Dominick Salvatore Schaums Outline of Microeconomics, 4th edition Schaums Outline Series 2006

40 THE MEASUREMENT OF ELASTICITIES [CHAP. 3
From B to D, e ¼ Q D Q B
P D P B
P B
Q B
¼
From D to B, e ¼ Q B Q D
P B P D
P D
Q D
¼
2000 7
¼ 7
2 1000
2000 5
ffi 1:67
2 3000
(The symbol ffi means approximately equal to.) Thus, we get a different value for e if we move from B to D than if we move
from D to B. This difference results because we used a different base in computing the percentage changes in each case.
We can avoid getting different results by using the average of the two prices [(P B þ P D )/2] and the average of the two
quantities [(Q B þ Q D )/2] instead of either P B and Q B or P D and Q D in the formula to find e. Thus,
e ¼
DQ
DP (P B þ P D Þ=2
(Q B þ Q D )=2 ¼ DQ
DP P B þ P D
Q B þ Q D
Applying this modified formula to find e either for a movement from B to D or for a movement from D to B, we get
e ¼
2000
12
2 4000
This is the equivalent of finding e at the point midway between B and D (i e., at point C).
¼ 3
EXAMPLE 2. Given the market demand schedule in Table 3.2 and the market demand curve in Fig. 3-2, we can find e for
a movement from point C to point F, from F to C and midway between C and F, as follows:
Table 3.2
Point P y ($) Q x
A 7 500
B 6 750
C–––– 5 ––– 1250
D 4 2000
F–––– 3 ––– 3250
G 2 4750
H 1 8000
Fig. 3-2
From C to F, e ¼ DQ
DP P C
Q C
¼
From F to C, e ¼ DQ
DP P F
Q F
¼
2000 5
¼ 4
2 1250
2000 3
ffi 0:92
2 3250
At the point midway between C and F (point D 0 on the dashed chord),
e ¼
DQ
DP (P
C þ P F )
(Q C þ Q F ) ¼ 2000 8
ffi 1:78
2 4500
3.2 ARC AND POINT ELASTICITY
The coefficient of price elasticity of demand between two points on a demand curve is called arc elasticity.
Thus, in Examples 1 and 2, we found arc elasticity. Later we will see that the coefficient of price elasticity of
demand in general differs at every point along a demand curve. Arc elasticity is, therefore, only an estimate.