Equilibrium Location with Elastic Demand in Mixed Duopoly Joint work with Minoru Kitahara OT 2010 1
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 OT 2010 2
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 OT 2010 3
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 OT 2010 4
Classical discussions of public firms Why do public firms exist? (1) Natural monopoly (a) Public firm monopoly (b) Regulated private firm monopoly OT 2010 5
Natural Monopoly P D AC 0 OT 2010 Ｙ 6
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) OT 2010 7
Non-Profitable Market P AC D 0 OT 2010 Y 8
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. OT 2010 9
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. OT 2010 10
Problem(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. OT 2010 11
Problem(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 OT 2010 12
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 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. OT 2010 13
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. OT 2010 14
Intuition (1) Privatization of the public firm reduces public firm's output q 0 (2) Privatization increases each private firm's output q 1 →production substitution from the public firm to the private firms. (3) Privatization decreases total output q 0 +nq 1 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. OT 2010 15
Production substitution reaction curve before privatization q 1 reaction curve of the private firm reaction curve after privatization 0 OT 2010 q 0 16
More detailed explanation of intuition Privatization of the public firm reduces q 0 and increases q 1 (production substitution). Before Privatization p=c 0' >c 1' →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. OT 2010 17
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 OT 2010 18
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. OT 2010 19
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. OT 2010 20
How to avoid this problem (1) Using constant marginal costs and assuming cost differences between public and private firms. Mujumdar and Pal (1998), Matsumura (2003 a), 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. OT 2010 21
How to avoid this problem (2) Using increasing marginal costs. De Fraja and Delbono (1989), Fjell and Pal (1996), White (1996), Matsumura and Kanda (2005), Heywood and Ye (2009 a), 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. OT 2010 22
How to avoid this problem (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 (2009 b) OT 2010 23
How to avoid this problem? More general Costs : Matsumura (1998, 2003 b), Kiyono and Tomaru (forthcoming) Discuss both (2) and (3): Matsumura and Shimizu (forthcoming) OT 2010 24
Shopping Model in Mixed 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 OT 2010 25
Maximal Differentiation in Private Duopoly 企業１の立地 ０ OT 2010 企業２の立地 １ 26
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 OT 2010 27
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P 2を所与とし て公企業の最適な価格は？（最適反応は？） OT 2010 28
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P 2を所与 として公企業の最適な価格は？（最適反応は？） OT 2010 29
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 OT 2010 30
Efficient Differentiation in Mixed Duopoly Cremer et al (1991) 企業１の立地 ０ OT 2010 1/4 企業２の立地 3/4 １ 31
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 OT 2010 32
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） OT 2010 33
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c 1>c 2とする。私企業（企業２）の価 格P 2を所与として公企業の最適な価格は？（最適 反応は？） P 1= P 2 ？, P 1> P 2 ？, P 1< P 2 ？ OT 2010 34
Mixed Duopoly Second Stage 問題：Second Stageを考える（費用を所与とする）。 仮にc 1>c 2とする。効率的な立地は？（均衡立地と は限らない） X 1= 1/4, X 1> 1/4, X 1< 1/4, X 2= 3/4, X 2> 3/4, X 2< 3/4 OT 2010 35
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 OT 2010 36
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 OT 2010 37
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 OT 2010 38
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？ OT 2010 39
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。 OT 2010 40
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 OT 2010 41
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 OT 2010 42
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 OT 2010 43
公企業の最適価格 企業２ の均衡 価格 需要非弾力的 0 需要弾力的 x 1 OT 2010 44
Shipping Model in Mixed Oligopoly OT 2010 45
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 OT 2010 46
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 OT 2010 47
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 OT 2010 48
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 OT 2010 49
Linear Cityなら？ 私企業の立地 ０ OT 2010 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 OT 2010 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？ OT 2010 52
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 OT 2010 53
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 OT 2010 外国企業 54
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 OT 2010 55
Equilibrium Location(外国企業３社) 外国企業間の differentiation OT 2010 一般性を失うこと なく企業０の立地 を０とする 56
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。 OT 2010 57
Matsushima and Matsumura (2003) Private Firms β =0 0 9/10 Private Firms 1/10 β=1 1/2 Public Firm OT 2010 delivered pricing, linear demand, constant marginal cost, no cost asymmetry, linear transport cost, Cournot, 58 domestic private
Results Private Firms β =0 0 9/10 1/10 β≧ 2/5 1/2 Public Firm OT 2010 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？ OT 2010 60
Matsushima and Matsumura (2003) Private Firms α =0 0 9/10 1/10 α=1 1/2 Public Firm OT 2010 Private Firms delivered pricing, linear demand, constant marginal cost, no cost asymmetry, linear transport cost, Cournot 61
Abina et al (2009) Private Firms α =0 0 9/10 1/10 α≧ 2/5 1/2 Public Firm OT 2010 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？ OT 2010 63
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