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Willingness to Pay, Death, Wealth and Damages

20 Mar 2011-American Law and Economics Review (Oxford University Press)-Vol. 13, Iss: 1, pp 45-102

AbstractWillingness to Pay, Death, Wealth and Damages (November 11, 2010) American Law and Economics Review (forthcoming 2011) Ariel Porat & Avraham Tabbach * When people face the risk of death, and when they ascribe no value to their wealth post-death, they over-invest in precautions in order to reduce that risk. There are two main reasons for such over-investment. First, people under risk of death discount their risk-reduction costs by the probability of death following precautions. Second, people facing the risk of death consider the consumption of their wealth when alive to be part of their benefit from risk- reduction. From a social perspective, people's wealth does not cease to exist after death. Therefore, discounting costs by the probability of death and taking into account the benefit of wealth-consumption are socially inefficient. But more interestingly, even from the perspective of the individual facing the risk of death, the investment in risk reduction is only optimal as a second-best alternative. We show that if markets were complete and people could contract with an annuity firm, who would inherit their assets upon death while paying them a sum of money during their lifetimes in accordance with the expected value of the inheritance, such contracts would make those people better off and, more importantly, would align the private and the social incentives to invest in risk reduction. Furthermore, we show how the insights developed in the paper should significantly change the application of Willingness to Pay (WTP) as a criterion for valuing life. In particular, we suggest that the WTP be discounted by the ex-post probability of death and that the value of life be determined irrespective of wealth. Finally, we argue that the results derived from traditional tort models for both unilateral and bilateral accidents should be substantially revised when applied to fatal accidents. In particular, we show that in bilateral accidents, contrary to conventional wisdom, negligence and strict liability rules lead to the same inefficient equilibrium. We also demonstrate how liability rules could be modified to increase efficiency. Ariel Porat is the Alain Poher Professor of Law at Tel Aviv University and Fischel-Neil Distinguished Visiting Professor of Law at the University of Chicago. Avraham Tabbach is Assistant Professor of Law at Tel Aviv University. Special thanks are due to Omri Yadlin, for helping us in developing the ideas underlying this paper, and to Steve Shavell for invaluable comments and suggestions. For very helpful comments and discussions, we thank Benjamin Alarie, Ronen Avraham, Oren Bracha, Omri Ben Shahar, Mira Ganor, Mark Geistfeld, David Gilo, Massimo D’antoni, Sharon Hannes, Alon Harel, Shelly Kreiczer-Levy, Bruce Hay, Saul Levmore, Jacob Nussim, Mitch Polinsky, Eric Posner, Ricky Revesz, Nicholas Quinn Rosenkranz, Ariel Rubinstein, Kathryn Spier, Steve Sugarman, Lior Strahilevitz, Richard Zeckhauser, the participants in workshops at the universities of Bar Ilan, Chicago, Harvard, Siena, Stanford, Texas and Yale, the participants at the Israeli Law and Economics Annual Meeting of 2010, at the NYC Tort Group at New York University, and at the Siena-Toronto-Tel Aviv Workshop in Law and Economics of 2010. Finally, we are grateful to Omer Yehezkel for providing excellent research assistance.

Topics: Poison control (53%), Tort (53%), Strict liability (51%), Israeli law (50%), Inheritance (50%)

Summary (5 min read)

Introduction

  • People with no family often do not leave much wealth behind them after their deaths.
  • That latter value, however, is not necessarily a social value, because other people could consume this wealth as well, once the particular individual under risk dies.
  • Once one has accepted the discounting costs effect and inflating benefits effect identified in the paper, one understands that the conventional law and economics analysis is misguided.

I. Self-Risk-Reduction

  • Conventional law and economics suggests that rational people take efficient precautions to reduce the risk of death to themselves, so long as this does not produce external effects on others.
  • For the purpose of simplicity and clarity, the authors will assume that people ascribe no value to their wealth upon death.
  • Later, in section I.E, the authors will show that their arguments are also valid in the more general case in which individuals are altruistic and do ascribe value to their wealth after death.
  • Formal proofs of the arguments presented below can be found in Appendices A and B. 7 See Viscusi, 2007, p. 598.
  • Compare also Posner (1992, p. 163: ―When … the person taking precautions and the person who may be injured if they are not taken are the same, the optimal precautions will be achieved without legal intervention.‖).

