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454 CHAPTER 11 MONOPOLY AND MONOPSONY

LEARNING-BY-DOING EXERCISE 11.4
S
E D
Computing the Optimal Monopoly Price for a Linear Demand Curve
Along a linear demand curve, the price Thus, the IEPR for this example is
elasticity of demand is not constant. Nevertheless, we
can still use the IEPR to compute the profit-maximizing P 50 1 200 2P
price (and then use that result to compute the profit- P ( 2P ) 2P
maximizing quantity). Also, we can get the same results 200 2P
by applying the profit-maximizing condition expressed If we multiply each side of this expression by 2P, we
in equation (11.1)—MC MR. get a simple linear equation: 2P 100 200 2P, or
Suppose a monopolist has a constant marginal cost P 75. Thus, the profit-maximizing monopoly price is
MC $50 and faces the demand curve P 100 Q/2 $75. We find the profit-maximizing monopoly quantity
(which can be rewritten as Q 200 2P).
by substituting this price into the demand curve:
Q 200 2(75) 50.
Problem
(b) To solve the problem by equating MR and MC, re-
(a) Find the profit-maximizing price and quantity for call Learning-By-Doing Exercise 11.1. In that exercise,
the monopolist using the IEPR. we showed that, for a linear demand curve of the form
P a bQ, marginal revenue MR a 2bQ. In this
(b) Find the profit-maximizing price and quantity for example, then, MR 100 Q. Since MR MC and
the monopolist by equating MR to MC.
MC 50, 50 100 Q, or Q 50. Substituting this
quantity back into the demand curve, we find that P
Solution 100 50/2 75.
(a) For a linear demand curve, the price elasticity of Thus, the IEPR and the MR MC condition give
demand is given by a formula derived from the general the same results for the profit-maximizing price and
expression for elasticity, Q,P (¢Q/¢P )(P/Q). 6 In this quantity (this is as it should be, of course, since the IEPR
particular example, Q/ P 2, so was derived from the MR MC condition). Also, note
that for a linear demand curve, where price elasticity of
demand is not constant, we have to begin with the gen-
P
Q,P 2 eral formula for Q,P when applying the IEPR.
Q
Similar Problem: 11.11
Since Q 200 2P,

2P
Q,P
200 2P

THE MONOPOLIST ALWAYS PRODUCES ON THE
ELASTIC REGION OF THE MARKET DEMAND CURVE

Although a monopolist could, in theory, set its price anywhere along the market
demand curve, a profit-maximizing monopolist will only want to operate on the elastic
region of the market demand curve (i.e., the region in which the price elasticity of
demand Q,P is between 1 and q). Figure 11.9 illustrates why. If you were a monop-
olist and you contemplated operating at a point such as A at which demand was in-
elastic, you could always increase profit by raising your price, reducing your quantity,
and moving to point B. When you move from point A to point B, your total revenue
goes up by the difference between area I and area II, and your total costs go down be-
cause you are producing less. If your total revenue goes up and your total costs go
6 For discussion of how the price elasticity of demand varies along a linear demand curve, see Chapter 2.