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Lecture # 16
Monopoly
Lecturer: Martin Paredes
1. The Monopolist's Profit Maximization Problem
 The Profit Maximization Condition
 Equilibrium
2. The Inverse Elasticity Pricing Rule
3. The Welfare Economics of Monopoly
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Definition: A monopoly market consists of a single
seller facing many buyers.
Assumption: There are barriers to entry.
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 The monopolist's objective is to maximise
profits:
Max (Q) = TR(Q) – TC(Q) = P(Q)· Q – C(Q)
Q
where P(Q) is the (inverse) market demand
curve.
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 Profit maximizing condition for a monopolist:
dTR(Q) = dTC(Q)
dQ
dQ
…or…
MR(Q) = MC(Q)
 In other words, the monopolist sets output so
that the marginal profit of additional
production is just zero.
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 Recall that a perfect competitor sets P = MC,
because MR = P.
 This is not true for the monopolist because the
demand it faces is NOT flat.
 As a result, MR < P
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 Since TR(Q) = P(Q) · Q, then:
dTR(Q) = MR(Q) = P(Q) + dP(Q) · Q
dQ
dQ
 In perfect competition, demand is flat, meaning
dP(Q)/dQ = 0, so MR = P.
 For a monopoly, demand is downwardsloping, meaning dP(Q)/dQ < 0, so MR < P.
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Example: Marginal Revenue
Price
Price
Competitive firm
Monopolist
Demand facing firm
Demand facing firm
P0
P0
P1
A
B
q q+1
C
A
Firm output
B
Q0 Q0+1
Firm output
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Price
Example: Marginal Revenue Curve and Demand
The MR curve lies below
the demand curve.
P(Q0)
P(Q), the (inverse) demand curve
Q0
Quantity
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Price
Example: Marginal Revenue Curve and Demand
The MR curve lies below
the demand curve.
P(Q0)
P(Q), the (inverse) demand curve
MR(Q0)
MR(Q), the marginal revenue curve
Q0
Quantity
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Example: Marginal revenue for linear demands

Suppose demand is linear:

Total revenue is

P(Q) = a – bQ
TR = Q*P(Q) = aQ – bQ2
Marginal revenue is: MR = dTR = a – 2bQ
dQ
 So, for linear demands, marginal revenue has twice
the slope of demand.
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Definition: An agent has market power if she can
affect the price that prevails in the market
through her own actions.
 Sometimes this is thought of as the degree to
which a firm can raise price above marginal
cost.
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 In the short run, the monopolist shuts down if
the profit-maximising price does not cover
AVC (or average non-sunk costs).
 In the long run, the monopolist shuts down if
the profit-maximising price does not cover AC.
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Example: Profit maximisation
 Suppose:
P(Q) = 100 – Q
TC(Q) = 100 + 20Q + Q2



Marginal revenue is: MR = dTR = 100 – 2Q
dQ
Marginal cost is:
MC = dTC = 20 + 2Q
dQ
MR = MC ==> 100 – 2Q = 20 + 2Q ==> Q* = 20
P* = 80
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Example: Profit maximisation
 In equilibrium
Q* = 20
P* = 80


Observe that:
AVC = 20 + Q* = 40
AC = 100 + 20 + Q* = 45
Q*
Hence, P* > AVC and P* > AC
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Price
Example: Positive Profits for Monopolist
100
Demand curve
100
Quantity
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Price
Example: Positive Profits for Monopolist
100
MR
Demand curve
50
100
Quantity
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Price
Example: Positive Profits for Monopolist
MC
100
20
MR
Demand curve
50
100
Quantity
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Price
Example: Positive Profits for Monopolist
MC
100
MR
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Demand curve
20
50
100
Quantity
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Price
Example: Positive Profits for Monopolist
MC
100
80
E
MR
20
Demand curve
20
50
100
Quantity
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Price
Example: Positive Profits for Monopolist
MC
AVC
100
80
E
MR
20
Demand curve
20
50
100
Quantity
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Price
Example: Positive Profits for Monopolist
MC
AVC
100
80
E
AC
MR
20
Demand curve
20
50
100
Quantity
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Price
Example: Positive Profits for Monopolist
MC
AVC
100
80
E
AC
: Profits
MR
20
Demand curve
20
50
100
Quantity
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Notes:
1. A monopolist has less incentive to increase
output than the perfect competitor: for the
monopolist, an increase in output causes a
reduction in its price.
2. Profits can remain positive in the long run
because of the assumption that there are
barriers to entry.
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Notes:
3. A monopolist does not have a supply curve:
because price is determined endogenously by
the demand:
 The monopolist picks a preferred point on
the demand curve.
 Alternative view: the monopolist chooses
output to maximize profits subject to the
constraint that price be determined by the
demand curve.
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 We can rewrite the MR curve as follows:
MR = P + dP · Q
dQ
= P + dP · Q · P
dQ P
= P 1 + dP · Q
dQ P
= P 1 + 1