A. Discounting-Costs Effect

  • Example 3. Eliminating Risks by the State. 28.
  • The proposition that the WTP to eliminate risk is linear in relation to the initial probability of death, while the WTP to reduce risk by a small percentage is nonlinear, may appear confusing.
  • Here, the social, rather than the private, value of those lives should be taken into account, and any value an individual ascribes to his life that is transferable to other individuals should not count.

C. Self Risk Reduction versus Redistribution

  • As the authors have argued above, individuals will over-invest in reducing their risk of death, since they ascribe no value to their wealth after death, although its social value is positive.
  • The authors explained that since individuals ascribe no value to their wealth after 14 Indeed, one can imagine situations where people’s investment in reducing the risk of death is inefficiently too low from a social perspective, even if they take their ability to consume their wealth into account, since they confer much benefit on society.
  • While there is some superficial resemblance between the two, they are distinct from one another in several important respects.
  • According to the redistribution argument, it is only the consumption by the rich, but not the poor, which could raise a social welfare concern.
  • 18 Finally, the redistribution argument calls for determining a social sub-optimal distribution of wealth in society, while their argument, as the authors make clear in the next Section, also calls for determining a sub-optimal allocation of resources by the individual over his lifetime.

D. Correcting the Inefficiencies

  • This is a problem not only for society, but also for A himself (i.e., A himself may agree that he is investing too much given the circumstances).
  • Since A ascribes no value to his wealth after death, and since he has a strong preference for living, he will invest excessively in protecting his life.
  • As will be explained below, the problem stems from the fact that contingent claims markets are incomplete; indeed, a market mechanism, which the authors call "improved annuity", would make A better off, bring down A's investment in risk reduction, and correct the social inefficiencies.
  • 19 Thus the improved annuity mechanism shows that A’s investment in self-risk reduction in the absence of improved annuity is not Paretooptimal .
  • Alternatively, if market mechanisms fail, an individual's over-investing in self-riskreduction can be corrected by using direct steps.

1. Market Mechanisms

  • The straightforward solution for the problem of overinvestment in safety is improved annuity (IA).
  • In that case, from A's ex ante perspective, he would be better off without the IA payments; at this point in time, it would be better for A—again, from his ex ante perspective—to have less resources for risk-reduction than what he would have but for the IA payments.
  • Alternatively, the annuity firm and A can agree that the amount that A would get if he survives would depend on his investment in risk-reduction.
  • With a viatical settlement, A purchases B’s life insurance policy (or part of it) at a price that is less than the death benefit of the policy.

2. State Intervention

  • The authors believe that the answer is probably no, for reasons related to the theory of the second-best.
  • Aside from the infringement of individual autonomy and privacy, which may be sufficient reason in itself to preclude state intervention, any intervention in people’s risk-reduction measures when at risk of death would encourage them to shift resources from riskreduction to consumption.
  • In other words, instead of over-investing in risk-reduction, they would over-consume.
  • This problem could theoretically be resolved if consumption were regulated, or taxed, but for both substantial and practical reasons, that is not a reasonable solution.

E. Generalizing the Arguments

  • So far the authors have assumed that people ascribe no value to their wealth after death.
  • Why the arguments pursued in this paper are valid also in cases where people do ascribe value to their wealth after death, but that value is lower than the value they ascribe to it when they are alive, is self-explanatory.
  • 22 strict sense the divergence between the private and the social perspective is unchanged.
  • That is because from a social perspective altruistic behavior creates a double benefit: the benefit to the benefactor from his altruistic behavior, and the benefit derived by the beneficiaries of the altruistic behavior.
  • This paper is about the risk of death, but some of its insights could apply to other situations where individuals face a risk other than death, that could affect their marginal utility of money.

II. Willingness to Pay and the Value of Life

  • The authors turn from the private to the public arena.
  • It is the state (or the government), not the individual, that should decide how 24 Things become more complicated if the heirs who are expected to inherit the individual under risk of death are also altruistic toward him.
  • Note that in this paper the authors do not discuss the value other people ascribe to the life of the individual under risk of death.
  • 23 much to invest in people's safety and accordingly needs to value people's lives.

C. Policy Implications

  • WTP is commonly measured by agencies by looking into both the stated and revealed preferences of individuals.
  • As long as the ex post probability of death is small, ignoring the discounting costs effect does not create a meaningful distortion in valuing people’s lives based on WTP.
  • They probably do so in the belief that such application is fairer and more just than ascribing different values to the wealthy and the poor (Revesz & Livermore, 2008; p. 14).
  • The authors remind their readers that their analysis ignores 33 See, for example, Weinstein, Shepard and Pliskin (1980, p. 384); Philipson, Becker, Goldman and Murphy (2010).
  • 30 possible positive externalities associated with individuals’ lives as well as the issue of productivity which sometimes is correlated with wealth.

