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

convincing case for leaving distribution to one side and focus on e¢ ciency?
To set the stage, let us return to the framework from section ?? but instead
of assuming that all consumers are identical, let us assume that they di¤er
in their tastes (i.e., have di¤erent utility function), that they have di¤erent
levels of income (e.g., because they got di¤erent types of human capital that
allow them to hold di¤erent types of jobs or got other sources of income than
wage income), and that the social welfare function is individualistic, but not
necessarily utilitarian. More speci…cally, replace assumptions 1, 3 and 7 from
lecture note 13-14 by 1’, 3, and 7’:
1’ The economy is populated by many di¤erent consumers, h = 1; ::; H.
1. There are two goods x1 and x2 with consumer prices q = (q1; q2) and
producer prices p = (p1; p2). The two goods are private goods and they
are sold in markets, i.e., a market price exists for both of them.
3’ The direct utility function of consumer h is Uh(x h 1; x h 2) and the budget
constraint is q1x h 1 + q2x h 2 = m h where m h is the given income of consumer
h.
2. Each consumer maximizes utility subject to the budget constraint. This
involves buying each of the two goods up to the point where
@Uh
@x1
@Uh
@x2
= hq1 (1)
= hq2; (2)
where h is the marginal utility of income (the Lagrange multiplier on the
budget constraint) for consumer h.
3. The two goods are produced with capital and labour, l0 and k. The total
supply of these are assumed to be …xed. The producer prices of labour
and capital, respectively, are p0 and pk.
4. The production functions are x1 = F 1 (l 1 0; k 1 ) and x2 = F 2 (l 2 0; k 2 ) where
l j
0 and kj is the amount of labour and capital, respectively employed in
the production of the two goods.
7’ Social welfare is individualistic, i.e.,
with
@SW F
@Uh
SW F (U1; :::; UH) (3)
0. This includes as a special case the utilitarian social
welfare function SW F = P H
h=1 Uh but we shall also consider other speci-
…cations.
Suppose that we want to evaluate the net social value of a (small) project
that increases the supply of x1 by x h 1 and, as a consequence, reduces the supply
2