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Liability for Third-Party Harm When Harm-Inflicting Consumers Are Present Biased

Liability for Third-Party Harm When Harm-Inflicting Consumers Are Present Biased Abstract This article analyzes the workings of liability when harm-inflicting consumers are present biased and both product safety and consumer care influence expected harm. We show that present bias introduces a rationale for shifting some losses onto the manufacturer, in stark contrast with the baseline scenario in which strict consumer liability induces socially optimal product safety and precaution levels. In addition, we establish that strict liability with contributory negligence may induce socially optimal product safety and precaution choices. 1. Introduction 1.1. Motivation and Main Results Time preferences are crucial to almost all choices and critically affect life outcomes (e.g., DellaVigna and Paserman, 2005; Meier and Sprenger, 2010; Sutter et al., 2013; Golsteyn et al., 2014; Koch et al., 2015). Time preferences are also important in the context of choices influenced by liability. Clearly, in that domain of decision-making, present choices have implications for later behavior and future payoff consequences. For example, an individual’s decision of whether or not to buy a car with a specific product safety level today will be guided by how carefully the individual expects to drive it and by the level of expected liability payments due after a possible car accident. Time preferences are commonly represented by the exponential discounting model introduced by Samuelson (1937), which assumes that the discount rate is constant and choices are time-consistent. However, data on intertemporal decision-making strongly suggest that immediate payoffs are special relative to future ones (i.e., that a bias favoring the present exists). This is incorporated in applied work using the |$\beta-\delta$| framework introduced by Laibson (1997), which departs from the exponential discounting setup only in that there is additional discounting between the present and any point in time in the future (e.g., Frederick et al., 2002; DellaVigna, 2009; O’Donoghue and Rabin, 2015). The |$\beta-\delta$| framework greatly improves the match between predictions and choice data. For example, Burks et al. (2012) emphasize that the |$\beta-\delta$| model best predicts their data from a large-scale field experiment. This article considers the workings of liability when harm-inflicting parties have |$\beta-\delta$| preferences. Specifically, in our setup, present-biased consumers cause harm to third parties; the expected value of harm is determined by both product safety and consumer care. Consumers may principally be naive or sophisticated about their present bias, meaning that they may or may not understand that, in the future, they will make decisions subject to present bias (e.g., O’Donoghue and Rabin, 1999). In our main analysis, we focus on sophisticated consumers but refer to naive consumers in our discussion. The sequence of our framework is important for understanding the role of present bias. In our model, a monopolist first chooses the product’s safety and price level. Next, consumers determine whether or not to buy a single unit of the product, anticipating how much precaution they will invest later on when actually using the product. At this point in time, payoff consequences from both taking precautions and possibly having to pay damages lie in the future (and are thus equally discounted by present-biased agents). When considering the purchase, sophisticated present-biased consumers understand that—at the later point in time when the choice about consumer precaution is due—they will discount only expected liability payments and not precaution costs and that they will therefore end up choosing suboptimal precautions. After the purchase, consumers use the product and invest in precaution. In the event of an accident, consumers and/or the firm may have to pay damages to the victim in the very last stage (depending on the liability regime). For illustration, assume that a consumer orders and pays for a car today, begins using the car a month later (thereby introducing the possibility of an accident), and ultimately pays damages for any harm suffered according to strict consumer liability several months after the accident. In this example, the lags between choices are at least 1 month. For present bias to influence decision-making, lags need not even be as long. The relevant literature emphasizes that it is primarily about distinguishing the present from the future. For example, the evidence in Shapiro (2005) is consistent with a daily|$\beta \approx 0.9$| and a daily |$\delta \approx 1$|⁠. Estimates in Augenblick and Rabin (2019) suggest an immediate gratification parameter of about |$0.83$|⁠.1 Strict consumer liability for third-party harm is our benchmark regime, building on the efficiency properties highlighted by Hay and Spier (2005) for the setup we adopt.2 For this benchmark liability arrangement, we find that there are three distortions when harm-inflicting consumers are present biased relative to the case when they are not. First, consumers underinvest in precaution due to the delayed payment of damages. Second, the firm underinvests in product safety. The firm’s product safety incentives stem either from firm liability or consumers’ demand for safety. Present-biased consumers undervalue product safety due to the delayed payment of damages, leading to the firm’s underinvestment when consumers are strictly liable for all harm. As a result, making the firm liable for a share of the expected harm may increase the level of product safety (at the cost of reducing consumer precaution) and thereby increase welfare. The third distortion arising from the consumers’ present bias concerns the level of output. Consumers perceive the price, that must be paid in the present, to be relatively more important than the consumption utility that is incurred only in the future. When we focus on a fully covered market, we find that making consumers strictly liable for a multiple of the harm (i.e., using a damages multiplier) induces the first-best outcome (i.e., socially optimal product safety and precaution levels) by debiasing the concern about damages payment.3 While a damages multiplier tailored to the present bias of single consumers is in all likelihood not a realistic policy option, using strict liability with a defense of contributory negligence is. We establish that there are circumstances under which the care incentives of both the firm and the consumer are aligned with that of the social planner when that liability rule is in place. However, when present bias is severe or consumers are naive, the use of strict liability with a defense of contributory negligence may no longer be socially desirable. The present article contributes to the literature on the economics of tort law by highlighting that time preferences can be an important moderator of the performance of different liability rules. The frameworks analyzed in this article are simple and leave room for future research. Nevertheless, against the background of the empirical evidence on intertemporal decision-making, the present study illustrates that time preferences should be taken seriously in policymaking. 1.2. Related Literature That timing is important for legal incentives is well established. For example, Gravelle (1990) and Friehe and Miceli (2017) consider endogenous trial delay, Miceli (1999) explores the strategic use of delay during settlement negotiations, and Kessler (1996) empirically explores institutional causes of settlement delay. Our article builds on Hay and Spier (2005). They study consumer-induced harm to others and highlight, for example, that some firm liability is optimal when consumers’ assets are insufficient to compensate harm. In our setup, we derive the same result—that is, firm liability may be socially desirable—albeit for a different reason, namely consumers’ present bias. Our contribution is related to Daughety and Reinganum (2013a) in that they also study a bilateral-care framework in the context of liability for harm resulting from product use. However, the two papers are clearly distinct because Daughety and Reinganum (2013a) study cumulative harm incurred by the consumer and we seek to establish the influence of present bias on the workings of liability. The literature on the economics of product liability considered a specific kind of bias early on, namely the possibility that consumers misperceive—usually underestimate—the expected harm (e.g., Spence, 1977; Polinsky and Rogerson, 1983; Geistfeld, 2009). Miceli et al. (2015) provide a recent contribution on this topic. Contributions to this literature assume that only the firm influences the expected harm incurred by consumers. Accordingly, strict liability of the firm may be proposed as an easy fix of the underestimation-problem in many circumstances. Our article considers a setup in which the expected harm is incurred by third parties and influenced by both the firm’s product safety and consumers’ precaution investments. Whereas the misestimation of expected harm can be remedied by an information policy, we are describing a phenomenon that is a consequence of non-standard preferences. Moreover, the distinction between naive and sophisticated consumers is not covered in existing liability literature but relevant in our context. Baniak and Grajzl (2017) consider how another behavioral aspect influences the workings of liability, analyzing consumers who mispredict the extent to which they will use a durable product in the future. A common example of what they are interested in is projection bias where, for instance, somebody buying a sports car is likely to overestimate the extent to which he will enjoy the product in the future. Since the expected consumer harm in their framework is a function of the level of product usage, the implications of consumers’ mispredictions are contingent on the prevailing liability regime. Key distinctions between our work and theirs include our focus on harm to others, a direct regulatory control regarding consumer behavior via a possible consumer precaution standard, and the distinction between players who are aware of their bias and players who are naive about it. Furthermore, there are potentially two decisions that are distorted due to the present bias in our setup whereas they are interested in only one choice. To the best of our knowledge, this article introduces present bias into the literature on the economics of tort law. In contrast, present bias has been considered in other domains of law and economics (see, e.g., McAdams 2011; Baumann and Friehe, 2012 for studies on criminal law and economics, and Friehe and Rössler, forthcoming for a study on litigation). Present bias has been dealt with in the literature in industrial organization (e.g., Spiegler, 2011; Heidhues and Köszegi, 2018). In many contributions from that branch of the literature, the focus is firms using multiple prices to potentially exploit consumers’ bias, exploring in particular the relevance of back-loaded fees (e.g., DellaVigna and Malmendier, 2004; Heidhues and Köszegi, 2010). In the present article, consumers pay a price upfront for a unit of the product. 1.3. Plan for the Article Section 2 presents the model. Section 3 discusses socially optimal choices. Section 4 elaborates on whether or not socially optimal incentives can be induced using liability law. Section 5 provides a discussion, and Section 6 concludes. 2. The Model 2.1. Firm A monopolistic firm offers a product whose use has a tendency to harm others.4 The expected harm that a single unit of the product causes to third parties is |$\mathcal{L}(x,y)=L-s(x)-p(y)$|⁠, where |$x$| denotes the firm’s product safety and |$y$| the consumer’s precaution level. Product safety and precaution reduce expected harm at a diminishing rate (i.e., |$s'>0>s''$| and |$p'>0>p''$|⁠). Our specification of expected harm is inspired by the representation in Chen and Hua (2017). The firm’s cost of product safety is |$k(x)$|⁠, with |$k(0)=0=k'(0)$|⁠, |$k'(x)>0$| and |$k''(x)\geq 0$| for all |$x>0$|⁠, and is incurred as a fixed cost (as in Daughety and Reinganum, 2006, for example). Product safety is observable by the consumer at the time of purchase. Production costs other than |$k$| are set to zero. The product’s price is denoted by |$P$|⁠. 2.2. Consumers Consumers either buy one or no unit of the product. Consumers differ in their (gross) valuation of the product’s use denoted |$v$|⁠. We assume that the valuation is uniformly distributed in the interval |$[\underline{v},\bar{v}]$|⁠, with |$V=\bar{v}-\underline{v}$|⁠. We normalize the number of potential consumers to one. Consumers incur a cost |$c(y)$| when they invest precaution |$y$| while using the product, where |$c(0)=0=c'(0)$|⁠, |$c'(y)>0$| and |$c''(y)\geq 0$| for all |$y>0$|⁠. Consumers are assumed to exhibit |$\beta-\delta$| preferences. Under that assumption, intertemporal preferences from the perspective of period |$t$| can be represented by |$U^t=u_t+\beta \sum_{\tau=t+1}^T \delta^\tau u_\tau$| with |$\delta$| as the standard discount factor, such that |$\beta=1$| corresponds to exponential discounting while |$\beta \in (0,1)$| reflects present bias (e.g., O’Donoghue and Rabin, 2015). We set |$\delta=1$| for notational simplicity and in order to focus on the implications of present bias alone. Note that the individual in period |$t$| considers utils in period |$t+1$| to be as valuable as utils in |$t+2$| when |$\delta=1$| and |$\beta<1$| apply. It is only when period |$t+1$| is reached that the same individual views utils in period |$t+1$| as more desirable than utils in period |$t+2$|⁠. This change in the relative desirability is important in our analysis and implies a stark contrast to the standard exponential discounting model. We consider sophisticated consumers who anticipate that future decision problems will be influenced by present bias, and comment on the analysis for naive consumers (i.e., consumers who fail to foresee that they will be subject to a present bias in the future) in our discussion in Section 5. As is standard (see, e.g., Heidhues and Köszegi, 2018), we assume that the firm is aware of the consumers’ bias and their sophistication about it. 2.3. Timing The interaction between firm, consumers, and nature unfolds as follows: (0) Nature allocates product valuation $v$ to individual consumers according to a uniform distribution in the interval $[\underline{v},\bar{v}]$⁠. The firm chooses product safety $x$ and price $P$⁠. (1) Consumers observe both the price and product safety level and choose whether or not to purchase a single unit of the product. Consumers transfer $P$ to the firm in case of purchase. (2) Consumers use the product and choose precautions $y$⁠. Accordingly, the product valuation $v$ and the precaution cost $c(y)$ are incurred only in Stage 2. An accident may occur. (3) If an accident occurred in Stage 2, possible damages payments are transferred. 