uniform liability exposure. The firm’s safety choices are distorted in both regimes under consideration: consumer-only liability and residual-manufac- turer liability. We find that residual-manufacturer liability dominates consumer-only liability if the monopolistic firm can observe consumers’ types, or if consumers’ types are not observable but heterogeneity stems only from their asset levels. However, if the monopolistic firm cannot observe consumers’ types and heterogeneity stems from their harm levels, it is more difficult to make a case for residual-manu- facturer liability. Keywords Liability· Judgment proofness· Safety· Precaution· Consumer JEL Classification K13· L12 1 Introduction When consumers’ use of a product may harm third parties, and potentially to the extent that consumers cannot fully compensate, the question arises whether the product’s manufacturer should be liable for the residual harm. Such an extension * Tim Friehe [email protected] 1 University ofMarburg, MACIE andPublic Economics Group, Am Plan 2, 35037Marburg, Germany 2 CESifo, Munich, Germany 3 University ofMarburg, Public Economics Group, Am Plan 2, 35037Marburg, Germany 4 University ofMarburg, MACIE andInstitutional Economics Group, Barfüssertor 2, 35037Marburg, Germany 444 European Journal of Law and Economics (2023) 56:443–460 1 3 of liability may be likened to vicarious liability where a party related to the tortfeasor and with some control over the expected harm is (partly) liable for harm done.1 The question about extended liability in the consumer context has long vexed courts in the United States where these issues are hotly debated in the legal and political arenas (Hay & Spier, 2005: 1700). However, the topic remains understudied. This comes even though consumers frequently harm others, and many consumers cannot undo the harm done entirely (i.e., they are judgment-proof).2 Examples of the setting under scrutiny in our paper range from drivers harming pedestrians in a car accident to limited-liability firms harming other firms or individuals via accidental data loss. Three policy targets seem relevant in this context: The manufacturer’s product safety, the precautions consumers take while using the product, and the output level. In a setting with a perfectly competitive product market and a representative consumer, Hay and Spier (2005) have shown that it is optimal to hold the consumer liable up to the level of their assets, and to hold the manufacturer liable for the residual harm. On a perfectly competitive market with homogeneous consumers, such a residual-manufacturer liability regime induces consumers to demand optimal safety from firms and exert a second-best level of precaution while ensuring that the combination of price and liability cost reflects the total social cost and, thus, induces socially optimal output. We complement the analysis in Hay and Spier (2005) by investigating the effects of the liability regimes on market outcomes in a setting with consumer heterogeneity and market power on the manufacturer’s part. In particular, we analyze how (i) the manufacturer’s choices concerning the product’s safety and market coverage and (ii) the social surplus depends on the liability rule. In a setup in which the effects of safety and precaution are independent, we compare two possible liability regimes, consumer-only and residual-manufacturer liability.3 In the former regime, only the consumer is held liable for the harm inflicted on the third party; in the latter regime, the consumer is again liable up to the own asset level, and the manufacturer is held liable for the residual harm that a consumer cannot compensate. Even scholars with a skeptical attitude towards product liability vis-a-vis consumers recommend that firms be held liable when a product potentially harms third parties (Polinsky & Shavell, 2010). They also advocate product liability when market forces are less effective in promoting product safety. Our analysis will demonstrate that when third-party harm and market power both play a role, the question of whether the manufacturer should be held liable for (residual) harm is difficult to answer. 1 Vicarious liability can take very different forms. For example, parents may be liable for harms caused by their children, contractors for harms caused by subcontractors, and firms for the harms caused by their employees. (Shavell, 2007). For environmental risk, Pitchford (1995) analyzes the optimal lender liability when the tortfeasor is a borrower. Arlen and MacLeod (2005) show that managed care organizations liable for medical malpractice by their physicians can be beneficial, that is, they find thatextending liabilityis preferred to the current treatment of physicians as independent contractors. 