Price and Output Determination:
Monopoly and Dominant Firms
Managerial Economics
Econ 340
Lecture 7
Christopher Michael
Trent University
© 2006 by Nelson, a division of Thomson Canada Limited
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Topics
● Sources of Market Power
● Unregulated Monopoly
● Optimal Markups
● Limit Pricing
● Regulated Monopolies
● Peak Load Pricing
© 2006 by Nelson, a division of Thomson Canada Limited
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Overview
"Monopoly" conjures images of huge profits,
great wealth, and indiscriminate power,
labeled robber barons.
• But some monopolies are NOT very profitable
• Others dominate their industry
• Still others are regulated and may have very low
rates of return on invested capital.
• Regulated monopolies are known as utilities.
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Sources of Market Power
for a Monopolist
» Legal restrictions -- copyrights & patents.
» Control of critical resources creates market power.
» Government-authorized franchises, such as provided to
cable TV companies.
» Economies of size allow larger firms to produce at lower cost
than smaller firms.
» Brand loyalty and extensive advertising makes entry
highly expensive.
» Increasing returns in network-based businesses compatibilities increase market penetration.
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What Went Wrong
With Apple?
• Apple tried to pursue increasing returns by
trying to be the industry standard
• Tried to protect its graphical interface code
from infringement
• Led to Apple being less compatible with
software being developed by third parties
• Microsoft recognized and became the
industry standard
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An Unregulated Monopoly
Monopoly is a single seller
P = 100 - Q
where entry is prohibited and
there are no close substitutes
1. FIRM = INDUSTRY
2. MR < P
TR1 = 60•40 = 2400
TR2 = 59•41 = 2419
19
© 2006 by Nelson, a division of Thomson Canada Limited
60
59
D
40 41
Q
So, MR = 19
where MR <
6
3.
At output where MR = MC,
profit is maximized
MC
Proof: Max  = TR – TC
Find where d/dQ = 0
PM
D
d/dQ = dTR/dQ - dTC/dQ = 0
MR – MC = 0
So: MR = MC
4.
Charge highest price
that the market will bear, PM
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QM
MR
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If we use a linear demand curve:
MARGINAL REVENUE is twice as steep
as a linear demand curve
If P = a - b•Q, then
TR = aQ - bQ2
so
MR = a - 2b•Q
This is twice as steep
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A Monopoly Problem
• Find the monopoly quantity if: P = 100 - Q,
and where MC = 20.
Answer this by starting where MR = MC
» TR = P•Q = 100•Q - Q2
» MR = 100 - 2•Q = 20
» 80 = 2•Q
» QM = 40
Find Monopoly Price:
» PM = 100 - 40 = 60
© 2006 by Nelson, a division of Thomson Canada Limited
The highest price
that the market will
bear.
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The Importance of Price Elasticity
of Demand for a Monopoly
MONOPOLY has MR = MC
TR = Q•P(Q)
dTR/dQ = MR = P + (dP/dQ)Q = P [1 + (dP/dQ)(Q/P)]
= P[1 + 1/ ED ]
As ED goes to
negative infinity,
MR approaches P
© 2006 by Nelson, a division of Thomson Canada Limited
P [ 1 + 1/ ED ] = MC
Marginal Revenue
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Optimal Markups
• The optimal markup can be found using this same
formula. P = [ED /( ED+1)]•MC.
• The optimal markup m is: (1+m) = [ED /( ED+1)]
• For example, if ED = -3, the markup is 50%, since
= [-3/( -3 +1)] = 1.5.
• If ED = -4, the markup is 33.3%, since his is where
[-4/( -4 +1)] = 1.333.
• If the price elasticity is infinite, the markup is zero.
This occurs in competition.
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Find the Monopoly Price in these
Problems
ANSWER
If ED = - 3
& MC = 100
What’s PM ?
• P[ 1 + 1/( - 3) ] = 100
• P[ 2/3 ] = 100
So, P = $150.
• If ED = -5, then optimal
monopoly price falls to
$125.
• The more elastic is the
demand, the closer is
price to MC.
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A Monopoly Pricing Problem
• Regression results for Land’s End
Women’s light-weight coats:
• Log Q = - 0.4 -1.7 Log P + 1.2 Log Y
( 3 . 2)
( 4. 5)
• Let MC of imported women’s light-weight
coats be $19.50.
• Find the Monopoly Price for a Land’s End
light-weight coat.
• ANSWER: P( 1 + 1/ED ) = MC
» P ( 1 + 1/(-1.7) ) = 19.50
» P = $47.36
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Limit Pricing
• An established firm considers the
possibility of new entrants with distaste.
• Suppose a new entrant would have a
U-shaped average cost curves.
• Suppose also that the established firm has
created some brand loyalty, such that
entrants must under-price them to take
away their customers.
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AC
14
The potential competitor (PC) has no demand at
limit price PL and DPC is below ACPC
Profit Profile
PL
ACPC
ACestablished
D
II
I
Q
time
DPC
Which profit profile (I or II) represents monopoly pricing?
Would a shareholder prefer profile I or II?
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Regulated Monopolies
•
•
•
•
Electric Power Companies
Natural Gas Companies
Communication Companies
Often, Water Companies
» All are examples of regulated companies
» They are all “naturally monopolistic” as they
all have significant declining cost curves.
» Suppose we examine railways before
regulation as an example of a natural
monopoly.
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Natural Monopolies
• Declining Cost
Industries
» economies in
distribution
» economies of scale
• Without Regulation
they face Cyclical
Competition with
prices gyrating
between PM and PC.
» railway history includes
periods of huge profits
then bankruptcies
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DEMAND
PM
AC
PR = AC
PC = MC
QM
QR QC
MR
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Solutions to the
Problem of Natural Monopolies
• PREVENT ENTRY, set
P = MC and subsidize.
• REGULATE, prevent
entry, & set P = AC
» common for local water,
» subsidies require some form of
telephone, electricity
taxation, which will tend to distort
work effort.
• FRANCHISE through
» subsidies to Via Rail
a bidding war, likely
• NATIONALIZE, prevent entry,
set price typically low
» governments find changing price a
highly political event
» once popular solution in Europe
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P = AC
» Cable TV
» concessions at various
stadiums
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Peak Load Pricing
• Examples: long distance calls,
electrical prices, seasonal pricing at
amusement parks
• Conditions:
» Not Storable
» Same Facilities
» Demand Variation
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Peak and Off-Peak Demand
What price
should we
charge for peak
and off-peak
users?
price
Pp
Po
Off-Peak
Demand
Peak-Load Demand
Q0 QP
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General Solution
• P(peak) = variable costs + capital costs
• P(off-peak) = variable costs only
• Some argue that off-peak users benefit from
capacity
» Electrical Case: Less chance of a brown out
» Amusement Park: Off-peak users
enjoy more space
» Then off-peak users should pay
for some part of the capacity
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