Page 473 - Microeconomics, Fourth Edition

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11.1 PROFIT MAXIMIZATION BY A MONOPOLIST 447
Combining these insights with the discussion in the preceding section, we can see
that, if output is positive (Q 0):

• Marginal revenue is less than price (MR P).
• Because average revenue is equal to price, marginal revenue is less than average
revenue (MR AR).
• Since the average revenue curve coincides with the demand curve, the marginal
revenue curve must lie below the demand curve.

Figure 11.4 shows the relationships among price, quantity, total revenue, average rev-
enue, and marginal revenue.
The relationship between average revenue and marginal revenue is consistent
with other average–marginal relationships we have seen elsewhere in the book. When
the average of something is falling, the marginal of that thing must be below the
average. Because market demand slopes downward (i.e., is falling) and the average rev-
enue curve corresponds to the demand curve, the marginal revenue curve must be
below the average revenue curve.

LEARNING-BY-DOING EXERCISE 11.1
S
E D
Marginal and Average Revenue for a Linear Demand Curve

Suppose that the equation of the market Thus, the marginal revenue curve for a linear demand
demand curve is P a bQ . curve is also linear. In fact, it has the same P-intercept
as the demand curve (i.e., at a), with twice the slope.
Problem What are the expressions for the average This implies that the marginal revenue curve intersects
and marginal revenues curves? the Q-axis halfway between the origin and the horizon-
tal intercept of the demand curve, which occurs at
Solution Average revenue coincides with the de-
mand curve. Thus, AR a bQ. Q a/(2b). For quantities greater than this halfway
point, marginal revenue not only lies below the demand
Per equation (11.2), marginal revenue is
curve, it is also negative. Notice that the shape of the
marginal curve in Figure 11.4(b) is consistent with these
¢P
MR(Q) P Q properties.
¢Q
Similar Problems: 11.1, 11.2
Now note that P/ Q b (since P a bQ is in the
general form of a linear equation). Substituting into the
equation above:

MR(Q) a bQ Q( b)
a 2bQ

THE PROFIT-MAXIMIZATION CONDITION
SHOWN GRAPHICALLY
Figure 11.5 illustrates the profit-maximization condition MR MC for our monopolist.
The marginal revenue curve MR is decreasing and lies below the demand curve D (which
is also the average revenue curve) for all positive output levels. The marginal cost curve