2 Shavell (1986) was probably the first to denote an injurer unable to fully compensate the victim after an accident as judgment-proof. We will also employ this terminology. 3 Hay and Spier (2005) also assume that the effects are independent in their Sect.3. Other papers with similar assumptions include Chen and Hua (2017). 445 1 3 European Journal of Law and Economics (2023) 56:443–460 We find that if the monopolistic firm can (i) observe consumers’ types, or (ii) cannot observe the types of consumers who differ only in their asset level, residual-manufacturer liability dominates consumer-only liability. However, if the monopolistic firm cannot observe the types of consumers who differ in their harm level, it is more difficult to establish that residual-manufacturer liability always induces weakly better market outcomes. We can thus provide at least some policy guidance regarding the policy debates occurring in the United States by identifying circumstances in which residual-manufacturer liability is socially preferred to consumer-only liability. In our analysis, we describe several distortions: first, judgment-proof consumers choose inefficiently low precaution levels in both regimes. Second, consumers with different harm or asset levels cannot be separated in an incentive-compatible manner when they have the same liability exposure. Third, product differentiation along the dimension of product safety can interfere with the manufacturer’s motive of rent extraction. Fourth, when different consumer types are pooled, the manufacturer’s safety investment targets the liability exposure of a product variety’s marginal consumer in the consumer-only liability regime and the harm caused by the marginal consumer in the residual-manufacturer liability regime while, from a social welfare perspective, the target should be the average harm inflicted by a product variety’s consumers. While we add new elements to the analysis in Hay and Spier (2005) with the second and third distortion, the fourth one differs as they consider consumers making continuous consumption choices, whereas we study binary consumption choices. The firm’s liability cost from serving judgment-proof consumers is substantially smaller under consumer-only liability. This fact counteracts the firm’s motive to limit market coverage to extract higher rents from consumers being served. Thus, if it is socially desirable to serve judgment-proof consumers, consumer-only liability can produce better market outcomes than residual-manufac- turer liability. However, in the consumer-only liability regime, the firm might invest insufficiently in the product’s safety due to the failure to internalize the harm that the consumer cannot compensate for. When the firm markets more than one product safety variant, the incentivecompatibility constraints induce an inter-dependency between the product variants, which tends to cause excessive safety for the highest-safety product variant in both liability regimes. In the consumer-only liability regime, it partially counteracts the under-investment in safety due to uncompensated harm. Under residual-manufacturer liability, when considering the group of judgment-proof consumers in isolation, the firm internalizes all marginal welfare effects of its own choices. In this regime, the rent-extraction motive induces the firm to offer an excessively safe product variant to judgment-proof consumers when they are served. The rest of the paper is structured as follows: We discuss the related literature in Sect.2 and present the model in Sect.3. Our analysis is contained in Sect.4. 446 European Journal of Law and Economics (2023) 56:443–460 1 3 2 Literature Our paper contributes to the literature on the economics of tort law [e.g., (Shavell, 2007)]. In our analysis, potentially judgment-proof injurers are crucial. Shavell (1986) provided the first formal analysis of the distortions arising from insufficient assets on behalf of the injurer and contributed to the discussion concerning instruments to amend the problem in Shavell (2005). Our framework does not consider minimum asset or mandatory-insurance requirements [e.g., (Polborn, 1998)]. Numerous contributions elaborated on the judgment-proof problem after (Shavell, 1986). These papers distinguished, for example, the impact of monetary and non-monetary care [e.g., (Miceli & Segerson, 2003)], different precaution technologies (Dari Mattiacci & de Geest, 2005), and different risk attitudes (Friehe, 2007). Hay and Spier (2005) is the paper most closely related to ours. Their main analysis examines the scenario with competitive firms and