Dr. Seiji Steimetz
ECON 101
Department of Economics
California State University, Long Beach
Page 1 of 12
A
NSWERS FOR
P
ROBLEM
S
ET
4
LEARNING
OBJECTIVE
LEARNING OBJECTIVE 6.1 Define the price elasticity of demand and understand how to measure it.
Review Questions
1.1
Price elasticity of demand = (percentage change in quantity demanded)/(percentage change in
price).
It isn’t measured by the slope of the demand curve because the slope depends arbitrarily on what
units you are using.
Slope will change by a factor of 100 if you use cents instead of dollars, for example.
Or, to take another example, consider the case of six-packs of soda versus cans of soda: If the price drops
by $1.00 per six-pack and this causes quantity demanded to increase by two six-packs, that is the same
thing as demand going up by 12 cans.
So, you could either calculate the slope as
−
1/2 six-packs, or you
could calculate it as
−
1/12 cans.
In addition, using percentage changes in the elasticity formula allow for
meaningful comparisons of demand responsiveness between very different kinds of goods:
for example,
breakfast cereal versus health care.
Because the slope uses physical units of quantities, such comparisons
become impossible.
1.2
The price elasticity = (percentage change in quantity demanded)/(percentage change in price) = –
25%/10% = –2.5.
This is elastic.
1.3
In calculating the percentage change in price and quantity, the midpoint formula divides by the
average of the starting and ending values.
Midpoint Formula
:
(Q
2
−
Q
1
)
Q
1
+
Q
2
2
⎛
⎝
⎜
⎞
⎠
⎟
÷
(P
2
−
P
1
)
P
1
+
P
2
2
⎛
⎝
⎜
⎞
⎠
⎟
Percentage changes can also be calculated by using the starting or ending value without averaging, but
this gives different results depending on whether the starting or ending value is used.

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Dr. Seiji Steimetz
ECON 101
Department of Economics
California State University, Long Beach
Page 2 of 12
1.4
A perfectly inelastic demand curve is shown by a vertical line, as shown at the bottom of Table 6-1.
Such a good will have no substitutes; for example, a life-saving drug.
Problems and Applications
1.5
a.
000
,
000
,
4
00
.
3
$
00
.
2
$
000
,
000
,
8
000
,
000
,
12
−
=
−
−
b.
4
00
.
3
$
00
.
2
$
8
12
−
=
−
−
. This is a much smaller value than in a.
c.
We can calculate the price elasticity using the midpoint formula as follows:
Percentage change in quantity demanded =
%
40
100
000
,
000
,
10
000
,
000
,
8
000
,
000
,
12
=
×
−
Percentage change in price =
%
40
100
50
.
2
$
00
.
3
$
00
.
2
$
−
=
×
−
So, the price elasticity of demand =
1
%
40
%
40
−
=
−
Notice that this value is significantly different than the ones calculated in a. and b.