4820–8
Natural
monopoly
Geir B.
Asheim
Introduction
Fight for a natural monopoly
Benchmark
4820–8
Short-run
commitments –
Capacity
competition
Geir B. Asheim
War of
attrition
Department of Economics, University of Oslo
ECON4820
Spring 2010
Last modified: 2010.03.09
In markets with economies of scale . . .
4820–8
Natural
monopoly
Geir B.
Asheim
. . . firms will compete for the monopoly rent
Questions:
Will the monopoly rent accrue to the winner?
Introduction
Benchmark
Short-run
commitments –
Capacity
competition
War of
attrition
Or will the fight between the firms lead to rent dissipation?
To the advantage of the consumers
Or wasted through costly competition
Topic today:
Provide a positive & normative benchmark
for the rent dissipation/no wastefulness case when
there are economies of scale (and economies of scope)
Present different well-specified models which lead to
different degrees of rent dissipation and wastefulness.
Theory of perfectly competitive markets
Positive and normative benchmark when firms have convex costs
4820–8
Natural
monopoly
Geir B.
Asheim
Introduction
Benchmark
Contestability
Modeling
Short-run
commitments –
Capacity
competition
War of
attrition
(a) Preferences are convex and consumers are price takers
(b) Costs are convex and firms are price takers
Positive conclusion: Existence of equilibrium
(c) Free entry
Positive conclusion: Zero profit
Normative implications for competition policy
Assumptions are satisfied: Do nothing.
If not, try change the market conditions.
If that’s not possible, regulate.
Theory of perfectly contestable markets
Positive and normative benchmark when firms do not have convex costs
4820–8
Natural
monopoly
Geir B.
Asheim
(a) Preferences are convex and consumers are price takers
Introduction
Benchmark
Contestability
Modeling
Short-run
commitments –
Capacity
competition
War of
attrition
(c) Free entry
Positive conclusion: Zero profit
Normative implications for competition policy
Assumptions are satisfied: Do nothing.
If not, try change the market conditions.
If that’s not possible, regulate.
Contestability theory: Definitions
4820–8
Natural
monopoly
Geir B.
Asheim
Introduction
Benchmark
Contestability
Modeling
All firms have the same technology:
Output q costs C (q) with C (0) = 0.
Two kinds of firms: Incumbents are firms i = 1, . . . , m
Potential entrants are firms i = m + 1, . . . , n
An industry configuration is a set of outputs {q1 , . . . , qm } for
the incumbents and a price p charged by all incumbents
Short-run
commitments –
Capacity
competition
Definition (Feasible industry configuration)
An industry configuration is feasible if m
i=1 qi = D(p) (markets
clear) and pqi ≥ C (qi ) for all i = 1, . . . , m (non-negative profits)
War of
attrition
Definition (Sustainable industry configuration)
An industry configuration is sustainable if p e q e ≤ C (q e ) for all
p e ≤ p and q e ≤ D(p e ) (entry is not profitable)
Definition (Perfectly contestable market)
is one in which any ind. conf. is feasible and sustainable
Contestability theory: Results
4820–8
Natural
monopoly
Geir B.
Asheim
Result
A long-run perfectly competitive equilibrium is a feasible and
sustainable ind. conf., while the converse need not hold.
Introduction
Result
Benchmark
A feasible and sustainable ind. conf. is characterized by
All firms earn zero profit
Price is equal to or exceeds marginal cost
No firm cross-subsidizes
Contestability
Modeling
Short-run
commitments –
Capacity
competition
War of
attrition
Result
In a feasible and sustainable ind. conf. with two producing firms,
price equals marginal cost (generalization of Bertrand comp.)
Result
In a feasible and sustainable ind. conf., total costs are minimized
How does potential competition
discipline the incumbent(s)?
4820–8
Natural
monopoly
In a perfectly contestable market, potential competition ensures
Geir B.
Asheim
Rent dissipation
Introduction
No wastefulness
Benchmark
Contestability
Modeling
Short-run
commitments –
Capacity
competition
War of
attrition
Is it possible to provide a game theoretic foundation
for an equilibrium in a perfectly contestable market?
(1) Prices adjust more slowly than quantities and entry
(Procurement by reverse auctions: Competitive bidding)
(2) Strategic defense against potential competition leads to
perfectly contestable behavior. Maskin, Tirole, A theory of
dynamic oligopoly, I: Overview and quantity competition
with large fixed costs, Ecma 56 (1988) 549–569
Short-run commitments
Capacity competition
4820–8
Natural
monopoly
Geir B.
Asheim
Introduction
Benchmark
Short-run
commitments –
Capacity
competition
Markovperfect
equilibrium
High δ
Low δ
A variant
War of
attrition
Motivation: Show . . .