3. The Social Optimum Before we describe the behavior that we will classify as socially optimal, we must first elaborate on the understanding of welfare in our context. Our article contributes by bringing present bias to the evaluation of liability rules. Zeiler (2019) distinguishes between two cases of using behavioral insights to analyze the law, the first being the incorporation of human fallibility and the second being the allowance of non-standard preferences. Whereas deviations of choices from standard theory predictions in the first category are certainly undesirable from a social point of view (e.g., subjects choosing wrong products due to a misperception of risk), deviations of choices from standard theory predictions in the second category do not similarly qualify as mistakes. Prima facie, present-biased preferences fall into the second category of non-standard preferences. However, the literature is divided about whether deviations due to present bias are to be seen as mistakes (e.g., Bernheim and Taubinsky, 2018).5 Importantly, in contrast to other non-standard preferences such as inequity aversion, for example, the very premise of present-biased preferences is that the preferences of an individual at different points in time are in conflict, meaning that a modification of behavior may benefit some selves and harm other selves. Giving in to temptation will in most circumstances do good only to the self of that period, for instance. Accordingly, O’Donoghue and Rabin (2006a) explain that a person able to choose future incentives would select long-run preferences. For that reason, we follow O’Donoghue and Rabin (1999, 2006a; 2006b) and Heidhues and Köszegi (2010) and others by treating consumers’ present bias as a “mistake,” but acknowledge that there may be diverging opinions and approaches (e.g., Goldman, 1979). We thus specify a “standard” welfare measure that features no discounting as a result of a taste for immediate gratification and classify behavior that maximizes this measure as socially optimal. The social planner would select the provision of the product and both product safety and precaution investments at levels to $$\begin{equation} \max_{\hat{v},x,y} W=\frac{1}{V} \int_{\hat{v}}^{\bar{v}}\big(v-c(y)-\mathcal{L}(x,y)\big)dv-k(x), \end{equation}$$(1) where |$\hat{v}$| is the valuation of the marginal consumer such that consumers with |$v\geq \hat{v}$| obtain a single unit of the product. The social planner’s first-order conditions result as $$\begin{align} W_{\hat{v}}=&-\frac{1}{V} \big[\hat{v}-c(y)-\mathcal{L}(x,y)\big]\leq 0 \label{1}\\ \end{align}$$(2) $$\begin{align} W_x=& Q(\hat{v}) s'(x)-k'(x)=0 \label{2}\\ \end{align}$$(3) $$\begin{align} W_y=&-Q(\hat{v}) \big[c'(y)-p'(y)\big]=0 \label{3}, \end{align}$$(4) where |$Q(\hat{v})=\frac{\bar{v}-\hat{v}}{V}$| denotes the quantity, that is, the share of consumers who obtain a single unit. The socially optimal marginal consumer has a valuation equal to the sum of precaution costs and expected harm (see condition (2)) and may be characterized by |$\underline{v}$|⁠, meaning that full-market coverage is socially optimal. In condition (3), the marginal influence of product safety on the expected harm is weighted by the level of output to represent the marginal benefit of higher product safety. This results from the fixed-cost character of product safety investments. For socially optimal precaution, the marginal increase in costs incurred by the consumer balance the marginal reduction in the third-party’s expected harm in (4). Condition (3) defines the socially optimal product safety level for a given output level |$Q$|⁠, |$x^{O}(Q)$|⁠. Likewise, condition (4) defines the socially optimal consumer precaution level which is independent of the output level |$Q$|⁠, that is, |$y^{O}(Q)$| with |$dy^{O}/dQ=0$|⁠. The socially optimal level of product safety |$x^{O}$| is independent of the socially optimal level of victim precaution |$y$| and vice versa. 4. Decentralized Decision-Making under Liability We consider a monopolistic firm. In our main analysis, we assume that the firm prefers to serve the full market (as in, e.g., Hua and Spier, 2018). In our discussion in Section 5, we refer to some effects from variable output (which are derived in Appendix B). We will explore decision maker incentives under different liability schemes. In our baseline scenario, the consumer is strictly liable for a share |$\alpha$| of the third-party’s expected harm, where |$\alpha \in [0,1]$|⁠, whereas the firm is responsible for the share |$1-\alpha$| of the expected harm. Our model follows Hay and Spier (2005). We depart from their framework by assuming consumers with present bias and by assuming a monopolist. Hay and Spier (2005) emphasize that setting |$\alpha=1$| yields optimal incentives. Accordingly, the policy |$\alpha=1$| will serve as a benchmark in our analysis. 4.1. Strict Consumer Liability for Share $\alpha \in [0,1]$ of Expected Harm Applying backward induction, our analysis starts in Stage 2, the last stage with modeled decision-making (as Stage 3 includes only a possible and mandated compensation payment). Stage 2 Consumers choose their level of precaution in Stage 2, seeking to $$\begin{equation} \min_y c(y)+\alpha \beta \mathcal{L}(x,y). \end{equation}$$(5) The consumer is assumed to be liable for a share |$\alpha$| of the third-party’s expected harm, a payment that would be due only in Stage 3 which is why it is discounted by the present bias |$\beta$|⁠. The privately optimal level of precaution as a function of the consumer’s liability |$\alpha$| and the consumer’s present bias |$\beta$|⁠, |$y^*(\alpha,\beta)=y^*$|⁠, solves $$\begin{equation}\label{ystern} c'(y^*)=\alpha \beta p'(y^*), \end{equation}$$(6) and is increasing in both |$\alpha$| and |$\beta$|⁠, since $$\begin{align} \frac{dy^*}{d\alpha}=&\frac{\beta p'}{c''}>0 \label{yalpha} \\ \end{align}$$(7) $$\begin{align} \frac{dy^*}{d\beta}=&\frac{\alpha p'}{c''}>0 \label{ybeta} . \end{align}$$(8) Clearly, the socially optimal level of precaution results for |$\alpha=1=\beta$|⁠, that is, when the consumer is fully responsible for third-party losses and is not present biased (refer to condition (4) for the comparison with the social planner’s incentives). Stage 1 Knowing product safety (that was set by the firm in Stage 0), consumers choose whether or not to purchase a unit of the product. We normalize consumers’ outside utility to zero. Taking into account the timing of the payoff flows, a consumer with valuation |$v$| chooses to buy the firm’s dangerous product if $$\begin{equation}\label{BVB} \beta v-P-\beta \big(c(y^*)+\alpha \mathcal{L}(x,y^*)\big)\geq 0. \end{equation}$$(9) The payment of the price is directly relevant to the consumer’s utility and is experienced in the present, whereas the consumption benefit and both precaution and liability costs are realized in the future (and are thus discounted by the factor |$\beta$|⁠). Stage 0 The firm chooses product safety and price in Stage 0, anticipating how consumers decide in later stages. When the firm prefers full-market coverage, this implies a price level at the level that makes the consumer with the lowest valuation indifferent between buying and not buying, that is, we get $$\begin{equation}\label{critv} P=\beta \big(\underline{v}-c(y^*)-\alpha \mathcal{L}(x,y^*)\big). \end{equation}$$(10) Using this price level to attain full-market coverage, expected firm profits can be stated as $$\begin{equation} \label{Pi1} \Pi=\beta \big(\underline{v}-c(y^*)-\alpha \mathcal{L}(x,y^*))\big)-(1-\alpha)\mathcal{L}(x,y^*)-k(x). \end{equation}$$(11) Maximizing |$\Pi$| with respect to product safety and rearranging the first-order condition, we obtain $$\begin{equation} (\beta \alpha+1-\alpha)s'(x^*)=k'(x^*), \label{FOCsafety} \end{equation}$$(12) where $$\begin{align} \frac{dx^*}{d\alpha}=&\frac{(1-\beta) s'}{(\beta \alpha+1-\alpha)s''-k''}<0 \label{xalpha} \\ \end{align}$$(13) $$\begin{align} \frac{dx^*}{d\beta}=&-\frac{\alpha s'}{(\beta \alpha+1-\alpha)s''-k''}>0 \label{xbeta} . \end{align}$$(14) The important difference between condition (12) and the one from the social planner’s problem (i.e., condition (3)) is due to the term |$(\beta \alpha+1-\alpha)$|⁠, which is strictly less than one when present-biased consumers bear liability, that is, when |$\beta<1$| and |$\alpha>0$|⁠. In other words, the firm has lower product safety incentives than the social planner. This is due to the fact that present-biased consumers discount their share of the expected harm as it is a future cost. Consequently, in Stage 1, present-biased consumers underappreciate a marginal increase in product safety and this is reflected in their willingness to pay. Considering the consumer’s payoff in Stage 1, the acceptable level of price increase after a marginal increase in product safety is only |$\alpha \beta s'(x)$| whereas it would be |$\alpha s'(x)$| without the present bias. Because the firm in contrast does not discount future liability payments, the privately optimal level of product safety is decreasing in the consumer’s share of expected losses, that is, the level of |$\alpha$|⁠. We now summarize our results by first attending to the benchmark scenario in which consumers are not present biased. Proposition 1 (Consumers without present bias) Assume that the market is fully covered and that |$\beta=1$|⁠. (i) Strict consumer liability for total harm (i.e., |$\alpha=1$|⁠) induces consumers to take optimal precaution and the firm to implement the socially optimal level of product safety. (ii) Sharing of liability between the firm and consumers (i.e., |$\alpha<1$|⁠) induces inefficient precaution by consumers, whereas the firm’s product safety is socially optimal. Considering only time-consistent consumers, our analysis delivers results similar to those derived in Hay and Spier (2005). Strict consumer liability for total harm induces first-best incentives with respect to both product safety and precaution. This result uses the common reasoning that consumer’s demand for product safety will induce firms without legal responsibility for expected losses to implement socially optimal product safety (e.g., Daughety and Reinganum, 2013b). Next, we return to our main research question, that is, the possible consequences of present bias for the workings of liability. We summarize our results in: Proposition 2 (Present-biased consumers) Assume that the market is fully covered and that |$\beta<1$|⁠. Then: (i) For all |$\alpha\in (0,1]$|⁠, present-biased consumers take fewer precautions than consumers without bias. (ii) For all |$\alpha\in (0,1]$|⁠, present-biased consumers obtain products with a lower level of product safety than consumers without bias. (iii) A more pronounced present bias (i.e., a lower |$\beta$|⁠) decreases both product safety and precaution. (iv) Full consumer liability cannot induce the socially optimal levels of both product safety and precaution, such that |$\alpha=1$| may not be the socially optimal allocation of expected harm. Proof. Claim (i) follows from the consumers’ first-order condition for privately optimal precautions. Claim (ii) results from the firm’s first-order condition for privately optimal product safety, since a positive |$\alpha$| implies that |$\beta<1$| will cause an underestimation of social marginal benefits in the private optimization. Claim (iii) is clear from the comparative-statics results explained above. We elaborate on Claim (iv) below. ☐ In the setup with full-market coverage, we identify two distortions when consumers are present biased. First, present bias directly bears on consumers’ precaution incentives in Stage 2 due to the discounting of future costs. This influence is apparent and intuitive. More importantly, consumers’ present bias implies that relying on consumer liability as an instrument to induce product safety works only imperfectly, because the consumer discounts expected liability payments using the factor |$\beta$| and the firm simply responds to the implications therefrom for the consumers’ willingness to pay in Stage 1. As a result, strict consumer liability for total harm cannot induce the socially optimal levels of product safety and precaution due to the distortions of present bias. Starting from the benchmark of full consumer liability (i.e., |$\alpha=1$|⁠), lowering the consumers’ share of expected harm means that precaution falls whereas product safety increases. This makes it possible that some |$\alpha<1$| is preferred relative to |$\alpha=1$|⁠. To be more precise, the relevant welfare formulation for the scenario with full-market coverage as a function of |$\alpha$| is $$\begin{align} \widetilde{W}(\alpha)=E[v]-c(y^*(\alpha))-\mathcal{L}(x^*(\alpha),y^*(\alpha))-k(x^*(\alpha)), \end{align}$$(15) which yields the derivative $$\begin{align} \frac{d \widetilde{W}}{d\alpha}=&\underbrace{\big(p'(y^*)-c'(y^*)\big)}_A \frac{dy^*}{d\alpha}+\underbrace{\big(s'(x^*)-k'(x^*)\big)}_B \frac{dx^*}{d\alpha} \nonumber \\ =&\frac{\beta (1-\alpha \beta)(p'(y^*))^2}{c''}+\frac{\alpha (s'(x^*))^2(1-\beta)^2}{(\beta \alpha+1-\alpha)s''-k''}. \end{align}$$(16) Referring to the first line, we know that at |$\alpha=1$|⁠, Terms A and B are positive since |$\beta p'(y^*)=c'(y^*)$|⁠, |$\beta s'(x^*)=k'(y^*)$|⁠, and |$\beta<1$|⁠. Moreover, we have derived that a marginal decrease in the level of |$\alpha$| will increase product safety and decrease consumer precaution. The restatement of the second line uses the private first-order conditions and the comparative-statics results. The first term represents the socially desirable impact of increasing the level of victim precaution via an increase in |$\alpha$|⁠, while the second term illustrates the socially undesirable effect of lower product safety. When the derivative is negative at |$\alpha=1$|⁠, it is socially preferable to shift some of the expected harm to the firm. This is more likely to hold true, for example, when product safety is relatively productive in terms of lowering expected losses at the private optimum. Numerical illustration. To highlight the possibility that imposing some share of the third-party’s losses on the firm can be socially optimal, we assume |$\mathcal{L}(x,y)=1-x-y$|⁠, |$c(y)=a y^2$|⁠, |$k(x)=3 x^2$|⁠, and |$\beta=4/5$|⁠. For example, we obtain that |$\alpha=10/13<1$| minimizes social costs |$\mathcal{L}(x,y)+c(y)+k(x)$| when |$a=30$| whereas |$\alpha=1$| is optimal when |$a=10$| (see Figure 1). Figure 1. Open in new tabDownload slide Social Costs as a Function of |$\alpha$|⁠. Figure 1. Open in new tabDownload slide Social Costs as a Function of |$\alpha$|⁠. 