Product Diversification, Entry

Privatization Waves
Joint work with Daisuke Shimizu
2005/10/26 寡占理論
1
Plan of the presentation
(1) Rough sketch of the model and results
(2) Explanation of mixed oligopoly
(3) Overview of related works on mixed
oligopoly
(4) Formal explanation of our model
(5) Results and implications
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Rough sketch of the model
・m state-owned public firm compete against
N-m private firms.
・Each public firm maximizes welfare, while
each private firm maximizes its own profits.
・N firms face Cournot competition.
Our main concerns: Relationship between
m and welfare.
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Motivation
We focus on the following situations
Large scale of privatization program in
developing or former communist
transitional economies
Sequential privatizations
←There are so many public firms that the
government cannot privatizes all public
firms at the same time.
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Problem
Dose a privatization of a public firm improve
welfare more likely when the number of
remaining public firm is large or small?
If large, the success of the earlier stage
privatization does not guarantee the
subsequent privatizations.
If small, the fail of the earlier stage
privatization does not imply the fail of the
subsequent privatization.
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Result 1


(1) W(m) is decreasing if the public firms
are significantly less efficient than the
private firms.
If public firms are sufficiently less efficient
than the private firms, privatization
improves welfare regardless of m and N
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Result 1
W
0
m (the number of public firms)
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Result 2
(2) W(m) is increasing if the cost difference
between public firms and private firms are
sufficiently small and the number of total
number of firm N is small.
The government should improve the
competitiveness of the market before
privatizing the public firms.
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Result 2
W
0
m (the number of public firms)
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Result 3


(3) W(m) is U-shape if the cost difference
between public firms and private firms are
sufficiently small and the number of total
number of firm N is large.
This is the most interesting case
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Result 3
W
0
m (the number of public firms)
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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
W
0
m1
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m
12
Larger scale privatization program
eventually more likely end up with
great success
W
0
m3
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m2
m1
m
13
Welfare-gains of privatizations is
accelerating
W
0
m3
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m2 m1
m
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Mixed Oligopoly, Mixed Market
Public firms compete against
private firms
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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
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Examples of mixed oligopoly in
other countries
Banking: Postal Banks (New Zealand, U.K., Germany,...)
Automobiles: Renault, VW
Medicine: Public Institute in Brazil
National Defense, Aviation: \ EADS, Airbus
Airline: National airlines (Swiss, Belgian, France,...)
Overnight Delivery: USSP
Energy: Electricite de France, Gas de France
Broadcasting: BBC
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Differences between public and
private firms
(1) Public firms are less efficient than private firms.
→Many empirical works does not support this view
(and many other papers support this view).
(2) Difference of objective function
→private firm maximize its own profits, public firm
care about social welfare
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Classical discussions of public
firms
Why do public firms exist?
(1) Natural monopoly
(a) Public firm monopoly
(b) Regulated private firm monopoly
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Non-Profitable Market
Ｐ
ＡＣ
Ｄ
0
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Ｙ
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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)
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Natural Monopoly
Ｐ
Ｄ
ＡＣ
0
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Ｙ
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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 faces
significant economy of scale, which
guarantees the monopoly by the
public firm
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Problems
(1) How to provide an incentives for welfare
maximization?
→ This is the central issue for the public
firm‘s monopoly
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Problems
(2) Is the welfare-maximizing behavior by the public
firm is efficient?
→This problem never appears in the public firm's
monopoly.
This question makes sense in mixed oligopoly
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 the mixed oligopoly
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Issues of mixed oligopoly
・Is welfare-maximizing behavior by the
public firm desirable in mixed oligopoly ?
・What distortion does welfare-maximizing
behavior by the public firm yield ?
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This paper's approach
(1) We do not make restrictions on the difference of
production efficiency between public and private firms.
(For the discussion of endogenous cost differences, see
Matsumura and Matsushima (2004).)
(2) Private firm maximizes its own profits, public firm
maximizes social welfare. （For more general objective
function, see Matsumura (1998).
(3) The number of firms is given exogenous.
（For endogenous number of private firms, see Matsumura
and Kanda (2004).）
(4) Simultaneous-move game (For sequential or
endogenous move game, see Pal (1998), and
Matsumura(2003a, 2003b).)
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De Fraja and Delbono(1989)
・ Cournot-type
(quantity-setting competition,
simultaneous-move game)
・No cost differences between public and private
firms.
・Linear demand and Quadratic cost function.
・The private firm maximizes its own profits.
・The public firm maximizes social welfare.
→The public firm chooses its output level so as
to the price equal to its marginal cost.
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Results
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.
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Intuition
・ Privatization of the public firm reduces x0 and
increases x1 (production substitution).
An increase of x1 improves welfare.
A decrease of x0 reduces welfare.
It is possible that the former effect dominates the
latter effect.
→Privatization might improve welfare.
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Production substitution
reaction curve
after privatization
q1
reaction curve of
the private firm
reaction curve
after privatization
0
q0
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More detailed explanation of intuition
Privatization of the public firm reduces x0 and increases
x1 (production substitution).
Before Privatization p=c0' >c1'
→ Public firm's marginal cost is higher than private firm's
→ Production substitution from public to private
economize production costs}
→Welfare-improving
→Privatization reduces total production level and so
consumer surplus
→ Welfare-impairing
It is possible that the former effect dominates the latter
effect.
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Contribution of De Fraja and Delbono (1989)
・No cost difference between public and private firms
→ privatization does not improves production
efficiency
・Public firm's objection: welfare
→No agency problem in the public firm
・No additional policies by regulation , tax, or subsidy
⇒Ideal circumstances for the existence of public firm.
Against assumptions for the advocators of
privatizations.
→ Nevertheless, privatization might improves
welfare
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Assumptions of De Fraja and Delbono (1989)
Many researchers in this filed believe that the
assumptions above are plausible,
but many other researchers (as well as I) make
these assumptions for strategic purposes.
・ Even without cost differences, privatization
improves welfare.
→If public firm is less efficient, much more.
・ Even without any agency problem in the public
firm, privatization improves welfare.
→If public firm has agency problem, much more.
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Assumptions of single public firm
Most existing works consider models with single public firm.
If this single public firm is privatized, the market becomes
pure market economy.
Considering desirable reform of the economic system in
former communist transitional countries, this is not a plausible
assumption. In reality numerous public firms exists 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 remains
after the privatization of several firms).
→Existing works cannot analyze these markets effectively.
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公企業１社のモデルでは分析が難しい事例

