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Oligopoly Theory 1
Oligopoly Theory (14)
Mixed Oligopoly
Aim of this lecture
(1) To understand the concept of mixed oligopoly.
(2) To understand the result that welfare-
maximizing behavior by a public firm can yield
suboptimal outcome.
Plan of the presentation
(1) Mixed Oligopoly
(2) Classical Discussion of Public Enterprises
(3) Welfare-Improving Privatization
(4) Three Typical Model Formulations of Mixed Oligopoly
(5) Partial Privatization
(6) International Competition
(7) Endogenous Competition Structure
(8) Multiple Public Enterprises
(9) Privatization Neutrality Theorem
(10) Other topics
Oligopoly Theory 2
Mixed Oligopoly, Mixed Market
State-owned public firms compete against private
firms
Oligopoly Theory 3
Examples of mixed oligopoly in
Japan
Banking: Postal Bank, DBJ, Iwate Bank
Housing Loan: the Public House Loan Corporation
Private Funds: DBJ, Industrial Revitalization
Corporation of Japan
Life Insurance: Postal Life Insurance (Kampo)
Overnight Delivery: Japan Post
Energy: Public Gas Corps (Narashino, Fukui,...)
Broadcasting: NHK
Oligopoly Theory 4
Examples of mixed oligopoly in
other countries
Banking: Postal Banks (New Zealand, U.K., Germany,...)
Automobiles: Renault, VW
Medicine: Public Institute in Brazil
Defense, Aviation: EADS, Airbus
Airline: airlines (Swiss, Belgian, France,...)
Overnight Delivery: USSP
Energy: Electricite de France, Gas de France
Broadcasting: BBC
Oligopoly Theory 5
Differences between public and
private firms
(1)Public firms are less efficient than private firms.
→Many empirical works do not support this view
(and many other papers do support this view).
(2) Difference of objective function
→Private firms maximize their own profits, whereas
public firms might care about social welfare.
Oligopoly Theory 6
Classical discussions of public
firms
Why do public firms exist?
(1) Natural monopoly
(a) Public firm monopoly
(b) Regulated private firm monopoly
Oligopoly Theory 7
Classical discussions of public
firms(2)
Why do public firms exist?
(2) Unprofitable market
(a) Public firm monopoly
(b) Private firm monopoly with subsidy
(compensation of deficit from public funds)
Oligopoly Theory 9
Oligopoly Theory 11
Classical discussions on state-
owned public firms→Public firm is the monopolist
In real economies, public firms are not always
monopolists.
Public firms do not always face significant economy
of scale, which guarantees monopoly by the
public firm.
Problem(1)
Oligopoly Theory 12
(1) How to provide incentives for welfare
maximization?
→ This is the central issue for the public firm's
monopoly
If we assume that the public firm is a welfare-
maximizer under the monopoly, it is absolutely
obvious that the first best is achieved by definition.
→No unsolved research problem exists. Thus,
researchers never assume that the public firm is a
welfare maximizer when they consider monopoly
situations.
Problem(2)
Oligopoly Theory 13
(2) Is the welfare-maximizing behavior by the public
firm efficient?
→This problem never appears in the public firm's
monopoly.
This question makes sense in mixed oligopolies
because welfare-maximizing behavior by the public
firm might worsen welfare through strategic
interaction between public and private firms.
→This is the central issue of mixed oligopolies.
Issues of mixed oligopoly
Oligopoly Theory 14
・Is welfare-maximizing behavior by the public firm
desirable in mixed oligopoly ?
・What distortion does welfare-maximizing
behavior by the public firm yield ?
De Fraja and Delbono(1989)
Oligopoly Theory 15
(1) Cournot-type (quantity-setting competition,
simultaneous-move, no product differentiation)
(2) No cost difference between public and private firms.
(3) Linear demand and quadratic cost function.
(4) The private firm maximizes its own profits given
outputs of other firms.
(5) The public firm maximizes social welfare
given outputs of other firms.
→The public firm chooses its output level so that the
price equals to its marginal cost.
Results
Oligopoly Theory 16
Compare the pure economy (after the
privatization) to the mixed economy (before the
privatization)
→Privatization of the public firm might improve
welfare
WP >WM or WP<WM.
WP >WM more likely takes place when the
number of private firms are large.
Intuition
Oligopoly Theory 17
(1) Privatization of the public firm reduces public firm's
output q0
(2) Privatization increases each private firm's output q1
→production substitution from the public firm to the
private firms.