4.2. Strict Consumer Liability with a Damages Multiplier In Section 4.1, |$\alpha$| was meant to represent different possible allocations of the expected harm between the firm and the consumer. Now, we address the possibility of a damages multiplier such that the consumer pays a multiple of expected harm in damages.6 Suppose that the consumer is obliged to pay |$\gamma \mathcal{L}(x,y)$| when a judge rules in the case, where |$\gamma\geq 1$|⁠. The idea of the damages multiplier in our context counters the discounting of the expected liability payments stemming from present bias. In Stage 2, first-best precaution results when the damages multiplier |$\gamma_I=\beta^{-1}$| is implemented by the policy maker. This is clear from the first-order condition $$\begin{equation}\label{DAMy} c'(y)=\beta \gamma p'(y). \end{equation}$$(17) Let us denote the level of precaution that solves (17) by |$\tilde{y}(\beta,\gamma)=\tilde{y}$|⁠. In Stage 1, with the use of a damages multiplier, a consumer with valuation |$v$| will buy the product when $$\begin{equation} \beta v-P-\beta [c(\tilde{y})+ \gamma \mathcal{L}(x,\tilde{y})]\geq 0.\label{BUY} \end{equation}$$(18) In Stage 0, with full-market coverage, the price is dictated by the expected payoffs of the consumer with the lowest valuation and thus follows as $$\begin{equation} P=\beta \big(\underline{v}-c(\tilde{y})-\gamma \mathcal{L}(x,\tilde{y})\big). \end{equation}$$(19) Using this price level for the fully covered market, expected profits can be stated as $$\begin{equation} \Pi=\beta \big(\underline{v}-c(\tilde{y})- \gamma \mathcal{L}(x,\tilde{y})\big)-k(x). \end{equation}$$(20) Maximizing |$\Pi$| with respect to product safety and rearranging the first-order condition, we obtain $$\begin{equation} \beta \gamma s'(\tilde{x})=k'(\tilde{x}). \label{FOCsafetyMultiplier} \end{equation}$$(21) We summarize our findings in: Proposition 3 (Present-biased consumers and damages multiplier) Assume that the market is fully covered and that |$\beta<1$|⁠. Strict consumer liability with a damages multiplier |$\gamma_I=\beta^{-1}>1$| induces socially optimal precaution and product safety. With respect to the consumer’s precaution incentives, the critical level of the multiplier offsets the present bias and induces first-best incentives. With respect to the product safety incentives of the firm, the multiplier raises the consumers’ willingness to pay for a marginally safer product to |$s'(x)$|⁠. In other words, in the setup currently considered, the damages multiplier is sufficient for inducing the first-best outcome. However, when the market is not fully covered, the damages multiplier bears on consumers’ willingness to pay, implying that coupling strict liability with a damages multiplier |$\gamma_I$| can no longer induce the first-best outcome (to see this, refer to inequality (18)). Generally, when it comes to practical policy questions, it is not reasonable to expect that a regulation using |$\gamma_I=\beta^{-1}$| is practically feasible. Courts would have to assess the present bias of specific consumers and this assessment must be correctly anticipated by the firm. Critically, there will be variation in this regard across potential victims and private information about it (e.g., Wang et al., 2016; Friehe and Pannenberg, 2020). Relatedly, Craswell (1999) is critical of the multiplier principle as the multiplier would have to be calculated on a case-by-case basis.7 4.3. Negligence-based Liability Rules Our analysis above shows that incentivizing both socially optimal product safety and socially optimal precaution is difficult using a variant of strict consumer liability with consumer liability for share |$\alpha$|⁠. In the following paragraphs, we discuss the outcomes that negligence-based liability rules can induce. We turn to the standard negligence rule that addresses a standard of conduct at the consumer and strict liability with a defense of contributory negligence, where the expected harm is fully shifted to the firm as long as the consumer complies with a precaution standard. 4.3.1. Consumer negligence Under consumer negligence, the firm is never held liable for third-party harm. The consumer is held liable if she chooses a precaution level below the due precaution level and is exempted from liability if she complies or chooses a precaution level above the due level. Accordingly, the result will be similar to the analysis of strict consumer liability when precaution falls short of the standard and the consumer will lose any interest in firm product safety when precaution weakly exceeds the standard (as we are considering third-party harm). Socially optimal incentives with regard to both product safety and precaution levels thus cannot result in this institutional setting. 4.3.2. Strict liability with a defense of contributory negligence Under strict liability with a defense of contributory negligence, the consumer is held liable for harm when the level of precaution is substandard while the firm is held liable otherwise. There thus no longer exists a risk of externalizing third-party harm, in contrast to what was true under consumer negligence. Daughety and Reinganum (2013a) find that strict liability with a defense of contributory negligence induces socially desirable incentives in a bilateral-care setup in which consumer harm is cumulative. We will arrive at a similar conclusion, but also highlight that this need not result in our setting. In Stage 2, the consumer compares the cost of complying with the precaution standard |$c(y^{O})$| to the cost of non-compliance |$c(y_1^*)+\beta \mathcal{L}(x,y_1^*)$|⁠, where |$y_1^*=y^*(1,\beta)$| as defined in equation (6). Since |$y_1^*<y^{O}$|⁠, the consumer may prefer to violate the standard when the present bias is significant. A consumer with a present bias |$\beta$| will comply with the precaution standard when the firm’s product safety is set at |$x$| when |$\Delta(\beta,x)<0$|⁠, where $$\begin{equation} \Delta(\beta,x)=c(y^{O})-c(y_1^*)-\beta \mathcal{L}(x,y_1^*). \end{equation}$$(22) Clearly, |$\Delta(\beta,x)<0$| at |$\beta=1$| and (at least) in an |$\epsilon$| neighborhood to the left of |$\beta=1$|⁠. Moreover, we know that |$\Delta(\beta,x)>0$| when |$\beta \rightarrow 0$|⁠. The level of product safety influences the incentives to obey the standard of precaution, which is illustrated by the fact that a higher product safety increases the level of |$\Delta$|⁠. The compliance choice resulting in Stage 2 is anticipated by sophisticated consumers in earlier stages of the game. In Stage 1, when consumers anticipate complying with the standard, the expected payoffs of a consumer with valuation |$v$| result as $$\begin{equation} \beta v-P^C-\beta c(y^{O}),\label{COM} \end{equation}$$(23) where |$P^C$| describes the price charged from complying consumers. When consumers anticipate non-compliance, their expected payoffs amount to $$\begin{equation} \beta v -P^N-\beta \big(c(y_1^*)+\mathcal{L}(x,y_1^*)\big),\label{NON} \end{equation}$$(24) where |$P^N$| describes the price charged from non-complying consumers. In Stage 0, the level of the price ensuring full-market coverage follows as $$\begin{align} P^{C}=&\beta \big(\underline{v}-c(y^{O})\big) \label{Pc} \\ \end{align}$$(25) $$\begin{align} P^{N}=&\beta \big(\underline{v}-c(y_1^*)-\mathcal{L}(x,y_1^*)\big), \end{align}$$(26) where |$P^C>P^N$| as |$y^{O}$| is socially optimal (i.e., as it maximizes |$p(y)-c(y)$|⁠). Using these prices, we obtain that the expected payoff from buying a product at |$P^C$| and obeying the standard is |$\beta (v-\underline{v})$|⁠, which is the same expected payoff as if the product is sold at |$P^N$| and the consumer does not obey the standard. This means that consumers are indifferent between compliance and non-compliance ex ante. In contrast, the firm will typically not be indifferent between these two outcomes. For any level of product safety that induces consumers to ultimately comply, the firm’s expected profits amount to $$\begin{equation} \Pi^C(x)=\beta \big(\underline{v}-c(y^{O})\big)-\mathcal{L}(x,y^{O})-k(x) \end{equation}$$(27) and are maximized by |$x^{O}$|⁠, where we use the statement of the price from equation (25). When consumers choose non-compliance in Stage 2, the firm’s expected profits are given by $$\begin{equation} \Pi^N(x)=\beta \big(\underline{v}-c(y_1^*)-\mathcal{L}(x,y_1^*)\big)-k(x), \end{equation}$$(28) and are maximized by |$x^*_1$|⁠, that is, the level of product safety that results from (12) when |$\alpha=1$|⁠. Note that we always obtain |$x_1^*<x^{O}$| when consumers are present biased (i.e., when |$\beta<1$|⁠). Comparing the two profit levels, compliant consumers mean that the firm bears expected harm, which signifies relatively lower profits than when consumers bear expected harm because consumers discount expected harm due to present bias. This first aspect, from the firm’s point of view, speaks in favor of having non-compliant consumers. However, the precaution level ultimately chosen by non-complying consumers may be very inadequate from the firm’s point of view, implying a possible preference for the compliance scenario. In the following argumentation, we distinguish three different scenarios. First, we may have that |$\Delta(\beta,x_1^*)<\Delta(\beta,x^{O})<0$|⁠, meaning that the consumer responds with compliance to a product safety choice of |$x^{O}$|⁠. The firm can induce the first-best compliance outcome. Based on our argument above, the firm may also increase product safety to a level |$x_s$| where this level is defined by making |$\Delta(\beta,x_s)=0$| hold. In this first case, the firm must accordingly compare |$\Pi^C(x^{O})$| to |$\Pi^N(x_s)$| to arrive at a decision about which product safety level to implement. Second, the circumstances may be such that |$\Delta(\beta,x_1^*)<0<\Delta(\beta,x^{O})$|⁠, which means that the consumer chooses (non-)compliance when |$x_1^*$| (⁠|$x^{O}$|⁠) is implemented by the firm. In this case, implementing what would be optimal for compliant consumers (i.e., |$x^{O}$|⁠) induces non-compliance and using product safety that is optimal for non-compliant consumers invites consumer compliance. The best adaptation for the firm in this circumstance is choosing a level of product safety that yields about |$\Delta(\beta,x)\approx 0$| and select whether to marginally induce compliance using |$x_s-\varepsilon$| (where |$\varepsilon\rightarrow 0$|⁠) for a profit |$\Pi^C(x^s-\varepsilon)$| or induce non-compliance using |$x_s$| for a profit |$\Pi^N(x_s)$|⁠.8 Third, it may hold that |$0<\Delta(\beta,x_1^*)<\Delta(\beta,x^{O})$|⁠. In such circumstances, the firm would have to distort product safety to |$x_s-\varepsilon$|⁠, where in this case |$x_s-\varepsilon<x^*_1$|⁠, to induce consumer compliance for a profit |$\Pi^C(x^s-\varepsilon)$| or otherwise implement |$x^*_1$| and earn |$\Pi^N(x^*_1)$|⁠. We summarize our results from above as follows: Proposition 4 (Strict liability with a defense of contributory negligence) Assume that the market is fully covered and that |$\beta<1$|⁠. (i) If |$\Delta(\beta,x_1^*)<\Delta(\beta,x^{O})<0$|⁠, then the socially optimal outcome |$(x^{O},y^{O})$| results when |$\Pi^C(x^{O})\geq \Pi^{N}(x_s)$|⁠. This is true for sufficiently large levels of |$\beta$|⁠. Otherwise, |$(x_s,y_1^*)$| obtains, where |$x_s>x^{O}$|⁠. (ii) If |$\Delta(\beta,x_1^*)<0<\Delta(\beta,x^{O})$|⁠, the outcome is |$(x_s-\varepsilon,y^{O})$| when |$\Pi^C(x_s-\varepsilon)\geq \Pi^N(x_s)$|⁠, and |$(x_s,y_1^*)$| otherwise, where |$x^{O}>x_s>x_1^*$|⁠. (iii) If |$0<\Delta(\beta,x_1^*)<\Delta(\beta,x^{O})$|⁠, the outcome is |$(x_s-\varepsilon,y^{O})$| when |$\Pi^C(x_s-\varepsilon)\geq \Pi^N(x_1^*)$|⁠, and |$(x_1^*,y_1^*)$| otherwise, where |$x_s<x_1^*$|⁠. Strict liability with a defense of contributory negligence can induce the socially optimal outcome in terms of product safety by the firm and precaution by the consumer.9 In order to obtain the socially optimal outcome, we note that having |$\Delta(\beta,x_1^*)<\Delta(\beta,x^{O})<0$| is a necessary condition. This in turn requires that the discounting due to the present bias is not too strong. In fact, we know that |$\Delta (\beta,x)>0$| when |$\beta \rightarrow 0$|⁠, such that the socially optimal outcome is not possible in such circumstances. Numerical illustration. In this example, we only want to highlight that the firm sometimes prefers to induce the socially optimal outcome under strict liability with a defense of contributory negligence. We also want to illustrate that this need not result. For this purpose, we suppose again that |$c(y)=a y^2$|⁠, |$k(x)=3 x^2$|⁠, and |$\mathcal{L}(x,y)=1-x-y$|⁠. The socially optimal levels of product safety and precaution result as |$(x^{O},y^{O})=(1/6,1/(2a))$|⁠. In Stage 2, the non-compliant consumer would choose |$y_1^*=\beta/(2a)$| instead of |$y^{O}$| when the cost comparison $$\Delta(\beta,x)=\frac{1-\beta^2}{4a^2}-\beta \frac{2a-\beta-2ax}{2a}$$ is positive at the given product safety level. The firm chooses |$x_1^*=\beta/6$| when it is clear that the consumer will not comply and considers $$\Pi^{N}(x)-\Pi^{C}(x^{O})=\frac{11}{12}-\frac{(2-\beta) (1-\beta) (1+\beta)}{4 a}-3 x^2-\beta (1-x).$$ We now focus on a severe present bias by assuming |$\beta=0.35$| and consider two possible scenarios for the cost function, |$a_1=1$| and |$a_2=7/4$|⁠. These assumptions imply that circumstances are characterized by |$\Delta(\beta,x_1^*)<\Delta(\beta,x^{O})<0$| which is described in Part (i) of Proposition 4, meaning that consumers prefer compliance in response to |$x^{O}=1/6$|⁠. To “lure” consumers into non-compliance, the firm must invest into product safety such that |$x>0.2$| (⁠|$x>0.54$|⁠) in Scenario 1 (2). This can be seen in Figure 2 as |$\Delta<0$| results for smaller levels of product safety. In contrast, the firm prefers consumer non-compliance for |$x\in (0,0.33)$| in Scenario 1 and for |$x\in (0,0.41)$| in Scenario 2. As explained above, non-compliance profits are maximized by |$x^*_1=0.06$| in both cases (profits peak at the same |$x$| in Figure 2). In Scenario 1, the firm chooses |$x_s=0.2$| to induce the consumer’s non-compliance. In contrast, in Scenario 2, the upward distortion of product safety required to make the consumer disobey the standard in Stage 2 is too high. Figure 2. Open in new tabDownload slide |$\delta=\Pi^{N}(x)-\Pi^{C}(x^{O})$| and |$\Delta(\beta,x)$| as a Function of |$x$| When |$\beta=0.35$| and Either |$a_1=1$| or |$a_2=7/4$|⁠. Figure 2. Open in new tabDownload slide |$\delta=\Pi^{N}(x)-\Pi^{C}(x^{O})$| and |$\Delta(\beta,x)$| as a Function of |$x$| When |$\beta=0.35$| and Either |$a_1=1$| or |$a_2=7/4$|⁠. 5. Discussion In this section, we will discuss the implications of changing some assumptions used in our main analysis. Appendices A and B provide formal derivations to back up the claims made in this section. 