III Applications to Tort Law

  • In particular, the authors analyze the effects of different liability rules on the incentives of potential injurers and victims to take precautions in situations where the harm is the victim's death.
  • The authors assume that both injurers and victims are risk-neutral with respect to wealth and strangers to one another.
  • The authors further assume, as before, that victims ascribe no value to their wealth after their deaths.
  • The authors analyze situations of unilateral and bilateral accidents and show that the fundamental results of the law and economics literature should be substantially revised following their analysis .

A. Unilateral Accidents

  • In unilateral accidents the injurer can take precautions to reduce the expected harm of his activity; by contrast, the victim can do nothing to affect the expected harm.
  • For similar reasons, the injurer's standard of care under a negligence rule should not be dependent on the victim's wealth:.
  • The standard of care should reflect the magnitude of the risk created by the injurer, since the higher that risk the higher the expected harm.

Strict Liability

  • The standard results of law and economics, namely that under a rule of strict liability victims do not take any precautions, do not hold when the harm is not fully compensable, as is the case with many types of bodily injury.
  • These other references mentioned by Arlen analyze the standard results.
  • In such cases the victims' inclination to take excessive precautions to reduce the risk of death would offset their inclination to take deficient precautions with respect to the risk of compensable harms.
  • Thus, in contrast to the view of conventional law and economics, in wrongful death cases, under a rule of strict liability, when damages equal social harm, injurers take efficient precautions, while victims take excessive precautions.
  • Changing the amount of damages, however, would affect the injurer’s incentives to take precautions.

Negligence

  • Under negligence, the injurer is liable for damages in the event of an accident if and only if he took less than due care.
  • Proposition (8) should be contrasted with standard results in the law and economics literature concerning pecuniary losses.
  • The injurer behaves e¢ ciently given that the victim takes too much care.
  • The victim decreases his care not because his care becomes less e¤ective as the injurer takes more care.
  • 58 the injurer to take e¢ cient care by the threat of liability, and since the victim is not compensated, the victim bears the residual harm and therefore takes e¢ cient care as well.

C. Transaction Costs

  • The authors analysis shows that in unilateral accident cases, efficiency mandates that damages, as well as the injurer's standard of care, should be set lower than what the WTP-based method dictates.
  • It also shows that in bilateral accident cases, first-best efficiency cannot be achieved, but second-best efficiency dictates that the injurer’s standard of care and damages (if causation is properly taken into account) should be set higher than what is required by the best solution.
  • He is therefore willing to pay a huge amount of money to induce the doctor who is performing the operation to take excessive precautions, much above the efficient level.
  • If transaction costs between the parties were prohibitively high, following their analysis, the patient's WTP should have been adjusted for the two aforementioned effects, and both damages and the doctor's standard of care would have been set lower than what the patient would have wanted.
  • But if transaction costs are low, those adjustments would fail to achieve their goal.

Conclusions

  • When people take too few precautions to protect themselves, it is often said that they lack information about the risks to their lives or an understanding of their own good.
  • Arguably, this is not a problem that the law should care about: so long as people do not externalize costs to third parties and so long as they have not lost their minds, they are free to use their own resources as they see fit.
  • As the authors have shown here, the discounting-costs effect and inflating-benefits effect produce a discrepancy between the private and social perspectives regarding risk-of-death reduction, for the precautions taken by people at risk of death are inefficiently excessive from the social perspective.
  • When it is just about people's choices regarding their lives, the authors believe the state should not intervene, except to facilitate the creation of complete markets and enable people to enter into IA contracts if they so desire.
  • But as the authors have explained, their conclusions would not change in substance if they relaxed this assumption and assumed instead that those individuals ascribe value to their wealth after death.

