9781118041581

where, for simplicity, MC is assumed to be constant. How should the firm set

its price to maximize its contribution (and, therefore, its profit)? The answer

depends on how responsive demand is to changes in price, that is, on price

elasticity of demand. Raising price increases the firm’s contribution per unit (or

margin), P MC. But to a greater or lesser degree, a price hike also reduces

the total volume of sales Q. If sales are relatively unresponsive to price (i.e.,

demand is relatively inelastic), the firm can raise its price and increase its mar-

gin without significantly reducing quantity. In this instance, the underlying

trade-off works in favor of high prices.

Alternatively, suppose demand is very elastic. In this instance, a price

increase would bring a large drop in sales to the detriment of total contribu-

tion. Here, the way to maximize contribution (and profit) is to play the other

side of the trade-off. The firm should pursue a policy of discount pricing to

maximize profitability. As we shall see, the correct pricing policy depends on a

careful analysis of the price elasticity of demand. Indeed, when the firm has

the ability to segment markets, it may benefit by trading on demand differ-

ences. As noted in this chapter’s opening example, airlines set a variety of dif-

ferent ticket prices—charging high fares to less price-sensitive business travelers

and discounting prices to economy-minded vacation travelers.

In Chapter 2, we focused on the application of the MR MC rule as a way

to determine the firm’s optimal level of output. It is possible to write down and

apply a modified (but exactly equivalent) version of the MR MC rule to

derive a simple rule for the firm’s profit-maximizing price.The firm’s optimal

price is determined as follows:

[3.12]

This equation, called the markup rule,indicates that

The size of the firm’s markup (above marginal cost and expressed as a percentage

of price) depends inversely on the price elasticity of demand for a good or service.

The markup is always positive. (Note that EPis negative, so the right-hand

side is positive.) What happens as demand becomes more and more price

elastic (i.e., price sensitive)? The right-hand side of the markup rule

becomes smaller, and so does the optimal markup on the left-hand side. In

short, the more elastic is demand, then the smaller is the markup above mar-

ginal cost.^11

PMC

P



1

EP

.

96 Chapter 3 Demand Analysis and Optimal Pricing

(^11) Here is how the markup rule is derived. From Equation 3.11, we know that MR P[1 1/EP].
Setting MR MC, we have P P/EPMC. This can be written as P MC P/EPand, finally,
[P MC]/P 1/EP, the markup rule. Thus, the markup rule is derived from and equivalent to
the MR MC rule.
c03DemandAnalysisAndOptimalPricing.qxd 8/18/11 6:48 PM Page 96