Product Diversification, Entry

Oligopoly Theory
3. Mixed Oligopoly in International
Markets
今日の講義の目的
（１）混合寡占の基本的な発想を理解する
（２）国際競争と国内競争の構造の違いを理解する
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Outline of the Third Lecture
3-1 Overview (第２講の続き) Free Entry
3-2 Overview (第２講の続き) Multiple Public
Enterprises
3-3 Overview (第２講の続き) Optimal Degree of
Privatization and Market Competition
3-4 Overview (第２講の続き) Relative Performance
and Market Competition
3-5 Overview (第２講の続き) Optimal Degree of
Privatization and Relative Performance
3-6 Competition against Foreign Competitors
3-7 Optimal Degree of Privatization and Foreign
Competition
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Matsumura and Kanda(2005)
Long-run analysis on mixed oligopoly
(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.
U0= (1-α) W+ α π0
(4) General demand and general cost (increasing
marginal costs).
(5) Free entry of private firms.
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自由参入市場
（１）政府が公企業（企業０）を作るか否かを決める。
政府がそれを作る場合、設立費用としてF0かかる。
（２）政府は企業０に対する持ち株比率s∈ [0,1]を決
め、間接的にαをコントロールする。
（３）各私企業はαを観察し、参入するか否かを決め
る。各私企業は同質的である。
（４）私企業数が確定した後、参入した企業は
Cournot競争。
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（２）から始まる部分ゲーム
（最適なαの分析）
αが与えられたもとで決まる内生変数：
n（企業数）、q1（各私企業の生産量）、q0（公企業の生
産量）、Ｑ（総生産量）
これらの変数に関する比較静学
(a) q1、Ｑともにαと独立
(b) q0はαの減少関数。
(c) nはαの増加関数。
政府の持ち株比率sの増加は公企業の生産量を増加
させ、参入企業数を減らすが、個別私企業の生産量と
公・私企業の総生産量に影響を与えない。
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Free entry equilibrium
P
private firm's residual demand
private firm's AC
0
private firm's output
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Y
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an decrease in α
P
private firm's residual demand
private firm's AC
0
Y
private firm's output
long run : reduction of the number of private firms
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Results
α =0 is optimal.（公企業の生産量は適正である。）
←限界費用価格付けによって無駄な私企業の参入
が抑えられるから。
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Intuition
α をほんの少し下げる。
(1) Qは不変→消費者余剰は不変
(2) q0が増加→ 公企業の限界費用・Δq0だけ費用増加。
(3) nが減少→私企業の平均費用・私企業の１社あたり生
産量・Δnだけ費用増加
私企業の１社あたり生産量・Δn =Δq0
私企業平均費用＝価格＞公企業の限界費用
⇒αの引き下げで生産費用が削減される。(Welfareimproving production substitution)
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公企業を設立すべきだったか
・企業０の設立が経済厚生を改善する必要十分条
件はπ＞ 0である
～公企業が黒字であれば公企業を参入させるべき
だった。逆に赤字を生むような公企業は不要だった。
・公企業と私企業の生産性が同じなら公企業は超過
利潤を得られる。
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No Cost Difference
P
AC
public firm's output
MC
0
private firm's output
Public firm obtains positive profits
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Y
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Brandao and Castro
(2007)
・民営化後の参入規制を考える。企業数を最適に
設定
～公企業を民営化すると経済厚生が改善することも
悪化することもある。
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Matsumura and Shimizu
(forthcoming)
(1) Cournot-type (quantity-setting competition,
simultaneous-move)
(2) No restrictions on the cost differences between
public and private firms.
(3) Linear demand and quadratic costs
(4) m public firms, N-m private firms.
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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
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.
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Examples of economies with
multiple public firms
(1) Former communist transitional countries
(examples) Russia, Many of Eastern and
Central European countries, China, Vietnam,
Mongolia...
(2) Developing and emerging countries
(examples) Brazil, India, Iran, Indonesia,
Thailand, Korea, Chinese Taipei...
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Examples of economies with
multiple public firms
(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
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Why did existing works consider
models with single public firm?
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.
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The assumption of no cost
difference between public and
private firms
(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.)
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The assumption of no cost
difference between public and
private firms
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.
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This paper's approach
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.
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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=0.5α(qi)２ +K (public firm),
c=0.5β(qi)２ +K (private firm), α≧β
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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 improves welfare regardless of N and m.