(3) Privatization decreases total output q0 +nq1.
Effects (1) and (3) reduce welfare and effect (2)
improves welfare. Effect (2) may be the strongest,
leading to an improvement of welfare.
(2) is stronger and (3) is weaker when m is larger
→Privatization morel likely improves welfare when n is
larger.
Production substitution
Oligopoly Theory 18
q1
reaction curve
after privatization
reaction curve of
the private firm
0
reaction curve
before privatization
q0
More detailed explanation of
intuition
Oligopoly Theory 19
Privatization of the public firm reduces q0 and
increases q1 (production substitution).
Before Privatization p=c0' >c1'
→Public firm's marginal cost is higher than private
firm's
→ Production substitution from public to private
economizes production costs →Welfare-improving
→Privatization reduces total production level and so
consumer surplus → Welfare-reducing
It is possible that the former effect dominates the latter
effect.
Contribution of De Fraja and
Delbono (1989)
Oligopoly Theory 20
(1) No cost difference between public and private firms
→ privatization does not improve production efficiency
(2) Public firm's objection: welfare →No agency
problem in the public firm
(3) No additional policies by regulation, tax, or subsidy
after privatization.
⇒Ideal circumstances for the existence of public firm.
Against assumptions for the advocators of
privatizations. → Nevertheless, privatization might
improve welfare
Assumptions of De Fraja and
Delbono(1989)
Oligopoly Theory 21
Many researchers in this field believe that the
assumptions above are plausible, but many other
researchers (as well as I) make these assumptions for
strategic purposes.
(1) Even without cost differences, privatization
improves welfare.
→If public firm is less efficient, much more.
(2) Even without any agency problem in the public firm,
privatization improves welfare.
→If public firm has agency problem, much more.
Why quadratic costs?
Oligopoly Theory 22
Constant marginal cost yields problems
If marginal costs are constant and no cost differences
exists, the public firm's monopoly yields the first
best.
→ It is nonsense to discuss mixed oligopolies in such
a circumstance.
How to avoid this problem?
Oligopoly Theory 23
(1) Using constant marginal costs and assuming cost
differences between public and private firms.
Mujumdar and Pal (1998),Pal (1998),Matsumura
(2003a),Matsumura and Ogawa (2010)
First best is achieved by the marginal cost pricing of
the private firm.
The private leadership yields the second best where
only private firms produce and the price is equal to
the marginal cost of the public firm.
It is the equilibrium in the observable delay game.
How to avoid this problem?
Oligopoly Theory 24
(2) Using increasing marginal costs. De Fraja and
Delbono (1989),Fjell and Pal (1996), White (1996),
Matsumura and Kanda (2005), Heywood and Ye
(2009a), Wang et al. (2009).
If there is no cost difference between public and
private firms, at the first best all firms choose the
same output level. It is not always achieved in
mixed oligopoly since public and private firms have
different objectives.
How to avoid this problem?
Oligopoly Theory 25
(3) Dropping the assumption of homogenous goods.
Monopolistic competition: Anderson et al. (1997),
Matsumura et al. (2009)
Linear demand (quadratic utility function) with product
differentiation: Fujiwara (2007), Matsumura and
Ogawa (2012), Haraguchi and Matsumura
(2014,2016)
Mill pricing location model: Cremer et al. (1992),
Matsumura and Matsushima (2003,2004), Inoue et al.
(2008)
Delivered pricing location model: Matsushima and
Matsumura (2003,2006), Heywood and Ye (2009b)
How to avoid this problem?
Oligopoly Theory 26
More general Costs : Matsumura (1998, 2003b),
Kiyono and Tomaru (2013)
Discuss both (1) and (2): Matsumura and Okamura
(2015).
Discuss both (2) and (3): Matsumura and Shimizu
(2010)
Partial Privatization
Oligopoly Theory 27
De Fraja and Delbono: The public sector holds whole
shares in the firm (nationalization) or the private
sector holds whole shares in the firm (privatization)
In the real world, we observe many firms with mixture
ownership (partial privatization)
NTT, JT, JP, Iwate Bank, Hokuriku Electric Power
Company, VW, Renault
Matsumura (1998)
Oligopoly Theory 28
(1) Cournot-type (quantity-setting competition,
simultaneous-move, no product differentiation)
(2) No restrictions on the cost differences between
public and private firms.
(3) The objective function of the public firm is the
weight sum of social welfare and its own profits.