homogeneous consumers with downward-sloping demand. In extensions, they first discuss results from a setting in which (i) consumers differ in both their price sensitivities and their harm levels, and (ii) safety and precaution are abstracted from; afterward, they turn to a case where some consumers have zero assets and others are fully solvent. Whereas residual-manufacturer liability is preferred in their main analysis, the two extensions show that this regime can introduce undesirable distortions with consumer heterogeneity. We consider a monopolistic firm that seeks to extract surplus from consumers who decide whether or not to buy a unit of output and continuous consumer heterogeneity either along the harm or the asset dimension where safety and precaution are always endogenous. The fact that there is only one firm on the supply side enables equilibria that cannot be reached with competitive firms, a fact particularly acute in product-differentiation scenarios. In its quest for rents, the monopolistic firm may seek to contract market coverage and distort product differentiation. This produces contrasting results: For example, when considering consumers differentiated only by their asset levels, Hay and Spier (2005) find that solvent consumers’ output is at the first-best level which does not hold in our framework. Our focus on a firm with market power represents the most critical departure from Hay and Spier (2005). The previous literature has considered the incentives of a monopolistic firm when consumers are potential victims. For example, Baumann etal. (2016) analyze loss shifting when a monopolistic firm serves consumers with different harm levels by providing a product with a uniform safety level. It is explained that shifting more losses to the firm can signify lower product safety levels because the firm’s focus moves from the marginal consumer’s harm to average harm. The firm’s focus on the marginal consumer type and the implied contrast to the average type is also relevant in our paper. This source of distortion has already been pointed out in Spence (1975). In our setting, when the level of assets is the same for all consumers and the level of harm varies from consumer to consumer, the consumer’s valuation of the firm’s marginal safety investment increases in the harm level that the consumer potentially imposes on others (up to the point where the consumer becomes judgmentproof). If a single product variant is offered, we can directly apply Proposition 1 in Spence (1975) to conclude that when the firm only serves solvent consumers, it oversupplies safety. When it also serves judgment-proof consumers, the firm in a residual 447 1 3 European Journal of Law and Economics (2023) 56:443–460 liability regime has even stronger incentives to supply safety, whereas in the consumeronly liability regime, the firm neglects the social cost of uncompensated harm, which induces a distortion of safety provision in the opposite direction. In contrast, for example, Endres and Lüdecke (1998) and Hua and Spier (2020) analyze the case in which a monopolist seeks to separate different consumer types by providing products with different safety attributes. We will also elaborate on product differentiation and emphasize that a uniform liability exposure of heterogeneous judgment-proof consumers implies that they cannot be disentangled in an incentive-compatible way. Whereas most papers consider consumers as possible victims, Rössler and Friehe (2020) find that the monopoly may yield greater welfare when individuals with moral or image concerns may harm third parties in product accidents. Regarding the implications of market power, Polinsky and Rogerson (1983) provide a contribution in which consumers misperceive product risk and firms interact in a Cournot oligopoly. They show that the optimal liability rule depends on the consumers’ risk misperception and the number of firms in the industry. We assume that consumers understand the risk and the firm’s safety level. Many economic transactions are nowadays channeled via platforms. Hua and Spier (2023) analyze whether two-sided platforms should be (partly) liable for harm caused by potentially judgment-proof firms and imposed on users operating on the platform. This platform liability may be beneficial because the platform has some control over expected harm. It can use the interaction price to deter firms more likely to impose harm and invest resources to weed them out. Platform liability can be beneficial independent of whether users are bystanders or consumers internalizing the expected harm when entering transactions. In two other recent contributions on platform liability as a type of indirect liability, Buiten etal. (2020) discuss the e-com- merce Directive of the European Union and Lefouili and Madio (2022) analyze the promises and pitfalls of platform liability as a means to stop online misconduct. 