Dominick Salvatore Schaums Outline of Microeconomics, 4th edition Schaums Outline Series 2006
50 THE MEASUREMENT OF ELASTICITIES [CHAP. 3Midway between F and H (point G 0 in Fig. 3-8) 4750 4e ¼ffi 0:842 11,250(For the elasticity from point C to point F, from F to C and midway between C and F, see Example 2.)3.7 For the market demand schedule in Table 3.9, (a) find e at points B, G, and D and (b) state what happensto total expenditures on commodity Y when P y falls.(a) We can find e at points B and G geometrically from Fig. 3-8.At point B,e ¼ RNOR ¼ 2500 ffi 3:3750At point G,e ¼ MLOR ¼ 4000 ffi 0:844750At point D, e ¼ 2(see Example 2).Fig. 3-8(b)Column (3) of Table 3.10 shows that as P y falls, total expenditures on commodity Y rise as long as e . 1 andfall when e , 1. Notice that as we move down along D y , price elasticity falls. This is usually the case forcurvilinear demand curves.Point(1)P y ($)Table 3.10(3)(2) Total ExpendituresQ y ($)A 7 500 3500B 6 750 4500 3.3C 5 1250 6250D 4 2000 8000 2.0F 3 3250 9750G 2 4750 9500 0.84H 1 8000 8000(4)e
CHAP. 3] THE MEASUREMENT OF ELASTICITIES 513.8 (a) Show that when QD y ¼ 600/P y (a rectangular hyperbola), the total expenditures on commodity Yremain unchanged as P y falls. (b) From (a), derive the value of e along the hyperbola. (c) Verify (b) byfinding e geometrically at P y ¼ $4 and at P y ¼ $2.(a) Table 3.11Point(1)P y ($)(3)(2) TotalQ y Expenditures ($)A 6 100 600B 5 120 600C 4 200 600D 3 200 600F 2 300 600G 1 600 600(b) Since QD y ¼ $600P yFig. 3-9(QD y )(P y ) ¼ $600 regardless of P y . Thus, for any given percentage fall in P y , QD y will increase by the samepercentage. Because the percentage changes in QD y and P y are always equal, e ¼ 1 at every point on therectangular hyperbola, D y .(c) See Fig. 3-9.At point C,At point F;e ¼ MLOM ¼ 150150 ¼ 1e ¼ LHOL ¼ 300300 ¼ 13.9 Table 3.12 gives two demand schedules. Using only the total expenditure criterion, determine if thesedemand curves are elastic or inelastic.Table 3.12P ($) 6 5 4 3 2 1Q x 100 110 120 150 200 300Q z 100 150 225 325 500 1100Since total expenditures on commodity X fail continuously as P x falls [see column (3) of Table 3.13], e , 1throughout the observed range of D x . Total expenditures on commodity Z rise continuously as P z falls [see column(5) of the table], so e . 1 throughout the observed range of D z ,D x ,D z , and D y (from Problem 3.8) are sketched inFig. 3-10.
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50 THE MEASUREMENT OF ELASTICITIES [CHAP. 3
Midway between F and H (point G 0 in Fig. 3-8)
4750 4
e ¼
ffi 0:84
2 11,250
(For the elasticity from point C to point F, from F to C and midway between C and F, see Example 2.)
3.7 For the market demand schedule in Table 3.9, (a) find e at points B, G, and D and (b) state what happens
to total expenditures on commodity Y when P y falls.
(a) We can find e at points B and G geometrically from Fig. 3-8.
At point B,
e ¼ RN
OR ¼ 2500 ffi 3:3
750
At point G,
e ¼ ML
OR ¼ 4000 ffi 0:84
4750
At point D, e ¼ 2
(see Example 2).
Fig. 3-8
(b)
Column (3) of Table 3.10 shows that as P y falls, total expenditures on commodity Y rise as long as e . 1 and
fall when e , 1. Notice that as we move down along D y , price elasticity falls. This is usually the case for
curvilinear demand curves.
Point
(1)
P y ($)
Table 3.10
(3)
(2) Total Expenditures
Q y ($)
A 7 500 3500
B 6 750 4500 3.3
C 5 1250 6250
D 4 2000 8000 2.0
F 3 3250 9750
G 2 4750 9500 0.84
H 1 8000 8000
(4)
e
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