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

Exercise 1 Suppose an analyst decided to ignore distribution and simply use
the market price of good 1, q1, as the shadow price and not qSP 1 . Would doing
so over-estimate or under-estimate the social value of a unit of output from the
project?
As noted in Lecture note 13-14, we do not observe the opportunity cost
of foregone consumption directly, so, in practice, it is, typically, estimated as
the monetary cost of the project or policy programme. For this reason, the
practical starting point for a social cost bene…t analysis that takes distribution
into account is often an expression such as
NB = P H
h=1
b
h x h 1 C (18)
where C is the monetary cost of the project. Given that, there are two broad
approaches to incorporating distribution into social cost bene…t analysis that
are widely used in practice: the "adjusted social weights approach" and the
"marginal cost of public funds approach". We shall discuss the two in detail
below, but …rst a little aside that you can jump if you are familiar with the
concept of inequality aversion. It plays a key role in what follows, so make sure
you know what it is.
3.1 Aside: Inequality aversion
An important consideration in calculating social welfare weights is the degree
of inequality aversion embodied in the social welfare function. We make a
distinction between inequality aversion de…ned over utility allocations (call this
utility inequality aversion) and inequality aversion de…ned over consumption
allocations (call this consumption inequality aversion). In practice, they often
get confounded but conceptually they are di¤erent things. Let us begin by
de…ne inequality aversion in general using a function g with constant relative
inequality aversion:
g(y) =
a
y1
: (19)
1 a
We de…ne the degree of inequality aversion (with respect to the variable y) as
a =
@ 2 g
@y2 y: (20)
@g
@y
The parameter a controls the degree of inequality aversion exhibited by the
function g. The higher is a, the greater the degree of aversion. To see the
intuition, let us think of y as income and g as a utility function. If g is a
linear function of income y, then a = 0 and the marginal utility is the same
irrespective of the level of income, i.e., rich and poor will get the same amount
of utility out of an extra unit of income. If a > 0, marginal utility is @g
@y = y a .
This is falling with income, so the marginal utility that a rich person gets from
an extra unit of y is lower than the marginal utility that a poor person gets
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