3 The model A risk-neutral monopolistic firm serves risk-neutral consumers who buy at most one product unit. When using the product, consumers may accidentally harm third parties. The accident probability 𝜋(x,y) decreases at a diminishing rate with the firm’s product safety and the consumer’s precaution investment (i.e., 𝜕2 𝜋 ∕ 𝜕 x2 > 0 > 𝜕𝜋 ∕ 𝜕 x and likewise for y). In order to simplify the exposure of our analysis, we assume that the marginal productivity of precaution in reducing the accident probability is independent of the firm’s safety level and vice versa (i.e., 𝜕2 𝜋 ∕ 𝜕 x 𝜕 y=0 ).4 A consumer of type i has a consumption value v, causes third-party harm hi in an accident, and incurs precaution costs c×yi when choosing precaution level yi , which 4 This simplifying assumption allows us to avoid qualifications in our statements. For example, when allowing for an interdependence between the firm’s safety and the consumer’s precaution choices, the comparison of the consumer’s choice to the socially optimal precaution level could only be made conditional on the firm’s safety investment. It would also be less clear how to evaluate an over-investment in safety from a social perspective, if, due to strategic complementarity, it is accompanied by an increase in the level of precaution of a consumer who tends to under-invest. 448 European Journal of Law and Economics (2023) 56:443–460 1 3 are assumed to be non-monetary (e.g., Beard, 1990; Friehe & Tabbach, 2014). The level of assets available for compensation in case of an accident amount to 𝜔i>0 . The monopolistic firm may offer only one kind of product with one price p and safety level x (due to external constraints) or may diversify and offer a product variety with safety level xi to consumers of type i at a price pi . The firm incurs a safety cost xi per unit of output of this product variety. We consider two different liability regimes, namely residual-manufacturer and consumer-only liability (Hay & Spier, 2005). Consumer i is always legally responsible to compensate 𝛿C i =min{h i ,𝜔 i} . Under residual-manufacturer liability, the firm is liable for 𝛿M i =max{0, h i −𝜔 i} . The consumer is legally responsible for the full harm when the private assets are weakly greater than the harm, and compensates the maximum amount possible (i.e., the level of assets) otherwise. We label a consumer of type i with liability exposure 𝛿C i <h i as judgment-proof. In the residual-manufac- turer liability regime, the firm compensates the difference between the consumer’s liability payment and the victim’s level of harm. For a given level of product safety xi , the consumer of type i can attain the private product value of by implementing the privately optimal precaution level The privately optimal precaution level is equal to (less than) the socially optimal precaution level for financially unconstrained (potentially judgment-proof) consumers independent of the liability regime.5 The consumer of type i buys a product if and only if the private product value exceeds the product’s price, that is, if Vi≥pi . We introduce two different social product values for consumer i conditional on the firm’s product safety choice xi . The maximum social product value supposes that the consumer’s precaution is at the first-best level, and is given by As privately optimal precaution is at the socially optimal level for financially unconstrained consumers, we obtain Vi=Wi . However, for judgment-proof consumers (i.e., if 𝛿C i <h i ), the personal product value exceeds the maximum social product value, that is, we have Vi>Wi . The second-best social product value amounts to Vi (x i )=v−𝜋(x i ,y i )𝛿 C i −cy i  yi (𝛿 C i )=arg min{𝜋(x i ,y i )𝛿 C i +cy i } . y∗ i(hi)=arg min{𝜋(xi,yi)hi+cyi}, Wi (x i )=v i −𝜋(x i ,y ∗ i )h i −cy ∗ i. 5 The level yi is independent of the firm’s level of safety xi by our assumption that the decrease of 𝜋 with safety is independent of precaution, and vice versa. 