9781118041581

Demand Analysis and Optimal Pricing 95

tickets are sold. The cost of an additional passenger or spectator is negligible

once the flight or event has been scheduled. As for inventory, production costs

are sunk; selling costs are negligible or very small. Thus, in each case the firm

maximizes profits by setting price and output to maximize revenue.

How does the firm determine its revenue-maximizing price and output?

There are two equivalent answers to this question. The first answer is to apply

Chapter 2’s fundamental rule: MR MC. In the case of a pure selling problem,

marginal cost is zero. Thus, the rule becomes MR 0, exactly as one would

expect. This rule instructs the manager to push sales to the point where there

is no more additional revenue to be had—MR 0—and no further.

From the preceding discussion, we have established a second, equivalent

answer: Revenue is maximized at the point of unitary elasticity. If demand were

inelastic or elastic, revenue could be increased by raising or lowering price,

respectively. The following proposition sums up these results.

Revenue is maximized at the price and quantity for which marginal revenue is zero

or, equivalently, the price elasticity of demand is unity (1).

Note that this result confirms that the point of unitary elasticity occurs at the

midpoint of a linear demand curve. For the sales quantity at the midpoint,

marginal revenue is exactly zero (since the MR curve cuts the horizontal axis

at the midpoint quantity). But when MR 0, it is also true that EP1.

CHECK

STATION 4

The management of a professional sports team has a 36,000-seat stadium it wishes to fill.

It recognizes, however, that the number of seats sold (Q) is very sensitive to average

ticket prices (P). It estimates demand to be Q60,0003,000P. Assuming the team’s

costs are known and do not vary with attendance, what is management’s optimal pricing

policy?

Optimal Markup Pricing

There is a close link between demand for a firm’s product and the firm’s

optimal pricing policy. In the remainder of this chapter, we will take a close

and careful look at the trade-off between price and profit. Recall that in

Chapter 2, the focus was squarely on the firm’s quantity decision. Once the

firm determined its optimal output by weighing marginal revenue and mar-

ginal cost, it was a simple matter to set price in order to sell exactly that

much output. Now we shift our focus to price and consider a somewhat dif-

ferent trade-off.

To illustrate this trade-off, we can write the firm’s contribution as

Contribution(PMC)Q ,

c03DemandAnalysisAndOptimalPricing.qxd 8/18/11 6:48 PM Page 95