(Partial Privatization)
U0 = (1-θ) W + θπ0
(4) General demand and general costs.
The government chooses s and s affects θ. After
observing θ firms compete in the product market.
Results
Oligopoly Theory 29
θ =0 is optimal only if it yields public monopoly.
→If we allow partial privatization, no privatization (full
nationalization) never becomes optimal.
Oligopoly Theory 30
Intuition
(1) Suppose that θ =0. A slight increase of θ from 0
reduces public firm's output q0 .
Since p=c0‘ when θ =0, this effect is negligible
(second order) ←envelope theorem
(2) An increasing in θ increases private firm's output
q1. Since p>c1', this effect is nonnegligible (first order)
⇒(2) dominates (1).
Partial Privatization
Oligopoly Theory 31
Free Entry: Matsumura and Kanda (2005), Wang et al.
(2010)
Product Differentiation: Fujiwara (2007)
Spatial Model: Lu and Poddar (2007)
Environmental Policy: Kato (2006), Ohori (2006)
Anti-Trust: Barcena-Ruiz and Garzon (2003)
Labour Market: Beladi and Chao (2006)
Subsidization: Tomaru (2006)
Endogenous Timing: Matsumura and Ogawa (2010),
Barcena-Ruiz and Garzon (2010)
Optimal degree of privatization
Oligopoly Theory 32
If we adopt partial privatization approach, we can
investigate the optimal degree of privatization (optimal
degree of θ.
Optimal degree of privatization depends on
(i) the number of private firms
(ii) the degree of foreign penetration
(iii) cost difference between public and private firms
(iv) existence of other policy instruments such as tax-
subsidy policy and shadow cost of public funding
(vi) Competition structure (free entry, role of public firm
and so on)
Optimal degree of privatization
Oligopoly Theory 33
Suppose that firms face Cournot competition. Optimal
degree of privatization is increasing in the number of
private firms. (Han and Ogawa, 2007, Lin and
Matsumura, 2012, Matsumura and Okamura, 2015).
It is decreasing in the foreign penetration in product
markets in the short run (Han and Ogawa, 2007, Lin
and Matsumura, 2012), and the result is inversed in
the long run (free entry markets). The latter result is
robust because it does not depend on the strategic
substitutability in product markets (Cato and
Matsumura, 2013).
Optimal degree of privatization
and the number of firms
Oligopoly Theory 34
The number of firms is larger.
(1) Marginal cost of each private firm is smaller when
marginal cost is increasing.
(2) Price-cost margin is smaller.
An increase in θ reduces the total output (welfare loss)
and induces welfare-improving production substitution.
The welfare loss is less significant because of (2) and
welfare gain is more significant because of (1).
Both increase the optimal degree of privatization.
Optimal degree of privatization and
the toughness of competition
Oligopoly Theory 35
Consider a relative-profit-maximization approach. α is
larger (the competition is tougher).
(1) Marginal cost of each private firm is larger when
marginal cost is increasing.
(2) Price-cost margin is smaller.
An increase in θ reduces the total output (welfare loss)
and induces welfare-improving production substitution.
The welfare loss is less significant because of (2) and
welfare gain is less significant because of (1).
Optimal degree of privatization and
the toughness of competition
Oligopoly Theory 36
When marginal cost is constant, only (2) matters. The
optimal degree of privatization is increasing in α.
When the marginal cost is increasing , (1) and (2) has
different effects. When the production cost is quadratic,
(1) dominates (2). → The optimal degree of
privatization is decreasing in α.
The two popular models yield the opposite policy
implications. (Matsumura and Okamura, 2015.)
Foreign Competitors
Oligopoly Theory 37
Public firm maximizes domestic welfare
→The public firm's behavior is dependent on whether
its rivals are domestic or foreign
If the rivals are foreign, the public firm becomes more
aggressive.
Fjell and Pal (1996)←De Fraja and Delbono (1989)
Pal and White (1998) ← Strategic Trade Policy
Mukherjee and Suetrong (2009) ← FDI
Chang (2005), Chao and Yu (2006), Fujiwara (2006)
← partial privatization version
Cato and Matsumura (2015) ← Strategic Trade Policy
at Free Entry Markets.
Optimal degree of privatization and
foreign ownership share in private
firms
Oligopoly Theory 38
The foreign ownership share in private firms is larger,
a lower price benefits for domestic welfare more.
An increase in θ reduces the total output (welfare loss)
and induces welfare-improving production substitution.
