9781118041581

Our discussion has suggested an interesting and important relationship

between marginal revenue and price elasticity. The same point can be made

mathematically. By definition, MR dR/dQ d(PQ )/dQ. The derivative of

this product (see Rule 5 of the appendix to Chapter 2) is

[3.11]

For instance, if demand is elastic (say, EP3), MR is positive; that is, an

increase in quantity (via a reduction in price) will increase total revenue. If

demand is inelastic (say, EP.6), MR is negative; an increase in quantity

causes total revenue to decline. If elasticity is precisely 1, MR is zero. Figure

3.3a shows clearly the relationship between MR and EP.

Maximizing Revenue

As we saw in Chapter 2, there generally is a conflict between the goals of max-

imizing revenue and maximizing profit. Clearly, maximizing profit is the appro-

priate objective because it takes into account not only revenues but also

relevant costs. In some important special cases, however, the two goals coin-

cide or are equivalent. This occurs when the firm faces what is sometimes called

a pure selling problem: a situation where it supplies a good or service while

incurring novariable cost (or a variable cost so small that it safely can be

ignored). It should be clear that, without any variable costs, the firm maximizes

its ultimate profit by setting price and output to gain as much revenue as pos-

sible (from which any fixedcosts then are paid). The following pricing problems

serve as examples.

• A software firm is deciding the optimal selling price for its software.


• A manufacturer must sell (or otherwise dispose of) an inventory of
  unsold merchandise.


• A professional sports franchise must set its ticket prices for its home
  games.


• An airline is attempting to fill its empty seats on a regularly scheduled
  flight.

In each of these examples, variable costs are absent (or very small). The cost

of an additional software copy (documentation and disk included) is trivial. In

the case of airline or sports tickets, revenues crucially depend on how many

P 31 1/EP 4.

P 31 (dP/dQ )(Q /P) 4

PP(dP/dQ )(Q /P)

MRP(dQ /dQ )(dP/dQ )Q

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