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

where the social weight attached to the bene…ts of individual h is simply h =
. Since marginal utility is falling with the level of consumption, we put
1
x h 1
less weight on individuals 3 and 4 (1=2000) who consume a lot of the project
output to begin with and higher weight on individuals 1 and 2 (1=1000) who
consume less of the project output initially. Table 1 shows what happens when
we apply these weights to a project that takes $1 of uncommitted public funds
and distribute it equally across the four individuals (through a non-distortionary
lump sum transfer). The last column shows the welfare increments ( 1
xh x
1
h 1) for
each consumer. We see that the sum of these bene…ts adds up to a very small
amount, namely 0:00075. This is a lot less than the $1 cost of the project, so it
should be rejected. But this does not seem to make any sense. We got a pound
of uncommitted funds, how can dividing it equally amongst individuals be such
a bad idea?
The issue is that we have (without saying it out load..) chosen to use public
funds as the numeraire, i.e., as the unit in which we measure the cost of the
project ($1 of public funds is worth $1). The bene…ts, however, 1
xh x
1
h 1, are
measured in units of utility. So the problem is that we are not comparing like
with like. More fundamentally, the problem is that the choice of the utility functions
must in practice be understood as the choice of ordinal utility functions.
This means that we can subject it to any positive transformation and it will
still represent the same underlying preferences over consumption. To see what
this implies more clearly, let us transform the utility function and represent the
individuals’preferences by the function e Uh = 10000 log(xh 1). Table 2 shows the
re-calculated bene…ts of the divided-a-pound-equally project. Now, they add up
to 7:5 and we conclude that the project is a good idea after all.
Exercise 2 Does this logic strengthen or weaken Harberger’s case for not applying
welfare weights at all?
Clearly, to reach a sensible decision and avoid leaving the analysis wide open
to manipulation by special interests, we need a principle that can tell us how
to normalize or anchor the social welfare weights so that the costs and bene…ts
become comparable.
The Green Book suggests the following normalization. Begin by de…ning as
the benchmark the social value of a uniform lump sum transfer, i.e., the social
value of dividing $1 of uncommitted public funds equally amongst all citizens.
This benchmark de…nes the opportunity cost of spending a pound on some other
project or programme. The logic is that any project or programme would have
to be better than simply spending the funds on a uniform lump sum transfer in
order to be socially justi…ed.
How does one implement this principle? What we need to do is to normalize
the welfare weights of the four individuals in such a way that a project that
divides $1 equally amongst them breaks even, i.e., yields a social bene…t equal
to the cost of $1. Formally, we want the normalized social weights –denoted
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