Welfare loss effect becomes more significant
→The optimal degree of privatization is decreasing in
the foreign ownership share in private firms.
Optimal degree of privatization and
foreign ownership share in
privatized firms
~ Lin and Matsumura (2012)
Oligopoly Theory 39
The foreign ownership share in the privatized firm is
larger, the privatized firm becomes more aggressive
after privatization. Expecting this aggressive behavior,
the stock price of the former public firm falls, resulting
in a welfare loss. Thus, the government chooses a
larger degree of privatization sells more when foreign
ownership in the privatized firm is larger.
→The optimal degree of privatization is decreasing in
the expected foreign ownership share in privatized firm.
Free Entry Equilibrium
Oligopoly Theory 40
In the first stage, the government chooses the degree
of privatization.
In the second stage, each private firm chooses
whether or to enter the market.
In the third stage, all firms face Cournot cometition.
Consider the subgame starting at the beginning of the
second stage.
→The equilibrium price is independent of θ.
Oligopoly Theory 41
Long-Run Equilibrium under Cournot Competition
DMR
MC
AC
AC>MC
D’
P>MR
equilibrium output of each firm0
Free Entry Equilibrium
Oligopoly Theory 42
Welfare = CS+ profit of the public firm (privatized firm).
CS is independent of θ.
Price is independent of θ.
→Only the public firm’s profit matters.
Because the price is constant, marginal cost pricing is
the best.
When the private firms are domestic, θ=1 is
optimal.←Matsumura and Kanda (2005).
The optimal degree of privatization is increasing in the
foreign ownership share in private firms. ←Cato and
Matsumura (2013).
Ex ante and ex post privatization
Oligopoly Theory 43
Ex ante privatization ~ The same time structure as
Matsumura and Kanda (2005).
Ex post privatization
In the first stage, each private firm chooses whether or
to enter the market.
In the second stage, the government chooses the
degree of privatization.
In the third stage, all firms face Cournot cometition.
Question: The equilibrium price of the ex ante
privatization is (higher than, lower than, the same as)
that in the ex post privatization model.
Private Leadership, Public
Leadership
Oligopoly Theory 44
Consider a duopoly model with quantity competition
under strategic substitutes. Consider two
Stackelberg models.
One is Public Leadership (the public firm is the
Stackelberg Leader) and the other is Private
Leadership (the public firm is the Stackelberg
follower).
Private Leadership
Oligopoly Theory 45
The public firm plays a passive role as a potential
competitor of the private firm.
The public firm supplies only when the private firm's
supply is insufficient. ~ Public firm plays a
complementarity role of the private sector.
This role is intensively discussed in Canada and in
Japan (when Koizumi was prime minister)
Public Leadership
Oligopoly Theory 46
The public firm leads the private sector, a positive
role.
Question: The public firm produces (less, more)
under public leadership than under simultaneous
production of public and private firms.
Free Entry Version of Public
Leadership
Oligopoly Theory 47
In the first stage, each private firm chooses whether or
to enter the market.
In the second stage, one public firm produces and then
all private firms produce simultaneously (Public
leadership).
Question: The equilibrium price of the public leadership
is (higher than, lower than, the same as) that in the
Cournot model.
Free Entry Version of Public
Leadership
Oligopoly Theory 48
In the first stage, each private firm chooses whether
or to enter the market.
In the second stage, one public firm produces and
then all private firms produce simultaneously (Public
leadership). Private firms are domestic.
Question: The total social surplus under the public
leadership is (larger than, smaller than, the same as)
that under the Cournot competition.
Free Entry Version of Private
Leadership
Oligopoly Theory 49
In the first stage, each private firm chooses whether or
to enter the market.
In the second stage, all private firms produce
simultaneously, and then, one public firm produces
(Private leadership)
Question: The equilibrium price of the private
leadership is (higher than, lower than, the same as)
that in the Cournot model.
Endogenous Role
Oligopoly Theory 50
Consider the observable delay game.
There are two possible time periods for output choice .
In the first stage, firm i simultaneously chooses
whether it likes to be the leader (ti=L) or the follower
(ti=F). If two players' choices are consistent, i.e., one
chooses to be the leader and the other does to be the
follower, they get the equilibrium payoffs of a agreed
timing Stackelberg. Otherwise, they receive the
equilibrium payoffs in Cournot.
Desirable Role, Endogenous Role
Oligopoly Theory 51
Quantity Competition.