449 1 3 European Journal of Law and Economics (2023) 56:443–460 which is second-best (SB) in the sense that it takes as given that judgment-proof consumers implement a socially suboptimal precaution level. When the second-best social product value differs from the maximal one, the judgment-proof consumer type i perceives a product value above the socially relevant one, that is, we have When added to the cost of product safety, we arrive at a social cost of producing private product value The comparison of Vi and Ci is relevant for whether serving consumer type i is socially desirable. The monopolistic firm bears Ci when residual-manufacturer liability applies. All constructs defined so far depend on product safety. Now, consider how a marginal change in xi affects the values Vi , WSB i , and Ci : The marginal social benefit from greater product safety exceeds the marginal benefit for a judgment-proof consumer. The marginal social cost of increasing product safety for a judgment-proof consumer may be positive or negative, depending upon the difference between the level of harm and the consumer’s asset level. Given that consumers choose precautions subject to either liability regime, the socially optimal level of product safety for consumer type i, if served, follows from maxxi W SB i −x i =V i −C i . It is socially optimal to serve consumers of type i only if WSB i >x i , that is, if Vi>Ci . 4 Analysis 4.1 Benchmark: full differentiation Suppose the firm can charge the private product value of each consumer type (i.e., pi=Vi ) and is subject to residual-manufacturer liability. In that case, it maximizes ∫ V i −C idi and thus has socially optimal incentives for product safety and market WSB i (x i ,h i ,𝛿 C i )=v i −𝜋(x i ,y i )h i −cy i, Vi −W SB i =𝜋(x i ,y i )(h i −𝛿 C i ) . Ci (x i )=x i +𝜋(x i ,y i )max{(h i −𝛿 C i ),0} . (1) 𝜕V i 𝜕 xi =− 𝜕𝜋 𝜕 xi 𝛿C i> 0 (2) 𝜕 W SB i 𝜕 xi =− 𝜕𝜋 𝜕 xi hi> 0 (3) 𝜕C i 𝜕x i =1+𝜕𝜋 𝜕x i max{(hi−𝛿C i),0 } 450 European Journal of Law and Economics (2023) 56:443–460 1 3 coverage.6 When choosing product safety, the firm internalizes the total harm. In terms of which consumers to serve, the firm serves consumers of type i only if Vi≥Ci , which is consistent with the social criterion. If consumer-only liability applies, the firm maximizes ∫ V i −x idi and thus has distorted safety and market coverage incentives as some consumers are judgment-proof. For judgment-proof consumers, the firm chooses safety because of the consumer’s liability exposure instead of the level of harm. In addition, the firm may serve consumers even though it reduces social welfare, which obtains when Ci>Vi>xi . We summarize our finding for the benchmark case in Proposition1: Proposition 1 (Benchmark) Suppose the monopolistic firm can observe consumers’ types and offer its consumers individualized product varieties. A firm subject to residual-manufacturer liability implements product safety and market coverage choices that maximize second-best welfare. A firm subject to the consumer-only liability regime serves too many judgment-proof consumers and offers them varieties with a too low product safety level. 4.2 Incentive compatible differentiation If the firm cannot observe consumer types, it must respect incentive compatibility when offering a menu of varieties. A variety xi meant for consumers of type i needs to be offered at a price pi such that only consumers of type i (weakly) prefer to buy that variety over another one. As higher product safety increases the private product value for all consumer types, incentive compatibility requires that higher-safety varieties are offered at higher prices. For any pair of varieties (xi,pi) and (xj,pj) with xi>xj , incentive compatibility for consumers of type i and type j requires: The assumption 𝜕2 𝜋 ∕ 𝜕 x 𝜕 y=0 allows us to write the difference of consumer i’s product values at two different product safety levels as7 Using the notation Δ 𝜋 (xi,xj)=𝜋(xi,yi)−𝜋(xj,yi) , we present the following restatement of the incentive compatibility constraints (4): (4) Vi(xi)−Vi(xj)≥pi−pj≥Vj(xi)−Vj(xj). Vi (x i )−V i (x j )=𝛿 C i (𝜋(x i ,y i )−𝜋(x j ,y i)) (5) 𝛿 C i ≥ p i −p j Δ𝜋(x i ,x j ) ≥ 𝛿C j . 6 We do not impose a specific assumption on the distribution. 7 In general, the difference of the personal product values of a consumer of type i at two different product safety levels follows as Vi (x i )−V i (x j )=−𝛿 C i Δ𝜋(x i ,x j )−c(y i (𝛿 C i ,x i )−y i (𝛿 C i ,x j )) . 457 1 3 European Journal of Law and Economics (2023) 56:443–460 4.2.3 Heterogeneous asset levels butsymmetric harm level In this section, we discuss the role of heterogeneity concerning the asset level. Figure3 sketches the relation between Wi ,W SB i ,V i ,C i for this case. When consumers differ only in their asset level, the personal product value and the social product value are inversely related for the judgment-proof consumers. In Fig.3, only consumers with asset levels above 𝜔SB should be served from a (second-best) welfare perspective because WSB i≥x only holds for them. However, without minimum asset requirements, excluding consumers with lower asset levels is impossible. Their valuation for the product is the highest for any safety level. In