Tuesday, April 21, 2009

This is a small and abridged segment from Allan Feldman's "Welefare Economics and Social Choice Theory, 2nd Ed." It is somewhat disturbing to me to know that there is a clear calculus for a man's worth. This is only one of the models presented in this book.

Chapter 11


1. Introduction

…what if the population changes? For instance, what if a set of individuals {1, 2, . . . , n} is attempting to choose between alternatives x and y, but x will kill off some of the people, and y will add additional people?

In fact, this is an extremely common question that policy makers and economists face almost every day. For instance: Should a state spend $5 million replacing a highway if those repairs will likely result in 1 less traffic fatality in the next year? Should a government spend $10 billion on AIDS drugs if those drugs will prevent 1,000 deaths? Should a government prohibit a sport or leisure activity if that sport creates a 1/6 probability of death per play (e.g., Russian roulette with a 6-chamber revolver)? Should it prohibit a sport or leisure activity if that sport creates a 1/1,000,000 probability of death per day (e.g., downhill skiing)?

Is it better for a country to have a higher population or lower? If it is better to have more people, should this be done by encouraging births, or increasing life expectancy? If it is better to have fewer people, is it better to reduce birth rates or increase deaths? …

2. Economic Model

The Money Value of a Life Placing a money value on a life in legal disputes is an ancient practice. The modern Anglo-American legal treatment of accidental killing, which started in the mid 19th century, typically provides that dependents of a deceased person may recover for pecuniary losses they suffer, especially lost wages the deceased would have provided. The deceased is primarily viewed as a money making machine. The value of his life is mainly given by lifetime income or earnings, possibly net of expenses needed to maintain the machine (e.g., food, clothing, etc.), possibly discounted to present value, and possibly augmented by the value of non-paid services provided. This can be called the human capital approach: the person is valued as a (human) money making machine.

The human capital approach to valuing lives, however, ignores how much the deceased himself would value being alive.

3. A Formal Version of the Economic Model

We will now develop a relatively simple model to show how one individual “computes” the value of his life.

In this model there is just one person, so we will dispense with an identifying subscript. There are two time periods. In period 1, the planning or ex-ante period, he decides on how to allocate his spending. He can spend on consumption, on precaution, or on insurance. Between period 1 and period 2, the ex-post period, events unfold, which leave him either alive, or dead. The probability that he ends up alive in period 2 depends on how much he spends on precaution in period 1. If he is alive, he consumes the amount he chose in period 1. If he is dead, the amount he would have consumed, plus the value of any insurance policy he bought, is bequeathed to his heirs.

We use the following notation:

x = consumption in period 2 (or part of bequest, if he is dead)

y = precaution expenditure

z = insurance expenditure

w = x + y + z = initial cash endowment

q(y) = probability he is alive in period 2

V = face value of any life insurance policy he buys

We assume the q(y) function is nicely behaved: 0 <>

y, q(y) increasing in y, concave, and smooth.

We assume that the cost of life insurance would reflect the actual odds that he will die, so that z = V · (1 − q(y)). That is, the price of insurance

is “actuarially fair.”

f (x) = xα if alive

g (x + V ) = (x + V )α − K if dead.

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