Chapter 9: As Much as Your Life is Worth


Your money or your life.

Take my life; I'm saving my money for my old age.


In chapter 3 I described one approach to producing efficient outcomes: If someone imposes costs on others, charge him an amount equal to the damage done in order to force him to take those costs into account in his decisions. This chapter will deal with a problem raised by that approach, one that may have occurred to you during the discussion of auto accidents in chapter 7. Some accidents destroy cars; we know, at least roughly, how to measure the cost of a car. But other auto accidents destroy people. How does one price a life?

Economists measure costs and value by revealed preference, by people's actual behavior. If someone offered to buy your heart for a million dollars, even ten million, it is unlikely that you would agree. By that standard it looks as though most people put an infinite value on their life.

But consider the decision of how often to get a medical checkup or have your brakes checked. Such activities buy you life in the form a slightly lower chance of an undetected heart blockage or a lethal skid. If life is of infinite value to you, you ought to divert time and money from activities that do not prolong your life to activities that do as long as the latter have any payoff at all, however small.

For the same reason, somebody who puts infinite value on his life ought to avoid all dangerous activities: hang gliding, skiing, or driving a car for any purpose not directly related to survival. He should not smoke, drink only on doctor's orders, and never touch ice cream or spare ribs. Exercise should be half an hour on a treadmill, avoiding the risk of unlikely but potentially lethal accidents on a tennis court or a jogging track. The result would be a long life. If you call it living.


The Problem Isn't Multiplying by Infinity but Dividing by Zero.


That is not how the people I know act. It is not the way I act. I doubt it is the way you act.

Consider again your reaction to an offer of a million dollars for your life. Why do you refuse, and keep refusing even when the buyer offers to raise his price? The obvious answer is not because your life is of infinite value but because money is of no use to a corpse.

Suppose we switch to a probabilistic version of the same deal: Someone offers you a gamble based on the roll of a hundred-sided die. On any roll from 1 to 99 he pays you a hundred thousand dollars. If it comes up 100, he shoots you. You might still decline the offer, but not as fast. If he raises the offer to a million dollars and a thousand-sided die, you may change your mind.

The decrease in the probability of death from 100 percent to 1 percent or .1 percent explains why the price you charge falls, but not why it falls from infinity to a million dollars, perhaps much less. What explains that is the increase in the chance of being able to collect the money from zero to a near certainty. Zero times a hundred million dollars is still zero. Ninety-nine hundredths times a hundred thousand dollars is a substantial sum.

This way of looking at the problem also explains why people sometimes do accept a near certainty of death—charging into machine-gun fire in the First World War, piloting a kamikaze bomber in the Second, or giving someone dear to you the last seat in the lifeboat. Those are all cases where you can die and still collect. One can even imagine someone accepting a million dollars in cash for his life if there were some person or cause sufficiently important to him that could make good use of the money. What makes no sense is accepting a million dollars for your life with the intention of spending the money on yourself.


Back to Law


The economic question of how to value a life is also a legal question. If someone accidentally destroys your car under circumstances in which he is legally liable, he owes you the price of a new car. What should he owe you—or your heirs—if he also destroys you?

The traditional common law answer, oddly enough, was "nothing." This may have been a consequence of the unwillingness of tort law to treat civil claims as transferable property, which meant that your claim for being killed died with you. Alternatively, it may have been a result of viewing tort damages as compensation to the victim rather than disincentive to the tortfeasor. It is hard to compensate someone for being dead. Legal reforms in the mid-nineteenth century made it possible for your wife and children to sue for the cost to them of your dying, roughly speaking for your future income minus the amount of it that you would have spent on yourself. But nobody could claim for the cost to you of losing your life.

Suppose, however, that we are constructing our own legal system along the general lines suggested by Pigou's analysis of externalities—ignoring, for the moment, the problems with that analysis raised by Coase. We want to impose a cost on those whose actions destroy or injure people for the same reason we want to impose a cost on those whose actions destroy or injure property, in order that the actor will take proper account of those consequences in deciding what to do. How, in principle, should we set the price?

Start with an actor who already bears all of the costs: yourself, deciding whether to take risks, spend money on medical care, or in other ways trade off your own life against other values. Even quite risky activities only rarely result in immediate death, so you expect the payment for the little bit of life you are sacrificing to be in a form that you can almost certainly collect. Under those circumstances, your behavior demonstrates that your value for your life is high but not infinite.

How might we measure that value? One way is by looking at the wage premium for risky professions. Trucking companies have to pay more to get people to drive trucks full of dynamite than trucks full of sand. By estimating the risk of death in risky jobs and measuring their wage premium relative to safer jobs that are otherwise similar, we get at least a rough estimate of the value of life to the people accepting those risky jobs: the amount they have to be paid to take them. Such calculations have been done; the result is a value of life, for ordinary Americans, ranging from about one to ten million dollars.

