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Demand Analysis and Optimal Pricing 91

How does one estimate the impact on sales from changes in two or more

factors that affect demand? A simple example can illustrate the method. In

Table 3.1, the price and income elasticities for nonbusiness air travel are esti-

mated to be EP.38 and EY1.8, respectively. In the coming year, average

airline fares are expected to rise by 8 percent and income by 5 percent. What

will be the impact on the number of tickets sold to nonbusiness travelers? The

answer is found by adding the separate effects due to each change:

[3.10]

Therefore, Q /Q (.38)(8%) (1.8)(5%) 6%. Sales are expected to

increase by about 6 percent.

DEMAND ANALYSIS AND OPTIMAL PRICING

In this section, we put demand analysis to work by examining three important

managerial decisions: (1) the special case of revenue maximization, (2) opti-

mal markup pricing, and (3) price discrimination.

Price Elasticity, Revenue, and Marginal Revenue

What can we say about the elasticity along any downward-sloping, linear

demand curve? First, we must be careful to specify the starting quantity and

price (the point on the demand curve) from which percentage changes are

measured. From Equation 3.8b, we know that EP(dQ /dP)(P/Q). The slope

of the demand curve is dP/dQ (as it is conventionally drawn with price on the

vertical axis). Thus, the first term in the elasticity expression, dQ /dP, is simply

the inverse of this slope and is constant everywhere along the curve. The term

P/Q decreases as one moves downward along the curve. Thus, along a linear

demand curve, moving to lower prices and greater quantities reduces elastic-

ity; that is, demand becomes more inelastic.

As a concrete illustration of this point, consider a software firm that is try-

ing to determine the optimal price for one of its popular software programs.

Management estimates this product’s demand curve to be

where Q is copies sold per week and P is in dollars. We note for future refer-

ence that dQ /dP 4. Figure 3.3a shows this demand curve as well as the

associated marginal revenue curve. In the figure, the midpoint of the demand

curve is marked by point M: Q 800 and P $200. Two other points, A and

B, along the demand curve also are shown.

Q1,6004P,

¢Q/QEP(¢P/P)EY(¢Y/Y)

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