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

CHAP. 3] THE MEASUREMENT OF ELASTICITIES 43
(1)
Income (M)
($/year)
(2)
Quantity of X
(units/year)
Table 3.4
(4)
(3)
in Q x in M
Percent Change Percent Change
(5)
(6)
e M Type of Good
8,000 5
_____________________ 100
_______________ 50
_______________ 2
________ luxury
12,000 10
______________________ 50
______________ 33.33
____________ 1.50
______ luxury
16,000 15
______________________ 20
_______________ 25
______________ 0.80
___ necessity
20,000 18
______________________ 11.11
____________ 20
_______________ 0.56
___ necessity
24,000 20
_____________________ 2 5
_____________ 16.67
____________ 20.30
______ inferior
28,000 19
____________________ 2 5.26
___________ 14.29
____________ 20.37
______ inferior
32,000 18
3.5 CROSS ELASTICITY OF DEMAND
The coefficient of cross elasticity of demand of commodity X with respect to commodity Y(e xy ) measures
the percentage change in the amount of X purchased per unit of time (DQ x =Q x ) resulting from a given percentage
change in the price of Y(DP y =P y ). Thus
e xy ¼ DQ x=Q x
DP y =P y
¼ DQ x
DP y
P y
Q x
If X and Y are substitutes, e xy is positive. On the other hand, if X and Y are complements, e xy is negative.
When commodities are nonrelated (i.e., when they are independent of each other), e xy ¼ 0.
EXAMPLE 7. To find the cross elasticity of demand between tea (X) and coffee (Y) and between tea (X) and lemons (Z)
for the data in the next table, we proceed as follows [Table 3.5(a) and (b) is the same as Tables 2.11 and 2.12 in Chapter 2]:
e xy ¼ DQ x
P
y
¼
þ10
40
¼þ0:5
DP y Q x þ20 40
e xz ¼ DQ x
P
z 5 10
¼
¼ 0:125
DP z Q x þ10 40
Since e xy is positive, tea and coffee are substitutes. Since e xz is negative, tea and lemons are complements. Problem 3.24
provides some empirical estimates of price, income, and cross elasticity of demand, while Problems 3.25 to 3.29 show
some important applications of the concept of price elasticity of demand.
Table 3.5(a)
Before
After
Commodity
Price
(cents/cup)
Quantity
(units/month)
Price
(cents/unit)
Quantity
(units/month)
Lemon (Y) 40 50 60 30
Tea (X) 20 40 20 50