Specifying Empirical Func2ons
for Welfare Measurement
Welfare measurement in cost-benefit analysis
Welfare Measurement in Cost-Benefit Analysis

Suppose we don’t know this
en=re demand curve.
We observe the equilibrium
price and quan=ty of P* and X*
and want to es=mate a change
in consumer surplus.
With an elas=city we can
es=mate the change in CS for
any change in price.
Change in Consumer Surplus (CS)
Welfare Measurement in Cost-Benefit Analysis

Change in CS as func2on of elas2city
Price elas=city of demand
ε
d
= (%
Δ
X
d
)/(%
Δ
P) = (
Δ
X
d
/ X
d
)/(
Δ
P/P)
= (
Δ
X
d
/ X
d
)
⋅
(P/
Δ
P) = (
Δ
X
d
/
Δ
P)
⋅
(P/X
d
)
This implies:
Δ
X
d
=
ε
d
⋅
(
Δ
P
⋅
X
d
)/P
So the change in consumer surplus (for linear demand) is
Δ
CS = [(-
Δ
P)
⋅
X*] + [½
⋅Δ
X
⋅
(-
Δ
P)]
SeRng X
d
=X* and P=P*, this can be wriTen as
Δ
CS =
[(-
Δ
P)
⋅
X*] + [½
⋅
[
ε
d
(
Δ
P
⋅
X*)/P*]
⋅
(-
Δ
P)]
[(-
Δ
P)
⋅
X*]
⋅
[1+(½
⋅ε
d
⋅Δ
P/P*)]
Welfare Measurement in Cost-Benefit Analysis