5.1. Competitive Firm We focus on a monopolistic firm which is important for the firm’s output decision. In our main analysis, the firm chooses to serve the full market, implying that the distinction between monopoly and perfect competition in terms of output is not relevant for our main results. With respect to the level of product safety, both the competitive and the monopolistic firm will effectively maximize the consumer’s utility in Stage 1 net of product safety costs. 5.2. Naive Consumers In our main analysis, we assume that consumers are present biased and correctly anticipate that this bias will impact on future decision-making problems. In the literature on time preferences, this kind of agent is considered to be sophisticated and contrasted with the naive agent who mistakenly believes that future decision-making problems will not be plagued by present bias. This distinction is relevant in our framework because sophisticated consumers anticipate that they will discount the expected liability by the present bias (and thus take too little precaution from the point of view of the consumer in Stage 1), while naive agents anticipate no such discounting of expected liability. For example, when strict liability with a defense of contributory negligence applies, this may mean that, in Stage 1, the naive consumer anticipates to comply with the precaution standard but ultimately fails to do so in Stage 2. The firm will clearly take the consumer’s naivety into account. 5.3. Endogenous Output The main analysis was presented for the scenario in which the firm finds it optimal to serve all consumers. When the pricing of the firm induces some consumers to drop out of the market, the present bias becomes relevant for the level of output that results in the market. Endogenous output is also relevant to the analysis because it bears on the performance of liability regimes. For example, the level of |$\alpha$| in the strict consumer liability setting will influence product safety, precaution, and the level of output in equilibrium. 5.4. Second-Party Harm Our main analysis concerns a product that may cause harm to third parties. When harm instead falls onto consumers, we obtain a key distinction relative to our main analysis in that consumers bear expected harm in Stage 2 (i.e., in the period in which precaution is determined) and may receive compensation from the firm in Stage 3. Considering the outcome for strict consumer liability, we find that the major problem—the consumers’ present bias leading to an insufficient willingness to pay for higher product safety—is still relevant, explaining that strict consumer liability also cannot induce overall efficiency in the case of second-party harm. 6. Conclusion Decisions and events in the context of liability are often spread out over time. For example, the time period between an accident and the payout of damages is significant in many (if not most) jurisdictions. This article brings this important aspect from the tort setting to the time preferences postulated in much of the behavioral economics literature to inquire about repercussions of present bias for the actual workings of liability. In a setup in which harm-inflicting consumers are present biased, we have established that the liability rule that is considered as the optimal one without present bias—strict consumer liability for total harm (see Hay and Spier, 2005)—cannot induce the first-best allocation. Our analysis produces arguments for shifting (at least) some losses to the firm. Along these lines, we document that strict firm liability with a defense of contributory consumer negligence may attain desirable outcomes under many circumstances. The present article presents a first inquiry into the matter, neglecting many aspects that deserve future research. For example, we have assumed that the productivity of product safety is independent of the level of precaution to simplify our discussion. However, with these assumptions, we exclude, for example, that sophisticated consumers may demand a higher level of product safety in order to compensate for the anticipated underinvestment in precaution. Acknowledgements We thank Peter Grajzl, Jerg Gutmann, Stephan Michel, Gerd Mühlheusser, Urs Schweizer, Kathy Spier, Stefan Voigt, and participants of the 2018 Annual Meeting of the American Law and Economics Association in Boston and the 2018 International Meeting in Law and Economics in Paris for valuable suggestions on earlier versions of the article. We gratefully acknowledge the very helpful suggestions received from two anonymous reviewers and the editor-in-charge, Albert Choi. Appendix A. Competitive Firms A competitive firm seeks to maximize the expected utility of consumers subject to a non-negative profit constraint. For our context, it is important to note that the firm is concerned about the consumer when he or she is faced with the purchasing choice. This implies that the firm tries to maximize the expected payoffs of an individual in Stage 1, using the instruments of the price and the level of product safety. In our main analysis, we analyze the scenario in which the market is fully covered. Consider a representative competitive firm that maximizes the consumer’s well-being in Stage 1 |$\beta v-P-\beta \big(c(y)+\alpha \mathcal{L}(x,y)\big)$| with respect to the level of product safety subject to the zero-profit constraint made concrete via |$P=k(x)+(1-\alpha)\mathcal{L}(x,y)$|⁠. The optimality condition results as $$(\beta \alpha +1-\alpha)s'(x)=k'(x)$$ which is exactly the condition derived for the monopolist. B. Endogenous Output and Naive Agents In this section, we revisit our analysis from Section 4.1, considering both endogenous output and agents which are possibly naive about their present bias. In order to distinguish between sophisticated and naive agents, we introduce |$\beta_R$| (⁠|$\beta_A$|⁠) as the level of present bias that is relevant for the current (anticipated for any future) decision-making problem and note that |$\beta_R=\beta_A<1$| for sophisticated agents and |$\beta_R<\beta_A=1$| for naive agents. Stage 2 As before, consumers choose their level of precaution in Stage 2, seeking to $$\begin{equation} \min_y c(y)+\alpha \beta_R \mathcal{L}(x,y). \end{equation}$$(A.1) The privately optimal level of precaution |$y^*(\alpha,\beta_R)=y^*_R$| solves $$\begin{equation} c'(y^*_R)=\alpha \beta_R p'(y^*_R). \end{equation}$$(A.2) Stage 1 Consumers choose whether or not to purchase a unit of the product. A consumer with valuation |$v$| chooses to buy the firm’s dangerous product if $$\begin{equation}\label{BVB2} \beta_Rv-P-\beta_R[c(y_A^*)+\alpha \mathcal{L}(x,y_A^*)]\geq 0. \end{equation}$$(A.3) With respect to the precaution and liability costs, it is the anticipated level of precaution |$y^*_A$| which depends on the anticipated present bias—|$y^*_A=y^*(\alpha,\beta_A)$|—that is relevant. The weak inequality in (9) yields a valuation of the marginal consumer equal to $$\begin{equation} \tilde{v}(P,x;\alpha,\beta_A,\beta_R)=\frac{P}{\beta_R}+c(y_A^*)+\alpha \mathcal{L}(x,y_A^*), \end{equation}$$(A.4) such that consumers with |$v\geq \tilde{v}$| purchase the product. The statement in (A.4) highlights that a significant present bias tends to deter consumers from purchasing the product since an important part of the consumer’s total cost is relevant in Stage 1 (namely the payment of the price), whereas benefits (and other costs, including those associated with liability damages) lie in the future. In addition, we see that the distinction between naive and sophisticated consumers is relevant at this stage because the former (latter) agents anticipate minimizing |$c(y)-\alpha p(y)$| (⁠|$c(y)-\alpha \beta p(y)$|⁠) with their choice of precaution. Stage 0 The firm chooses product safety and price in Stage 0, anticipating how consumers decide in later stages. Profits can be stated as $$\begin{equation} \Pi=\left[P-(1-\alpha)\mathcal{L}(x,y_R^*)\right]Q(\tilde{v}(P,x;\alpha,\beta_A,\beta_R))-k(x). \end{equation}$$(A.5) While the ultimately implemented level of consumer precaution |$y_R^*$| features in the firm’s price-cost margin, the valuation of the marginal consumer builds upon the anticipated level |$y_A^*$|⁠. Maximizing |$\Pi$| with respect to the price yields |$P$| as a function of the level of product safety $$\begin{equation}\label{Pstern} P^*(x;\alpha,\beta_A,\beta_R)=\frac{\beta_R[\bar{v}-c(y_A^*)-\alpha \mathcal{L}(x,y_A^*)]+(1-\alpha)\mathcal{L}(x,y_R^*)}{2}{.}\quad \end{equation}$$(A.6) Since naive consumers mistakenly anticipate that they will minimize |$c(y)-\alpha p(y)$|⁠, the price for naive present-biased consumers exceeds the price for sophisticated consumers for a given level of product safety. Intuitively, sophisticated consumers understand ex ante that using the product will be associated with higher costs than the naive consumer anticipates. Using the price in Equation (A.6) to restate the valuation of the marginal consumer as a function of the level of product safety, we obtain $$\begin{equation}\label{margval} \tilde{v}(x;\alpha,\beta_A,\beta_R)=\frac{\bar{v}+c(y_A^*)+\alpha \mathcal{L}(x,y_A^*)+\frac{1-\alpha}{\beta_R}\mathcal{L}(x,y_R^*)}{2}. \end{equation}$$(A.7) The implied level of output is distorted relative to the first-best outcome due to the supply from a monopolistic firm and consumers’ present bias. The valuation of the marginal consumer is lower when consumers are naive instead of sophisticated, leading to a greater output with naive consumers (despite the fact that the price charged to naive consumers is higher).10 Using (A.6) and (A.7) to restate (A.5), we can state the firm’s first-order condition for the optimal level of product safety as $$\begin{equation} Q(\tilde{v}(x;\alpha,\beta_A,\beta_R)) (\beta_R \alpha+1-\alpha)s'(x)=k'(x). \label{FOCsafetyI} \end{equation}$$(A.8) Matching the statements made in our main analysis, only when |$\beta_A=\beta_R=1$| applies will strict consumer liability for total harm (i.e., |$\alpha=1$|⁠) induce consumers to take optimal precaution and the firm to implement the socially optimal level of product safety for the given level of output. In addition to the insights obtained in the main text, we find that (i) present bias bears on the level of output, (ii) naive consumers demand more of the product than sophisticated consumers (as naive consumers mistakenly anticipate private-cost-minimizing precautions), and that (iii) naive consumers obtain safer products (as output with naive consumers is higher than that with sophisticated consumers). Footnotes 1. " The existence and policy relevance of present bias has been the subject of an ever growing empirical literature. Early work is reviewed in DellaVigna (2009), for instance. More recently, Wang et al. (2016), for example, provide measurements of present bias and patience for 53 countries, highlighting that the heterogeneity between countries is much more pronounced in terms of present bias. Friehe and Pannenberg (2020) explore potential sources of differences in time preferences. 2. " We depart from Hay and Spier (2005) by focusing on a monopolistic instead of a perfectly competitive market structure. Importantly, this departure is inconsequential for the induced care incentives when consumers are time-consistent. 3. " Note that the damages multiplier does not induce the first-best outcome in a setup in which only some consumers are served by the firm because the multiplier exacerbates an output distortion (while it still induces socially optimal care levels for the given level of output). 4. " Focusing on a monopolistic firm is a common approach in the literature on the economics of liability (see, e.g., Daughety and Reinganum, 1995, 2013a; Spier, 2011). We thereby abstract from additional strategic effects due to the interdependence among firms in an oligopoly. In our discussion in Section 5, we briefly refer to the alternative benchmark scenario, that is, the case of a competitive firm. 5. " Zeiler (2019) documents very well the heterogeneity of opinions in this regard. 6. " The idea of a damages multiplier was prominently raised in the rationalization of punitive damages (Polinsky and Shavell, 1998), for example. 7. " For instance, Chu and Huang (2004) emphasize that payments exceeding the level of harm are in practice awarded only for “outrageous” conduct, which further questions the practical implementability of any multiplier in excess of one. 8. " The intuition runs as follows: conditional on consumer compliance, the firm would prefer to implement |$x^{O}$| but cannot do so without inducing consumer non-compliance. Likewise, conditional on consumer non-compliance, the firm would prefer to implement only |$x_1^*$| but induces non-compliance only with a greater product safety. The curvature of profits ensures that the firm will pick that limit value of product safety for the respective condition. 9. " It is important to note that the performance of strict liability with a defense of contributory negligence is not compromised when the firm serves only a part of the market (as was true for the damages multiplier). When the consumer complies with the precaution standard, the firm takes full expected harm into account. 10. " Sophisticated consumers with |$\beta_A=\beta_R$| consume less than in the benchmark with time-consistent consumers—which already features too little consumption due to the supply from a monopolistic firm—because they anticipate that they will not minimize |$c(y)-\alpha p(y)$| with their precaution (i.e., they correctly predict their future costs from using the product). Additionally, there is a direct effect when |$\alpha<1$| from the firm’s shifting expected liability payments via the price (the last term in the numerator of (A.7)). It is not clear that naive consumers consume less than what would result with time-consistent consumers given the precaution that they actually choose in Stage 2. They underestimate the future cost from consumption due to |$\beta_A=1$| leading them to think that they will minimize |$c(y)-\alpha p(y)$|⁠. However, since there is an artificial scarcity introduced by the monopolistic firm, it is unlikely that naive consumers will actually overconsume relative to the efficient threshold |$\hat{v}=c(y)+\mathcal{L}(x,y)$| derived in Section 3 (where |$V$| from (A.7) must exceed |$c+\mathcal{L}$| in the statement of socially optimal valuation in order to have any consumers buying the product). References Augenblick, N. , and Rabin M.. 2019 . “ An Experiment on Time Preference and Misprediction in Unpleasant Tasks ,” 86 Review of Economic Studies 941 – 75 . 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Evidence from food stamp nutrition cycle ,” 89 Journal of Public Economics 303 – 25 . Google Scholar Crossref Search ADS WorldCat Spence, M . 1977 . “ Consumer Misperceptions, Product Failure and Producer Liability ,” 44 Review of Economic Studies 561 – 72 . Google Scholar Crossref Search ADS WorldCat Spiegler, R . 2011 . Bounded Rationality and Industrial Organization . Oxford : Oxford University Press . Google Scholar Crossref Search ADS Google Scholar Google Preview WorldCat COPAC Spier, K. E . 2011 . “ Product Safety, Buybacks, and the Post-Sale Duty to Warn ,” 27 Journal of Law, Economics, & Organization 515 – 39 . Google Scholar Crossref Search ADS WorldCat Sutter, M. , Kocher M. G., Daniela G.-R., and Trautmann S. T.. 2013 . “ Impatience and Uncertainty: Experimental Decisions Predict Adolescent’s Field Behavior ,” 103 American Economic Review 510 – 31 . Google Scholar Crossref Search ADS WorldCat Wang, M. , Oliver R. M., and Hens T.. 2016 . “ How Time Preferences Differ: Evidence from 53 Countries ,” 52 Journal of Economic Psychology 115 – 35 . Google Scholar Crossref Search ADS WorldCat Zeiler, K . 2019 . “ Mistaken About Mistakes ,” 48 European Journal of Law and Economics 9 – 27 . Google Scholar Crossref Search ADS WorldCat © The Author 2020. Published by Oxford University Press on behalf of the American Law and Economics Association. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com This article is published and distributed under the terms of the Oxford University Press, Standard Journals Publication Model (https://academic.oup.com/journals/pages/open_access/funder_policies/chorus/standard_publication_model) http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png American Law and Economics Review Oxford University Press

