Product Diversification, Entry

Equilibrium Location with Elastic
Demand in Mixed Duopoly
Joint work with Minoru Kitahara
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Plan of the presentation
(1) Mixed Oligopoly
(2) Classical discussion of Public Firms
(3) Theory of Mixed oligopoly
(4) Mixed Oligopoly with Shopping Models
(5) Mixed oligopoly with Shipping Models
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Mixed Oligopoly, Mixed Market
State-owned public firms compete against private firms
Examples 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 (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,
Italy, Indonesia...)
Overnight Delivery: USSP
Energy: Electricite de France, Gas de France,
Macquarie,
Broadcasting: BBC
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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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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, however, 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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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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Problem(1)
(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 welfaremaximizer under the monopoly, it is absolutely
obvious that the first best is achieved by definition.
→No unsolved research problem remains. Thus,
researchers never assume that the public firm is a
welfare maximizer when they consider monopoly
situation.
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Problem(2)
(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 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 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.
WP >WM more likely takes place when the
number of private firms are large.
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Intuition
(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 more likely improves welfare when n is
larger.
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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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Contribution of De Fraja and
Delbono(1989)
(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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Assumptions of De Fraja and
Delbono(1989)
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.
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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)
(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 (forthcoming)
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.
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How to avoid this problem (2)
(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), The paper presented
yesterday.
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.
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How to avoid this problem (3)
(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)
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)
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How to avoid this problem?
More general Costs : Matsumura (1998, 2003b),
Kiyono and Tomaru (forthcoming)
Discuss both (2) and (3): Matsumura and Shimizu
Shimizu (forthcoming)
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Shopping Model in Mixed Duopoly
Duopoly Model、長さ１の直線都市。公企業１（企
業１）。私企業１（企業２）。私企業は国内企業。
移動費用は距離の２乗に比例。各消費者１単位の
財を企業１ないし企業２から購入。企業１の利得
は総余剰、企業２の利得は自社の利潤。両企業の
限界費用は一定でｃ（費用格差なし）。
各企業は第１期に独立に立地を決める。
立地を見た後第２期にBertrand競争。
shopping model
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Maximal Differentiation in Private
Duopoly
企業１の立地
０
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企業２の立地
１
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Why Maximal Differentiation in
Private Duopoly?
企業２が少し離れる
(1) 企業１需要の価格弾力性が小さくなる
→企業１の価格が上がる(直接効果)
(2) 企業２の需要の価格弾力性が小さくなる
→企業２の価格が上がる→企業１の最適価格が上が
る(間接効果、戦略的効果)
２つの効果によって離れる誘因が生まれる
この２つのHotellingが示した需要量減少効果を
dominateして最大距離の均衡が生まれる
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Mixed Duopoly
公企業はライバルと自分の需要の分割が効率的にな
るように配慮
問題：Second Stageでの競争を考える（立地を所与
とする）。私企業（企業２）の価格P2を所与とし
て公企業の最適な価格は？（最適反応は？）
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脱線：もし私企業が外国企業なら？
問題：Second Stageでの競争を考える（立地を所与
とする）。海外私企業（企業２）の価格P2を所与
として公企業の最適な価格は？（最適反応は？）
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Mixed Duopoly
First Stage
企業２が離れる
（１）企業１の需要の価格弾力性が小さくなる
→企業１は価格を上げない⇒ Private Duopolyで存在
した直接効果が消える
（２）企業２の需要の価格弾力性が小さくなる
→企業２の価格が上がる→企業１の最適価格が上が
る（間接効果、戦略的効果）
Private Duopolyに比べて離れる誘因が小さい
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Efficient Differentiation in Mixed
Duopoly
Cremer et al (1991)
企業１の立地
０
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1/4
企業２の立地
3/4
１
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Endogenous Cost Differentials
between Public and Private Firms
Matsumura and Matsushima (2004)
設定は生産費用を内生化する以外Cremer et al
(1991)のDuopoly versionと同じ。
Hotelling, Shopping Model, Domestic Private Firm
(Firm 2), Public Firm (Firm 1)
企業の費用内生化：企業努力によって費用下がる。
努力にはdisutilityが伴う
(1) 費用削減努力 (2)立地選択 (3) 価格競争
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Maximal Differentiation in Private
Duopoly at the second stage
企業１の立地
企業２の立地
０
１
費用をgivenとすると極端な費用格差がない限り
均衡立地は費用格差のない時と同じ
費用格差がかなりあったら？
→純粋戦略均衡無くなる（第６講参照）
