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

48 THE MEASUREMENT OF ELASTICITIES [CHAP. 3
(b) For a movement from D to G,
e ¼
40,000
2
3
60,000
¼ 1
For a movement from G to D,
e ¼
40,000
2
1
100,000
¼ 0:2
At the point midway between D and G (i.e., at point F),
40,000 4
e ¼
2 160,000
¼ 0:5
3.4 For the market demand schedule in Problem 3.3, (a) finde at point C geometrically, and (b) derive the
formula for finding e geometrically at point C. (c) What happens to e as we approach point A? Aswe
approach point H? Why?
(a) At point C,
(see Fig. 3-7.)
e ¼ LH
OL ¼ 80,000
40,000 ¼ 2
Fig. 3-7
(b) e ¼ DQ
DP P Q ¼ LH
LC LC
OL ¼ LH
OL
(c)
Notice that DQ=DP is the reciprocal of the slope of D x . Since the slope of a straight line remains constant
DQ
DP ¼ OH
OA ¼ LH
LC
We have used LH/LC above in order to make the cancellations shown and express e as the ratio of two distances.
The value of e at point C above coincides with the value found in Problem 3.3. By similar triangles
e ¼ LH
OL ¼ CH
AC ¼ RO
AR
Thus, by dropping a perpendicular from any point on the demand curve to either the quantity or price axis, we
can find the price elasticity of demand at that point as the ratio of the two distances defined.
As we move toward point A, price elasticity increases and approaches infinity, since the numerator of the elasticity
fraction increases while its denominator decreases. As we move toward point H, price elasticity decreases
and approaches zero, since the numerator of the elasticity fraction decreases while its denominator increases.
3.5 (a) Find e geometrically at points B, D, F, and G for the market demand curve in Problem 3.4(a). What
happens to total expenditures on commodity X as the price of X falls? (b) State and explain the general
rule relating total expenditures on commodity X to e when P x falls.