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UC Berkeley
Law and Economics Workshop
Title
Willingness to Pay, Death, Wealth and Damages
Permalink
https://escholarship.org/uc/item/1h40h660
Author
Porat, Ariel
Publication Date
2010-11-01
eScholarship.org Powered by the California Digital Library
University of California

Willingness to Pay, Death, Wealth and Damages
(November 11, 2010)
American Law and Economics Review (forthcoming 2011)
Ariel Porat & Avraham Tabbach
*
When people face the risk of death, and when they ascribe no value to their wealth post-death,
they over-invest in precautions in order to reduce that risk. There are two main reasons for
such over-investment. First, people under risk of death discount their risk-reduction costs by
the probability of death following precautions. Second, people facing the risk of death
consider the consumption of their wealth when alive to be part of their benefit from risk-
reduction. From a social perspective, people's wealth does not cease to exist after death.
Therefore, discounting costs by the probability of death and taking into account the benefit of
wealth-consumption are socially inefficient.
But more interestingly, even from the perspective of the individual facing the risk of
death, the investment in risk reduction is only optimal as a second-best alternative. We show
that if markets were complete and people could contract with an annuity firm, who would
inherit their assets upon death while paying them a sum of money during their lifetimes in
accordance with the expected value of the inheritance, such contracts would make those
people better off and, more importantly, would align the private and the social incentives to
invest in risk reduction. Furthermore, we show how the insights developed in the paper
should significantly change the application of "Willingness to Pay" (WTP) as a criterion for
valuing life. In particular, we suggest that the WTP be discounted by the ex-post probability
of death and that the value of life be determined irrespective of wealth. Finally, we argue that
the results derived from traditional tort models for both unilateral and bilateral accidents
should be substantially revised when applied to fatal accidents. In particular, we show that in
bilateral accidents, contrary to conventional wisdom, negligence and strict liability rules lead
to the same inefficient equilibrium. We also demonstrate how liability rules could be modified
to increase efficiency.
*
Ariel Porat is the Alain Poher Professor of Law at Tel Aviv University and Fischel-Neil
Distinguished Visiting Professor of Law at the University of Chicago. Avraham Tabbach is
Assistant Professor of Law at Tel Aviv University. Special thanks are due to Omri Yadlin, for
helping us in developing the ideas underlying this paper, and to Steve Shavell for invaluable
comments and suggestions. For very helpful comments and discussions, we thank Benjamin
Alarie, Ronen Avraham, Oren Bracha, Omri Ben Shahar, Mira Ganor, Mark Geistfeld, David
Gilo, Massimo D’antoni, Sharon Hannes, Alon Harel, Shelly Kreiczer-Levy, Bruce Hay, Saul
Levmore, Jacob Nussim, Mitch Polinsky, Eric Posner, Ricky Revesz, Nicholas Quinn
Rosenkranz, Ariel Rubinstein, Kathryn Spier, Steve Sugarman, Lior Strahilevitz, Richard
Zeckhauser, the participants in workshops at the universities of Bar Ilan, Chicago, Harvard,
Siena, Stanford, Texas and Yale, the participants at the Israeli Law and Economics Annual
Meeting of 2010, at the NYC Tort Group at New York University, and at the Siena-Toronto-Tel
Aviv Workshop in Law and Economics of 2010. Finally, we are grateful to Omer Yehezkel for
providing excellent research assistance.

2
Introduction
People with no family often do not leave much wealth behind them after their deaths.
People with family leave, on average, much more.
1
This might seem odd: people
without family would be expected to spend less on living expenses than people with
family and therefore to leave more wealth. But in fact, it is not strange at all: there is
no reason for someone to leave anything after his death, if, as is often the case, the
value he ascribes to his wealth after death is less than the value he ascribes to it while
alive.
2
Should this bother us? Maybe not. After all, individuals without family choose
how much to work and how much to spend, and if they leave no wealth behind after
their deaths, this presumably indicates that they planned their lives wisely. In
economics terms, they fully internalized all the costs and benefits of their lives and
therefore lived efficiently from both private and social perspectives.
But sometimes, when people are subject to risk of death and, in particular, to
substantial risk of death, the fact that they ascribe much less value to their wealth after
they die than when alive should bother us. In this paper we discuss two reasons why it
should bother us. Both relate to investment in reducing the risk of death. The first
reason is that people discount the costs of reducing their risk of death by the
probability that they will die anyway. We call this the ―discounting costs effect‖. The
second reason is that people ascribe a high value to their lives not only because they
highly value their lives as such, but also because they value the consumption of their
wealth while they are alive. That latter value, however, is not necessarily a social
value, because other people could consume this wealth as well, once the particular
individual under risk dies. Therefore, people ascribe a higher value to their lives than
the social value. We call this the ―inflating benefits effect‖. For the sake of simplicity
we will assume throughout the paper that people ascribe no value to their wealth after
1
See for example Wilhelm (1996) "Hundreds of billions of dollars per year are bequeathed by
people in the United States, and about two thirds of this passes from parents to children".
Another form of this observation is that people with family often carry life insurance while
people without family do not.
2
Empirical evidence indicates that the value individuals place on bequests is less than the value
they place on consumption during their lives. See Viscusi & Moore (1989).

