Equilibrium Location with Elastic Demand in Mixed Duopoly Joint work with Minoru Kitahara OT2010

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 OT2010

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 OT2010

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 OT2010

Classical discussions of public firms Why do public firms exist? (1) Natural monopoly (a) Public firm monopoly (b) Regulated private firm monopoly OT2010

Natural Monopoly P D AC Ｙ OT2010

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) OT2010

Non-Profitable Market AC D Y OT2010

Classical discussions on state-owned 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. OT2010

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. OT2010

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 welfare-maximizer 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. OT2010

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 OT2010

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. OT2010

Results →Privatization of the public firm might improve welfare 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. OT2010

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. OT2010

Production substitution reaction curve before privatization q1 reaction curve of the private firm q0 reaction curve after privatization q0 OT2010

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. OT2010

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 OT2010

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. OT2010

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. OT2010

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. OT2010

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. OT2010

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) OT2010

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) OT2010

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 OT2010

Maximal Differentiation in Private Duopoly 企業１の立地 企業２の立地 ０ １ 企業１の立地 OT2010

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 OT2010

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？） OT2010

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？） OT2010

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 OT2010

Efficient Differentiation in Mixed Duopoly Cremer et al (1991) 企業１の立地 企業２の立地 企業１の立地 １ 1/4 ０ 3/4 OT2010

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 OT2010

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） OT2010

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 ？ OT2010

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 OT2010

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 OT2010

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 OT2010

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 OT2010

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？ OT2010

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。 企業１の立地 OT2010

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 OT2010

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 OT2010

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 OT2010

公企業の最適価格 企業２の均衡価格 需要非弾力的 W 需要弾力的 x1 OT2010

Shipping Model in Mixed Oligopoly OT2010

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 OT2010

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 OT2010

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 OT2010

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 OT2010

Linear Cityなら？ 私企業の立地 公企業の立地 私企業の立地 ０ １ 企業１の立地 OT2010

Linear Cityなら？ 公企業の立地 私企業の立地 ０ １ 企業１の立地 OT2010

外国企業がいたら？ Matsushima and Matsumura (2006) OT2010

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 OT2010

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 OT2010

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 OT2010

Equilibrium Location(外国企業３社) 外国企業間のdifferentiation 一般性を失うことなく企業０の立地を０とする OT2010

General Model of Linear and Circular City ここを跨ぐ 時βの費用 market size 1 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。 OT2010

Matsushima and Matsumura (2003) Private Firms β =0 Private Firms Private Firms 1/10 delivered pricing, linear demand, constant marginal cost, no cost asymmetry, linear transport cost, Cournot, domestic private firms 9/10 β=1 1/2 Public Firm OT2010

Results Private Firms β =0 Private Firms Private Firms 1/10 9/10 Private Firms Private Firms 1/10 9/10 delivered pricing, linear demand, constant marginal cost, no cost asymmetry, linear transport cost, Cournot β≧2/5 1/2 Public Firm OT2010

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？ OT2010

Matsushima and Matsumura (2003) Private Firms α =0 Private Firms Private Firms 1/10 9/10 delivered pricing, linear demand, constant marginal cost, no cost asymmetry, linear transport cost, Cournot α=1 1/2 Public Firm OT2010

Abina et al (2009) Private Firms α =0 Private Firms Private Firms 1/10 Private Firms Private Firms 1/10 9/10 delivered pricing, linear demand, constant marginal cost, no cost asymmetry, linear transport cost, Cournot α≧2/5 1/2 Public Firm OT2010

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？ OT2010