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

42 THE MEASUREMENT OF ELASTICITIES [CHAP. 3
EXAMPLE 5. In Fig. 3-5 and Table 3.3, we find e at points B, C, D, F, G, H, and L for the demand curve of Example 1 and
can observe what happens.to total expenditures on commodity X as P x falls. At point B, e ¼ TM/OT ¼ 7000/1000 ¼ 7 (see
Fig. 3-5). The coefficient of price elasticity of D x at other points is found in a similar way. As we approach point A, e
approaches infinity. As we approach point M, e approaches zero. (For the factors affecting e, see Problem 3.10.)
Table 3.3
Point P x ($) Q x Total Expenditures ($) e
A 8 0 0
B 7 1,000 7,000 7
C 6 2,000 12,000 3
D 5 3,000 15,000 5/3
F 4 4,000 16,000 1
G 3 5,000 15,000 3/5
H 2 6,000 12,000 1/3
L 1 7,000 7,000 1/7
M 0 8,000 0
Fig. 3-5
3.4 INCOME ELASTICITY OF DEMAND
The coefficient of income elasticity of demand (e M ) measures the percentage change in the amount of a
commodity purchased per unit time (DQ/Q) resulting from a given percentage change in a consumer’s
income (DM/M). Thus
e M ¼ DQ=Q
DM=M ¼ DQ
DM M Q
When e M is negative, the good is inferior. If e M is positive, the good is normal. A normal good is usually a
luxury if its e M . 1, otherwise it is a necessity. Depending on the level of the consumer’s income, e M for a good
is likely to vary considerably. Thus a good may be a luxury at “low” levels of income, a necessity at “intermediate”
levels of income and an inferior good at “high” levels of income.
EXAMPLE 6. Columns (1) and (2) of Table 3.4 show the quantity of commodity X that an individual would purchase per
year at various income levels. Column (5) gives the coefficient of income elasticity of demand of this individual for commodity
X between the various successive levels of available income. Column (6) indicates the range of income over which
commodity X is a luxury, a necessity or an inferior good. Commodity X might refer to bottles of champagne. At income
levels above $24,000 per year, champagne becomes an inferior good for this individual (who presumably substitutes rare
and very expensive wines for champagne).