→This is because privatization improves production
efficiency
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Proposition 1（the case where
public firms are extremely
inefficient）
W
0
m (the number of public firms)
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Proposition 2
If α<(β+1)2 /(β+2) and
N ≦((β+1)2 -α(β+1) (β+2))/(1-β2+αβ) (1)
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 α<(β+1)2 /(β+2) and (1) is not satisfied, then
(i) W* is decreasing in m for [0, mMIN)
is minimized at mMIN and increasing in m
for ( mMIN, N] where
mMIN≡α [N(β2 –αβ-1)+(β+1)3- α(β+1)(β+2)]
/(β+1-α){αβ- (β+1)2} ∈[0,N]
(ii) W* is convex with respect to m for
[0, mMIN)
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Proposition 3:cost difference
between public and private firms is
small and the market is sufficiently
competitive
W
0
mMIN
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m
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・Larger scale privatization program
eventually more likely ends up with great
success
・Failures at early stages do not imply the
failure of the whole privatization program
W
0
m2
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mMIN m2’ m1
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Welfare-gains of privatizations are
accelerating
W
m3 m2 m1 m0
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mMIN
m
30
Intuition
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.
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Summary
(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, the latter
stage of privatization program is.
→Once we reach the critical stage, the privatization
automatically proceeds with larger support.
(4) Similar results are obtained under constant
marginal cost if we introduce product differentiation.
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Optimal Degree of Privatization
One Public Firm, m Private firms.
The public firm's objective is U0= (1-α) W+ απ0
No cost difference between public and private firms.
Linear demand and quadratic cost function.
The private firm maximizes its own profits given
outputs of other firms.
Exactly the same as in De Fraja and Delbono (1989)
except for the objective of the public firm.
In the first stage the government chooses α. The
government's objective is W.
In the second stage firms face Cournot competition.
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Second Stage
Equilibrium output of the public firm is (increasing,
decreasing) in α.
Equilibrium output of the each private firm is
(increasing, decreasing) in α.
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First Stage
Equilibrium level of α is (increasing, decreasing) in m.
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Relative Performance
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相対利潤
各企業が自社の利潤ではなくライバルとの相対利潤
を最大化したら？（利潤の差を最大化）
→よりaggressiveに生産する
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均衡
最大化の一階条件
P+P'Y1-C1' -P'Y2=0
→symmetricな均衡(Y1=Y2)では価格＝限界費用となる
（完全競争の世界）
⇒数量競争の文脈で、寡占市場でも激しい競争になる
典型例
この状態がevolutionary stable (Vega-Redondo, 1997)
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相対利潤
U1=π1-απ2
α=1 完全競争 α=0 Cournot α=-1 Collusion
完全競争からカルテルまで競争度を連続的に表現可能
応用例
カルテルの安定性はαに関して単調減少
R&Dの水準はαに関して非単調ーU字型
プロセスイノベーションとプロダクトイノベーション
の選択に影響
製品差別化の程度はαに関して単調減少
自由参入市場の企業数と価格はαに関して単調減少
αが十分大きい・小さいときMulti-Storeが均衡に
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相対利潤・相対評価の正当化
（１）CEOの市場での評価
（２）evolutionary approach
（３）ねたみ、利他主義（実験経済学・経済心理学
の成果）
（４）Fershtman and Judd (1987)の応用
（５）政治学の分野への応用
（６）ステータスの議論
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Conjectural Variation
conjectural variation（推測変動）
自社が１単位生産量を増やすとｒだけ市場全体の全体の
生産量が増えると仮定して各企業が行動する。
Cournotならr=1。
Conjectural Variation Model~Cournotを特殊ケースとし
て含む一般的モデル（？）
でもr=1以外のケースは意味あるのか？
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Conjectural Variation Modelの解
Duopoly, 同質財市場、限界費用一定で両企業の限界費
用は同じ（ｃ）
企業１の一階条件
P+P'rＹ1 =c
２階条件は満たされているものとする
均衡の導出
P+P'rＹ1 =c、P+P'rＹ2 =cの連立方程式を解く
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Conjectural Variation Model
r≠1とする
企業１の生産量の変化は企業２の生産量も変化させる
→企業１の生産量を見てから企業２が生産量を決めるの
でないとおかしい
企業２の生産量の変化は企業１の生産量も変化させる
→企業２の生産量を見てから企業１が生産量を決めるの
でないとおかしい
⇒静学的なモデルとしては論理的に破綻している
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論理的に破綻しているのになぜ
Conjectural Variation Modelが使わ
れるのか？
（１）an unmodeled dynamic model
～動学的なinteractionを考えている
→もしそうなら動学モデルを作るのが筋
（２）市場の競争度を表現
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Conjectural Variation Modelの解
CV Modelでの企業１の一階条件 P+P'rＹ1 =c
Cournot Model での企業１の一階条件
P+P'Ｙ1 =c ｒ＝１に対応
Bertrand Model~完全競争モデルでの一階条件
P =c ｒ＝０に対応
Joint Profit Maximization(カルテル）での一階条件
P+P'(Ｙ1+Ｙ2) =c ｒ＝２に対応
それぞれ競争度の違うモデルに対応。ｒが小さいほど競争
が激しい。競争度を特定化しないでモデル化できる。
～実証系の論文で特にadvantageがある。
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相対利潤アプローチのadvantage
(1) 静学的モデルとして破綻していない（コンシステ
ントなモデル）。
(2) Cournot, Bertrand, Collusionの３つの間の競争状
態に対してもちゃんとしたfoundationがある。
(3) 静学的な文脈ではより現実的（おそらく賛否両論
ある）
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Relative Profit Approach: Mixed
Oligopoly
Vi=πi-α(他社の利潤）
私企業は上記の相対利潤を、公企業はU0= (1-θ) W+
θπ0を最大化。
私企業数はｍ。需要・費用関数等はDe Fraja and
Delbono (1989)と同じ。
In the first stage the government chooses θ. The
government's objective is W.
