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2.2 PRICE ELASTICITY OF DEMAND 47
Equation (2.4) highlights the difference between the slope of the demand curve,
b, and the price elasticity of demand, b(P Q) . The slope measures the absolute
change in quantity demanded (in units of quantity) brought about by a one-unit change
in price. By contrast, the price elasticity of demand measures the percentage change in
quantity demanded brought about by a 1 percent change in price.
You might wonder why we do not simply use the slope to measure the sensitivity
of quantity to price. The problem is that the slope of a demand curve depends on the
units used to measure price and quantity. Thus, comparisons of slope across different
goods (whose quantity units would differ) or across different countries (where prices
are measured in different currency units) would not be very meaningful. By contrast,
the price elasticity of demand expresses changes in prices and quantities in common
terms (i.e., percentages). This allows us to compare the sensitivity of quantity
demanded to price across different goods or different countries.
constant elasticity
Constant Elasticity Demand Curves demand curve A
Another commonly used demand curve is the constant elasticity demand curve, demand curve of the form
b
b
given by the general formula: Q aP , where a and b are positive constants. For the Q aP where a and b
are positive constants. The
constant elasticity demand curve, the price elasticity is always equal to the exponent term b is the price elas-
11
b. For this reason, economists frequently use the constant elasticity demand curve ticity of demand along this
to estimate price elasticities of demand using statistical techniques. curve.

LEARNING-BY-DOING EXERCISE 2.6
S
D
E
Elasticities along Special Demand Curves
Problem Q, P ( b)(P Q) Since b 10 and Q 400 10P,
when P 30,
(a) Suppose a constant elasticity demand curve is given
1
by the formula Q 200P 2 . What is the price elasticity 30
of demand? Q,P 10 a 400 10(30) b 3
(b) Suppose a linear demand curve is given by the and when P 10,
formula Q 400 10P . What is the price elasticity of
demand at P 30? At P 10? 10
Q,P 10 a b 0.33
400 10(10)
Solution
Note that demand is elastic at P 30, but it is inelastic at
(a) Since this is a constant elasticity demand curve, the P 10 (in other words, P 30 is in the elastic region of
price elasticity of demand is equal to 1 2 everywhere the demand curve, while P 10 is in the inelastic region).
along the demand curve.

(b) For this linear demand curve, we can find the price Similar Problems: 2.5, 2.6, 2.13
elasticity of demand by using equation (2.4):

PRICE ELASTICITY OF DEMAND AND TOTAL REVENUE

Businesses, management consultants, and government bodies use price elasticities of
demand a lot. To see why a business might care about the price elasticity of demand,
let’s consider how an increase in price might affect a business’s total revenue, that is, total revenue Selling
the selling price times the quantity of product it sells, or PQ. You might think that price times the quantity of
product sold.

11 We prove this result in the appendix to this chapter.