Figure 2.2). This price equation usually is referred to as the firm’s inverse

demand equation.^2

Equation 2.1 (or the equivalent, Equation 2.2) contains all the informa-

tion the firm needs to predict revenue. However, before launching into the

revenue analysis, we should pause to make two points. First, the demand equa-

tion furnishes a quantitative snapshot of the currentdemand for the firm’s prod-

uct as it depends on price. Of course, many other factors, including competing

firms’ products and prices and the general strength of the computer industry,

affect the firm’s chip sales. The demand prediction of Equation 2.1 is based on

the current state of these factors. If economic conditions change, so too will the

firm’s sales at any given price; that is, Equation 2.1 would no longer be a valid

representation of the new demand conditions. Keep in mind that our use of the

demand equation takes other demand-relevant factors as given, that is,

unchanged. (Chapters 3 and 9 take up the effects of changing market condi-

tions and competitor behavior on a firm’s demand.)

The second point is that we view the demand curve as deterministic;that

is, at any given price, the quantity sold can be predicted with certainty. For a

given price, Equation 2.1 furnishes a precise sales quantity. Conversely, for any

targeted sales quantity, Equation 2.2 provides a precise market-clearing price.

We acknowledge that such certainty is hardly the norm in the real world.

Nonetheless, the demand equation representation remains valid as long as the

margin of error in the price-quantity relationship is relatively small. To become

comfortable with the demand equations, think of a product with a long and sta-

ble history, allowing sales predictions to be made with very little error. (A deter-

ministic demand equation would be inappropriate in the case of a new product

launch. Other methods, discussed in Chapters 12 and 13, would be used to

provide probability forecasts of possible sales levels.)

Let’s use Equation 2.2 to predict the revenues generated by alternative sales

policies of the microchip manufacturer. Figure 2.3 contains the pertinent infor-

mation and provides a graph of revenue. Column 1 of the tabular portion lists

a spectrum of possible sales quantities ranging from 0 to 8.5 lots. It will be con-

venient to think of the sales quantity, Q, as the firm’s decision variable, that is,

the variable it explicitly chooses. For each alternative choice of Q, column 2 lists

the corresponding sales price obtained from Equation 2.2. (Be sure you under-

stand that the firm cannotset both Q and P independently. Once one is set, the

other is determined by the forces of demand embodied in the demand equa-

tion.) Finally, column 3 lists the resulting revenue earned by the firm, where

revenue is defined as R P Q. From the table, we observe that revenue is zero

when sales are zero (obviously). Then as Q increases, revenue initially rises,

34 Chapter 2 Optimal Decisions Using Marginal Analysis

(^2) An important special case occurs when the firm produces for a perfectly competitive market. (An
extensive discussion appears in Chapter 7.) There the firm faces a horizontal demand curve instead
of a downward-sloping curve. For example, suppose the inverse demand equation is P 170. The
firm can sell as much or as little output as it wishes at $170,000 per lot, the competitive price, and
its actions will have no effect on this price.
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