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A Simple Model of the Firm 33

sales will be 2 lots (or 200 chips). If the firm cut its price to $100,000, its sales

would increase to 3.5 lots (point B). A dramatic reduction to a price of $50,000

would increase sales to 6 lots (point C). Thus, the demand curve shows the

firm’s predicted sales over a range of possible prices. The downward slope of

the curve embodies the law of demand: A lower price brings forth an increased

quantity of sales.

Demand curves and demand equations have a wide variety of uses in eco-

nomics. Predicting the profit consequences of selective fare discounts by air-

lines, the impact of higher oil prices on automobile travel, and the effect of

government day-care subsidies for working mothers all require the use of

demand curves. The properties of demand curves and the ways of estimating

demand equations are important topics in Chapters 3 and 4. At present, we

will focus on the firm’s main use of the demand relationship:

The firm uses the demand curve as the basis for predicting the revenue conse-

quences of alternative output and pricing policies.

Quite simply, the demand curve allows the firm to predict its quantity of sales

for any price it charges. In turn, revenue can be computed as the product of

price and quantity. The most useful way to begin the revenue estimation task

is to work with the mathematical representation of the demand curve. An alge-

braic representation of the demand curve in Figure 2.2 is

[2.1]

where Q is the quantity of lots demanded per week and P denotes the price per

lot (in thousands of dollars). In this form, the demand equation predicts the

quantity of microchips sold at any given price. For instance, if P equals $50

thousand, then, according to Equation 2.1, Q equals 6 lots (point C in the fig-

ure); if P equals $130 thousand, Q equals 2 lots, and so on. For any price the firm

charges, the demand equation predicts the resulting quantity of the good that will be sold.

Setting different prices and computing the respective quantities traces out the

demand curve in Figure 2.2.

With a bit of algebraic rearrangement, we can derive an equivalent version

of Equation 2.1, namely,

[2.2]

This equation generates exactly the same price-quantity pairs as Equation

2.1; thus, the two equations are equivalent. The only difference is the vari-

able chosen for placement on the left-hand side. Note the interpretation of

Equation 2.2. For any quantity of microchips the firm plans to sell, Equation

2.2 indicates the price needed to sell exactly this quantity. For instance, setting

Q 3.5 lots in Equation 2.2, we find that P equals $100 thousand (point B in

P 170 20Q,

Q8.5.05P,

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