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