Dominick Salvatore Schaums Outline of Microeconomics, 4th edition Schaums Outline Series 2006
44 THE MEASUREMENT OF ELASTICITIES [CHAP. 3Table 3.5(b)BeforeAfterCommodityPrice(cents/unit)Quantity(units/month)Price(cents/unit)Quantity(units/month)Lemon (Z) 10 20 20 15Tea (X) 20 40 20 353.6 PRICE ELASTICITY OF SUPPLYThe coefficient of price elasticity of supply (e s ) measures the percentage change in the quantity supplied ofa commodity per unit of time (DQ=Q) resulting from a given percentage change in the price of the commodity(DP=P). Thuse s ¼ DQ=QDP=P ¼ DQDP P QWhen the supply curve is positively sloped (the usual case), price and quantity move in the same directionand e s . 0. The supply curve is said to be elastic if e s . 1, inelastic if e s , 1, and unitary elastic if e s ¼ 1. Arcand point e s can be found in the same way as arc and point e. When the supply curve is a positively slopedstraight line, then, all along the line, e s . 1, if the line crosses the price axis; e s , 1, if it crosses the quantityaxis; and e s ¼ 1, if it goes through the origin.EXAMPLE 8. To find e x for a movement from point A to point C, from C to A and midway between A and C (i.e., at pointB) and midway between C and F (i.e., at point D) for the values of Table 3.6, we proceed as follows:Table 3.6Point P x ($) Q xA——— 6 ––––8000B 5 6000C——— 6 ––––4000D 3 2000F——— 2 ——— 0From A to C,e s ¼ DPDP P AQ A¼From C to A, e s ¼ 4000 2At point B,At point D,4000244000e s ¼ DQDP P A þ P C¼ 4000 Q A þ Q C 268000¼ 2e s ¼ DQDP P C þ P F¼ 4000 Q C þ Q F 2¼ 1:51012,00064000ffi 1:67¼ 3
CHAP. 3] THE MEASUREMENT OF ELASTICITIES 45EXAMPLE 9. We can find e s at points B and D geometrically from Fig. 3-6.Fig. 3-6At Point B,e s ¼ DQDP P B¼ GLQ B LB LBOL ¼ GLOL ¼ 10,000 ffi 1:676000At point D,e s ¼ GHOH ¼ 60002000 ¼ 3To find point e s , for a curvilinear supply curve, we draw a tangent to the supply curve at the point and then proceed as above(see Problems 3.21 and 3.22).GlossaryArc elasticity of demandThe coefficient of price elasticity of demand between two points on a demand curve.Cross elasticity of demand (e xy ) The ratio of the percentage change in the amount of commodity X purchased per unitof time to the percentage change in the price of commodity Y. If e xy . 0, X and Y are substitutes; if e xy , 0, X and Y arecomplements; and if e xy ¼ 0, X and Y are nonrelated (i.e., independent).Income elasticity of demand (e M ) The ratio of the percentage change in the amount of a commodity purchased perunit of time to the percentage change in the consumer’s income. If e M . 0, the commodity is normal, and if e M , 0, it isinferior; if e M . 1, it is a luxury, and if 0 , e M , 1, it is a necessity.Point elasticity of demandThe coefficient of price elasticity of demand at a particular point on a demand curve.Price elasticity of demand (e) The ratio of the percentage change in the quantity of a commodity demanded per unit oftime to the percentage change in the price of the commodity. If e . 1, demand is elastic; if e , 1, demand is inelastic; and ife ¼ 1, demand is unitary elastic.Price elasticity of supply (e s ) The ratio of the percentage change in the quantity of a commodity supplied per unit oftime to the percentage change in the price of the commodity.Review Questions1. If the percentage increase in the quantity of a commodity demanded is smaller than the percentage fall in its price,the coefficient of price elasticity of demand is (a) greater than 1, (b) equal to 1, (c) smaller than 1, or (d) zero.Ans. (c) See Section 3.1.
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44 THE MEASUREMENT OF ELASTICITIES [CHAP. 3
Table 3.5(b)
Before
After
Commodity
Price
(cents/unit)
Quantity
(units/month)
Price
(cents/unit)
Quantity
(units/month)
Lemon (Z) 10 20 20 15
Tea (X) 20 40 20 35
3.6 PRICE ELASTICITY OF SUPPLY
The coefficient of price elasticity of supply (e s ) measures the percentage change in the quantity supplied of
a commodity per unit of time (DQ=Q) resulting from a given percentage change in the price of the commodity
(DP=P). Thus
e s ¼ DQ=Q
DP=P ¼ DQ
DP P Q
When the supply curve is positively sloped (the usual case), price and quantity move in the same direction
and e s . 0. The supply curve is said to be elastic if e s . 1, inelastic if e s , 1, and unitary elastic if e s ¼ 1. Arc
and point e s can be found in the same way as arc and point e. When the supply curve is a positively sloped
straight line, then, all along the line, e s . 1, if the line crosses the price axis; e s , 1, if it crosses the quantity
axis; and e s ¼ 1, if it goes through the origin.
EXAMPLE 8. To find e x for a movement from point A to point C, from C to A and midway between A and C (i.e., at point
B) and midway between C and F (i.e., at point D) for the values of Table 3.6, we proceed as follows:
Table 3.6
Point P x ($) Q x
A——— 6 ––––8000
B 5 6000
C——— 6 ––––4000
D 3 2000
F——— 2 ——— 0
From A to C,
e s ¼ DP
DP P A
Q A
¼
From C to A, e s ¼ 4000
2
At point B,
At point D,
4000
2
4
4000
e s ¼ DQ
DP P
A þ P C
¼ 4000
Q A þ Q C 2
6
8000
¼ 2
e s ¼ DQ
DP P
C þ P F
¼ 4000
Q C þ Q F 2
¼ 1:5
10
12,000
6
4000
ffi 1:67
¼ 3