Wednesday, July 27, 2011

What is a life worth?

Well, on the one hand, it is priceless. But from an economic point of view, a life is only worth about $4,000,000. Of that, $2,000,000 is the person’s worth to himself, and any others he provides for. The other $2,000,000 is the person’s worth to the rest of the economy. How much the rest of the economy benefits from his life’s labor. These figures are very rough, the mean, and of course vary greatly from person to person.

But how do we figure? First, we figure a person is only worth to an economy what he contributes to society. So we figure from a labor force of 150 Million we have a GDP of 14 Trillion. Round that to make the annual contribution to the economy per worker an even $100,000. Times say 40 years labor, about the number of years we suppose the average worker to work in a lifetime. $4,000,000. About half of that goes to the worker, about half to the rest of the economy. That’s the mean. The median worker only gets about$1.4M, but the median worker also probably contributes less than $4M. But what about the people who don’t contribute to the GDP? Well, here we’re counting them the same. Perhaps we shouldn’t. After all, someone who is compensated more than he contributes to society has a negative value to society. But we can also figure not all contributions to an economy show up in the GDP.

This has important ramifications. Such a heartless calculation actually suggests important ways individuals, and society, benefit. It means, for instance, that it is beneficial to individuals if we don’t spend too much saving a life. For instance, we wouldn’t want to spend $1 Trillion to save one life. Everyone else would be that much poorer. The economy would be out $999,996,000,000. That’s just dollars, but the equivalent in lives (valued at $4,000,000) is 249,999. It is 499,999 lives if we take the value a life is worth to the rest of the economy. We would be trading that many lives for one life. This is a bad deal for an economy. If it did this too much, it would literally kill itself.

What about pain and suffering? People are not just economic mechanisms. They have feelings. They feel pain. Can we put a dollar value on that? Sure. Let’s say $1 Trillion on a person’s feelings. Would we want to spend $1 Trillion on a person’s life? We just went through that calculation, and the point is the same. It would overvalue that life, and be a bad deal for the rest of the economy, which is to say, everyone else. It wouldn’t be fair. You can spend $1 Trillion to save one life, but you can’t spend $1 Trillion per person on everybody else, to save their lives. In fact, it works out you can only spend less than $100,000 per year per person. On average.

We can look at it this way: The economy exists to save, and is essentially saving, everybody’s lives, all the time. We’re all on life support. And since the average each worker contributes is less than $100,000 per year, that is all we can spend, on average, per person, per year.

This shows that it is important not to overvalue life. A society which takes excess precautions against the loss of life is the poorer for it. In a sense, it is literally killing more people to prevent the loss of fewer.

Hospitals already often use a rule of thumb. Their guideline is, (often) for spending up to $100,000 per year of life extension. This is equal to our total annual contribution to the economy per worker. For instance, consider extending the life of an elderly person. On the one hand, society typically does not gain any benefit. On the other, the elderly person has already contributed his share to society, and in a sense has earned this consideration, as a kind of savings. And it provides an incentive for people to keep working. But the figure of $100,000 per year is probably too high, considering the limits of the current health care system’s ability to supply health care, and the high rents already collected from it, and contributes to the high costs of medicine today. The rents imply that the benefits to the patient are far less than the $100,000 expended, so the actual value of life is lower than the nominal one. Indeed, if we consider the rent to be 40% of the system, that is, 40% is ‘wasted’ compared to the health care systems of other advanced economies, then the actual value of a person-year is $60,000. This suggests an economic value of $2.4M for a life, lower than our calculated value of $4M.

One interesting, if perverse, example of the extreme is the California death penalty, reinstituted in 1978, which has cost $308M per person (13) executed. Indeed, its total cost $4B, is a substantial share of the California deficit. We can make this calculation: $308M divided by $4M is the total destruction of the lifetime production of 77 people. In this case, the state is effectively killing (the productive capacity of) more people than the criminal ever did. From another perspective, the annual cost of $184M is equal to the total annual contribution of 1840 workers to the economy, almost twice as many as are actually on death row. The work of 1840 workers, wasted.

The EPA, now, gives a figure of $7.9 Million for the value of one life, almost twice the total economic value we calculated, or 4 times the net value of a life to the economy.

Not a very good trade off. Of course, there is also quality of life. Clean air is better than polluted air, even if the polluted air doesn’t kill you.

Regulations impose costs on producers. By not permitting the externalization of costs, (pollution of one sort or another for the EPA) which by the EPA’s calculations, would cause an increase in death (and disease,) things cost more to produce, and these costs are passed on to consumers. But it also results in less of those things being produced, and since resources are consumed in all production, less being consumed. So in the case of environmental regulations, other benefits accrue than just the saving of lives. Resources are conserved, other things which might be expensive to remedy are reduced. Such things might be considered to be included when the value of a life is overestimated.