Pal (1998): When the private firm is domestic, the
private leadership is better than the public leadership
and it is an equilibrium in the observable delay game.
It is a unique equilibrium if the number of private firm
is larger than 3.
In a mixed duopoly, both private leadership and public
leadership constitute equilibria, but the former is risk
dominant (Matsumura and Ogawa 2012).
Matsumura (2003a): In the two—production-period
model, only the robust equilibrium is private
leadership.
Desirable Role, Endogenous Role
Oligopoly Theory 52
Quantity Competition.
Matsumura (2003b): When the private firm is foreign,
the public leadership is better than the private
leadership and it is an equilibrium in the observable
delay game.
Endogenous Price-Quantity Choice
Oligopoly Theory 53
Matsumura and Ogawa (2012) investigate price-quantity
choice in a mixed duopoly, using the model of Singh
and Vives (1984) . →choosing a price contract is a
dominant strategy for both firms, resulting in Bertrand
competition in mixed duopolies, in contrast to the results
in private duopolies.
Bertrand yields larger profit in the private firm and
greater welfare than Cournot.
These results hold true even if the private firm is owned
by foreign investors (Haraguchi and Matsumura 2014)
but not in an oligopoly (Haraguchi and Matsumura
2016) .
Assumptions of single public firm
Oligopoly Theory 54
Most existing works consider models with single
public firm.
If this single public firm is privatized, the market
becomes pure market economy.
Assumptions of single public firm
Oligopoly Theory 55
Considering desirable reform of the economic system
in former communist transitional countries, this is not a
plausible assumption. In reality numerous public firms
exist in such countries and it is politically impossible to
privatize all of the public firms at the same time.
Considering large scale privatization program in
traditional mixed economies, one privatization does not
yield pure market economy (because substantial public
firms remain after the privatization of several firms).
→Existing works cannot analyze these markets
effectively.
Examples of economies with
multiple public firms
Oligopoly Theory 56
(1) Former communist transitional countries
(examples) Russia, Many of Eastern and Central
European countries, China, Vietnam, Mongolia...
(2) Developing, recently developed, and emerging
countries
(examples) Brazil, India, Iran, Indonesia, Thailand,
Korea, Taiwan...
Examples of economies with
multiple public firms
Oligopoly Theory 57
(3) Successful privatization programs in developed
countries
(examples) UK, Japan, Germany, Australia, NZ
(4) Traditional mixed economies in developed
countries
(examples) Japan, France, Germany, Korea
Why did existing works consider
models with single public firm?
Oligopoly Theory 58
If no cost differences between public and private
firms exists, obviously N = m yields the first best
outcome.
→Full nationalization of the economy (complete
communist economy) yields the first best.
→ It is nonsense to discuss mixed oligopoly under
such assumptions.
But the result (complete communist economy yields
the first best) is so unrealistic and implausible.
The assumption of no cost
difference between public and
private firms
Oligopoly Theory 59
(1) Strategic assumption. (Even if no cost difference, privatization can improve welfare.)
→Much more if cost difference exits.
(2) Realistic assumption. (In mixed market, the public firm faces tough competition with private firms. If the public firm is extremely less efficient than private firms, it would not be able to survive.)
The assumption of no cost
difference between public and
private firms
Oligopoly Theory 60
If m = N (pure planned economy), no competitive
pressure exists and the assumption of no cost
difference is not plausible.
→Restricting attentions to single public firm and
avoiding the nonsense result that the first best is
achieved by pure nationalized economy.
Approach of Matsumura and
Shimizu (2010)
Oligopoly Theory 61
Suppose that the economy has 100 firms and 25 of them are public firms.
Then the number of public firms becomes 24,23,22,... by privatization.
What happens in the process of this privatization?
We believe that it is worth discussing this problem.
We dare to deviate from the traditional single public firm model.
Matsumura and Shimizu (2010)
m state-owned public firms compete against N-m
private firms. N firms face Cournot competition.
Each public firm maximizes welfare, while each private
firm maximizes its own profits.
Quadratic costs:
C = 0.5θ(qi)2 + K (public firm),
C = 0.5β(qi)2 + K (private firm), θ≧ β
Oligopoly Theory 62
Main concerns: Relationship between m and welfare.
Result 1
(1) W(m) is decreasing if the public firms are
significantly less efficient than the private firms.
