Product Diversification, Entry

Oligopoly Theory
2. Overview on Mixed Oligopoly
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）厚生最大化行動が必ずしも厚生最大化をもたらさ
ないメカニズムを理解する
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Outline of the Second Lecture
2-1 State-Owned Public Firm and Mixed Oligopoly
2-2 Public Monopoly
2-3 Production Substitution
2-4 Privatization and Welfare Implications
2-5 Partial Privatization
2-6 Long-Run Competition and Mixed Oligopoly
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Mixed Oligopoly, Mixed Market
State-owned 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
Life Insurance: Postal Life Insurance (Kampo)
Overnight Delivery: Japan Post
Energy: Public Gas Corps (Sendai,Narashino,
Fukui,...)
Broadcasting: NHK
Telecommunication: NTT
Tobacco: JT
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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,
Italy, Indonesia...)
Overnight Delivery: USSP
Energy: Electricite de France, Gas de France,
Macquarie,
Broadcasting: BBC
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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.
This paper, as well as many other papers on mixed
oligopoly, assume that the public firm’s objective is
welfare.
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Classical discussions of public
firms(1)
Why do public firms exist?
(1) Natural monopoly
(a) Public firm monopoly
(b) Regulated private firm monopoly
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Natural Monopoly
P
D
AC
0
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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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Non-Profitable Market
P
AC
D
0
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Classical discussions on stateowned 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.
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Problem(1)
(1) How to provide incentives for welfare maximization?
→ The central issue for the public firm's monopoly
If we assume that the public firm’s objective is welfare
and the public firm is the monopolist, it is absolutely
obvious that the first best is achieved.
No research problem remains unsolved under such
nonsense assumption.
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Problem(2)
(2) Is the public firm’s welfare-maximizing behavior
efficient?→never appears in public firm's monopoly.
This question makes sense in mixed oligopoly since
public firm’s welfare-maximizing behavior might
worsen welfare through strategic interaction between
public and private firms.
→The central issue of mixed oligopoly
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De Fraja and Delbono(1989)
(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.
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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
(1) Privatization of the public firm reduces public firm's
output q0
(2) Privatization increases private firm's output q1
→production substitution from the public firm to the
private firm.
(3) Privatization decreases total output q0 +q1
Effects (1) and (3) reduces welfare and effect (2)
improves welfare. Effect (2) may be the strongest,
leading to an improvement of welfare.
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Production Substitution
reaction curve
before privatization
q1
reaction curve of
the private firm
reaction curve
after privatization
0
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q0
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More detailed explanation of
intuition
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.
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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 mixed oligopoly in such a
circumstance.
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How to avoid this problem?
(1) Using constant marginal costs and assuming cost
differences between public and private firms.
Mujumdar and Pal(1998),Pal(1998),
Matsumura(2003a), Lu (2007)
(2) Using increasing marginal costs. De Fraja and
Delbono (1989), Fjell and Pal (1996),White (1996),
Matsumura and Kanda (2005), Heywood and Ye
(forthcoming) , Matsumura and Shimizu
(forthcoming)
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How to avoid this problem?
(3) Dropping the assumption of homogenous goods
and or introducing spatial components. Cremer et
al. (1992), Anderson et al. (1997), Matsumura and
Matsushima (2003,2004), Matsushima and
Matsumura (2003,2006), Fujiwara (2007), Heywood
and Ye (forthcoming, forthcoming), Ishibashi et al
(forthcoming)
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Contribution of De Fraja and
Delbono
(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
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Partial Privatization
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, Iwate Bank, Hokuriku Electric Power
Company, VW, Renault
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Matsumura (1998)
(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-α) W+ απ0
(4) General demand and general costs.
The government chooses s and s affects α. After
observing α firms compete in the product market.
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Results
α =0 is optimal only if it yields public monopoly.
→If we allow partial privatization, no privatization (full
nationalization) never becomes optimal.
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Intuition
(1) Suppose that α =0. A slight increase in α reduces
public firm's output q0 .
Since p=c0', this effect is negligible (second order)
←envelope theorem
(2) Increasing α increases private firm's output q1
Since p>c1', this effect is nonnegligible (first order)
⇒(2) dominates (1).
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Partial Privatization
Free Entry: Matsumura and Kanda (2005)
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)
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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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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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