Liability for Third-Party Harm When Harm-Inflicting Consumers Are Present Biased

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Abstract

Abstract This article analyzes the workings of liability when harm-inflicting consumers are present biased and both product safety and consumer care influence expected harm. We show that present bias introduces a rationale for shifting some losses onto the manufacturer, in stark contrast with the baseline scenario in which strict consumer liability induces socially optimal product safety and precaution levels. In addition, we establish that strict liability with contributory negligence may induce socially optimal product safety and precaution choices. 1. Introduction 1.1. Motivation and Main Results Time preferences are crucial to almost all choices and critically affect life outcomes (e.g., DellaVigna and Paserman, 2005; Meier and Sprenger, 2010; Sutter et al., 2013; Golsteyn et al., 2014; Koch et al., 2015). Time preferences are also important in the context of choices influenced by liability. Clearly, in that domain of decision-making, present choices have implications for later behavior and future payoff consequences. For example, an individual’s decision of whether or not to buy a car with a specific product safety level today will be guided by how carefully the individual expects to drive it and by the level of expected liability payments due after a possible car accident. Time preferences are commonly represented by the exponential discounting model introduced by Samuelson (1937), which assumes that the discount rate is constant and choices are time-consistent. However, data on intertemporal decision-making strongly suggest that immediate payoffs are special relative to future ones (i.e., that a bias favoring the present exists). This is incorporated in applied work using the |$\beta-\delta$| framework introduced by Laibson (1997), which departs from the exponential discounting setup only in that there is additional discounting between the present and any point in time in the future (e.g., Frederick et al., 2002; DellaVigna, 2009; O’Donoghue and Rabin, 2015). The |$\beta-\delta$| framework greatly improves the match between predictions and choice data. For example, Burks et al. (2012) emphasize that the |$\beta-\delta$| model best predicts their data from a large-scale field experiment. This article considers the workings of liability when harm-inflicting parties have |$\beta-\delta$| preferences. Specifically, in our setup, present-biased consumers cause harm to third parties; the expected value of harm is determined by both product safety and consumer care. Consumers may principally be naive or sophisticated about their present bias, meaning that they may or may not understand that, in the future, they will make decisions subject to present bias (e.g., O’Donoghue and Rabin, 1999). In our main analysis, we focus on sophisticated consumers but refer to naive consumers in our discussion. The sequence of our framework is important for understanding the role of present bias. In our model, a monopolist first chooses the product’s safety and price level. Next, consumers determine whether or not to buy a single unit of the product, anticipating how much precaution they will invest later on when actually using the product. At this point in time, payoff consequences from both taking precautions and possibly having to pay damages lie in the future (and are thus equally discounted by present-biased agents). When considering the purchase, sophisticated present-biased consumers understand that—at the later point in time when the choice about consumer precaution is due—they will discount only expected liability payments and not precaution costs and that they will therefore end up choosing suboptimal precautions. After the purchase, consumers use the product and invest in precaution. In the event of an accident, consumers and/or the firm may have to pay damages to the victim in the very last stage (depending on the liability regime). For illustration, assume that a consumer orders and pays for a car today, begins using the car a month later (thereby introducing the possibility of an accident), and ultimately pays damages for any harm suffered according to strict consumer liability several months after the accident. In this example, the lags between choices are at least 1 month. For present bias to influence decision-making, lags need not even be as long. The relevant literature emphasizes that it is primarily about distinguishing the present from the future. For example, the evidence in Shapiro (2005) is consistent with a daily|$\beta \approx 0.9$| and a daily |$\delta \approx 1$|⁠. Estimates in Augenblick and Rabin (2019) suggest an immediate gratification parameter of about |$0.83$|⁠.1 Strict consumer liability for third-party harm is our benchmark regime, building on the efficiency properties highlighted by Hay and Spier (2005) for the setup we adopt.2 For this benchmark liability arrangement, we find that there are three distortions when harm-inflicting consumers are present biased relative to the case when they are not. First, consumers underinvest in precaution due to the delayed payment of damages. Second, the firm underinvests in product safety. The firm’s product safety incentives stem either from firm liability or consumers’ demand for safety. Present-biased consumers undervalue product safety due to the delayed payment of damages, leading to the firm’s underinvestment when consumers are strictly liable for all harm. As a result, making the firm liable for a share of the expected harm may increase the level of product safety (at the cost of reducing consumer precaution) and thereby increase welfare. The third distortion arising from the consumers’ present bias concerns the level of output. Consumers perceive the price, that must be paid in the present, to be relatively more important than the consumption utility that is incurred only in the future. When we focus on a fully covered market, we find that making consumers strictly liable for a multiple of the harm (i.e., using a damages multiplier) induces the first-best outcome (i.e., socially optimal product safety and precaution levels) by debiasing the concern about damages payment.3 While a damages multiplier tailored to the present bias of single consumers is in all likelihood not a realistic policy option, using strict liability with a defense of contributory negligence is. We establish that there are circumstances under which the care incentives of both the firm and the consumer are aligned with that of the social planner when that liability rule is in place. However, when present bias is severe or consumers are naive, the use of strict liability with a defense of contributory negligence may no longer be socially desirable. The present article contributes to the literature on the economics of tort law by highlighting that time preferences can be an important moderator of the performance of different liability rules. The frameworks analyzed in this article are simple and leave room for future research. Nevertheless, against the background of the empirical evidence on intertemporal decision-making, the present study illustrates that time preferences should be taken seriously in policymaking. 1.2. Related Literature That timing is important for legal incentives is well established. For example, Gravelle (1990) and Friehe and Miceli (2017) consider endogenous trial delay, Miceli (1999) explores the strategic use of delay during settlement negotiations, and Kessler (1996) empirically explores institutional causes of settlement delay. Our article builds on Hay and Spier (2005). They study consumer-induced harm to others and highlight, for example, that some firm liability is optimal when consumers’ assets are insufficient to compensate harm. In our setup, we derive the same result—that is, firm liability may be socially desirable—albeit for a different reason, namely consumers’ present bias. Our contribution is related to Daughety and Reinganum (2013a) in that they also study a bilateral-care framework in the context of liability for harm resulting from product use. However, the two papers are clearly distinct because Daughety and Reinganum (2013a) study cumulative harm incurred by the consumer and we seek to establish the influence of present bias on the workings of liability. The literature on the economics of product liability considered a specific kind of bias early on, namely the possibility that consumers misperceive—usually underestimate—the expected harm (e.g., Spence, 1977; Polinsky and Rogerson, 1983; Geistfeld, 2009). Miceli et al. (2015) provide a recent contribution on this topic. Contributions to this literature assume that only the firm influences the expected harm incurred by consumers. Accordingly, strict liability of the firm may be proposed as an easy fix of the underestimation-problem in many circumstances. Our article considers a setup in which the expected harm is incurred by third parties and influenced by both the firm’s product safety and consumers’ precaution investments. Whereas the misestimation of expected harm can be remedied by an information policy, we are describing a phenomenon that is a consequence of non-standard preferences. Moreover, the distinction between naive and sophisticated consumers is not covered in existing liability literature but relevant in our context. Baniak and Grajzl (2017) consider how another behavioral aspect influences the workings of liability, analyzing consumers who mispredict the extent to which they will use a durable product in the future. A common example of what they are interested in is projection bias where, for instance, somebody buying a sports car is likely to overestimate the extent to which he will enjoy the product in the future. Since the expected consumer harm in their framework is a function of the level of product usage, the implications of consumers’ mispredictions are contingent on the prevailing liability regime. Key distinctions between our work and theirs include our focus on harm to others, a direct regulatory control regarding consumer behavior via a possible consumer precaution standard, and the distinction between players who are aware of their bias and players who are naive about it. Furthermore, there are potentially two decisions that are distorted due to the present bias in our setup whereas they are interested in only one choice. To the best of our knowledge, this article introduces present bias into the literature on the economics of tort law. In contrast, present bias has been considered in other domains of law and economics (see, e.g., McAdams 2011; Baumann and Friehe, 2012 for studies on criminal law and economics, and Friehe and Rössler, forthcoming for a study on litigation). Present bias has been dealt with in the literature in industrial organization (e.g., Spiegler, 2011; Heidhues and Köszegi, 2018). In many contributions from that branch of the literature, the focus is firms using multiple prices to potentially exploit consumers’ bias, exploring in particular the relevance of back-loaded fees (e.g., DellaVigna and Malmendier, 2004; Heidhues and Köszegi, 2010). In the present article, consumers pay a price upfront for a unit of the product. 1.3. Plan for the Article Section 2 presents the model. Section 3 discusses socially optimal choices. Section 4 elaborates on whether or not socially optimal incentives can be induced using liability law. Section 5 provides a discussion, and Section 6 concludes. 2. The Model 2.1. Firm A monopolistic firm offers a product whose use has a tendency to harm others.4 The expected harm that a single unit of the product causes to third parties is |$\mathcal{L}(x,y)=L-s(x)-p(y)$|⁠, where |$x$| denotes the firm’s product safety and |$y$| the consumer’s precaution level. Product safety and precaution reduce expected harm at a diminishing rate (i.e., |$s'>0>s''$| and |$p'>0>p''$|⁠). Our specification of expected harm is inspired by the representation in Chen and Hua (2017). The firm’s cost of product safety is |$k(x)$|⁠, with |$k(0)=0=k'(0)$|⁠, |$k'(x)>0$| and |$k''(x)\geq 0$| for all |$x>0$|⁠, and is incurred as a fixed cost (as in Daughety and Reinganum, 2006, for example). Product safety is observable by the consumer at the time of purchase. Production costs other than |$k$| are set to zero. The product’s price is denoted by |$P$|⁠. 