(
)
( )
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 Given that  is the price elasticity of demand:
 When demand is elastic ( < -1), then the
marginal revenue is positive (MR > 0).
 When demand is unit elastic ( = -1), then the
marginal revenue is zero (MR= 0).
 When demand is inelastic ( > -1), then the
marginal revenue is negative (MR < 0).
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Price
Example: Elastic Region of Linear Demand Curve
a
Demand
a/b
Quantity
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Price
Example: Elastic Region of Linear Demand Curve
a
MR
Demand
a/2b
a/b
Quantity
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Price
a
Example: Elastic Region of Linear Demand Curve
Elastic region ( < -1), MR > 0
MR
Demand
a/2b
a/b
Quantity
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Price
a
Example: Elastic Region of Linear Demand Curve
Elastic region ( < -1), MR > 0
Inelastic region (0>>-1), MR<0
MR
Demand
a/2b
a/b
Quantity
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Price
a
Example: Elastic Region of Linear Demand Curve
Elastic region ( < -1), MR > 0
Unit elastic (=-1), MR=0
Inelastic region (0>>-1), MR<0
MR
Demand
a/2b
a/b
Quantity
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 A monopolist will only operate on the elastic
region of the market demand curve
 Note: As demand becomes more elastic at each
point, marginal revenue approaches price.
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 The monopolist will produce at MR = MC, but
we also found that:
MR = P 1 + 1

 Then: P
or:
( )
( )
1 + 1

= MC
P – MC = – 1
P

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Definition: The Lerner Index of market power is
the price-cost margin, (P*-MC)/P*.
 It measures the monopolist's ability to price
above marginal cost, which in turn depends on
the elasticity of demand.
 The Lerner index ranges between 0 (for the
competitive firm) and 1 (for a monopolist
facing a unit elastic demand).
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 A monopoly equilibrium entails a dead-weight
loss.
 For the following analysis, suppose the supply
curve in perfect competition is equal to the
marginal cost curve of the monopolist.
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Example: Welfare Effects of Perfect Competition
Supply
PC
Demand
QC
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MR
Example: Welfare Effects of Perfect Competition
Supply
: Consumer Surplus
: Producer Surplus
PC
Demand
QC
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MR
Example: Welfare Effects of Monopoly
MC
PC
Demand
QC
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MR
Example: Welfare Effects of Monopoly
MC
PM
PC
Demand
QM
QC
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MR
Example: Welfare Effects of Monopoly
MC
PM
: Consumer Surplus
PC
Demand
QM
QC
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MR
Example: Welfare Effects of Monopoly
MC
PM
: Consumer Surplus
: Producer Surplus
PC
Demand
QM
QC
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MR
Example: Welfare Effects of Monopoly
MC
PM
: Consumer Surplus
: Producer Surplus
PC
: Deadweight Loss
Demand
QM
QC
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MR
1. A monopoly market consists of a single seller
facing many buyers (utilities, postal services).
2. A monopolist's profit maximization condition is
to set marginal revenue equal to marginal cost.
3. Marginal revenue generally is lower than price.
How much less depends on the elasticity of
demand.
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4. A monopolist never produces on the inelastic
portion of demand since, in the inelastic region,
raising price and reducing quantity make total
revenues rise and total costs fall!
5. The Lerner Index is a measure of market power,
often used in antitrust analysis.
6. A monopoly equilibrium entails a dead-weight
loss.
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