Dr. Steven Waters
Econ 380
Page 1 of 6
Lecture 8
Demand and Elasticity I
Can God be pleased by the vast and increasing inequities
among us?
Is he not grieved by our arrogant accumulation?
Foster, Richard J. Freedom of Simplicity
,
1981, Harper & Row, Publishers, p. 32
The Economics Outline
1.
Consumer Surplus
2.
CrossPrice Effects
3.
Substitutes (Gross & Net)
4.
Complements (Gross & Net)
The Mathematics Outline
1.
More Slutsky Equation!
2.
Young’s Theorem
Consumer Surplus
Consumer surplus is a measure of the value that consumers receive above and beyond
what they pay for.
How much a person is willing to pay for a good is different from what
she has to pay for a good.
In this graph, the shaded area is the consumer surplus.
There is a direct relationship between consumer surplus and expenditure functions.
Suppose we are thinking about a situation where the price of good x increases.
With the
increase in price, we are worse off because our real income goes down.
However, in the
compensated demand world (Hicksian demand) we have the situation that income is
compensated to assure that the same level of utility is attained.
How much income has to
be compensated is exactly what the expenditure function measures.
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Dr. Steven Waters
Econ 380
Page 2 of 6
Suppose price increases from
0
x
P
to
1
x
P
(i.e.,
0
1
x
x
P
P
>
):
Expenditures when price is
0
x
P
:
)
,
,
(
0
0
0
U
P
P
E
E
y
x
=
Expenditures when price is
1
x
P
:
)
,
,
(
0
1
1
U
P
P
E
E
y
x
=
The loss in welfare (consumer surplus) is measured as the increase in needed
expenditures.
Thus:
welfare change =
1
0
E
E
−
Since
0
1
E
E
>
, the welfare change is negative (i.e., the person is worse off).
It turns out that this change in expenditures can be written:
1
0
E
E
−
=
∫
∫
=
1
0
1
0
)
,
,
(
0
x
x
x
x
P
P
x
y
x
x
P
P
dP
U
P
P
h
dE
In other words, it is just the area under the Hicksian demand curve.
What happens if we look at the area under the Marshallian demand curve?
1.
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 Spring '11
 Stevens
 Consumer Surplus, Dr. Steven Waters

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