Chapter 24
NAME
Monopoly
Introduction.
The profitmaximizing output of a monopolist is found by
solving for the output at which marginal revenue is equal to marginal cost.
Having solved for this output, you find the monopolist’s price by plugging
the profitmaximizing output into the demand function. In general, the
marginal revenue function can be found by taking the derivative of the
total revenue function with respect to the quantity. But in the special case
of linear demand, it is easy to find the marginal revenue curve graphically.
With a linear inverse demand curve,
p
(
y
) =
a

by
, the marginal revenue
curve always takes the form
MR
(
y
) =
a

2
by
.
24.1 (0)
Professor Bong has just written the first textbook in Punk
Economics. It is called
Up Your Isoquant
. Market research suggests that
the demand curve for this book will be
Q
= 2
,
000

100
P
, where
P
is
its price. It will cost $1,000 to set the book in type. This setup cost is
necessary before any copies can be printed. In addition to the setup cost,
there is a marginal cost of $4 per book for every book printed.
(a)
The total revenue function for Professor Bong’s book is
R
(
Q
) =
20
Q

Q
2
/
100
.
(b)
The total cost function for producing Professor Bong’s book is
C
(
Q
) =
1
,
000 + 4
Q
.
(c)
The marginal revenue function is
MR
(
Q
) =
20

Q/
50
and
the marginal cost function is
MC
(
Q
) =
4
.
The profitmaximizing
quantity of books for professor Bong to sell is
Q
*
=
800.
24.2 (0)
Peter Morgan sells pigeon pies from a pushcart in Central Park.
Morgan is the only supplier of this delicacy in Central Park. His costs are
zero due to the abundant supplies of raw materials available in the park.
(a)
When he first started his business, the inverse demand curve for pigeon
pies was
p
(
y
) = 100

y
, where the price is measured in cents and
y
measures the number of pies sold.
Use black ink to plot this curve in
the graph below. On the same graph, use red ink to plot the marginal
revenue curve.
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310
MONOPOLY
(Ch.
24)
0
50
75
100
125
Pigeon pies
25
50
75
100
Cents
25
150
Black
lines
Blue line
Red line
(b)
What level of output will maximize Peter’s profits?
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 One '11
 Unknown
 Monopoly, Supply And Demand, Japanese government, Professor Bong

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