Elasticity of Demand 85The algebraic expressions in Equations 3.7 and 3.8a are referred to as point
elasticities because they link percentage quantity and price changes at a price-
quantity point on the demand curve.Although most widely used, point elasticity
measures are not the only way to describe changes in price and quantity. A
closely related measure is arcprice elasticity, which is defined aswhere Qis the average of the two quantities, Q (Q 0 Q 1 )/2,and isPEP
¢Q/Q
¢P/P
the average of the two prices, In the airline example, the
average quantity is 105 seats, the average price is $237.50, and the arc price
elasticity is (10/105)/(5/237.5) 4.5.
The main advantage of the arc elasticity measure is that it treats the prices
and quantities symmetrically; that is, it does not distinguish between the “initial”
and “final” prices and quantities. Regardless of the starting point, the elasticity is
the same. In contrast, in computing the elasticity via Equation 3.7, one must be
careful to specify P 0 and Q 0. To illustrate, suppose the initial airfare is $235 and
110 seats are filled. The elasticity associated with a price hike to $240 (and a drop
to 100 seats) is EP(10/110)/(5/235) 4.3. Thus, we see that the elastic-
ity associated with the change is 4.8 or 4.3, depending on the starting point.
The overriding advantage of point elasticities (Equation 3.8a) is their appli-
cation in conjunction with marginal analysis. For instance, a firm’s optimal
pricing policy depends directly on its estimate of the price elasticity, EP
(dQ /Q)/(dP/P). In this and later chapters, we will focus on point elasticities
in our analysis of optimal decisions.^7
Elasticity measures the sensitivity of demand with respect to price. In
describing elasticities, it is useful to start with a basic benchmark. First, demand
is said to be unitary elasticif EP1. In this case, the percentage change in
price is exactly matched by the resulting percentage change in quantity, but in
the opposite direction. Second, demand is inelasticif 1 EP0. The term
inelasticsuggests that demand is relatively unresponsive to price: The percent-
age change in quantity is less (in absolute value) than the percentage change
in price. Finally, demand is elasticif EP1. In this case, an initial change in
price causes a larger percentage change in quantity. In short, elastic demand
is highly responsive, or sensitive, to changes in price.
The easiest way to understand the meaning of inelastic and elastic demand
is to examine two extreme cases. Figure 3.2a depicts a vertical demand curve
representing perfectly inelasticdemand, EP0. Here sales are constant (atP (P 0 P 1 )/2.
(^7) As long as the price change is very small, the point elasticity calculated via Equation 3.7 will vary
little whether the higher or lower price is taken as the starting point. Furthermore, this value will
closely approximate the exact measure of elasticity given by Equation 3.8a.
c03DemandAnalysisAndOptimalPricing.qxd 8/18/11 6:48 PM Page 85