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Mixed Duopoly
Third Stage
公企業はライバルと自分の需要の分割が効率的にな
るように配慮
問題：Third Stageでの競争を考える（立地を所与と
する）。仮にc1>c2とする。私企業（企業２）の価
格P2を所与として公企業の最適な価格は？（最適
反応は？）
P1= P2 ？, P1> P2 ？, P1< P2 ？
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Mixed Duopoly
Second Stage
問題：Second Stageを考える（費用を所与とする）。
仮にc1>c2とする。効率的な立地は？（均衡立地と
は限らない）
X1= 1/4, X1> 1/4, X1< 1/4, X2= 3/4, X2> 3/4, X2< 3/4
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Efficient and Equilibrium
Differentiation in Mixed Duopoly
at the second stage
企業１の立地
企業２の立地
０
１
費用をgivenとするとfirst bestのoutcomeが実現
均衡立地の性質は費用格差のない時と同じ
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First stage in Private Duopoly
両私企業の努力過小。
企業１の費用下がる→企業１の価格下がる→企業２の
価格下げる（戦略的補完）⇒企業１の損失
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First Stage in Mixed Duopoly
私企業の努力過大⇒公企業と私企業の間に費用格差
が生じる。
企業２の費用下がる→企業１がより端に立地(second
stage)、より高い価格(third stage)
←より効率的な企業２に市場を譲るから
⇒企業２の利益～戦略的な理由からより多く（過大
に）投資する誘因
→公企業の民営化によって厚生が改善する可能性も
民営化の利益：投資と生産効率性の不均衡是正
民営化の不利益：過剰差別化、過小投資
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Elastic Demand
今までの話：全ての消費者が１単位財を買う
各企業の需要は弾力的、全体の需要は非弾力的
需要が弾力的でも立地パターンは効率的になる？
仮にならないとして、均衡における差別化の程度は
過大になるのか過小になるのか？
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Model
linear city, mill pricing, elastic demand, constant
marginal cost, no cost asymmetry, quadratic
transport
各消費者はどちらかの企業から財を購入。購入量は
価格に依存。需要の価格弾力性一定。但しあまり大
きくない。
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Proposition 1
私企業の顧客は左側の方が多い～需要の中点より私企
業の立地は公企業寄り。
私企業の立地
公企業の立地
１
０
私企業の顧客
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Proposition 2
inefficient location (too close,私企業が少し離れると
Welfareが改善) ~Proposition 2
私企業の立地
公企業の立地
１
０
経済厚生が改善
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Intuition
公企業は私企業が近づいてきてもあまり低い価格を付
けたがらない～不必要に顧客をとると移動費用が増す
から
私企業が近いほど、価格の小さな低下で不必要に顧客
を奪ってしまう～価格を下げる誘因が小さくなる
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公企業の最適価格
企業２
の均衡
価格
需要非弾力的
需要弾力的
0
x1
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Shipping Model in Mixed Oligopoly
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Shipping Model in Mixed Oligopoly
Matsushima and Matsumura (2003)
Oligopoly Model、長さ１の円環都市。各点線形の需
要関数。輸送費用は距離に比例。限界費用は一定
でゼロ。
企業０の利得は総余剰、私企業の利得は自社の利潤。
各企業は第１期に独立に直線都市上に立地を決める。
立地を見た後第２期期にCournot競争。
shipping model
Pal (1998)のmixed oligopoly version
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Equilibrium Location (Duopoly)
一般性を失うことなく
企業０の立地を０とする
企業１の最適反応
を考える
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Equilibrium Location (Duopoly)
一般性を失うことなく
企業０の立地を０とする
企業１の均衡立地
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Equilibrium Location (Oligopoly)
一般性を失うことなく
企業０の立地を０とする
私企業の集積
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Linear Cityなら？
私企業の立地
０
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公企業の立地私企業の立地
１
50
Linear Cityなら？
公企業の立地
０
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私企業の立地
１
51
外国企業がいたら？
Matsushima and Matsumura (2006)
Matsushima and Matsumura (2003)の私企業のうち
何社かが外国企業なら？
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Equilibrium Location(外国企業１社)
一般性を失うこと
なく企業０の立地
を０とする
外国企業
私企業の集積
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Equilibrium Location(外国企業２社)
一般性を失うこと
なく企業０の立地
を０とする
国内私企
業の戦略
が変わる
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外国企業
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Equilibrium Location(外国企業２社)
一般性を失うこと
なく企業０の立地
を０とする
国内私企
業の戦略
が変わる
外国企業
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Equilibrium Location(外国企業３社)
外国企業間の
differentiation
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一般性を失うこと
なく企業０の立地
を０とする
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General Model of Linear and
Circular City
ここを跨ぐ
時βの費用
0
1/2
β＝０ならCircular, 十分に大きければLinear。最初の
モデルと本質的には同じ。
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Matsushima and Matsumura (2003)
β =0
Private Firms
Private Firms
Private Firms
0
1/10
9/10
β=1
1/2
Public Firm
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delivered pricing,
linear demand,
constant
marginal cost,
no cost
asymmetry,
linear transport
cost, Cournot,
domestic private
58
firms
Results
Private Firms
Private Firms
β =0
0
1/10
9/10
β≧2/5
1/2
Public Firm
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Private Firms
delivered pricing,
linear demand,
constant
marginal cost,
no cost
asymmetry,
linear transport
cost, Cournot
59
Results
・均衡立地はjumpしないでなめらかに円から線へ
・β≧2/5で結果は線と同じに
→線型都市モデルの適用領域は広い
・partial agglomerationが現れない、という円の結
果はβ=0の時のみ成立～円は極めて特殊？
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Matsushima and Matsumura (2003)
Private Firms
Private Firms
α =0
0
1/10
9/10
α=1
1/2
Public Firm
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Private Firms
delivered pricing,
linear demand,
constant
marginal cost,
no cost
asymmetry,
linear transport
cost, Cournot
61
Abina et al (2009)
Private Firms
Private Firms
α =0
0
1/10
9/10
α≧2/5
1/2
Public Firm
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Private Firms
delivered pricing,
linear demand,
constant
marginal cost,
no cost
asymmetry,
linear transport
cost, Cournot
62
Results
・均衡立地はjumpしないでなめらかに円から線へ
・α≧2/5で結果は線と同じに
→線型都市モデルの適用領域は広い
・partial agglomerationが現れない、という円の結
果はα=0の時のみ成立～円は極めて特殊？
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