Spatial Cournot Equilibria in a Quasi-Linear City Joint work with Takeshi Ebina and Daisuke Shimizu OT2010 1 Plan of the presentation (1) Motivation (2) Shipping Model (3) Spatial Cournot Competition (4) Model Formulation (5) Equilibrium Outcomes (6) Welfare Implication OT2010 2 Linear-City 0 OT2010 1 3 Circular-City 0 1/2 OT2010 4 Two Standard Models of Space (1) Hotelling type Linear-City Model (2) Salop type (or Vickery type) Circular-City Model Linear-City has a center-periphery structure, while every point in the Circular-City is identical. →Circular Model is more convenient than Linear Model for discussing symmetric oligopoly except for duopoly. OT2010 5 Motivation Circular-City でモデル化する →Linear-City Modelだとどうなるの？と必ず聞かれる（除くfree entry の議論) Matsumura (2003), Matsushima and Matsumura (2003,2006), Matsumura and Matsushima (2005) Linear-City でモデル化しても、Circular-City Modelだとどうなるのとは聞かれなかった。 →でもその後refereeからやはり聞かれた Matsumura and Matsushima (2004, 2007) ⇒一つのモデルですっきり出来ないのか？２つのモデルを特殊ケースとして含む一般モデルで議論できないか？ OT2010 6 General Model α 0 1 αの費用で０から１、１から０へ輸送可能。 α＝０ならCircular, 十分に大きければLinear OT2010 7 General Model market size α 0 market size 1 1/2 α =0ならLinear, α=1ならCircular OT2010 8 General Model ここを跨ぐ時αの費用 0 1/2 α＝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 9 Application どの議論に適用するか？一番素直なのはmill pricingのlocation-price model。でも標準的なquadraticなtransport cost functionを使うと、円でも線でもどちらもmaximal differentiation。２つを区別する意味があまりない。（transport costを変えれば意味ある議論になるかも） delivered pricing model→linear-cityとcircular-cityでは均衡立地パターンが違う⇒とりあえずこれでやってみる。 OT2010 10 Mill Pricing Model (Shopping Model) 長岡京河原町高槻梅田茨木淡路 OT2010 11 Delivered Pricing Model (Shipping Model, Spatial Price Discrimination Model) 北海道東北九州 OT2010 関西東海関東 12 Hamilton, Thisse, and Weskamp (1989) duopoly, delivered pricing model, linear transport cost, linear demand at each point, Hotelling–type linear city In the first stage firms choose their locations. In the second stage firms face Bertrand or Cournot competition. OT2010 13 Bertrand Firm 1 0 OT2010 1/4 Firm 2 3/4 1 14 Cournot Firm 2 Firm 1 0 OT2010 1/2 1 15 Pal (1998) duopoly, delivered pricing model, linear transport cost, linear demand at point, Salop–type circular markets each In the first stage firms choose their locations In the second stage firms face Cournot competition OT2010 16 Cournot Firm 1 0 1/2 Firm 2 OT2010 17 Bertrand Firm 1 0 1/2 Firm 2 OT2010 18 Shipping modelのその他の研究 Oligopoly： Anderson and Neven(1991), Matsushima (2001),Shimizu and Matsumura (2003), Gupta et al (2004), Matsumura et al (2005) Welfare: Matsumura and Shimizu (2005a, 2005b, 2009) Different Production Costs across locations: Mayer (2000) OT2010 19 Shipping modelのその他の研究 General Transport Costs： Gupta (2004), Matsumura and Shimizu (2006) Mixed Strategy Equilibria: Matsumura and Shimizu (2008) Product Differentiation: Shimizu (2002), Yu and Lai (2003) Multi Plants: Chamorro-Rivas (2000), Pal and Sarkar (2002) OT2010 20 Shipping modelのapplications FMS Anderson and de Palma (1998), Eaton and Schmitt(1994), Norman and Thisse(1999). Antitrust Gupta, Kats, and Pal(1995), Matsumura(2003,2004), Matsumura and Matsushima (2005) ,Matsumura and Okamura (2006) Mixed Oligopoly Matsushima and Matsumura (2003, 2006) OT2010 21 Location-Quantity Model 0 Firm 2 3/4 α=0 1/4 Firm 1 1/2 OT2010 Firm 1 Firm 2 α =1 22 Results ・均衡はsymmetricなもののみ・均衡立地はjumpする・複数均衡 OT2010 23 Results 企業１の立地 1/2 1/4 0 α OT2010 24 Intuition なぜjump? なぜ複数均衡？ ←strategic complementarity ライバルが真ん中に寄ると真ん中による誘因が大きくなる～Matsumura (2004) OT2010 25 Complimentarity Firm 1 0 OT2010 Firm 1 1/2 Firm 2 1 26 Results ・均衡立地はjumpしないでなめらかに円から線へ OT2010 27 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 28