(W is total social surplus, consumer surplus +
profits of firms. m is the number of public firms)
If public firms are sufficiently less efficient than the
private firms, privatization improves welfare
regardless of m and N
Oligopoly Theory 63
Result 2
(2) W(m) is increasing if the cost difference
between public firms and private firms are
sufficiently small and the total number of firms N
is small.
The government should improve the
competitiveness of the market before privatizing
the public firms.
Oligopoly Theory 65
Result 3
(3) W(m) is U-shaped if the cost difference
between public firms and private firms are
sufficiently small and N (the total number of
firms) is large.
This is the most interesting case
Oligopoly Theory 67
Even if privatization does not improve
welfare at the early stages, it can
eventually lead to a point such that
privatizations after that point on are
beneficial to the society
Oligopoly Theory 69
W
mm1
0
Larger scale privatization
programs eventually more likely
end up with great success
Oligopoly Theory 70
W
m m1m2m3
0
Intuition
Oligopoly Theory 72
Suppose that m public firms and N - m private firms
exist. Suppose that one public firm is privatized.
→Production substitutions from the privatized firm
to m - 1 public firm and to N - m private firms
take place.
→The former production substitution reduces
welfare and the latter improves welfare.
→The latter becomes stronger when m is smaller
and N is larger.
Implications
Oligopoly Theory 73
(1) Failures at early stages do not imply the failure of
the whole privatization program (except for highly
concentrated markets).
→We should evaluate privatization program from the
long term viewpoint.
(2) Smaller size privatization programs more likely fail.
(3) Welfare-gains of privatizations are larger at the
latter stage of privatization program.
→Once we reach the critical stage, the privatization
automatically proceeds with larger support.
Privatization Neutrality Theorem
Oligopoly Theory 74
Privatization Neutrality Theorem: Privatization does not
matter under optimal subsidy policy.
It implies that if the optimal subsidy policy is adopted,
discussing mixed oligopoly or privatization policy
does not make sense.
Most of the results in mixed oligopoly literature have
quite limited implications and importance if this
theorem is really robust.
Distractive Result, Disaster for researchers in this field.
Intuition behind PNT
Oligopoly Theory 75
Suppose that all firms are symmetric. Consider the
private oligopoly.
The first best is achieved when P=ci' (price =marginal
cost) ~ all firms choose the same output level
It is achieved by the production subsidy s*.
Intuition behind PNT
Oligopoly Theory 76
Suppose that one firm is nationalized. Suppose that
all of remaining firms do not change their output.
The nationalized firm, which is welfare-maximizer,
never changes its output .
All remaining private firms obviously have no incentive
to change their outputs.
→s* yields the first best outcome in the mixed
oligopoly.
Condition for PNT
Oligopoly Theory 77
When I explain the intuition behind PNT, I do not use
any of
(1) Private firms are profit maximizers
(2) Homogeneous product market,
(3) Single public firm
and so on.
All we use is the condition that the first best is
achieved at the symmetric equilibrium, the first best
is achieved by the simple unit subsidy, and the pubic
firm is welfare maximizer.
White(1996)
Oligopoly Theory 78
Introducing subsidy policy into the Cournot-type
model of De Fraja and Delbono (1989).
The government chooses unit subsidy s so as to
maximize resulting welfare
Results: Privatization affects neither optimal subsidy
rate nor resulting welfare
→Privatization does not matter under optimal
subsidy policy (Irrelevance Results)
Subsequent works
Oligopoly Theory 79
Poyago-Theotoky (2001): public firms' leadership;
Myles (2002):general demand and cost functions;
Tomaru (2006): partial privatization approach;
Hashimzade et al. (2007): product differentiation;
Kato and Tomaru (2007): various payoff functions of
private firms.
Irrelevance result (especially irrelevance result on
welfare) is quite robust.
General formulation and general result → Matsumura
and Okumura (2013)
Exception
Oligopoly Theory 80
Fjell and Heywood (2004): Privatization is relevant
under asymmetric order of moves among private firms.
Robustness of PNT
Oligopoly Theory 81
Privatization Neutrality Theorem is far from robust:
(1) PNT obviously does not hold when there is cost
difference between public and private firms.
(2) PNT does not hold unless all firms are domestic.~
Matsumura and Tomaru (2012)
(3) PNT does not hold at free entry markets
~Cato and Matsumura (2013)
(4) If there is an excess burden of taxation, PNT does
not hold. ~Matsumura and Tomaru (2013)
(5) PNT does not hold if firms control two or more
independent variables
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