Price Elasticity
by Peter M. Kerr
© 2007 [2001]
This monograph borrows heavily from Chapters 4, 5, and 11
of the author’s A Backdoor to Economics (1999).
Demand
Elasticity refers to the responsiveness of one variable to
changes in another variable. Consider the demand for Coke and
changes in its price. If a small drop in the price of Coke
provokes a huge increase in the quantity demanded, then the
demand is said to be highly responsive to changes in its price,
or the demand is highly price elastic. A highly inelastic
demand for Coke would be one where a huge drop in price
results in a small increase in the quantity demanded. While
elasticity is in one sense a new word for responsiveness, it is
also a measure of this responsiveness.
A coefficient of own price elasticity (E) could be generally
defined as the percentage change (%Δ) in the quantity
demanded divided by the percentage change in price
(1) E = %Δ Qdemanded
÷
%Δ P
While this general definition is excellent for interpreting a
coefficient, for calculation purposes we must use the following
variant of this definition.
(2) Earc =
│Δ Q / Σ Q │
────────────
│Δ P / Σ P │
This formula prescribes the following steps:
(i) Subtract the original value of the quantity from
its new value.
(ii) Add the original value of the quantity to its new
value.
(iii) Divide (i) by (ii).
(iv) Subtract the original value of the price from its
new value.
(v) Add the original value of the price to its new
value.
(vi) Divide (iv) by (v).
(vii) Divide (iii) by (vi).
(viii) Erase the minus (-) sign, i.e., use the absolute
value.
To see how this formula might be used, consider an
individual’s demand for Coke diagrammed in
Figure 1. If the price drops from $.80 to $.60, the quantity
demanded will increase from 4 to 8 cans per week.
(i)
8 - 4 = 4 (ΔQ)
(ii) 8 + 4 = 12 (ΣQ)
(iii) 4 ÷ 12 = 1/3 (i ÷ ii)
(iv) .6 - .8 = -.2 (ΔP)
(v) .6 + .8 = 1.4 (ΣP)
(vi) -.2 ÷ 1.4 = -1/7 (iv ÷ v)
(vii) (1/3) ÷ (-1/7) = - 7/3 = -2.3 (iii ÷ vi)
(viii) │-2.3│ = 2.3 = EA
As a ratio of percentages, EA is a pure number, i.e., it has no unit
of measure like dollars or cans. The fact that EA equals 2.3 can
be interpreted as a "one percent drop in price will result in a 2.3
percent increase in quantity demanded." [Note that a 25 percent
drop in price was matched with a 100 percent increase in
quantity demanded. Using the general definition of the
coefficient, (1) above, would yield E = 4.]
Figure 1.
Oftentimes, new students of economics make the mistake of
assuming that slope (i.e., "rise over run") and elasticity are the
same. Clearly they are not. The slope of the demand curve is 20 and it is the same for any segment or arc of the demand
curve. If price goes down by a dime, the quantity demanded
goes up by 2 cans. What is the coefficient of elasticity in a
different region of the demand curve? In figure 2 suppose that
price began at $.40 and dropped to $.20. The coefficient of
elasticity would be .4. Whereas the slope of a straight line never
varies, the elasticity of a straight-line demand curve depends
upon the segment under consideration.
Figure 2.
In terms of magnitude only (aka, absolute value) EA is greater
then EB. Consider segment A; when price drops from $.80 to
$.60, this is a decrease of $.20 or 25 percent. In segment B, the
same decrease of $.20 is a 50 percent decrease. While both
segments have the same absolute drop in price, arc A has a
smaller relative drop. At the same time, both segments have the
same absolute increase in quantity demanded, i.e., 4. However,
arc A has a larger relative increase, 100 percent compared to arc
B's 33 2/3 percent. Comparing segment A to B, a relatively
smaller drop in price nets a relatively larger increase in quantity
demanded. Clearly, quantity demanded is more responsive to
price changes in region A than B, i.e., demand is more elastic in
region A than B. This, of course, is reflected in the measures of
elasticity. The greater the coefficient's absolute value, the
more elastic the demand. According to the coefficients, a one
percent drop in price would result in a 2.3 percent increase in
quantity demanded in arc A, but only a .4 percent increase in
arc B.
The absolute value or the magnitude of the coefficient of
elasticity allows economists establish categories for different
demands. If E > 1, then the demand is said to be elastic. If E <
1, then demand is said to be inelastic. If E = 1, then demand is
said to be unit elastic. In the latter case, the percentage change
in price is exactly matched by the percentage change in quantity
demanded. Table 1 summarizes this classification.
Table 1
Value of
E
________
Relationship between
%Δ Q and %Δ P
____________________
Type of
Demand
____________
E<1
%Δ Q < %Δ P
inelastic
E=1
%Δ Q = %Δ P
unit elastic
E>1
%Δ Q > %Δ P
elastic
Applying these criteria to the demand curve in Figure 3,
demand in arc A is elastic while demand in B is inelastic. The
coefficient of elasticity for a price drop from $.80 to $.20
(section C in Figure 3) is 1 which means that demand over C is
unit elastic. Elasticity's elusiveness stems from the fact that it is
a relative concept.
Figure 3.
Respond to the following questions.
1. Suppose that a 20 percent drop in the price of
bicycles resulted in a 10 percent increase in sales. In
this case, the elasticity of demand for bicycles would
be
A. elastic.
B. unit elastic.
C. inelastic.
D. indeterminate, not enough information
has been given.
2. When the Lasky Shoe Store dropped the price of a
canvas sneaker from $25 to $20, sales increased from
50 pairs to 70 pairs per week. The magnitude of the
coefficient of elasticity is
A. .66 2/3.
B. 1.5.
C. 2.0.
D. .5.