2.2. Consumers Consumers either buy one or no unit of the product. Consumers differ in their (gross) valuation of the product’s use denoted |$v$|⁠. We assume that the valuation is uniformly distributed in the interval |$[\underline{v},\bar{v}]$|⁠, with |$V=\bar{v}-\underline{v}$|⁠. We normalize the number of potential consumers to one. Consumers incur a cost |$c(y)$| when they invest precaution |$y$| while using the product, where |$c(0)=0=c'(0)$|⁠, |$c'(y)>0$| and |$c''(y)\geq 0$| for all |$y>0$|⁠. Consumers are assumed to exhibit |$\beta-\delta$| preferences. Under that assumption, intertemporal preferences from the perspective of period |$t$| can be represented by |$U^t=u_t+\beta \sum_{\tau=t+1}^T \delta^\tau u_\tau$| with |$\delta$| as the standard discount factor, such that |$\beta=1$| corresponds to exponential discounting while |$\beta \in (0,1)$| reflects present bias (e.g., O’Donoghue and Rabin, 2015). We set |$\delta=1$| for notational simplicity and in order to focus on the implications of present bias alone. Note that the individual in period |$t$| considers utils in period |$t+1$| to be as valuable as utils in |$t+2$| when |$\delta=1$| and |$\beta<1$| apply. It is only when period |$t+1$| is reached that the same individual views utils in period |$t+1$| as more desirable than utils in period |$t+2$|⁠. This change in the relative desirability is important in our analysis and implies a stark contrast to the standard exponential discounting model. We consider sophisticated consumers who anticipate that future decision problems will be influenced by present bias, and comment on the analysis for naive consumers (i.e., consumers who fail to foresee that they will be subject to a present bias in the future) in our discussion in Section 5. As is standard (see, e.g., Heidhues and Köszegi, 2018), we assume that the firm is aware of the consumers’ bias and their sophistication about it. 2.3. Timing The interaction between firm, consumers, and nature unfolds as follows: (0) Nature allocates product valuation $v$ to individual consumers according to a uniform distribution in the interval $[\underline{v},\bar{v}]$⁠. The firm chooses product safety $x$ and price $P$⁠. (1) Consumers observe both the price and product safety level and choose whether or not to purchase a single unit of the product. Consumers transfer $P$ to the firm in case of purchase. (2) Consumers use the product and choose precautions $y$⁠. Accordingly, the product valuation $v$ and the precaution cost $c(y)$ are incurred only in Stage 2. An accident may occur. (3) If an accident occurred in Stage 2, possible damages payments are transferred. 3. The Social Optimum Before we describe the behavior that we will classify as socially optimal, we must first elaborate on the understanding of welfare in our context. Our article contributes by bringing present bias to the evaluation of liability rules. Zeiler (2019) distinguishes between two cases of using behavioral insights to analyze the law, the first being the incorporation of human fallibility and the second being the allowance of non-standard preferences. Whereas deviations of choices from standard theory predictions in the first category are certainly undesirable from a social point of view (e.g., subjects choosing wrong products due to a misperception of risk), deviations of choices from standard theory predictions in the second category do not similarly qualify as mistakes. Prima facie, present-biased preferences fall into the second category of non-standard preferences. However, the literature is divided about whether deviations due to present bias are to be seen as mistakes (e.g., Bernheim and Taubinsky, 2018).5 Importantly, in contrast to other non-standard preferences such as inequity aversion, for example, the very premise of present-biased preferences is that the preferences of an individual at different points in time are in conflict, meaning that a modification of behavior may benefit some selves and harm other selves. Giving in to temptation will in most circumstances do good only to the self of that period, for instance. Accordingly, O’Donoghue and Rabin (2006a) explain that a person able to choose future incentives would select long-run preferences. For that reason, we follow O’Donoghue and Rabin (1999, 2006a; 2006b) and Heidhues and Köszegi (2010) and others by treating consumers’ present bias as a “mistake,” but acknowledge that there may be diverging opinions and approaches (e.g., Goldman, 1979). We thus specify a “standard” welfare measure that features no discounting as a result of a taste for immediate gratification and classify behavior that maximizes this measure as socially optimal. The social planner would select the provision of the product and both product safety and precaution investments at levels to $$\begin{equation} \max_{\hat{v},x,y} W=\frac{1}{V} \int_{\hat{v}}^{\bar{v}}\big(v-c(y)-\mathcal{L}(x,y)\big)dv-k(x), \end{equation}$$(1) where |$\hat{v}$| is the valuation of the marginal consumer such that consumers with |$v\geq \hat{v}$| obtain a single unit of the product. The social planner’s first-order conditions result as $$\begin{align} W_{\hat{v}}=&-\frac{1}{V} \big[\hat{v}-c(y)-\mathcal{L}(x,y)\big]\leq 0 \label{1}\\ \end{align}$$(2) $$\begin{align} W_x=& Q(\hat{v}) s'(x)-k'(x)=0 \label{2}\\ \end{align}$$(3) $$\begin{align} W_y=&-Q(\hat{v}) \big[c'(y)-p'(y)\big]=0 \label{3}, \end{align}$$(4) where |$Q(\hat{v})=\frac{\bar{v}-\hat{v}}{V}$| denotes the quantity, that is, the share of consumers who obtain a single unit. The socially optimal marginal consumer has a valuation equal to the sum of precaution costs and expected harm (see condition (2)) and may be characterized by |$\underline{v}$|⁠, meaning that full-market coverage is socially optimal. In condition (3), the marginal influence of product safety on the expected harm is weighted by the level of output to represent the marginal benefit of higher product safety. This results from the fixed-cost character of product safety investments. For socially optimal precaution, the marginal increase in costs incurred by the consumer balance the marginal reduction in the third-party’s expected harm in (4). Condition (3) defines the socially optimal product safety level for a given output level |$Q$|⁠, |$x^{O}(Q)$|⁠. Likewise, condition (4) defines the socially optimal consumer precaution level which is independent of the output level |$Q$|⁠, that is, |$y^{O}(Q)$| with |$dy^{O}/dQ=0$|⁠. The socially optimal level of product safety |$x^{O}$| is independent of the socially optimal level of victim precaution |$y$| and vice versa. 4. Decentralized Decision-Making under Liability We consider a monopolistic firm. In our main analysis, we assume that the firm prefers to serve the full market (as in, e.g., Hua and Spier, 2018). In our discussion in Section 5, we refer to some effects from variable output (which are derived in Appendix B). We will explore decision maker incentives under different liability schemes. In our baseline scenario, the consumer is strictly liable for a share |$\alpha$| of the third-party’s expected harm, where |$\alpha \in [0,1]$|⁠, whereas the firm is responsible for the share |$1-\alpha$| of the expected harm. Our model follows Hay and Spier (2005). We depart from their framework by assuming consumers with present bias and by assuming a monopolist. Hay and Spier (2005) emphasize that setting |$\alpha=1$| yields optimal incentives. Accordingly, the policy |$\alpha=1$| will serve as a benchmark in our analysis. 4.1. Strict Consumer Liability for Share $\alpha \in [0,1]$ of Expected Harm Applying backward induction, our analysis starts in Stage 2, the last stage with modeled decision-making (as Stage 3 includes only a possible and mandated compensation payment). Stage 2 Consumers choose their level of precaution in Stage 2, seeking to $$\begin{equation} \min_y c(y)+\alpha \beta \mathcal{L}(x,y). \end{equation}$$(5) The consumer is assumed to be liable for a share |$\alpha$| of the third-party’s expected harm, a payment that would be due only in Stage 3 which is why it is discounted by the present bias |$\beta$|⁠. The privately optimal level of precaution as a function of the consumer’s liability |$\alpha$| and the consumer’s present bias |$\beta$|⁠, |$y^*(\alpha,\beta)=y^*$|⁠, solves $$\begin{equation}\label{ystern} c'(y^*)=\alpha \beta p'(y^*), \end{equation}$$(6) and is increasing in both |$\alpha$| and |$\beta$|⁠, since $$\begin{align} \frac{dy^*}{d\alpha}=&\frac{\beta p'}{c''}>0 \label{yalpha} \\ \end{align}$$(7) $$\begin{align} \frac{dy^*}{d\beta}=&\frac{\alpha p'}{c''}>0 \label{ybeta} . \end{align}$$(8) Clearly, the socially optimal level of precaution results for |$\alpha=1=\beta$|⁠, that is, when the consumer is fully responsible for third-party losses and is not present biased (refer to condition (4) for the comparison with the social planner’s incentives). Stage 1 Knowing product safety (that was set by the firm in Stage 0), consumers choose whether or not to purchase a unit of the product. We normalize consumers’ outside utility to zero. Taking into account the timing of the payoff flows, a consumer with valuation |$v$| chooses to buy the firm’s dangerous product if $$\begin{equation}\label{BVB} \beta v-P-\beta \big(c(y^*)+\alpha \mathcal{L}(x,y^*)\big)\geq 0. \end{equation}$$(9) The payment of the price is directly relevant to the consumer’s utility and is experienced in the present, whereas the consumption benefit and both precaution and liability costs are realized in the future (and are thus discounted by the factor |$\beta$|⁠). Stage 0 The firm chooses product safety and price in Stage 0, anticipating how consumers decide in later stages. When the firm prefers full-market coverage, this implies a price level at the level that makes the consumer with the lowest valuation indifferent between buying and not buying, that is, we get $$\begin{equation}\label{critv} P=\beta \big(\underline{v}-c(y^*)-\alpha \mathcal{L}(x,y^*)\big). \end{equation}$$(10) Using this price level to attain full-market coverage, expected firm profits can be stated as $$\begin{equation} \label{Pi1} \Pi=\beta \big(\underline{v}-c(y^*)-\alpha \mathcal{L}(x,y^*))\big)-(1-\alpha)\mathcal{L}(x,y^*)-k(x). \end{equation}$$(11) Maximizing |$\Pi$| with respect to product safety and rearranging the first-order condition, we obtain $$\begin{equation} (\beta \alpha+1-\alpha)s'(x^*)=k'(x^*), \label{FOCsafety} \end{equation}$$(12) where $$\begin{align} \frac{dx^*}{d\alpha}=&\frac{(1-\beta) s'}{(\beta \alpha+1-\alpha)s''-k''}<0 \label{xalpha} \\ \end{align}$$(13) $$\begin{align} \frac{dx^*}{d\beta}=&-\frac{\alpha s'}{(\beta \alpha+1-\alpha)s''-k''}>0 \label{xbeta} . \end{align}$$(14) The important difference between condition (12) and the one from the social planner’s problem (i.e., condition (3)) is due to the term |$(\beta \alpha+1-\alpha)$|⁠, which is strictly less than one when present-biased consumers bear liability, that is, when |$\beta<1$| and |$\alpha>0$|⁠. In other words, the firm has lower product safety incentives than the social planner. This is due to the fact that present-biased consumers discount their share of the expected harm as it is a future cost. Consequently, in Stage 1, present-biased consumers underappreciate a marginal increase in product safety and this is reflected in their willingness to pay. Considering the consumer’s payoff in Stage 1, the acceptable level of price increase after a marginal increase in product safety is only |$\alpha \beta s'(x)$| whereas it would be |$\alpha s'(x)$| without the present bias. Because the firm in contrast does not discount future liability payments, the privately optimal level of product safety is decreasing in the consumer’s share of expected losses, that is, the level of |$\alpha$|⁠. We now summarize our results by first attending to the benchmark scenario in which consumers are not present biased. Proposition 1 (Consumers without present bias) Assume that the market is fully covered and that |$\beta=1$|⁠. (i) Strict consumer liability for total harm (i.e., |$\alpha=1$|⁠) induces consumers to take optimal precaution and the firm to implement the socially optimal level of product safety. (ii) Sharing of liability between the firm and consumers (i.e., |$\alpha<1$|⁠) induces inefficient precaution by consumers, whereas the firm’s product safety is socially optimal. Considering only time-consistent consumers, our analysis delivers results similar to those derived in Hay and Spier (2005). Strict consumer liability for total harm induces first-best incentives with respect to both product safety and precaution. This result uses the common reasoning that consumer’s demand for product safety will induce firms without legal responsibility for expected losses to implement socially optimal product safety (e.g., Daughety and Reinganum, 2013b). Next, we return to our main research question, that is, the possible consequences of present bias for the workings of liability. We summarize our results in: Proposition 2 (Present-biased consumers) Assume that the market is fully covered and that |$\beta<1$|⁠. Then: (i) For all |$\alpha\in (0,1]$|⁠, present-biased consumers take fewer precautions than consumers without bias. (ii) For all |$\alpha\in (0,1]$|⁠, present-biased consumers obtain products with a lower level of product safety than consumers without bias. (iii) A more pronounced present bias (i.e., a lower |$\beta$|⁠) decreases both product safety and precaution. (iv) Full consumer liability cannot induce the socially optimal levels of both product safety and precaution, such that |$\alpha=1$| may not be the socially optimal allocation of expected harm. Proof. Claim (i) follows from the consumers’ first-order condition for privately optimal precautions. Claim (ii) results from the firm’s first-order condition for privately optimal product safety, since a positive |$\alpha$| implies that |$\beta<1$| will cause an underestimation of social marginal benefits in the private optimization. Claim (iii) is clear from the comparative-statics results explained above. We elaborate on Claim (iv) below. ☐ In the setup with full-market coverage, we identify two distortions when consumers are present biased. First, present bias directly bears on consumers’ precaution incentives in Stage 2 due to the discounting of future costs. This influence is apparent and intuitive. More importantly, consumers’ present bias implies that relying on consumer liability as an instrument to induce product safety works only imperfectly, because the consumer discounts expected liability payments using the factor |$\beta$| and the firm simply responds to the implications therefrom for the consumers’ willingness to pay in Stage 1. As a result, strict consumer liability for total harm cannot induce the socially optimal levels of product safety and precaution due to the distortions of present bias. Starting from the benchmark of full consumer liability (i.e., |$\alpha=1$|⁠), lowering the consumers’ share of expected harm means that precaution falls whereas product safety increases. This makes it possible that some |$\alpha<1$| is preferred relative to |$\alpha=1$|⁠. To be more precise, the relevant welfare formulation for the scenario with full-market coverage as a function of |$\alpha$| is $$\begin{align} \widetilde{W}(\alpha)=E[v]-c(y^*(\alpha))-\mathcal{L}(x^*(\alpha),y^*(\alpha))-k(x^*(\alpha)), \end{align}$$(15) which yields the derivative $$\begin{align} \frac{d \widetilde{W}}{d\alpha}=&\underbrace{\big(p'(y^*)-c'(y^*)\big)}_A \frac{dy^*}{d\alpha}+\underbrace{\big(s'(x^*)-k'(x^*)\big)}_B \frac{dx^*}{d\alpha} \nonumber \\ =&\frac{\beta (1-\alpha \beta)(p'(y^*))^2}{c''}+\frac{\alpha (s'(x^*))^2(1-\beta)^2}{(\beta \alpha+1-\alpha)s''-k''}. \end{align}$$(16) Referring to the first line, we know that at |$\alpha=1$|⁠, Terms A and B are positive since |$\beta p'(y^*)=c'(y^*)$|⁠, |$\beta s'(x^*)=k'(y^*)$|⁠, and |$\beta<1$|⁠. Moreover, we have derived that a marginal decrease in the level of |$\alpha$| will increase product safety and decrease consumer precaution. The restatement of the second line uses the private first-order conditions and the comparative-statics results. The first term represents the socially desirable impact of increasing the level of victim precaution via an increase in |$\alpha$|⁠, while the second term illustrates the socially undesirable effect of lower product safety. When the derivative is negative at |$\alpha=1$|⁠, it is socially preferable to shift some of the expected harm to the firm. This is more likely to hold true, for example, when product safety is relatively productive in terms of lowering expected losses at the private optimum. Numerical illustration. To highlight the possibility that imposing some share of the third-party’s losses on the firm can be socially optimal, we assume |$\mathcal{L}(x,y)=1-x-y$|⁠, |$c(y)=a y^2$|⁠, |$k(x)=3 x^2$|⁠, and |$\beta=4/5$|⁠. For example, we obtain that |$\alpha=10/13<1$| minimizes social costs |$\mathcal{L}(x,y)+c(y)+k(x)$| when |$a=30$| whereas |$\alpha=1$| is optimal when |$a=10$| (see Figure 1). Figure 1. Open in new tabDownload slide Social Costs as a Function of |$\alpha$|⁠. Figure 1. Open in new tabDownload slide Social Costs as a Function of |$\alpha$|⁠. 