. . . the effect of potential competition in a market
which is a natural monopoly
(Fixed cost: f where f < Π̃m < 2f )
and where entry gives Cournot-competition
(Π̃i (Ki , Kj ) = P(Ki + Kj )Ki − (c + c0 )Ki )
. . . that contestability may be obtained when prices
adjust more rapidly than quantities and entry
Model: Firms alternate at choosing capacity. (If not . . . ?)
Per period profit: Πi (Ki , Kj ) = Π̃i (Ki , Kj ) − f
(Πi (0, Kj ) = 0)
Πij < 0 — Increased capacity is aggressive
Πiii < 0 — Second-order condition
Πiij < 0 — Strategic substitutes (e.g., Cournot competition)
∞
Intertemporal profit at time t: s=0 δ s Πi (Ki,t+s , Kj,t+s )
A Markov-perfect equilibrium (R1 , R2 ) satisfies:
4820–8
Natural
monopoly
Geir B.
Asheim
Introduction
Benchmark
Short-run
commitments –
Capacity
competition
Markovperfect
equilibrium
High δ
Low δ
A variant
War of
attrition
There exists functions V1 , W1 , V2 and W2 such that
1
V1 (K2 ) = maxK Π (K , K2 ) + δW1 (K )
Discounted profit given best choice now
and the players follow (R1 , R2 ) later.
R1 (K2 ) = arg maxK Π1 (K , K2 ) + δW1 (K )
The reaction function specifies a best choice.
W1 (K1 ) = Π1 (K1 , R2 (K1 )) + δV1 (R2 (K1 ))
Discounted profit when the opponent acts
and the players follow (R1 , R2 ).
and likewise for V2 and W2 .
Rent dissipation and no wastefulness when δ is high
4820–8
Natural
monopoly
Geir B.
Asheim
Introduction
Benchmark
Short-run
commitments –
Capacity
competition
Markovperfect
equilibrium
High δ
Low δ
A variant
War of
attrition
Suppose δ is so near 1 so that there exists K̄ ≥ K m determined
by
δ
Π1 (K̄ , 0) = 0
Π1 (K̄ , K̄ ) + 1−δ
Short-term loss
Long-term gain
Then 0 is a best a reaction to K ≥ K̄ :
V1 (K ) = 0 ≥ Π1 (K̄ , K ) +
1
δ
1−δ Π (K̄ , 0)
and K̄ is a best reaction to K < K̄ :
V1 (K ) = Π1 (K̄ , K ) +
1
δ
1−δ Π (K̄ , 0)
As δ → 1, Π1 (K̄ , 0) → 0: Price = AC
>0
Rent dissipation and no wastefulness when δ is high
4820–8
Natural
monopoly
Geir B.
Asheim
Introduction
Benchmark
Short-run
commitments –
Capacity
competition
Markovperfect
equilibrium
High δ
Low δ
A variant
War of
attrition
High capacity . . .
deters entry by making a challenge tougher
leads to lower prices if capacity is utilized
As δ → 1 (i.e., when the response time goes to 0):
Contestability
Short-run commitments in capacity yields contestability
provided that it is possible to react fast enough
Rent dissipation
No positive profit due to potential competition
No wastefulness
Benefits consumers through lower prices
No rent dissipation when δ is low
4820–8
Natural
monopoly
Geir B.
Asheim
Introduction
Suppose δ is so near 0 that no K̄ satisfies
Benchmark
Short-run
commitments –
Capacity
competition
Markovperfect
equilibrium
High δ
Low δ
A variant
War of
attrition
Π1 (K̄ , K̄ ) +
Short-term loss
δ
1−δ
Π1 (K̄ , 0) = 0
Long-term gain
Then the entrant stays out
even though the incumbent earns monopoly profit.
Eaton & Lipsey, Bell J Econ (1980)
4820–8
Natural
monopoly
Geir B.
Asheim
Introduction
Benchmark
Short-run
commitments –
Capacity
competition
Markovperfect
equilibrium
High δ
Low δ
A variant
War of
attrition
f < Π̃m < 2f
Π̃d = 0
Continuous time
Capital lasts for H periods. Only one unit is needed
Decision: When to replace capital?
Early replacement . . .
deters entry by making a challenge tougher
does not lead to lower prices
As δ → 1 (i.e., when the response time goes to 0):
Rent dissipation
No positive profit due to potential competition
Wastefulness
Does not benefit consumers through lower prices
War of attrition
4820–8
Natural
monopoly
Geir B.
Asheim
f < Π̃m Π̃d = 0 Continuous time
Each firm stays in hoping that the other withdraw first
Each firm is uncertain about whether the other withdraws
Introduction
Benchmark
Short-run
commitments –
Capacity
competition
War of
attrition
Decision: Probability with which to withdraw?
Duopoly (starting with two firms):
Complete rent dissipation
Firms have zero expected profit
Partial wastefulness
Constant price = AC increases consumer surplus
Monopoly (starting with one firm):
No rent dissipation