This is an imperfect measure for at least two reasons. First, the people who accept such jobs are the ones most willing to do so; all else being equal they will be the ones with the lowest value for their lives. Second, driving a dynamite truck may be less pleasant work than driving a truck loaded with sand; the driver is under more pressure, which some will see as an extra cost. Of course, there may also be people who regard the tension as a benefit—the sort of people who get their fun jumping out of airplanes or climbing cliffs. The protagonist of Neil Stephenson's Snow Crash, set in the twenty-first century, delivers pizza for the Mafia. He takes the job precisely because the Mafia has converted pizza delivery into a high-risk, high-pressure profession.

Problems such as these imply that estimates of value for life based on the risk premium for risky professions might be off in either direction. But they still provide at least a first approximation, and one that can be improved by more detailed studies.

If we accept this approach to calculating the value of life, we seem to have a simple solution to the optimal incentive problem. If someone causes another person's death under circumstances that make him liable for the loss—just what that means will be taken up in chapter 14—he owes his victim's estate damages corresponding to the value of the victim's life to himself, as reflected in his behavior. If we somehow know that the victim would have required an extra thousand dollars a year to agree to drive a dynamite truck instead of a sand truck, and if we also know that driving a dynamite truck increases the probability of dying each year by a tenth of a percentage point, the tortfeasor owes a million dollars to the victim's estate, since a million dollars times a probability of one in a thousand is equal to a thousand dollars.

To see the implications of this legal rule, imagine that you are considering dynamiting some tree stumps, which is a lot less work than digging them up. The only catch is that there is one chance in ten thousand of a lethal accident. If it happens, since the victim values his life at a million dollars, you will owe his heirs a million dollars in damages. In deciding whether to go ahead, you must add to the cost of the dynamite an additional expected cost of a hundred dollars, one chance in ten thousand of a million-dollar liability. That is precisely the price the victim would have required to accept a one in ten thousand chance of death. It is also what a fully informed insurance company would charge you (plus something extra for overhead) to insure your stump-removal project against liability. You use dynamite if it produces net benefits, if the cost savings to you outweigh the risk to third parties. That is the efficient outcome. Through the magic of the tort system, you have been induced to make the same choice the victim would have made.


Optimal Deterrence, Optimal Insurance, and Never the Twain Shall Meet


This provides the correct incentive to people not to take chances with other people's lives, but there is still a problem. Suppose the victim has no dependents and no worthy causes he cares about. The only thing he can buy with the million dollars (specified in his will, which happens to provide for the unlikely contingency that he will be tortiously blown up) is a spectacular tomb. We have provided the right deterrence to the tortfeasor, but we have done it at the cost of transferring money from people who can use it to someone who cannot.

The example is an extreme one, but it points to a general problem. Tort liability serves at least two different functions. One is to deter actions that injure others. Another is to compensate the victims, to insure them. There is no reason to expect the optimal damage payment for purposes of deterrence to be equal to the optimal damage payment for purposes of insurance.

Consider again our hypothetical victim. Given the choice, he would buy no life insurance, since money is more useful to him alive than dead. The fact that his optimal insurance is zero does not mean that someone who kills him has done him no damage.

This way of putting the question also suggests the solution. A potential victim with no need for life insurance wants to transfer his damage payment from the future in which he gets blown up to the future in which he is alive to enjoy the money. Our society has a very large industry in the business of transferring money from one future to another: the insurance industry. When you buy fire insurance you are giving up money in a future in which your house does not burn down in order to collect money in a future in which it does, transferring wealth from one future to another.

The potential victim whose damage award will overcompensate him solves the problem not by buying insurance but by selling it. In exchange for a fixed payment now he transfers to an insurance company the right to collect damages if he is ever tortiously killed. If he faces one chance in a thousand of being tortiously killed and getting a million dollars in damages, and if, for simplicity, we ignore the insurance company's operating costs and assume it buys and sells insurance at its actuarial value, the company will pay him a thousand dollars. They have bought life insurance on him, but insurance that only pays off if his death is the result of someone else's tort. To put the same thing in different words, they have bought an inchoate tort claim, a claim for a tort that has not yet happened.

This set of institutions not only provides potential tortfeasors with the right deterrence, assuming that we can estimate the value of life reasonably accurately, it also gives the payment to the victim when it is most valuable to him. If he wants to have money if he dies, if, in other words, he wants life insurance, he gets the damage payment then. If he doesn't want it then, he transfers the money back to when it is most useful to him.


A Perfect Information Fantasy and How to Get It


Imagine how we would handle risky activity in a world where all risks were known. Every time you imposed a risk on someone else, you would owe him the amount of money he would have required to voluntarily accept that risk. Not only would that give people whose actions might injure others the right incentives, it would also achieve, ex ante, the nominal objective of tort liability—compensating victims at the expense of tortfeasors—an objective that cannot be achieved ex post, since we have no way of adequately compensating someone for the loss of his life.

Now consider the system described in the previous section, with one addition: Potential tortfeasors buy insurance against their liability. The cost to me of risks I impose on others shows up in my insurance premium, representing the insurance company's estimate of the risk that they will have to pay out on the insurance. The cost to you of risks others impose on you is balanced by the money you can get by selling the right to collect damages if you are killed. It is just the result described in the previous paragraph, except that we are now in a world where risks can be estimated but not known with certainty, with the insurance companies providing a market mechanism to estimate the relevant risks.