3
death, but, as we will explain, our arguments are equally valid in the more general
case (see Section I.E.).
To illustrate and better understand the discounting costs and inflating benefits
effects, consider the following example:
Example 1. The Operation. Individual A is seriously ill. He knows his
chances of survival are estimated at 40%. A is a wealthy person and has no
family. His wealth amounts to $4M. He ascribes no value to his wealth after
his death. A decides to spend $500,000 on an operation that will increase his
chances of survival to 50% (i.e., by 10%). Is such an investment efficient
from a social perspective?
Conventional law and economics wisdom suggests that the answer is yes,
since A bears the costs and benefits of his investment. However, upon deeper
reflection, no would seem to be the correct answer. The first reason is the discounting
costs effect: A's investment of $500,000 does not reflect his true private costs, and
therefore it does not and cannot represent the true value A ascribes to his life. In
particular, A discounts the $500,000 he is willing to spend by the probability that he
will die after undergoing the operation (hereinafter: "ex-post probability of death"),
because he ascribes no value to his wealth after his death. So the true private costs to
A are only $250,000 ($500,000*50%). From a social perspective, however, the true
social costs of A’s investment is, of course, the full $500,000 (with no discount for the
probability of death). The fact that A ignores the value of his wealth after his death
creates a divergence between the private and social goals of maximizing welfare.
The second reason why A's spending on health is socially inefficient is the
inflating benefits effect: A ascribes a higher value to his life than what society
ascribes to it. Specifically, the value A ascribes to his life is composed of two
components: first, the value A ascribes to his life qua life and, second, the value A
ascribes to his ability to enjoy life through the consumption of his wealth. Assume, for
example, that the value A ascribes to his life qua life is $1M, and the value he ascribes
to his ability to consume his wealth is its equivalent in dollar terms, namely $4M. A,
who ascribes no value to his wealth after death, does not take into account the simple
fact that even if he should die and therefore cease to enjoy the consumption of his
wealth, other people will consume and enjoy it. Consumption by others of A’s
resources has, of course, social value. Since A ignores that social value, his decision
to invest resources in reducing his risk of death cannot reflect the social value of such
risk-reduction. In particular, A's investment in the operation reflects the value of his

4
life qua life ($1M) plus the value of his ability to consume his remaining wealth
($3.5M, which is left after spending $500,000 on the operation). But from a social
perspective, A’s life is worth only $1M. A's ability to consume his wealth has a
private, not a social, value, since A’s wealth is transferable and can be consumed by
other people. Thus, there are two distortions that have induced A to invest $500,000:
first, he discounted the $500,000 social costs of risk reduction by 50%, and second, he
inflated the social value of his life, which is $1M, by $3.5M. If only social costs and
social benefits had determined A’s investment in risk reduction instead, he should
have spent on the operation no more than $100,000 (10%*$1M), which is the
expected social benefit of the operation.
The above two effects imply that individuals will over-invest in reducing the
risk to their lives relative to the socially efficient level of risk reduction. This
argument is distinguishable from the familiar utilitarian argument for redistribution, as
we explain at length below in Part I.C. One important distinction is that individuals
overinvestment in reducing risks to their lives is also inefficient from the perspective
of the individuals themselves. In particular, A who faces the risk of death would be
better off if he could enter into an annuity contract, under which he would undertake
to leave his assets to the annuity firm after his death, in return for an undertaking by
the annuity to pay A the amount of the expected value of the inheritance when A is
alive (hereinafter: ―improved annuity‖). As we will demonstrate in Part I.D, if A were
to enter into such an annuity contract, A would invest no more than $100,000 in
reducing his risk of death. In other words, his investment in reducing his risk of death
would conform to what society would like him to invest. Thus, as the potential
utilization of the improved annuity indicates, A’s investment in self-risk reduction in
the absence of improved annuity is not Pareto-optimal. While annuities (hereinafter:
regular annuity‖) are common in the market today, they do not adjust for the
expected value of the wealth the individuals utilizing them will leave after death, and
therefore do not remove the inefficiencies which we have identified above.
Should the state intervene and prohibit people from overinvesting in safety?
Or should the law generally create incentives for people to behave efficiently under
such circumstances? We briefly discuss these questions in Part I.D of the paper and
argue that while the state should not intervene, it should facilitate people's entering
into improved annuity contracts, if they choose to do so. We explain the difficulties in
establishing a market for such annuities, but argue that it is nevertheless a plausible

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