4.2. Strict Consumer Liability with a Damages Multiplier In Section 4.1, |$\alpha$| was meant to represent different possible allocations of the expected harm between the firm and the consumer. Now, we address the possibility of a damages multiplier such that the consumer pays a multiple of expected harm in damages.6 Suppose that the consumer is obliged to pay |$\gamma \mathcal{L}(x,y)$| when a judge rules in the case, where |$\gamma\geq 1$|⁠. The idea of the damages multiplier in our context counters the discounting of the expected liability payments stemming from present bias. In Stage 2, first-best precaution results when the damages multiplier |$\gamma_I=\beta^{-1}$| is implemented by the policy maker. This is clear from the first-order condition $$\begin{equation}\label{DAMy} c'(y)=\beta \gamma p'(y). \end{equation}$$(17) Let us denote the level of precaution that solves (17) by |$\tilde{y}(\beta,\gamma)=\tilde{y}$|⁠. In Stage 1, with the use of a damages multiplier, a consumer with valuation |$v$| will buy the product when $$\begin{equation} \beta v-P-\beta [c(\tilde{y})+ \gamma \mathcal{L}(x,\tilde{y})]\geq 0.\label{BUY} \end{equation}$$(18) In Stage 0, with full-market coverage, the price is dictated by the expected payoffs of the consumer with the lowest valuation and thus follows as $$\begin{equation} P=\beta \big(\underline{v}-c(\tilde{y})-\gamma \mathcal{L}(x,\tilde{y})\big). \end{equation}$$(19) Using this price level for the fully covered market, expected profits can be stated as $$\begin{equation} \Pi=\beta \big(\underline{v}-c(\tilde{y})- \gamma \mathcal{L}(x,\tilde{y})\big)-k(x). \end{equation}$$(20) Maximizing |$\Pi$| with respect to product safety and rearranging the first-order condition, we obtain $$\begin{equation} \beta \gamma s'(\tilde{x})=k'(\tilde{x}). \label{FOCsafetyMultiplier} \end{equation}$$(21) We summarize our findings in: Proposition 3 (Present-biased consumers and damages multiplier) Assume that the market is fully covered and that |$\beta<1$|⁠. Strict consumer liability with a damages multiplier |$\gamma_I=\beta^{-1}>1$| induces socially optimal precaution and product safety. With respect to the consumer’s precaution incentives, the critical level of the multiplier offsets the present bias and induces first-best incentives. With respect to the product safety incentives of the firm, the multiplier raises the consumers’ willingness to pay for a marginally safer product to |$s'(x)$|⁠. In other words, in the setup currently considered, the damages multiplier is sufficient for inducing the first-best outcome. However, when the market is not fully covered, the damages multiplier bears on consumers’ willingness to pay, implying that coupling strict liability with a damages multiplier |$\gamma_I$| can no longer induce the first-best outcome (to see this, refer to inequality (18)). Generally, when it comes to practical policy questions, it is not reasonable to expect that a regulation using |$\gamma_I=\beta^{-1}$| is practically feasible. Courts would have to assess the present bias of specific consumers and this assessment must be correctly anticipated by the firm. Critically, there will be variation in this regard across potential victims and private information about it (e.g., Wang et al., 2016; Friehe and Pannenberg, 2020). Relatedly, Craswell (1999) is critical of the multiplier principle as the multiplier would have to be calculated on a case-by-case basis.7 4.3. Negligence-based Liability Rules Our analysis above shows that incentivizing both socially optimal product safety and socially optimal precaution is difficult using a variant of strict consumer liability with consumer liability for share |$\alpha$|⁠. In the following paragraphs, we discuss the outcomes that negligence-based liability rules can induce. We turn to the standard negligence rule that addresses a standard of conduct at the consumer and strict liability with a defense of contributory negligence, where the expected harm is fully shifted to the firm as long as the consumer complies with a precaution standard. 4.3.1. Consumer negligence Under consumer negligence, the firm is never held liable for third-party harm. The consumer is held liable if she chooses a precaution level below the due precaution level and is exempted from liability if she complies or chooses a precaution level above the due level. Accordingly, the result will be similar to the analysis of strict consumer liability when precaution falls short of the standard and the consumer will lose any interest in firm product safety when precaution weakly exceeds the standard (as we are considering third-party harm). Socially optimal incentives with regard to both product safety and precaution levels thus cannot result in this institutional setting. 4.3.2. Strict liability with a defense of contributory negligence Under strict liability with a defense of contributory negligence, the consumer is held liable for harm when the level of precaution is substandard while the firm is held liable otherwise. There thus no longer exists a risk of externalizing third-party harm, in contrast to what was true under consumer negligence. Daughety and Reinganum (2013a) find that strict liability with a defense of contributory negligence induces socially desirable incentives in a bilateral-care setup in which consumer harm is cumulative. We will arrive at a similar conclusion, but also highlight that this need not result in our setting. In Stage 2, the consumer compares the cost of complying with the precaution standard |$c(y^{O})$| to the cost of non-compliance |$c(y_1^*)+\beta \mathcal{L}(x,y_1^*)$|⁠, where |$y_1^*=y^*(1,\beta)$| as defined in equation (6). Since |$y_1^*<y^{O}$|⁠, the consumer may prefer to violate the standard when the present bias is significant. A consumer with a present bias |$\beta$| will comply with the precaution standard when the firm’s product safety is set at |$x$| when |$\Delta(\beta,x)<0$|⁠, where $$\begin{equation} \Delta(\beta,x)=c(y^{O})-c(y_1^*)-\beta \mathcal{L}(x,y_1^*). \end{equation}$$(22) Clearly, |$\Delta(\beta,x)<0$| at |$\beta=1$| and (at least) in an |$\epsilon$| neighborhood to the left of |$\beta=1$|⁠. Moreover, we know that |$\Delta(\beta,x)>0$| when |$\beta \rightarrow 0$|⁠. The level of product safety influences the incentives to obey the standard of precaution, which is illustrated by the fact that a higher product safety increases the level of |$\Delta$|⁠. The compliance choice resulting in Stage 2 is anticipated by sophisticated consumers in earlier stages of the game. In Stage 1, when consumers anticipate complying with the standard, the expected payoffs of a consumer with valuation |$v$| result as $$\begin{equation} \beta v-P^C-\beta c(y^{O}),\label{COM} \end{equation}$$(23) where |$P^C$| describes the price charged from complying consumers. When consumers anticipate non-compliance, their expected payoffs amount to $$\begin{equation} \beta v -P^N-\beta \big(c(y_1^*)+\mathcal{L}(x,y_1^*)\big),\label{NON} \end{equation}$$(24) where |$P^N$| describes the price charged from non-complying consumers. In Stage 0, the level of the price ensuring full-market coverage follows as $$\begin{align} P^{C}=&\beta \big(\underline{v}-c(y^{O})\big) \label{Pc} \\ \end{align}$$(25) $$\begin{align} P^{N}=&\beta \big(\underline{v}-c(y_1^*)-\mathcal{L}(x,y_1^*)\big), \end{align}$$(26) where |$P^C>P^N$| as |$y^{O}$| is socially optimal (i.e., as it maximizes |$p(y)-c(y)$|⁠). Using these prices, we obtain that the expected payoff from buying a product at |$P^C$| and obeying the standard is |$\beta (v-\underline{v})$|⁠, which is the same expected payoff as if the product is sold at |$P^N$| and the consumer does not obey the standard. This means that consumers are indifferent between compliance and non-compliance ex ante. In contrast, the firm will typically not be indifferent between these two outcomes. For any level of product safety that induces consumers to ultimately comply, the firm’s expected profits amount to $$\begin{equation} \Pi^C(x)=\beta \big(\underline{v}-c(y^{O})\big)-\mathcal{L}(x,y^{O})-k(x) \end{equation}$$(27) and are maximized by |$x^{O}$|⁠, where we use the statement of the price from equation (25). When consumers choose non-compliance in Stage 2, the firm’s expected profits are given by $$\begin{equation} \Pi^N(x)=\beta \big(\underline{v}-c(y_1^*)-\mathcal{L}(x,y_1^*)\big)-k(x), \end{equation}$$(28) and are maximized by |$x^*_1$|⁠, that is, the level of product safety that results from (12) when |$\alpha=1$|⁠. Note that we always obtain |$x_1^*<x^{O}$| when consumers are present biased (i.e., when |$\beta<1$|⁠). Comparing the two profit levels, compliant consumers mean that the firm bears expected harm, which signifies relatively lower profits than when consumers bear expected harm because consumers discount expected harm due to present bias. This first aspect, from the firm’s point of view, speaks in favor of having non-compliant consumers. However, the precaution level ultimately chosen by non-complying consumers may be very inadequate from the firm’s point of view, implying a possible preference for the compliance scenario. In the following argumentation, we distinguish three different scenarios. First, we may have that |$\Delta(\beta,x_1^*)<\Delta(\beta,x^{O})<0$|⁠, meaning that the consumer responds with compliance to a product safety choice of |$x^{O}$|⁠. The firm can induce the first-best compliance outcome. Based on our argument above, the firm may also increase product safety to a level |$x_s$| where this level is defined by making |$\Delta(\beta,x_s)=0$| hold. In this first case, the firm must accordingly compare |$\Pi^C(x^{O})$| to |$\Pi^N(x_s)$| to arrive at a decision about which product safety level to implement. Second, the circumstances may be such that |$\Delta(\beta,x_1^*)<0<\Delta(\beta,x^{O})$|⁠, which means that the consumer chooses (non-)compliance when |$x_1^*$| (⁠|$x^{O}$|⁠) is implemented by the firm. In this case, implementing what would be optimal for compliant consumers (i.e., |$x^{O}$|⁠) induces non-compliance and using product safety that is optimal for non-compliant consumers invites consumer compliance. The best adaptation for the firm in this circumstance is choosing a level of product safety that yields about |$\Delta(\beta,x)\approx 0$| and select whether to marginally induce compliance using |$x_s-\varepsilon$| (where |$\varepsilon\rightarrow 0$|⁠) for a profit |$\Pi^C(x^s-\varepsilon)$| or induce non-compliance using |$x_s$| for a profit |$\Pi^N(x_s)$|⁠.8 Third, it may hold that |$0<\Delta(\beta,x_1^*)<\Delta(\beta,x^{O})$|⁠. In such circumstances, the firm would have to distort product safety to |$x_s-\varepsilon$|⁠, where in this case |$x_s-\varepsilon<x^*_1$|⁠, to induce consumer compliance for a profit |$\Pi^C(x^s-\varepsilon)$| or otherwise implement |$x^*_1$| and earn |$\Pi^N(x^*_1)$|⁠. We summarize our results from above as follows: Proposition 4 (Strict liability with a defense of contributory negligence) Assume that the market is fully covered and that |$\beta<1$|⁠. (i) If |$\Delta(\beta,x_1^*)<\Delta(\beta,x^{O})<0$|⁠, then the socially optimal outcome |$(x^{O},y^{O})$| results when |$\Pi^C(x^{O})\geq \Pi^{N}(x_s)$|⁠. This is true for sufficiently large levels of |$\beta$|⁠. Otherwise, |$(x_s,y_1^*)$| obtains, where |$x_s>x^{O}$|⁠. (ii) If |$\Delta(\beta,x_1^*)<0<\Delta(\beta,x^{O})$|⁠, the outcome is |$(x_s-\varepsilon,y^{O})$| when |$\Pi^C(x_s-\varepsilon)\geq \Pi^N(x_s)$|⁠, and |$(x_s,y_1^*)$| otherwise, where |$x^{O}>x_s>x_1^*$|⁠. (iii) If |$0<\Delta(\beta,x_1^*)<\Delta(\beta,x^{O})$|⁠, the outcome is |$(x_s-\varepsilon,y^{O})$| when |$\Pi^C(x_s-\varepsilon)\geq \Pi^N(x_1^*)$|⁠, and |$(x_1^*,y_1^*)$| otherwise, where |$x_s<x_1^*$|⁠. Strict liability with a defense of contributory negligence can induce the socially optimal outcome in terms of product safety by the firm and precaution by the consumer.9 In order to obtain the socially optimal outcome, we note that having |$\Delta(\beta,x_1^*)<\Delta(\beta,x^{O})<0$| is a necessary condition. This in turn requires that the discounting due to the present bias is not too strong. In fact, we know that |$\Delta (\beta,x)>0$| when |$\beta \rightarrow 0$|⁠, such that the socially optimal outcome is not possible in such circumstances. Numerical illustration. In this example, we only want to highlight that the firm sometimes prefers to induce the socially optimal outcome under strict liability with a defense of contributory negligence. We also want to illustrate that this need not result. For this purpose, we suppose again that |$c(y)=a y^2$|⁠, |$k(x)=3 x^2$|⁠, and |$\mathcal{L}(x,y)=1-x-y$|⁠. The socially optimal levels of product safety and precaution result as |$(x^{O},y^{O})=(1/6,1/(2a))$|⁠. In Stage 2, the non-compliant consumer would choose |$y_1^*=\beta/(2a)$| instead of |$y^{O}$| when the cost comparison $$\Delta(\beta,x)=\frac{1-\beta^2}{4a^2}-\beta \frac{2a-\beta-2ax}{2a}$$ is positive at the given product safety level. The firm chooses |$x_1^*=\beta/6$| when it is clear that the consumer will not comply and considers $$\Pi^{N}(x)-\Pi^{C}(x^{O})=\frac{11}{12}-\frac{(2-\beta) (1-\beta) (1+\beta)}{4 a}-3 x^2-\beta (1-x).