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

CHAP. 3] THE MEASUREMENT OF ELASTICITIES 55
(c)
Fig. 3-12
3.15 (a) Does e M measure movements along the same demand curve or shifts in demand? (b) How can
we find the income elasticity of demand for the entire market? (c) Give some examples of luxuries,
(d) Since food is a necessity, how can we get a rough index of the welfare of a family or nation?
(a)
(b)
(c)
In measuring the income elasticity of demand, only income changes out of the factors affecting demand. Thus,
while the price elasticity of demand (e) refers to a movement along a specific demand curve, the income
elasticity of demand (e M ) measures a shift from one demand curve to another.
In Problem 3.14(a) we found e M for a single family. In getting the income elasticity of demand of a commodity
for the entire market, Q would have to refer to the market quantity and M to the money income of all the
consumers in the market (with the distribution of money incomes assumed to remain constant).
Expenditures on education and travel are usually considered luxuries by most people.
(d ) Roughly speaking, the smaller the proportion of income spent on food by a family or nation, the greater is its welfare.
3.16 (a) Find the cross elasticity of demand between hot dogs (X) and hamburgers (Y) and between hot dogs (X)
and mustard (Z), for the data in Table 3.17. (b) State the ceteris paribus conditions in finding e xy and e xz .
Table 3.17
Before
After
(a)
(b)
Commodity
Price
(dollars/unit)
Quantity
(units/month)
Price
(dollars/unit)
Quantity
(units/month)
Hamburgers (Y) 3.00 30 2.00 40
Hot dogs (X) 1.00 15 1.00 10
Mustard (jar) (Z) 1.50 10 2.00 9
Hot dogs (X) 1.00 15 1.00 12
e xy ¼ DQ x
P
y 5 3
¼
¼þ1
DP y Q x 1 15
e xz ¼ DQ x
P
z 3 1:50
¼
¼
DP z Q x 0:50 15
0:6
Since e xy is positive, hot dogs and hamburgers are substitutes. Since e xz is negative, hot dogs and mustard are
complements for this individual.
In finding e xy , we assumed that the prices of all other commodities (including the prices of X and Z), and the
individual’s money income and tastes remain unchanged. Similarly, e xz measures the responsiveness in Q x to
a change in P z only. Thus, like e M , e xy and e xz measure shifts in the demand curve for X.