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

y b h –to satisfy the following equation:
4X
h=1
b
1
h
4
1 = 0 (30)
where " 1
4 " is the extra consumption given to each consumer and " 1" is the
monetary cost of this policy. This equation implies that P 4
h=1 b h = 4 (or more
generally the number of individuals in society, H). The next step is to scale the
to make them sum to 4. The scaling factor –
sometime called the reference consumption level –can be de…ned as
original social weights h = 1
x h 1
bc =
4
P4 =
h=1 h
4
6=2000
4000
= ; (31)
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where we use the original weights associated with Uh = log(x h 1). The normalized
social weights (using this reference consumption level) are then calculated as
b h = hbc: (32)
Table 3 shows the normalized weights. Given these weights, we can now evaluate
di¤erent projects. If a project yields positive net (social) bene…ts at these
weights, the project dominates from a social point of view the next-best alternative
of allocating the funds lump sum to individuals.
Exercise 3 Verify that at the normalized social weights a project that divides
1£ equally amongst all individuals breaks even.
Exercise 4 Consider a project that allocates 1£ to consumers 1 and 2 and
nothing to consumers 3 and 4. Does that pass the cost bene…t test at the normalized
social weights? What about a project that allocates £ 1 to consumers 3
and 4 and nothing to the other two? Would you reach the same conclusion if
the assumed utility function was Uh = 20 log(x h 1) + 30 instead of Uh = log(x h 1)?
The proposed normalization – the "Green Book" normalization – is obviously
just one possibility. Many others could be considered. However, it is
based on a fairly strong rationale. Clearly, one way to dispose of a 1£ of uncommitted
funds is to give it back to individuals in a lump sum fashion. So in
that sense, it does de…ne a feasible benchmark, but one could also give the 1£
back as cut in the income tax or spend it on policing or something else. The
reason for using "divided-a-pound-equally" as the benchmark to normalize the
distributional weights is an argument that many actual tax systems, including
the UK system, can be approximated fairly well by a system where individuals
get the same universal bene…ts and pay into the system roughly in proportion to
their incomes, i.e., that the tax liabilities of an individual can be approximated
by T h = B + tm h where m h is the total income of individual h, B0 is the
(monetary) value of the universal bene…t, and t is the (average) tax rate per
unit of income.
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