$$ We now focus on a severe present bias by assuming |$\beta=0.35$| and consider two possible scenarios for the cost function, |$a_1=1$| and |$a_2=7/4$|⁠. These assumptions imply that circumstances are characterized by |$\Delta(\beta,x_1^*)<\Delta(\beta,x^{O})<0$| which is described in Part (i) of Proposition 4, meaning that consumers prefer compliance in response to |$x^{O}=1/6$|⁠. To “lure” consumers into non-compliance, the firm must invest into product safety such that |$x>0.2$| (⁠|$x>0.54$|⁠) in Scenario 1 (2). This can be seen in Figure 2 as |$\Delta<0$| results for smaller levels of product safety. In contrast, the firm prefers consumer non-compliance for |$x\in (0,0.33)$| in Scenario 1 and for |$x\in (0,0.41)$| in Scenario 2. As explained above, non-compliance profits are maximized by |$x^*_1=0.06$| in both cases (profits peak at the same |$x$| in Figure 2). In Scenario 1, the firm chooses |$x_s=0.2$| to induce the consumer’s non-compliance. In contrast, in Scenario 2, the upward distortion of product safety required to make the consumer disobey the standard in Stage 2 is too high. Figure 2. Open in new tabDownload slide |$\delta=\Pi^{N}(x)-\Pi^{C}(x^{O})$| and |$\Delta(\beta,x)$| as a Function of |$x$| When |$\beta=0.35$| and Either |$a_1=1$| or |$a_2=7/4$|⁠. Figure 2. Open in new tabDownload slide |$\delta=\Pi^{N}(x)-\Pi^{C}(x^{O})$| and |$\Delta(\beta,x)$| as a Function of |$x$| When |$\beta=0.35$| and Either |$a_1=1$| or |$a_2=7/4$|⁠. 5. Discussion In this section, we will discuss the implications of changing some assumptions used in our main analysis. Appendices A and B provide formal derivations to back up the claims made in this section. 5.1. Competitive Firm We focus on a monopolistic firm which is important for the firm’s output decision. In our main analysis, the firm chooses to serve the full market, implying that the distinction between monopoly and perfect competition in terms of output is not relevant for our main results. With respect to the level of product safety, both the competitive and the monopolistic firm will effectively maximize the consumer’s utility in Stage 1 net of product safety costs. 5.2. Naive Consumers In our main analysis, we assume that consumers are present biased and correctly anticipate that this bias will impact on future decision-making problems. In the literature on time preferences, this kind of agent is considered to be sophisticated and contrasted with the naive agent who mistakenly believes that future decision-making problems will not be plagued by present bias. This distinction is relevant in our framework because sophisticated consumers anticipate that they will discount the expected liability by the present bias (and thus take too little precaution from the point of view of the consumer in Stage 1), while naive agents anticipate no such discounting of expected liability. For example, when strict liability with a defense of contributory negligence applies, this may mean that, in Stage 1, the naive consumer anticipates to comply with the precaution standard but ultimately fails to do so in Stage 2. The firm will clearly take the consumer’s naivety into account. 5.3. Endogenous Output The main analysis was presented for the scenario in which the firm finds it optimal to serve all consumers. When the pricing of the firm induces some consumers to drop out of the market, the present bias becomes relevant for the level of output that results in the market. Endogenous output is also relevant to the analysis because it bears on the performance of liability regimes. For example, the level of |$\alpha$| in the strict consumer liability setting will influence product safety, precaution, and the level of output in equilibrium. 5.4. Second-Party Harm Our main analysis concerns a product that may cause harm to third parties. When harm instead falls onto consumers, we obtain a key distinction relative to our main analysis in that consumers bear expected harm in Stage 2 (i.e., in the period in which precaution is determined) and may receive compensation from the firm in Stage 3. Considering the outcome for strict consumer liability, we find that the major problem—the consumers’ present bias leading to an insufficient willingness to pay for higher product safety—is still relevant, explaining that strict consumer liability also cannot induce overall efficiency in the case of second-party harm. 6. Conclusion Decisions and events in the context of liability are often spread out over time. For example, the time period between an accident and the payout of damages is significant in many (if not most) jurisdictions. This article brings this important aspect from the tort setting to the time preferences postulated in much of the behavioral economics literature to inquire about repercussions of present bias for the actual workings of liability. In a setup in which harm-inflicting consumers are present biased, we have established that the liability rule that is considered as the optimal one without present bias—strict consumer liability for total harm (see Hay and Spier, 2005)—cannot induce the first-best allocation. Our analysis produces arguments for shifting (at least) some losses to the firm. Along these lines, we document that strict firm liability with a defense of contributory consumer negligence may attain desirable outcomes under many circumstances. The present article presents a first inquiry into the matter, neglecting many aspects that deserve future research. For example, we have assumed that the productivity of product safety is independent of the level of precaution to simplify our discussion. However, with these assumptions, we exclude, for example, that sophisticated consumers may demand a higher level of product safety in order to compensate for the anticipated underinvestment in precaution. Acknowledgements We thank Peter Grajzl, Jerg Gutmann, Stephan Michel, Gerd Mühlheusser, Urs Schweizer, Kathy Spier, Stefan Voigt, and participants of the 2018 Annual Meeting of the American Law and Economics Association in Boston and the 2018 International Meeting in Law and Economics in Paris for valuable suggestions on earlier versions of the article. We gratefully acknowledge the very helpful suggestions received from two anonymous reviewers and the editor-in-charge, Albert Choi. Appendix A. Competitive Firms A competitive firm seeks to maximize the expected utility of consumers subject to a non-negative profit constraint. For our context, it is important to note that the firm is concerned about the consumer when he or she is faced with the purchasing choice. This implies that the firm tries to maximize the expected payoffs of an individual in Stage 1, using the instruments of the price and the level of product safety. In our main analysis, we analyze the scenario in which the market is fully covered. Consider a representative competitive firm that maximizes the consumer’s well-being in Stage 1 |$\beta v-P-\beta \big(c(y)+\alpha \mathcal{L}(x,y)\big)$| with respect to the level of product safety subject to the zero-profit constraint made concrete via |$P=k(x)+(1-\alpha)\mathcal{L}(x,y)$|⁠. The optimality condition results as $$(\beta \alpha +1-\alpha)s'(x)=k'(x)$$ which is exactly the condition derived for the monopolist. B. Endogenous Output and Naive Agents In this section, we revisit our analysis from Section 4.1, considering both endogenous output and agents which are possibly naive about their present bias. In order to distinguish between sophisticated and naive agents, we introduce |$\beta_R$| (⁠|$\beta_A$|⁠) as the level of present bias that is relevant for the current (anticipated for any future) decision-making problem and note that |$\beta_R=\beta_A<1$| for sophisticated agents and |$\beta_R<\beta_A=1$| for naive agents. Stage 2 As before, consumers choose their level of precaution in Stage 2, seeking to $$\begin{equation} \min_y c(y)+\alpha \beta_R \mathcal{L}(x,y). \end{equation}$$(A.1) The privately optimal level of precaution |$y^*(\alpha,\beta_R)=y^*_R$| solves $$\begin{equation} c'(y^*_R)=\alpha \beta_R p'(y^*_R). \end{equation}$$(A.2) Stage 1 Consumers choose whether or not to purchase a unit of the product. A consumer with valuation |$v$| chooses to buy the firm’s dangerous product if $$\begin{equation}\label{BVB2} \beta_Rv-P-\beta_R[c(y_A^*)+\alpha \mathcal{L}(x,y_A^*)]\geq 0. \end{equation}$$(A.3) With respect to the precaution and liability costs, it is the anticipated level of precaution |$y^*_A$| which depends on the anticipated present bias—|$y^*_A=y^*(\alpha,\beta_A)$|—that is relevant. The weak inequality in (9) yields a valuation of the marginal consumer equal to $$\begin{equation} \tilde{v}(P,x;\alpha,\beta_A,\beta_R)=\frac{P}{\beta_R}+c(y_A^*)+\alpha \mathcal{L}(x,y_A^*), \end{equation}$$(A.4) such that consumers with |$v\geq \tilde{v}$| purchase the product. The statement in (A.4) highlights that a significant present bias tends to deter consumers from purchasing the product since an important part of the consumer’s total cost is relevant in Stage 1 (namely the payment of the price), whereas benefits (and other costs, including those associated with liability damages) lie in the future. In addition, we see that the distinction between naive and sophisticated consumers is relevant at this stage because the former (latter) agents anticipate minimizing |$c(y)-\alpha p(y)$| (⁠|$c(y)-\alpha \beta p(y)$|⁠) with their choice of precaution. Stage 0 The firm chooses product safety and price in Stage 0, anticipating how consumers decide in later stages. Profits can be stated as $$\begin{equation} \Pi=\left[P-(1-\alpha)\mathcal{L}(x,y_R^*)\right]Q(\tilde{v}(P,x;\alpha,\beta_A,\beta_R))-k(x). \end{equation}$$(A.5) While the ultimately implemented level of consumer precaution |$y_R^*$| features in the firm’s price-cost margin, the valuation of the marginal consumer builds upon the anticipated level |$y_A^*$|⁠. Maximizing |$\Pi$| with respect to the price yields |$P$| as a function of the level of product safety $$\begin{equation}\label{Pstern} P^*(x;\alpha,\beta_A,\beta_R)=\frac{\beta_R[\bar{v}-c(y_A^*)-\alpha \mathcal{L}(x,y_A^*)]+(1-\alpha)\mathcal{L}(x,y_R^*)}{2}{.}\quad \end{equation}$$(A.6) Since naive consumers mistakenly anticipate that they will minimize |$c(y)-\alpha p(y)$|⁠, the price for naive present-biased consumers exceeds the price for sophisticated consumers for a given level of product safety. Intuitively, sophisticated consumers understand ex ante that using the product will be associated with higher costs than the naive consumer anticipates. Using the price in Equation (A.6) to restate the valuation of the marginal consumer as a function of the level of product safety, we obtain $$\begin{equation}\label{margval} \tilde{v}(x;\alpha,\beta_A,\beta_R)=\frac{\bar{v}+c(y_A^*)+\alpha \mathcal{L}(x,y_A^*)+\frac{1-\alpha}{\beta_R}\mathcal{L}(x,y_R^*)}{2}. \end{equation}$$(A.7) The implied level of output is distorted relative to the first-best outcome due to the supply from a monopolistic firm and consumers’ present bias. The valuation of the marginal consumer is lower when consumers are naive instead of sophisticated, leading to a greater output with naive consumers (despite the fact that the price charged to naive consumers is higher).10 Using (A.6) and (A.7) to restate (A.5), we can state the firm’s first-order condition for the optimal level of product safety as $$\begin{equation} Q(\tilde{v}(x;\alpha,\beta_A,\beta_R)) (\beta_R \alpha+1-\alpha)s'(x)=k'(x). \label{FOCsafetyI} \end{equation}$$(A.8) Matching the statements made in our main analysis, only when |$\beta_A=\beta_R=1$| applies will strict consumer liability for total harm (i.e., |$\alpha=1$|⁠) induce consumers to take optimal precaution and the firm to implement the socially optimal level of product safety for the given level of output. In addition to the insights obtained in the main text, we find that (i) present bias bears on the level of output, (ii) naive consumers demand more of the product than sophisticated consumers (as naive consumers mistakenly anticipate private-cost-minimizing precautions), and that (iii) naive consumers obtain safer products (as output with naive consumers is higher than that with sophisticated consumers). Footnotes 1. " The existence and policy relevance of present bias has been the subject of an ever growing empirical literature. Early work is reviewed in DellaVigna (2009), for instance. More recently, Wang et al. (2016), for example, provide measurements of present bias and patience for 53 countries, highlighting that the heterogeneity between countries is much more pronounced in terms of present bias. Friehe and Pannenberg (2020) explore potential sources of differences in time preferences. 2. " We depart from Hay and Spier (2005) by focusing on a monopolistic instead of a perfectly competitive market structure. Importantly, this departure is inconsequential for the induced care incentives when consumers are time-consistent. 3. " Note that the damages multiplier does not induce the first-best outcome in a setup in which only some consumers are served by the firm because the multiplier exacerbates an output distortion (while it still induces socially optimal care levels for the given level of output). 4. " Focusing on a monopolistic firm is a common approach in the literature on the economics of liability (see, e.g., Daughety and Reinganum, 1995, 2013a; Spier, 2011). We thereby abstract from additional strategic effects due to the interdependence among firms in an oligopoly. In our discussion in Section 5, we briefly refer to the alternative benchmark scenario, that is, the case of a competitive firm. 5. " Zeiler (2019) documents very well the heterogeneity of opinions in this regard. 6. " The idea of a damages multiplier was prominently raised in the rationalization of punitive damages (Polinsky and Shavell, 1998), for example. 7. " For instance, Chu and Huang (2004) emphasize that payments exceeding the level of harm are in practice awarded only for “outrageous” conduct, which further questions the practical implementability of any multiplier in excess of one. 8. " The intuition runs as follows: conditional on consumer compliance, the firm would prefer to implement |$x^{O}$| but cannot do so without inducing consumer non-compliance. Likewise, conditional on consumer non-compliance, the firm would prefer to implement only |$x_1^*$| but induces non-compliance only with a greater product safety. The curvature of profits ensures that the firm will pick that limit value of product safety for the respective condition. 9. " It is important to note that the performance of strict liability with a defense of contributory negligence is not compromised when the firm serves only a part of the market (as was true for the damages multiplier). When the consumer complies with the precaution standard, the firm takes full expected harm into account. 10. " Sophisticated consumers with |$\beta_A=\beta_R$| consume less than in the benchmark with time-consistent consumers—which already features too little consumption due to the supply from a monopolistic firm—because they anticipate that they will not minimize |$c(y)-\alpha p(y)$| with their precaution (i.e., they correctly predict their future costs from using the product). Additionally, there is a direct effect when |$\alpha<1$| from the firm’s shifting expected liability payments via the price (the last term in the numerator of (A.7)). 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Published: Apr 1, 2020

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