In the second stage firms face Cournot competition.
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Second Stage
Equilibrium output of the public firm is (increasing,
decreasing) in θ.
Equilibrium output of the each private firm is
(increasing, decreasing) in θ.
Equilibrium output of the public firm is (increasing,
decreasing) in α.
Equilibrium output of the each private firm is
(increasing, decreasing) in α.
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First Stage
Equilibrium θ is (increasing, decreasing) in m.
Equilibrium θ is (increasing, decreasing) in α.
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First Stage
Equilibrium θ is increasing in m.
Equilibrium θ is (increasing, decreasing) in α.
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競争相手が外国企業だったら？
Private Duopolyならライバルの国籍は関係なし
公企業の目的関数がdomestic welfareなら、ライバ
ルの国籍と公企業の行動が関係している
問題：ライバルが外国企業なら公企業の最適生産
量は増えるか減るか？（反応曲線がどうシフトする
か？）
～ライバルの生産量ゼロならもちろん同じ。ライバル
の生産量が正の範囲では？
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公企業の反応曲線
ライバルが外国企業：P’’<0
Ｙ２
ライバルが外国企業
：線形需要
ライバルが
国内企業
0
OT:Mixed Oligopolt
ライバルが外国
企業：P’’<0
Y１
52
Optimal Degree of Privatization
One Public Firm, m Private firms. mβ is foreign private
firms, m(1-β) is domestic private firms.
The public firm's objective is U0= (1-α) W+ απ0
No cost difference between public and private firms.
Linear demand and quadratic cost function.
The private firm maximizes its own profits given
outputs of other firms.
In the first stage the government chooses α. The
government's objective is W.
In the second stage firms face Cournot competition.
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Second Stage
Equilibrium output of the public firm is (increasing,
decreasing) in α.
Equilibrium output of the each private firm is
(increasing, decreasing) in α.
Equilibrium output of the public firm is (increasing,
decreasing) in β.
Equilibrium output of the each private firm is
(increasing, decreasing) in β.
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First Stage
Equilibrium α is (increasing, decreasing) in m.
Equilibrium α is (increasing, decreasing) in β.
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Lin and Matsumura (unpublished)
Players: government, firm 0 (public firm), mβ foreign
private firms, m(1-β) domestic private firms,
Payoffs: domestic welfare (government),
Its own profits (private firms)
α(its own profit)＋(1-α) domestic welfare (firm 0)
(1) Government sells α shares at the price M= α π0e.
Infinitesimal foreign investors purchase αγ at the price
γM and domestic purchase at the price (1-γ)M .
(2) Given α and M, firms faces Cournot competition.
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Second Stage
Firm 0's payoff
απ0 +(1-α) domestic welfare
=απ0+(1-α)(CS+(1-αγ)π0+m(1-β)π1+γM)
q0S is decreasing in α and increasing in βand γ
Privatization makes firm 0 less aggressive.
An increase in the foreign presence makes firm 0
more aggressive.
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First stage
The government's payoff
domestic welfare
=CS+(1-αγ)π0+m(1-βγ)π1+γM
=CS+π0+m(1-β)π1
Important Point: In the second stage, M is given
exogenously, whereas in the first stage M depends
on α, so it is endogenous.
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Results
(i)α* is increasing in γ and (ii)α* is decreasing in β.
(i) An increase in foreign presence in the capital
market for privatization increases the optimal
degree of privatization
Complementarity between privatization policy and
open market policy
(ii) An increase in foreign presence in product
markets decreases the optimal degree of
privatization
Substitute between privatization policy and open
market policy
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Intuition (ii)
A decrease of α accelerates the competition,
resulting in a lower price and lower outputs of
foreign firms.
→It reduces the rent obtained by the foreign firms.
The government has a stronger incentive to commit
to larger output when β is large.
Exactly the same mechanism repeatedly appear in
the world of strategic trade policy.
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Intuition (i)
A decrease of α accelerates the competition,
resulting in a lower price and lower profits of firm 0.
This effect becomes stronger when γ is larger.
→It reduces M.
The government has a stronger incentive to commit
to smaller output (larger output) when γ is larger.
Time-inconsistency.
The government want to restrict aggressive
behavior of firm 0 before selling the stocks.
After selling the stocks, it has incentive to expand
the outputs of firm 0.
Committing to a smaller output by a larger α.
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