Lecture Note 15: Social Cost Benefit Analysis - University of ...

in the …rst place. This suggests that the …scal implications of a project (both
on the cost and bene…t side) should be adjusted for the marginal cost of public
funds in order to re‡ect the true social cost or bene…ts of the project. This line
of reasoning is based on e¢ ciency considerations. Second, the approach is also
occasionally justi…ed by noting that many projects and government programmes
distribute income or resources from the general taxpayer to the speci…c groups
that bene…t from the project or programme. This in undoubtedly true in many
cases: a new school will bene…t those who use it, but may be …nanced from
general revenues; a welfare bene…t programme will bene…t those how qualify
for it, but may be …nanced from general revenues, etc. Given that, one can
argue that di¤erent weights should be given to the bene…ts (the social surplus
created by the programme) than to the net revenue cost of the programme or
project, but without going the all the way and applying di¤erent weights to
each individual. That is, all "bene…ciaries" are treated as if they were the same
and all "contributors" are treated as if they were the same, but the two groups
are treated di¤erently. This is the distributional justi…cation for the approach.
To see the logic behind this approach more clearly and to make it clear under
which conditions it is valid, let us return to the example from section 3.2, but
instead of specifying the cost of the project in monetary terms at the outset, we
now assume that the opportunity cost is foregone consumption of some other
good x2 and that the utility function of individual h is
Uh = log x h 1 + log x h 2:
The bene…t of the project is as before x h 1 for individual h (which we assume
is provided free of charge) while the cost is a reduction in consumption of good
x2 in the order of x h 2. Under these assumptions, we can evaluate the project
by estimating:
NB = SW F +
SW F ;
where (recall that we assume that the social welfare function is utilitarian in
the example)
SW F + =
SW F + =
4X @SW F
h=1
@Uh
4X @SW F
h=1
@Uh
@Uh
@x h 1
@Uh
@x h 2
x h 1 =
x h 2 =
4X
h=1
4X
h=1
@Uh
@x h 1
@Uh
@x h 2
So far, this is invariant to the choice of utility function because we are specifying
the costs and bene…ts in the same units. Let us rewrite the bene…t di¤erential
= hq1 to get
( SW F + ) by exploring the utility maximization condition @Uh
@x h 1
SW F + = q1
4X
h=1
x h 1
x h 2:
h x h 1: (34)
The opportunity cost of the programme in terms of the units of good x2 that
must be scari…ed can be linked to the …nancial cost of the project, C. Let us
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