Undervaluing life has its own costs. Negative externalities, excess pollution, is encouraged. Overproduction of stuff is encouraged. (This could be an argument for undervaluing life, where increasing the amount of stuff is equated to economic progress!) There are more accidents, as insufficient precautions are taken. There is loss of life and quality of life.

Note, when an economy is poorer, the capitalization per person, and what depends on it, the individual’s ability to contribute to society, thus the value of life, is less. Kenya for instance has a GDP per capita of $1600, $66B/41M but a labor force of 18M, so the average economic contribution per worker is about $3700, times 40 years or about $150K over a lifetime, (average life expectancy about 60, but do they have retirement?) so that is the mean economic value of a life, there.

Back to the US:
A child, on the other hand, has the potential to contribute $4,000,000 to society. But society has not yet invested in him. In fact, (our) society, on the average will invest somewhere around $350,000 in raising a child to adulthood, not counting the opportunity cost of parenting. Most of this cost is born by the family, so does not subtract from the $2,000,000 net contribution. A six year old, for instance, has about $70,000 invested in him, by his family: $60,000 direct costs, and $10,000 or so for his first year of schooling, which one way or another is borne by taxes. Now families are not the only ones to pay these taxes, so there is some subsidy of education by the rest of society. This omits cost- the opportunity cost to the self for his education, when, instead of capitalizing in himself, he could be doing something else.

In fact, it could be argued that the only real loss to society is this investment, and not the inferred profits society takes from his labor. And this investment is all society should be insured against. (This argument is also carried out in: )

Of course, the actual capitalization may be more or less than that figure, depending on the efficiency of parenting and the educational system, and the social system of the community. Much of the cost of the educational system now seems to be going to rent, judging from the reported decline in results. So the actual capitalization is less.

Further consideration indicates that the health care system may be considered part of the capitalization of individuals. Consider a child who needs a $50,000 surgery to survive and be productive. He is capitalized, by age 20, to $400,000, and so similarly for all medicine. Currently about $2.4T total health care expenditure per year, or $8K per person per year. This ups the capitalization for our six year old to about $120K. (There seems to be some double counting here, unless the family is fully covered from other, social, sources. One might also consider the fact that, except for young children, the expenditure on health up to middle age is probably less than $8K per year, and higher than $8K afterward.) Anyway, the capital investment per person would be $600K ($8K x 75years) + $350K or essentially $1M invested by society in each person, over their lifetime. On an annual basis about $13 K per year per person..

Other considerations enter in. For instance the average life is that of a 38 year old, round off to 40 year old. He has cost $670K capitalization by society, and produced about $2M. Net contribution $1.33M to society. Should we make this the average economic value of a life?

Suppose we were to nuke a city of 1M people. Which would be the loss to society?
Well, the fixed assets would be $180B ($54T/300M x 1M.) But the total loss of human capital would be about $670K x 1M = $670B. So the total is $850B (Compare this calculation with:
Here we are just counting what we have invested in the city, rather than the loss of any potential gains we had hoped to obtain from it. Just by the way, The wars in Afghanistan and Iraq have cost $1.2T since 2001, the equivalent, in terms of capital investment, of a city of 1.4M people, or larger than San Antonio, the 7th largest city in the US. Estimates of the total costs of the War on Terror run to $4T, but a figure of $2.4T ( places the cost at slightly more than Chicago, 3rd largest city in US. (If we were just counting physical structure, no loss of life, it would be almost 5 times the city of Chicago, more than the entire state of Illinois, leveled. This is equivalent to the 28 million houses of my earlier post.) Annualized, we are nuking the equivalent, inhabitants included, of Newark, NJ (pop 277K), or Greensboro, NC, (pop 270K) every year. 40 Years of the War on Drugs has cost about $1T, or by this calculation a city almost 1.2M population, or about the size of Dallas, the 9th largest city in the US. (If it helps with the imagination, you can imagine slightly larger cities just depopulated, since the actual physical destruction of buildings, homes and factories just adds on about a quarter of the value of destruction.)

One thing we see is that the value of a life depends on the calculation we are performing with it.

There is an implied social/moral choice in undervaluing or overvaluing a life. When you overvalue a life, you are sacrificing society for the individual. When you undervalue a life, you are sacrificing the individual for society. But sometimes society pays, anyway, when many individuals are sacrificed.

But of course, society is just made up of individuals. Or, individuals make up society.