the market equilibrium, either only judgment-proof or all consumers are served, or no output is produced. When subject to residual-manufacturer liability, the firm has strictly weaker incentives to serve the market than in the consumer-only liability regime. Judgment-proof consumers are the least attractive in the former and the most attractive in the latter regime. Thus, serving only judgment-proof consumers can be a market outcome only in the consumer-only liability regime. Under residualmanufacturer liability, the market will be served if and only if a safety level exists such that the aggregate private product value exceeds the aggregate social costs. The valuation of a marginal safety investment increases in the consumer’s asset level (for judgment-proof consumers). As the consumers with the lowest asset levels have the highest willingness to pay, Spence (1975) implies an underinvestment in safety for any market coverage in the consumer-only liability regime, which is exacerbated by the failure to fully internalize the social cost. The firm subject to residual-manufac- turer liability selects the safety level which maximizes (second-best) social welfare. Proposition 4 (Symmetric harm and heterogeneous asset levels) When consumers differ only concerning their asset levels, and asset levels exceed the level of harm for some consumer types, then market outcomes under residual-manufacturer liability are weakly preferred to market outcomes under consumer-only liability. 5 Conclusion Consumers may harm third parties while using their products and may be unable to compensate victims fully. Holding the products’ manufacturers (partially) liable for the harm done by their consumers represents a potential policy. We have compared consumer-only liability with residual-manufacturer liability when the producer is a monopolistic firm, complementing earlier work done for competitive firms. The co-existence of several distortions in our framework complicates a general regime comparison. For example, the monopolistic firm focuses on the marginal consumer when assessing safety. This may mean that the firm’s internalization of harm under residual-manufacturer liability is socially undesirable concerning safety incentives because consumer-only liability can already induce excessive safety in some circumstances. In contrast, the firm’s internalization of 458 European Journal of Law and Economics (2023) 56:443–460 1 3 harm under residual-manufacturer liability tends to provide for a better alignment of privately optimal and socially optimal output but, interestingly, also doesn’t have to. In our paper, we assess the issues at stake and identify circumstances in which consumer-only liability performs better than residual-manufacturer liability and instances where the reverse is true. Given the importance of the matter and the limitations of our framework, we think that future research is warranted. Appendix: Proof ofProposition 2 (i) Suppose that V𝜔(x)<x∀x , but the firm serves the judgment-proof consumers, i.e., the safest product variety sells at a price pm≤V𝜔(xm)<xm . The firm makes losses with the judgment-proof consumers in either regime. Raising the price of this variety to xm , and adjusting all prices according to the incentive-compatible pricing scheme (6) deters only those consumers from buying the product with whom the firm makes losses and raises the profits earned with all consumers who still buy the product. Hence, the adjusted pricing scheme constitutes a profitable deviation for the firm. Next, suppose that the judgment-proof consumers are served despite their small mass. Denote the mass of judgment-proof consumers with mj . Accordingly, the mass of solvent consumers is 1−mj . The firm adheres to the incentive-compatible pricing scheme (6)—or gains from deviating to it. Increase the price pm of product variety xm to p� m=V 𝜔 (xm)+𝜀,𝜀∈(0, Δ 𝜋 (xm,xm−1))hm−1 , and adjust all other prices according to the pricing rule (6) by 𝜀 . If xm is the only product variety, set p′ m just slightly above V𝜔(xm) . The judgment-proof consumers now abstain from consumption, while for all other consumers, prices have Fig. 3 W i,W SB i ,Vi,C i for a fixed level of product safety. We assume vi=v , ci=c , hi=h∀i , whereas 𝜔i is different for each i 459 1 3 European Journal of Law and Economics (2023) 56:443–460 increased by 𝜀 , which is still below the rent they previously obtained. Hence, they continue to buy their original product variety. Profits have changed by −mj(Vm−xm)+(1−mj)𝜀 , which is positive if mj is sufficiently small. (ii) The statement follows from the fact that the safety investment has the additional benefit of reducing the firm’s