Lecture 9
Demand and Elasticity II
John D. Rockefeller was once asked how much was enough.
His answer? “Just a little bit more.”
The Economics Outline
1. Market Demand
2. OwnPrice Elasticity of Demand
3. Income Elasticity of Demand
4. Elasticity Relationships
4.1. From the Budget Constraint
4.1.1. Engel Aggregation
4.1.2. Cournot Aggregation
4.2. From the Slutsky Equation
4.3. From Homogeneity
The Mathematics Outline
1. Euler’s Theorem
Market Demand
Let’s suppose there are n goods and m people in the economy and let:
i
= 1 to n
(goods in the economy)
j
= 1 to m
(individuals in the economy)
(Marshallian demand for good i by individual j)
)
,
,...,
(
1
j
n
j
i
j
i
I
P
P
x
x
=
Then market demand is characterized by the equation:
∑
=
=
=
m
j
m
n
i
j
n
j
i
i
I
I
P
P
X
I
P
P
x
X
1
1
1
1
)
,...,
,
,...,
(
)
,
,...,
(
Graphically, market demand is the horizontal summation of individual demand.
OwnPrice Elasticity of Demand
Elasticity is a measure of responsiveness.
In the setting of demand, we are interested in
the response of demand to some change in the system.
In order to get things into a unit
free measure, elasticity is calculated in percentages.
With the Slutsky equation we looked at how
changes as
changes.
However, if we
find that the answer to this problem is –25 we need to put that in context.
Is –25 a lot or a
little.
If you are currently consuming 30 units and your consumption changes by 25, then
the change seems like a lot.
If you are currently consuming 1,000 units, a change of 25
i
x
i
P
Dr. Steven Waters
Econ 380
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doesn’t seem like much.
If we put things in percentage terms the change is put in
context.
Ownprice elasticity of demand is defined as:
Arc Elasticity
(Finite Changes):
Q
P
P
Q
P
P
Q
Q
P
P
Q
Q
P
Q
x
x
x
x
x
x
P
x
x
⋅
∆
∆
=
∆
∆
=
∆
∆
=
∆
∆
=
%
%
,
ε
Point Elasticity
(Infinitely Small Changes):
Q
P
P
Q
x
P
x
⋅
∂
∂
=
,
Sometimes I may drop the subscripts on ownprice elasticity (as I did here) and follow
the convention in economics of denoting quantities with the letter Q.
Up to this point in
time, I have denoted quantities with letters like
x
and
y
, or
.
Don’t get confused
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 Spring '11
 Stevens
 Supply And Demand, Dr. Steven Waters

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