Monopoly
Economics 302 - Microeconomic Theory II: Strategic Behavior
Shih En Lu
Simon Fraser University
(with thanks to Anke Kessler)
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Monopoly
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Topics
1
Monopoly: what and when
2
Pro…t maximization
3
Welfare
4
Government and Monopoly
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Most Important Things to Learn
1
How to …nd the market price and quantity under a monopoly
2
Relation between price, marginal cost and price elasticity of demand
3
Understand the source of deadweight loss and how to compute it
4
Pros and cons of various government policies dealing with monopolies
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What Is a Monopoly?
A …rm that is the only one in the market, i.e. no …rm produces a
close substitute.
(Use common sense - hard to think of a good with no substitute at
all.)
As a result, a monopoly does not lose all its demand when it raises
price above marginal cost: it has market power.
A monopoly picks a point on the market demand curve.
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Sources of Monopoly
Government policy
1
2
Directly owned/regulated by the state (utilities)
Patents (drugs), copyrights (music), trademarks (brand names),
licenses (nightclubs), etc.
Large e¢ cient scale
1
2
Natural monopoly: decreasing average cost over the relevant range of
quantities (utilities)
Network externalities on the demand side (Microsoft O¢ ce)
Firm actions
1
2
Control of essential input (DeBeers)
Being more e¢ cient than other …rms and/or preventing entry
(Walmart) - this is di¤erent
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Pro…t Maximization
Today, we assume that the monopoly charges the same price to every
customer. We will cover price discrimination later in the semester.
Notation: P = price per unit, q = quantity (use q and Q
interchangeably: …rm and market quantities are the same)
Inverse demand curve: P (q ), …rm’s cost function: C (q )
Pro…t: π (q ) = P (q )q
First-order condition:
ECON 302 (SFU)
C (q ) (Total Revenue - Total Cost)
π 0 (q )
= P (q ) + P 0 (q )q
Monopoly
C 0 (q ) = 0
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Pro…t Maximization (II)
Marginal Revenue = P (q ) + P 0 (q )q = C 0 (q ) = Marginal Cost
This pins down the monopoly quantity qm . Read the price o¤ the
demand curve: P = P (qm ).
Note: Because P 0 (q ) < 0, we have MR < P whenever q > 0.
In words: the monopolist chooses the quantity where marginal
revenue equals marginal cost and charges the maximum price that
bears that quantity.
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Pro…t Maximization: Some Caveats
We have assumed that the demand and cost functions are
di¤erentiable, and the good is perfectly divisible.
We have assumed that the second-order condition (π 00 (q ) < 0) holds,
i.e. that MR intersects MC from above. We will usually deal with
decreasing MR and increasing MC , in which case this automatically
holds.
Just like for perfectly competitive …rms, you need to check that the
monopoly wouldn’t prefer shutting down.
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Example
Demand: Q = 12
1
2P
Monopoly’s cost: C (q ) = q 2
Find price and quantity.
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Price, Marginal Cost and Elasticity at the Monopolist’s
Optimum
Remember FOC: P (q ) + P 0 (q )q = C 0 (q )
P
dP
dq q
MC =
P MC
P
=
dP q
dq P
Equivalently,
1
, where
jej
jej
P
MC = jej 1
=
e is the price elasticity of demand
These formulae only make sense if jej > 1. Why?
Markup over marginal cost gets lower as elasticity increases: the
…rm’s market power decreases.
What happens when jej ! 1? And when jej ! ∞?
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Example Continued
We found qm = 4 and P = 16.
Marginal cost is C 0 (q ) =
Thus jej =
P
P MC
=
16
16 8
d
2
dq (q )
= 2q, so it is 8 at qm .
= 2.
Now lets …nd jej directly using the demand Q = 12
jej =
dq P
dP q
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=
1
2
16
4
1
2 P.
= 2.
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Welfare
Continue with our example: MC (q ) = 2q and P = 24
2q.
We found qm = 4, but what is the socially optimal quantity?
Set equal the marginal social cost and bene…t
) 2q = 24 2q ) q = 6.
Units between 4 and 6 yield a bene…t between 16 and 12, but only
cost between 8 and 12.
Both the consumers and the …rm would be better o¤ if those two
units were produced and sold at a price of 12.
The monopoly outcome is not Pareto e¢ cient.
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Welfare (II)
Like with taxes on a perfectly competitive market, the deadweight
loss is the area between the demand and marginal cost curves, from
the actual quantity to the e¢ cient quantity.
In the example, it’s a triangle, so DWL =
1
2
(6
4)
(16
8) = 8.
In general, take an integral.
You can also analyze the consumer surplus and producer surplus
(which is just the monopoly’s pro…t plus its …xed cost). Again, it’s
similar to the situation with taxes on a perfectly competitive market,
except that the "Government revenue" area is part of producer
surplus.
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Why Would a Government Create a Monopoly?
Monopolies come with a deadweight loss. Why create them?
The government might take control of a monopoly that would exist
anyway (e.g. utilities).
The government can generate revenue or reduce expenditures by
selling the right to form a monopoly (e.g. certain toll highways).
The government might want to encourage innovation through patents
and copyright. The alternative would be to subsidize, which increases
the need for revenues and could therefore increase deadweight losses
elsewhere.
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What Can Government Do about Monopolies?
Divestiture: monopolies that control a key resource can be forced to
sell o¤ some of that resource. For example, AT&T had to sell o¤ its
local operations in 1982.
In other cases, such as natural monopolies, the government can still
a¤ect the price:
1
2
through taxes (or subsidies);
directly through regulation.
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Taxes and Monopolies
Does taxing a monopoly improve e¢ ciency?
It does redistribute money from the monopoly (and its customers)
toward the government.
Just like under perfect competition, there is a tax wedge between the
curves determining quantity.
Here, they are the MR and MC curves (rather than the supply and
demand curves).
Once you know the quantity, read the price paid by consumers (P c )
o¤ the demand curve.
The price received by the monopoly is P c less the tax.
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Taxes and Monopolies: Example
Return to our example: MC (q ) = 2q, P = 24
MR (q ) = 24 4q.
2q and
We found qm = 4 and P = 16 with no taxes. Now suppose there’s a
per unit tax of 6.
Find the new quantity, price paid by consumers and price received by
the …rm.
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Taxes and Monopolies: Ad Valorem Tax
Instead of a per unit tax of 6, suppose there’s a percentage tax of
100% of the price received by the monopoly (equivalently, 12 of the
price paid by consumers).
Total revenue is 21 of what it was without tax at every q. Thus so is
marginal revenue ) MR (q ) = 12 2q
Setting MR = MC gives: 12
per unit tax.
2q = 2q, or q = 3, just like with the
P c is still read o¤ the demand curve: P c = 18.
But what does the monopoly get now?
Why does the per unit/percentage distinction matter with a
monopoly, and not under perfect competition?
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Taxes and Monopolies: Price Can Increase by more than
Tax Amount!
Now suppose MC (q ) = 1, qD = P
With no taxes, P =
2.
2
2 1 MC
= 2.
With a per unit tax of 0.5, the e¤ective marginal cost becomes 1.5.
What is the new price paid by consumers? Has it increased by more
than the tax?
Convince yourself that this happens when demand is steeper than
MR (q ) MC (q ) between qm and qwith tax .
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Price Regulation
Ideally, P = MC . But this can lead to a loss: for example, with
constant MC and a …xed cost F , average cost is MC + Fq > MC .
Can instead set P = AC , but we then get away from e¢ ciency.
On top of these theoretical problems, in practice the government may
not know the cost curves.
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