General Description of Benefit/Cost
Benefit/cost analysis is a formal technique for balancing
the benefits which a project produces against the cost of producing that
benefit. It is not as easy as it sounds.
The first question is what is "a project."
Ideally, a project is a discrete unit of activity which is self-contained and
can be divided into smaller and smaller pieces with no change in the relation
of costs to benefits. In the real world, projects are frequently
"complementary": the benefits of one project depend at least in part
on benefits derived from other projects. Further, the benefits obtained are
frequently "lumpy"; they come in indivisible packages (such as
"1 60-person bus" or "1 30-pupil classroom"). It might be
desirable to provide the benefit of transportation for only 30 people;
"project indivisibility" means that the costs will be incurred the
same as if the benefits were provided for 60 people. It is possible to define
projects to account for complementarities and indivisibilities, but it makes
the model more complex and its interpretation less straightforward.
If what is meant by "project" is far from simple, what is meant by
"benefit" and "cost" are at least as problematic. The
problem with the term "project" is one of definition: one must
carefully distinguish each of the many facets of the program under
consideration. The problem with "benefit" and "cost" is
primarily one of measurement: one knows what the benefits and costs are, the
problem is to express them in a way that can be treated analytically
(quantitatively).
Benefits are particularly difficult to measure. Often dollar-value is used to
measure both costs and benefits. This has the advantage of relying on common
units of measure: a dollar is a dollar. For most program costs, this works
well: the annual budget specifies most of the costs associated with the
program. But it is less effective for measuring benefits: Does the flow of
revenue which they generate properly reflect the relationship between three
units of low-income housing and six units of job-training programs?
Further, many public-sector programs cannot assign dollar values to the
benefits they provide. There is no market for their services. Even when the
market supplies a comparable service, the purchase price of the service may not
adequately reflect its value. Is the true value of an education the sum of the
tuition paid? That is, after all, the price offered in the market to firms
providing that service. Part of the problem in this example is that not all of
the value of the service is paid to the supplier: students value an education
enough to forego the opportunity to earn full-time wages for the period of
their studies. This cost to the student is a "dead-weight loss"; it
goes to the benefit of no one. Another part of the problem is that much of the
benefit of an education is "intangible," it has no price in the
market because it is not a commodity which can be transferred. The value is immeasurable, it is both zero and infinite.
The value of a benefit may also vary depending on the recipient. A dollar to a
starving person has a very different value compared to a dollar to a wealthy
person. The benefits of a tax-relief project may be evaluated differently,
depending on whether they accrue primarily to the wealthy or to the poor. It is
possible to take account of the "differential impact" of projects on
different client groups, again at the price of complicating the analysis.
A project may also provide benefits for other programs, sometimes even for
programs serving goals which are different from those served by the original
project. Projects involving transportation or housing are notorious for
providing benefits that "spill over" the original project. It is very
difficult to include such "externalities" in a formal analysis,
simply because it is so easy to overlook them.
The problems in measuring costs are subtle, but no less significant. One is a
question of constraints: Often a project must not exceed specified thresholds,
such as acceptable levels of pollution, acceptable rates of unemployment, or
other considerations. If the analytical model is a simple one--if it treats
each constraint separately--the thresholds can be set as maximum values which
may not be exceeded. If the analyst wishes to consider multiple constraints
interacting on each other, "linear programming"
(a mathematical tool which uses the calculus to solve multiple equations
simultaneously) may be used.
Both techniques will result in a solution which comes as close as possible to
the constraining limits without crossing them. The analyst must decide whether
this course of action is, in fact, wise. Some constraints may be of the sort
that net benefits increase as the threshold is approached: The more people in
the stadium watching a homecoming game, the better--up to the point that the
crowding becomes a physical danger. Other constraints are of the sort that
there is always some "disbenefit," if not
directly attributable to the project, then to the total system. An industry may
carefully monitor its effluent into a stream, being careful not to exceed the
capacity of the stream to absorb it. If a similar industry on the opposite bank
follows the same procedure, severe pollution may occur in spite of the fact
that neither industry has exceeded the commonly agreed constraints.
Frequently the relationship between costs and benefits changes over time. Often
the costs of a project are incurred early and the benefits are spread out over
the life of the project. This is usually resolved by discounting future
benefits and costs to their present value. Most people prefer to enjoy the
fruits of their labor immediately; a reward a year from today is not as
gratifying as the same reward today. The future reward is "discounted,"
or marked down, by a certain amount. The size of the discount is usually
determined by the other available opportunities for using one's resources
(whether those resources are capital or labor). "
There is, also, the question of whether to categorize an item as a cost or a
"negative benefit." If benefit/cost analysis were simply a measure of
the surplus of benefits over costs, there would be no issue; a "negative
benefit" would have the same effect as a cost. The analysis is concerned,
however, not with the size of the difference, but with the ratio of their
differences.
For example, how should we include the impact of air and noise pollution
resulting from the construction of a new industrial plant? If the total value
of the pollution is small relative to the other costs and benefits of the
project, the point is probably not worth pursuing. Assume, for the purpose of
argument, that the other costs and benefits are roughly equal and the value of
the pollution is 25% of the costs (or the benefits). If the pollution is
considered as a cost of the project which is imposed on the public, the benefit/cost
ratio would be <1.0/1.25>, or 0.80. If, on the other hand, the pollution
is considered as an internal component of the system--a disbenefit
counterbalancing the other benefits of the project--then the benefit/cost ratio
would be <0.75/1.0>, or 0.75. The two projects are identical in
everything but definition, yet one is found to be clearly superior to the
other.
There is, finally, the question of when the analysis is complete. The answer
is, when all the costs and benefits have been included in the analysis.
Unfortunately, that is a practical impossibility. There is always the
possibility that one has failed to include a significant indirect cost or
benefit, or overlooked a linkage with another system, or underestimated the
joint impact of several projects together. This need not be considered a
failure on the analyst's part: Much of benefit/cost analysis is an attempt to
estimate the unmeasurable, to affix a quantitative
value on a qualitative variable.
© 1996 A.J.Filipovitch
Revised 11 March 2005