8. Consider the graph below, which illustrates the demand for Fluff. Fluff can be produced at a constant marginal and average total cost of $4 per case.Quantity ofFluff (cases)MCDPrice($/case)100$2040a. Draw in a carefully constructed marginal revenue curve.b. Apply the MR= MCrule to determine the profit-maximizing level of output. What price must the monopolist charge to maximize profit?c. Calculate the profit earned by the monopolist.d. The slope of the demand curve indicates that in order to sell one more unit, the price must fall by 20 cents. Verify that the seller cannot increase profit by reducing price and selling slightly more.e. The slope of the demand curve indicates that if the price of Fluff increases by 20 cents, consumers will buy one less unit. Verify that the seller cannot increase profit by increasing price and selling slightly less.
8. a. The inverse demand function is
P
= 20
–
0.2
Q
Thus, the total revenue is
TR
=
P
×
Q
= 20
Q
–
0.2
Q
2
Hence, the marginal revenue can be represented by
MR
= 20
–
0.4
Q
Quantity of
Fluff (cases)
MC
MR
D
Price
($/case)
$20
4
0
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Market Power and Monopoly
Chapter 9
111
Solution
e. Suppose that the seller increases the price by 20 cents and sells one less unit of the good. The profit
9. Irwin is a monopoly seller of specialty bearings. Con-sider the graph to the right, which illustrates the de-mand and marginal revenue curves for Irwin’s 30-weight ball bearings, along with the marginal and average total costs of producing bearings:a. Find the monopolist’s profit-maximizing level of output.b. Determine the price the monopolist should charge to maximize profit.c. Draw an appropriate rectangle on your graph to represent the total revenue the seller receives from selling the profit-maximizing quantity of bearings at the profit-maximizing price.d. Draw an appropriate rectangle on your graph to represent the total cost of producing ball bearings.e. The difference in the areas you drew in (c) and (d) represents profit. Calculate the profit Irwin earns from selling 30-weight ball bearings.
9. a.
The monopolist will maximize its profit by producing the level of output at which
MR = MC,
that is,
100 dozen bearings.
b. The monopolist should charge $100 per dozen to maximize profit.
c.
Quantity of bearings
(dozens)
Price
($/dozen)
$100
170
130 150
60 100
60
MC
ATC
0
MR
D
Total
revenue
Quantity of bearings
(dozens)
Price
($/dozen)
$100
170
130 150
60 100
60
MC
ATC
0
MR
D
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112
Part 3
Markets and Prices
Solution
d.