The Surpluses
R. Pope
Ordinary Surplus
Probably, no concept in economics is as discussed or even used as surplus analysis. It is
the bedrock of policy analysis. You have seen in Econ. 110 that consumer surplus was
used to discuss policy. This is properly called Marshallian surplus or ordinary surplus
because it was Marshall that developed the concept using ordinary demand curves. It is
the area under a demand curve and above price. Using a policy example involving x, let
1
x
p
is the initial situation and
2
x
p
, the subsequent situation, this surplus is
(1)
2
1
(
,
, )
.
x
x
p
x
y
p
S
x p
p
I dp
Δ
= 
∫
Example: As you will recall, for U=xy, the demand function is
(
, )
.
2
x
x
I
x p
I
p
=
Suppose
that
1
x
p
is 9,
2
x
p
=4, p
y
= 9and I is 100. Then,
4
9
100
[50(ln(4)
ln(9))]
$40.54
2
x
x
S
dp
p
Δ
= 
= 

=
∫
Now this may seem to you like a perfectly sensible money measure of the change in
consumer wellbeing. However, a lot of ink has been spent trying to dethrone it as a
useful policy notion. Hicks was the first to carefully consider these issues. I might add, I
don’t think ordinary surplus has been dethroned.
Contender 1: Compensating Variation.
It is rooted in the notion of willingness to pay. That is, what is the maximum amount that
a person is willing to pay for the change. It is like a purchase price or amount. It is
defined as
2
1
(
,
)
(
, )
x
x
V p
I
CV
V p
I

=
=U
1
where V is the indirect utility function and U
0
just denotes that we are on the original indifference curve. One can then invert the first V
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 Winter '08
 Showalter,M
 Economics, Consumer Surplus, Supply And Demand, Px, Hicksian demand function

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