Dominick Salvatore Schaums Outline of Microeconomics, 4th edition Schaums Outline Series 2006
54 THE MEASUREMENT OF ELASTICITIES [CHAP. 3INCOME ELASTICITY AND CROSS ELASTICITY OF DEMAND3.14 Table 3.15 shows the quantity of “regular cuts of meat” that a family of four would purchase per yearat various income levels. (“Regular cuts of meat” might refer to pork chops and pot roast; “superiorcuts of meat” might refer to steaks and roast beef while “cheap cuts” to hamburger and chicken.) (a)Find the income elasticity of demand of this family for regular cuts of meat between the various successivelevels of this family’s income. (b) Over what range of income are regular cuts of meat aluxury, a necessity, or an inferior good for this family? (c) Plot on a graph the income-quantityrelationship given above (measure income on the vertical axis and quantity on the horizontalaxis). The resulting curve is called an Engel curve; such curves are discussed in greater detail inChapter 4.Table 3.15Income ($/year) 4,000 6,000 8,000 10,000 12,000 14,000 16,000 18,000Quantity (1b/year) 100 200 300 350 380 390 350 250(a) See columns (5) and (6) of Table 3.16.(b) At very low levels of income (here, $8000 per year or less), this family presumably consumes mostlycheap cuts of meat, regular cuts representing a luxury. At intermediate levels of income (here, between$8000 and $14,000 per year) regular cuts of meat become a necessity. At high levels of income (here,above $14,000), this family begins to reduce its consumption of regular cuts of meat and consumes moresteaks and roast beef.(1)Income($/year)(2)Quantity(1b/year)Table 3.16(3)Percent Changein Q(4)Percent Changein M(5)e M(6)Type of GoodA 4,000 100———————— 100 ————— 50 ———— 2 ———— luxuryB 6,000 200——————— 50 —————— 33.33 ——— 1.50 ——— luxuryC 8,000 300——————— 16.67 —————— 25 ———— 0.67 — necessityD 10,000 350——————— 8.57 ——————— 20 ———— 0.43 — necessityF 12,000 380——————— 2.63 ——————— 16.67 ——— 0.16 — necessityG 14,000 390—————— 210.26 —————— 14.28 —— 20.72 — inferiorH 16,000 350—————— 228.57 —————— 12.50 ——— 22.29 — inferiorL 18,000 250
CHAP. 3] THE MEASUREMENT OF ELASTICITIES 55(c)Fig. 3-123.15 (a) Does e M measure movements along the same demand curve or shifts in demand? (b) How canwe 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 incomeelasticity 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 commodityfor the entire market, Q would have to refer to the market quantity and M to the money income of all theconsumers 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 3.17BeforeAfter(a)(b)CommodityPrice(dollars/unit)Quantity(units/month)Price(dollars/unit)Quantity(units/month)Hamburgers (Y) 3.00 30 2.00 40Hot dogs (X) 1.00 15 1.00 10Mustard (jar) (Z) 1.50 10 2.00 9Hot dogs (X) 1.00 15 1.00 12e xy ¼ DQ x P y 5 3¼¼þ1DP y Q x 1 15e xz ¼ DQ x P z 3 1:50¼¼DP z Q x 0:50 150:6Since e xy is positive, hot dogs and hamburgers are substitutes. Since e xz is negative, hot dogs and mustard arecomplements for this individual.In finding e xy , we assumed that the prices of all other commodities (including the prices of X and Z), and theindividual’s money income and tastes remain unchanged. Similarly, e xz measures the responsiveness in Q x toa change in P z only. Thus, like e M , e xy and e xz measure shifts in the demand curve for X.
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54 THE MEASUREMENT OF ELASTICITIES [CHAP. 3
INCOME ELASTICITY AND CROSS ELASTICITY OF DEMAND
3.14 Table 3.15 shows the quantity of “regular cuts of meat” that a family of four would purchase per year
at various income levels. (“Regular cuts of meat” might refer to pork chops and pot roast; “superior
cuts of meat” might refer to steaks and roast beef while “cheap cuts” to hamburger and chicken.) (a)
Find the income elasticity of demand of this family for regular cuts of meat between the various successive
levels of this family’s income. (b) Over what range of income are regular cuts of meat a
luxury, a necessity, or an inferior good for this family? (c) Plot on a graph the income-quantity
relationship given above (measure income on the vertical axis and quantity on the horizontal
axis). The resulting curve is called an Engel curve; such curves are discussed in greater detail in
Chapter 4.
Table 3.15
Income ($/year) 4,000 6,000 8,000 10,000 12,000 14,000 16,000 18,000
Quantity (1b/year) 100 200 300 350 380 390 350 250
(a) See columns (5) and (6) of Table 3.16.
(b) At very low levels of income (here, $8000 per year or less), this family presumably consumes mostly
cheap cuts of meat, regular cuts representing a luxury. At intermediate levels of income (here, between
$8000 and $14,000 per year) regular cuts of meat become a necessity. At high levels of income (here,
above $14,000), this family begins to reduce its consumption of regular cuts of meat and consumes more
steaks and roast beef.
(1)
Income
($/year)
(2)
Quantity
(1b/year)
Table 3.16
(3)
Percent Change
in Q
(4)
Percent Change
in M
(5)
e M
(6)
Type of Good
A 4,000 100
———————— 100 ————— 50 ———— 2 ———— luxury
B 6,000 200
——————— 50 —————— 33.33 ——— 1.50 ——— luxury
C 8,000 300
——————— 16.67 —————— 25 ———— 0.67 — necessity
D 10,000 350
——————— 8.57 ——————— 20 ———— 0.43 — necessity
F 12,000 380
——————— 2.63 ——————— 16.67 ——— 0.16 — necessity
G 14,000 390
—————— 210.26 —————— 14.28 —— 20.72 — inferior
H 16,000 350
—————— 228.57 —————— 12.50 ——— 22.29 — inferior
L 18,000 250
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