Why do these institutions not exist; why is there is no market on which you can sell your future claims for the tortious loss of your life? There are two answers. The first is that, as I mentioned earlier, traditional common law did not award you or your estate damages for the loss of your life, on the principle that your claim dies with you. This has changed in recent decades, as states have passed survival statutes allowing your heirs to collect damages for your de ath. While these laws permit your heirs to claim for your pain and suffering, they do not usually permit a claim based on the value to you of your life; as a result, they badly understate the real loss. The second and related reason is that the common law does not treat tort claims as transferable property. While you can, in principle, sell life insurance on yourself, subject to the restrictions of your state's regulatory regime, you cannot sell your claim to future damage payments.

This is an issue we will return to again in chapters 18 and 19. In the former I will argue that making tort claims, including claims for torts that have not yet occurred, marketable would help solve some of the problems of using tort law to replace criminal law. In the latter I will argue that the failure of the common law either to permit claims based on the value of the victim's life to himself (what have recently come to be called "hedonic damages") or to treat tort claims as property is evidence against Posner's thesis of the efficiency of the common law.


Damages for Injury


We have been considering the problem of compensating people for being killed, but similar arguments apply to lesser injuries as well. When someone is tortiously blinded or crippled, he is made worse off in at least three different ways. The injury imposes pecuniary costs: medical bills, lost wages, and the like. It imposes nonpecuniary costs; life is less fun from a wheelchair. Finally, the injury reduces the value to the victim of additional money, at least once the medical bills and the wheelchair are paid for, since many of the ways in which he could have used money in the past are no longer available to him.

How might we measure his loss in order to calculate the damages that someone responsible for it would owe? One way is to simply measure pecuniary loss: lost wages, medical expenses, and the like. To a considerable degree, this is the traditional common law approach; its obvious advantage is that these are the easiest costs to measure. Its obvious disadvantage is that it may badly underestimate total costs. Very few of us would be willing to give up our eyesight, or our legs, in exchange for full medical expenses plus lost wages.

An approach more consistent with the language of tort law would be to require the tortfeasor to fully compensate the victim, to "make him whole." That would mean paying him enough so that a potential victim, knowing he would be compensated, would not care whether or not the accident happened. One practical problem with doing that is that injuries not only make people worse off, they also make money less useful to them. Even if it were possible, by enormous payments, to just barely recompense the victim, it is not obvious that the creation of blind billionaires living in profligate luxury, and so just barely compensating with pleasures that large amounts of money can buy for lost pleasures that it cannot buy, is a good idea.

Another way of putting this is to observe that full compensation represents more insurance than a potential victim would want to buy. To see this, imagine that the victim first receives full compensation for his pecuniary losses, so that he can afford to consume exactly the same things as if he had not been injured. Since some of those things (color television if he has been blinded) are no longer useful to him, he will transfer some of his expenditure to things that before the accident were not worth their cost. He is worse off, since he is buying a thousand dollars of gourmet dinners worth a thousand units of happiness instead of a thousand dollar color television that would be worth two thousand—if he could see it. With fewer ways of spending the same amount of money, he is getting less happiness per dollar.

If we now award him enough more money to return him to his old level of happiness, he will be using that money to buy things even less valuable to him, with the result that the last dollar will provide even less happiness. This is a less extreme version of the reason you would not sell your life for a million dollars. It implies that the price for which you would sell your eyesight is high, perhaps infinite.

I have already offered the solution to this problem in the more extreme case: Award damages based on what potential victims would have accepted in exchange for the risk. Since that may well overcompensate from the insurance standpoint, permit potential victims to transfer part of their future awards to their uninjured state by selling part of their damage claim in advance.

The same solution applies here. It implies damage payments higher than mere compensation for pecuniary loss, since after suffering an injury and being compensated for pecuniary loss the victim is still worse off than if the injury did not occur. It implies damage payments lower than those that would fully compensate since, by allowing the victim to shift some of the money to his uninjured state, we increase the value to him of the compensation. The consequence, as in the earlier case, is full compensation ex ante. Ex post, potential victims who do not get injured are better off as a result of the risk imposed on them; they have the money from selling part of the damage claim for an accident that did not happen. Actual victims are worse off as a result of the risk.

I believe I have now solved the puzzle with which I started this chapter: How can we adequately compensate people for loss of life or limb. The answer is that, ex post, we often cannot and usually should not. But our inability to compensate ex post does not mean that life is infinitely valuable, nor does it imply that we should avoid any activity that imposes any risk of death on other people, any more than it is a reason to avoid any act that imposes any risk of death on oneself.

In both cases, the relevant question is whether the cost of the risk is worth paying for the associated benefit. We make that calculation implicitly for ourselves every time we drive, or eat ice cream, or decide to have a baby. We could force people to make the same calculation for risks they impose on others by imposing ex post liability sufficient to reimburse potential victims ex ante.

[article link:my Article on fair compensation for death or injury]

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