Chapter 11: Monopoly
• We are now back in partial equilibrium.
• So far we assumed perfect competition. In this chapter,
we study the other extreme, when there is only one
seller.
• Why do we care about monopoly? Because as
monopoly is the only seller, it can influence the market
equilibrium, i.e., they have market power. The
monopoly equilibrium is often inefficient.
Perfect
competition
Monopoly/
Monopsony
Oligopoly/ Oligopsony
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Monopoly Profit Maximization
• Being the only seller, monopoly can set price or quantity
to influence the market equilibrium.
• We know that all firms maximize their profits by setting
MR=MC (as π=R-C).
• Monopoly’s MC curve can be obtained in the same way
as the competitive firms.
• Difference is that monopoly faces a downward-sloping
demand curve, thus it faces a different MR curve.
competitive firm :   P  Q  C (Q)
monopoly :
  P(Q)  Q  C (Q)
2
Marginal Revenue
• Marginal revenue is the revenue the firm obtains from one
more additional q. The MR is p for a competitive firm.
• For monopoly: R  P(Q)  Q
MR 
dR  P  dQ  Q  dP
 P Q 
R
P
 1
 P
Q  P 1 

P
1   , where   0.


Q
Q
 
 Q P 
Thus, MR>0 if demand is elastic (ε<-1)
MR<0 if demand is inelastic (-1<ε≤0).
• If demand is inelastic, MR=MC is not optimum for a
monopolist since MR<0. Come back to this point later.
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MR= B
= P*△Q =P
B = P*△Q
C = Q*△P
MR = B +(-C)
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Unit Elastic Demand: What is MR?
Price
4
Example: Q = 4P -1
3
2
1
1
2
3
4
Quantity
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Linear Demand Curve and MR
For linear demand functions:
p = a – bq, where a>0, b>0.
R = pq = aq – bq2
MR= a – 2bq.
• Thus, MR curve and demand curve have the
same intercept, but MR is twice as steep as
demand curve.
• Elasticity at the mid-point is unity.
• The demand is elastic when price is higher and
inelastic when price is lower.
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Elasticity of a Linear Demand Curve
Price
a
ε< -1: elastic
Demand: P = a - bq
ε= -1
a/2
-1 < ε≤ 0: inelastic
Marginal Revenue:
P = a - 2bq
a/2b
a/b
Quantity
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• Monopoly profit is
maximized in the elastic
portion of the demand.
• A monopoly never
operates in the inelastic
portion of the demand.
• A monopoly shuts down:
– in LR if Pm<AC
– In SR if Pm<AVC
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Effects of a Shift of the Demand Curve
• Unlike a competitive firm, a monopoly does not have a supply
curve. Monopoly’s MC is not enough to know how much a
monopoly will sell at any given price.
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Market Power
• Market power: the ability of a firm to charge P above MC and earn
a positive profit.
Q: Can a monopoly always set a very high price?
• At profit-maximizing optimum:
p
1
 1
MR  p 1    MC 

MC 1  1
 

i.e., The ratio of P to MC depends only on the elasticity of
demand at the optimum.
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• Lerner Index: the ratio of the difference between P and
MC to the P (0≤LI ≤1).
p  MC
1
LI 

p

– The larger the LI, the greater the difference between
p and MC, and thus the greater the monopoly’s
market power.
– LI=0 for competitive firm as it faces a perfectly
elastic demand curve (ɛ=-∞).
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Welfare Effects of Monopoly
• Ch.9 showed that competitive equilibrium
maximizes social welfare.
• By setting higher price than MC, monopoly
causes consumers to buy less than competitive
equilibrium, which creates deadweight loss (DWL).
• Thus, monopoly creates inefficiency.
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Deadweight Loss of Monopoly
13
• Since MC<Pm*, if the transaction of extra output (from
Qm* to Qc*) takes place at MC<P<Pm*, both consumers
and producer can be made better-off theoretically.
• This is a Pareto improvement.
• Why doesn’t monopolist do this, i.e. set different prices
for the sale of extra output?
• Monopolist cannot set different price levels for different
consumers since resale is possible (but we study
exceptions in the next chapter).
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Imposing a tax on q
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Imposing Ad Valorem (Sales) tax
Because of the sales tax,
the demand curve tilt
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Effect of Ad Valorem Tax (1)
Price
MC
p mb
e* before tax
e* for competitive
market
Demand
MR
q mb
Quantity
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Effect of Ad Valorem Tax (2)
Price
e* after tax
pm
MC
a_consumer
p mb
D
MR
（1-τ) MR
q ma
（1-τ) D
Quantity
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Effects of Taxes on Welfare
1.
Specific tax of t per q on monopolist:
Max   P(q )  q  C (q )  t  q
FOC :
2.
P(q)
C (q) set
P
q
 t  0  MR  MC  t
q
q
Ad valorem tax of (τ×100)%:
Max   (1   )  P(q)  q  C (q)
FOC :
3.

P(q)  C (q) set
(1   )   P 
q 
 0  (1   )  MR  MC
q
q


Profit tax of (x×100)%
Max   (1  x)   P (q )  q  C (q ) 
FOC :

P(q )
C (q )  set
(1  x)   P 
q
  0  MR  MC
q
q


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What Create Monopolies?
Why does monopoly exist?
1. Natural monopoly: Small market demand relative to
minimum efficient scale. One firm can produce the
total output of the market at lower cost than several
firms could. With a natural monopoly, it is more
efficient to have only one firm produce than more
firms.
2.
Barriers to enter: Government grants monopoly
rights to operate through licenses and restrictions.
3.
Patent protection: Government provides monopoly
right to use new idea for a certain period, to provide
incentives to innovate.
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Demand Relative to Minimum
Efficient Scale (MES)
Price
Panel A: typical one firm’s
AC curve
If one firm produce Q*,
the cost is too high.
Price
Panel B: there is a firm with
Superior technology (ACs)
ACs
AC
P*
Demand
MES
Q*
P*
Demand
Output
MES
Q*
Output
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Cost Advantages that Create Monopolies
• Scale economies: Where MC curve =market demand
curve, AC of a firm is still decreasing (see natural
monopoly).
• Scale economies can rise when production function is
subject to increasing returns to scale.
• Scale advantage can rise when fixed cost is large and MC
is small.
• Examples are electricity, gas, telephone, and so on
requiring a lot of fixed costs. Other cases include superior
technology (e.g., patent) and management ability.
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A Natural Monopoly
Price
MC
AC
Demand
PM
PAC
Loss to the firm from
marginal cost pricing
(p=MC)
PMC
MR
qM qAC
qMC
Quantity
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• Dilemma is if p=MC by policy, profit is negative
(purple area).
• Solution I: Set p=MC and provide subsidy by the
same amount as the deficit.
• Solution II: Let public corporations supply.
• “Solution” III: Permit the company which is willing
to set the lowest price. This should be close to
PAC.
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