Public Finance, 2nd Edition

and others suggesting still diVerent approaches to the evaluation of a person's

life.

6

Even if one believes that the value of life is measurable in principle,

however, there remains the diYcult task of evaluating such concepts as

Mishan's individual HCVs or Kneese's economic value of life. In that

sense, Broome's general pessimism about valuing the loss of life is easily

shared.

Limit Values of Intangibles

The real danger with true intangibles is that they can easily undermine

objective cost±beneWt analysis in nondefense areas when they are realistically

only a fraction of overall beneWts or costs. Proponents and opponents will

undoubtedly be able to discover ``substantial'' intangible beneWts or costs in

any government project. By placing a suYciently large implicit dollar value

on some intangible element of a project, the project's present value can

arbitrarily be made positive or negative. Cost±beneWt analysis risks becoming

a blatantly political exercise.

The presence of intangibles should not preclude undertaking a careful

cost±beneWt analysis. To the contrary, the only plausible way of obtaining a

proximate valuation of the intangibles is by means of a cost±beneWt analysis

of the tangible project costs and beneWts. The tangible data can then be used

to place implicit lower or upper bounds on the value of the intangible

elements. For example, suppose the government must choose between two

mutually exclusive alternatives, A and B, with the following properties: The

quantiWable present value of A is greater than the quantiWable present value

of B, but B is perceived to contain some intangible beneWts. For B to be

chosen, the implicit dollar value of its intangible beneWts must be at least

(PV

A

 PV

B

). One can then ask whether society would conceivably be willing

to pay that much for the alleged intangible beneWts. Placing even a lower

(upper) bound on the value of intangible beneWts (costs) is impossible without

recourse to a careful cost±beneWt study.

LUMPINESS

Suppose a private Wrm invests in a new machine that increases its annual

production capacity by 1000 units. It typically measures the beneWts of the

machine as the increase in expected revenues from the 1000 units, equal to

1000 times the existing and expected future market price of the item each year

for the projected life of the machine. The revenue measure pDX is usually

6

J. M. Buchanan and R. L. Faith, ``Trying Again to Value a Life''; M. W. Jones-Lee,

``Trying To Value a Life: Why Broome Does Not Sweep Clean''; A. Williams, ``A Note on

`Trying to Value a Life' ''; and J. Broome, ``Trying To Value a Life: A Reply,'' Journal of Public

Economics, October 1979.

778 LUMPINESS

X

X

0

D

X

1

p

0

p

S

S'

FIGURE 26.1

considered to be a reasonable approximation of the social beneWts of the

machine as long as the 1000 units represent a ``small'' increment to overall

market capacity. As depicted in Fig. 26.1, (X

1

 X

0

 1000) is such a small

addition to the overall market that it has virtually no eVect on the market

price.

7

Government investments, in contrast, often represent substantial add-

itions to existing market capacity, enough that they do aVect prices. This

situation is depicted in Fig. 26.2. Obvious examples include hydroelectric

projects that substantially reduce the price of electricity to an entire region or

large additions to a public transportation network in an urban area that

substantially reduce travel and congestion costs. In these cases, pDX revenue

calculations are no longer good approximations of the beneWts. The proper

beneWt measures are a good deal more complex. They have been presented in

Chapter 9 for measuring the beneWts of decreasing-cost services and in

Chapter 13 for measuring the loss from taxation. Our purpose here will be

to collect and summarize these results in the context of beneWt measurement

when prices change discretely. The extension to cost measurement is straight-

forward.

First-Best Benefit Measures: A Single Price Change

As always in public sector analysis, it matters whether the underlying policy

environment is considered Wrst best or second best, although perhaps less so

here than in other areas. To keep matters straight, however, we will assume to

7

We are assuming a Wrst-best environment in which consumers and producers face the same

prices.

26. MEASUREMENT PROBLEMS IN COST±BENEFIT ANALYSIS 779