expected liability cost so that the optimal product safety that is offered by the firm when not held liable for residual harm is sub-optimally low from the point of view of the firm that is subject to residual manufacturer liability. (iii) In the consumer-only liability regime, the firm can earn a rent V𝜔(x𝜔)−x𝜔>0 with each judgment-proof consumer by offering the product variety x𝜔 at a price V𝜔(x𝜔) . Still, she has to grant a rent to the solvent consumers. If the mass of judgment-proof consumers is sufficiently high, the former effect dominates the latter. When subject to residual manufacturer liability, the firm faces additional costs ∫ h 𝜔 C i −x� 𝜔 when serving the judgment-proof consumers with (a possibly different) product variety x′ 𝜔 , earning a strictly lower rent (possibly negative) with each of them. Thus, when the mass of judgment-proof consumers surpasses the threshold, it becomes profitable for the firm in the consumeronly liability regime to serve them, when subject to residual manufacturer liability, the firm strictly prefers not to serve them. Funding Open Access funding enabled and organized by Projekt DEAL. The authors did not receive support from any organization for the submitted work. Declarations Conflict of interest The authors have no relevant financial or non-financial interests to disclose. Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/ licenses/by/4.0/. References Arlen, J., & MacLeod, W. B. (2005). Torts, expertise, and authority: Liability of physicians and managed care organization. Rand Journal of Economics, 36, 494–515. Baumann, F., Friehe, T., & Rasch, A. (2016). Why product liability may lower product safety. Economics Letters, 147, 55–58. Beard, T. R. (1990). Bankruptcy and care choice. Rand Journal of Economics, 21, 626–634. Buiten, M. C., de Streel, A., & Peitz, M. (2020). Rethinking liability rules for online hosting platforms. International Journal of Law and Information Technology, 28, 139–166. 460 European Journal of Law and Economics (2023) 56:443–460 1 3 Chen, Y., & Hua, X. (2017). Competition, product safety, and product liability. Journal of Law, Economics, & Organization, 33, 237–267. Dari Mattiacci, G., & de Geest, G. (2005). Judgment proofness under four different precaution technologies. Journal of Institutional and Theoretical Economics, 161, 38–56. Endres, A., & Lüdecke, A. (1998). Incomplete strict liability: Effects on product differentiation and information provision. International Review of Law and Economics, 18, 511–528. Friehe, T. (2007). A note on judgment proofness and risk aversion. European Journal of Law and Economics, 24, 109–118. Friehe, T., & Tabbach, A. (2014). Judgment proofness and the choice between monetary and nonmonetary care. Journal of Institutional and Theoretical Economics, 170, 249–274. Hay, B., & Spier, K. E. (2005). Manufacturer liability for harms caused by consumers to others. American Economic Review, 95, 1700–1711. Hua, X., & Spier, K. E. (2020). Product safety, contracts, and liability. Rand Journal of Economics, 51, 233–259. Hua, X., & Spier, K. E. (2023). Holding platforms liable. https:// doi. org/ 10. 2139/ ssrn. 39850 66 Lefouili, Y., & Madio, L. (2022). The economics of platform liability. European Journal of Law and Economics, 53, 319–351. Miceli, T. J., & Segerson, K. (2003). A note on optimal care by wealth-constrained injurers. International Review of Law and Economics, 23, 273–284. Pitchford, R. (1995). How liable should a lender be? The case of judgment-proof firms and environmental risk. American Economic Review, 85, 1171–1186. Polborn, M. K. (1998). Mandatory insurance and the judgement-proof problem. International Review of Law and Economics, 18, 141–146. Polinsky, A. M., & Rogerson, W. P. (1983). Products liability, consumer misperceptions, and market power. Bell Journal of Economics, 14, 581–589. Polinsky, A. M., & Shavell, S. (2010). The uneasy case for product liability. Harvard Law Review, 123, 1436–1492. Rössler, C., & Friehe, T. (2020). Liability, morality, and image concerns in product accidents with third parties. European Journal of Law and Economics, 50, 295–313. Shavell, S. (1986). The judgment proof problem. International Review of Law and Economics, 6, 45–58. Shavell, S. (2005). Minimum asset requirements and compulsory liability insurance as solutions to the judgment-proof problem. Rand Journal of Economics, 36, 63–77. Shavell, S. (2007). Liability for accidents. In: A. M. Polinsky & S. Shavell (Eds.), Handbook of Law and Economics (Vol. 1). Elsevier. Spence, A. M. (1975). Monopoly, quality, and regulation. Bell Journal of Economics, 6, 417–429. Publisher’s Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.