旧社会主義国・移行国の民営化プログラムの分析（ロシア等の
旧ソ連諸国、東欧、中国、ベトナム、モンゴル...）

歴史的に多くの公企業を抱えた途上国、新興国の公企業改革
プログラム（ブラジル、インド、イラン、ベネズエラ、インドネシア、
タイ、台湾、韓国...）

大規模で組織的な民営化プログラムを成功させた（？）先進国
の分析（英国、日本（？）、ドイツ（？）、豪州、NZ）

かなりの規模の公企業群がまだのこり、その一体改革が予想さ
れる先進国の分析（日本、ドイツ、フランス）
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なぜ既存研究が１国１公企業モデル
を扱うのか？
公私の費用格差がなければ、N=m でobviousにfirst
bestが達成される
→ 私的部門を全く持たない完全な計画経済で常にfirst
bestが達成される
→そもそも混合寡占を分析する意味がなくなる


しかしこの分野の人間は私的部門を全く持たない完全
な計画経済で常にfirst bestが達成されるという結果が
realisticだとは思っていない
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費用構造に関する仮定
公私の費用格差がないという仮定は戦略的な仮定で
あると同時に、現実的な仮定と考える研究者も多い
← 混合市場では公企業も私企業との競争を強いられる
ので、私企業に比べて極端に非効率的だと生き残れな
い（競争圧力）
 m=Nとなってしまうとこの競争圧力が減って、Ｘ非効率
の問題が深刻になる
→複数の公企業を抱える可能性をはじめから否定して
m=Nならfirst bestという無意味な議論を回避する

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この論文でやりたいこと

経済全体で１００社企業がありそのうち公企業
が２５社いる状態から出発して、公企業を２４社、
２３社、２２社と減らしていくと経済厚生はどうな
るのかを議論する意味はある。

この論文では、この分野のタブーを犯してでもあ
えてこの問題に挑戦する。
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Notations
N: Number of total firms
m: Number of public firms
qi: Firm i's output
Ci(qi) : Firm i's production cost
p(Q): demand function
Q: Total output
πi: Firm i's profit
CS: Consumer surplus
W: social surplus
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The model
Players: Identical m public firms,
identical N-m private firms.
Payoff: Welfare (Public firm),
Its own profits (Each private firm).
All firms simultaneously choose their outputs
（Cournot competition）.
Linear demand: p=A-Q.
Quadratic costs: c=0.5 α(qi)２ (public firm),
c=0.5 β(qi)２ (public firm),
α≧β
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Why quadratic costs？
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 to mixed
oligopoly in such a circumstances.
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How to avoid this problem?




(1) Using constant marginal costs and assuming
cost differences between public and private firms.
Pal (1998), Matsumura (2003)
(2) Using increasing marginal costs. De Fraja and
Delbono (1989), Matsumura and Kanda (2005),
This paper.
(3) Dropping the assumption of homogenous goods.
Cremer et al (1992), Anderson et al (1997),
Matsumura and Matsushima (2003, 2004),
Matsushima and Matsumura (2003).
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Proposition 1
Iｆ α>(β+1)2 /(β+2), then W* is decreasing in
m.
If cost difference between public and private
firms is sufficiently large, privatization of a
public firm always improve welfare regardless of
N and m.
→This is because privatization improves
production efficiency
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Proposition 1（the cases where public firms is
extremely inefficient）
W
0
m (the number of public firms)
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Proposition 2
Iｆ     12 /  2 and

  1     1  2
N
,
3
(1)
1   2  
then W* is non-decreasing in m and strictly
increasing if m>0 or (1) is satisfied with
strict inequality.
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Proposition 2（cost difference between
public and private firm is small and the
market is not sufficiently competitive）
W
0
m (the number of public firms)
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Proposition 3
Iｆ     12 /  2 and (1) is not satisfied,
then



0
,
m
,
(i) W* is decreasing in m for 

is minimized at m and increasing in m


m,
N

for  
where

 N  2    1    13     1  2
m
 0, N .
2
  1       1 


(ii) W* is convex with respect to m for
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


0
,
m




48
Proposition 3（cost difference between
public and private firm is small and the
W market is sufficiently competitive
0

m
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m (the number of public firms)
49
・Larger scale privatization program eventually
more likely ends up with great success
・Failureｓ at early stage do not imply the failure of
the whole privatization program
W
0
m2
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
m
m2’
m1
50
Welfare-gains of privatizations is
accelerating
W

m3 m2
m1
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m0
m
m
51
Intuition
Suppose that m public firms and N-m private firms
exit. 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 impairs
welfare and the latter improves welfare.
→The latter becomes stronger when m is smaller
and N is larger.
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まとめ
・初期の民営化の失敗がプログラム全体の失敗を意味
しない
→評価には長期的な視野が必要。
・小規模な民営化は失敗しやすい。
・民営化の利益は最終段階に近づくほど大きい
→民営化プログラムを一度軌道に乗せればあとは自
然にうまくいく。最初が一番しんどい。
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