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

CHAP. 3] THE MEASUREMENT OF ELASTICITIES 57
As shown in Fig. 3-13(a),
at point C on S,
at point F on S x ,
e s ¼ DQ
DP P C
Q C
¼ OH
HC HC
OH ¼ 1
e s ¼ DQ
DP P F
Q F
¼ OG
GF GF
OG ¼ 1
As shown in Fig. 3-13(b),
at point K on S y ,
at point L on S y ,
e s ¼ DQ
DP P K
Q K
¼ JN
NK NK
ON ¼ JN
ON , 1
e s ¼ DQ
DP P L
Q L
¼ JM
ML ML
OM ¼ JM
OM , 1
What was found to be true for points C and F on S x [Fig. 3-13(a)] is clearly true for all other points on S x . Similarly, e s ,1 all
along S y [Fig. 3-13(b)]. Thus, if a positively sloped straight-line supply curve goes through the origin, it has unitary elasticity;
if it crosses the quantity axis, it is inelastic; and if it crosses the price axis (see Example 9), it is elastic.
3.20 From the supply schedule in Table 3.18, find arc e s for a movement (a) from point D to point B,(b) from
B to D and (c) midway between D and B.
Table 3.18
Point P y ($) Q y
A 6 6000
B——-- 5 –––5500
C 4 4500
D——– 3 –––3000
F 2 0
(a) From D to B e s ¼ DQ
DP P
D
¼ 2500
Q D 2
3
3000
¼ 1:25
(b) From B to D e s ¼
2500
2
5
5500
ffi 1:11
(c) Midway between D and B e s ¼ DQ
DP P
D þ P B
¼ 2500
Q D þ Q B 2
8
8500
ffi 1:18
3.21 Plot the supply schedule of Problem 3.20 and find e s, at point C.
The elasticity of supply at point C in Fig. 3-14 is obtained by drawing a tangent to S y at C and then proceeding
as in Problem 3.19. Thus,
e s ¼ DQ
DP P C
Q C
¼ OG
GC GC
OG ¼ 1
Notice that the price elasticity of supply at point C 0 (found in Problem 3.20) differs slightly from the point elasticity
of S y at point C. The difference is due to the curvature of S y and diminishes as D and B move closer to each other.