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Recall the “Law of Demand”:
Other things equal, when the price of a good rises,
the quantity demanded of the good falls.
An example of qualitative information about the
relationship between two variables ( . . . relates
directions of changes).
Often we need quantitative information (relating
magnitudes of changes).
When price rises, does quantity demanded fall . . .
. . . a “little”?
. . . a “lot”?
How can we measure the degree of responsiveness of
quantity demanded to price changes?
p
p
D1
D2
p
“big” Q
Q
“small” Q
Q
It seems to be related to slope:
Relatively “flat” demand -- big response of Q to p
Relatively “steep” demand -- small response.
This suggests using either the slope or the reciprocal of
the slope of demand as a measure of the responsiveness
of Q to changes in p.
Reciprocal of the slope =
ΔQ
Δp
“change in Q / change in p”
Greater value for reciprocal of slope means quantity
demanded is “more responsive” to price changes?
Problems with the use of demand curve slope (or its
reciprocal) as a measure of responsiveness:
1. Numerical value has “units” attached.
-- can’t compare across goods measured in
different units.
-- can get any numerical value you want just by
changing units.
2. The slope (or its reciprocal) involves an implicit
comparison (ratio) of absolute changes.
-- may not be very informative.
Here’s an example to show why:
p
($/lb.)
Q
(lbs./day)
p1
($/lb.)
Q1
(lbs./day)
Good
A
+2
-100
1
10,000
Good
B
+10
-50
50
100
At first, the demand for good A seems more
responsive: a smaller price change produces
a bigger quantity response.
But when we think in terms of relative (rather than
absolute) changes, the demand for good B is clearly
more responsive than the demand for good A.
The lesson: A comparison of relative (or percentage)
changes gives a more informative measure of
responsiveness.
(own price) elasticity of demand =
%  in Q demanded
%  in p
Q
Q
x 100
" base Q"
" base Q"


p
p
x 100
" base p"
" base p"
One remaining question:
When quantity changes (from Q1 to Q2, say), what
quantity should be used as the “base Q” in a
percentage change calculation?
The usual choice: the initial quantity (Q1)
(A change from Q = 100 to Q = 110 is an increase of
10%, calculated by this method.)
Problem: This method gives a different (absolute) value
for the percentage change going in the other
direction.
(A change from Q = 110 to Q = 100 is a decrease of
9.09%)
Standard convention: The “Midpoint Method.” For the
“base Q” use the simple average of the initial and
final quantities:
(Q1 + Q2) ÷ 2
(Same for percentage changes in price)
Earlier, we had the (own price) elasticity of demand
expressed as:
Q
" base Q"
p
" base p"
=
(Q2 - Q1) / [ (Q2 + Q1) ÷ 2]
(p2 - p1) / [ (p2 + p1) ÷ 2 ]
or, more simply =
(Q2 - Q1) / (Q2 + Q1)
(p2 - p1) / (p2 + p1)
An example of an elasticity calculation:
($/lb.)
1.75
Pt. 2
Pt. 1
1.50
Demand
72
=
=
80
(lbs./day)
(Q2 - Q1) / (Q2 + Q1)
(p2 - p1) / (p2 + p1)
(72 - 80) / (72 + 80)
(1.75 - 1.50) / (1.75 + 1.50)
= -0.684
A brief digression for those who know some calculus:
The formula on previous slide gives “arc elasticity,”
because it assigns an elasticity value to any “arc,”
or segment, of a demand curve.
We can write arc elasticity as:
Q
Q " midpoint p"
" midpoint Q"

. . or, simplifying . .
p
p " midpoint Q"
" midpoint p"
. . . where “midpoint” p and Q are the average
values of p and Q over the arc.
Now let the arc gradually shrink to a single point.
“Midpoint” p and Q become the unique price and
quantity coordinates of the point . . .
. . . and the ratio of discrete changes in Q and p
converges to:
dQ
dp
-- the derivative of Q w.r.t. p.
“Point elasticity”:
dQ p

dp Q
(For the purposes of Econ 101, arc elasticity
is good enough.)
Now returning to the example of an elasticity
calculation:  = -0.684.
What do we make of this number?
First note negative sign.
Along a demand curve, price and quantity changes
are always of opposite signs . . .
. . . so (own price) elasticities of demand are
always negative.
Sometimes we automatically think in terms of absolute
values ( . . . but this can be a dangerous habit).
What information is conveyed by the numerical
value ( || = 0.684 )?
%Q
Let’s look at some cases, remembering  
%p
With vertical demand . . .
p
Pt. 1
%Q = 0 so  = 0
p
“perfectly” or (“completely”)
inelastic demand
Pt. 2
Q
Exactly the same quantity
demanded -- no matter
what the price.
With “relatively steep” demand . . .
| %p | > | %Q |
p
so . . .
p
0<||<1
Q
Q
“inelastic demand”
For certain special demand curves, the relative (%)
changes in price and quantity are the same
(in absolute value).
| %p | = | %Q |
p
so . . .
||=1
p
“unit elastic demand”
Q
Q
For “relatively flat” demand curves . . .
p
| %p | < | %Q |
so . . .
p
1<||<
Q
Q

“elastic demand”
For a horizontal demand curve . . .
p
%p = 0
so . . .
p1
||=
Q
Q

“perfectly” (or
“completely”)
elastic demand
At any price equal to or below p1, quantity demanded
is unlimited (for practical purposes). At any price
even slightly above p1, quantity demanded is zero.