1 / 37

Our works related to this paper

Multiple Long-Run Equilibria in a Spatial Cournot Model and Welfare Implications joint work with Takanori Ago. (1) Spatial Cournot Competition and Transportation Costs in a Circular City (ARS 2012, joint work with Noriaki Matsushima)

dara-dodson
Download Presentation

Our works related to this paper

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Multiple Long-Run Equilibria in a Spatial Cournot Model and Welfare Implications joint work with Takanori Ago

  2. (1) Spatial Cournot Competition and Transportation Costs in a Circular City (ARS 2012, joint work with Noriaki Matsushima) (2) Spatial Cournot Equilibria in a Quasi-Linear City (PiRS 2010, with Takeshi Ebina and Daisuke Shimizu) (3) Noncooperative Shipping Cournot Duopoly with Linear-Quadratic Transport Costs and Circular Space (JER 2008, with Daiskuke Shimizu). (4) Spatial Cournot Competition and Economic Welfare: A Note (RSUE 2005, with Daisuke Shimizu) (5) Partial Agglomeration or Dispersion in Spatial Cournot Competition (SEJ 2005, with Takao Ohkawa and Daisuke Shimizu) Our works related to this paper

  3. Mill Pricing Model (Shopping Model) Mitaka Kichijoji Musashisakai Tachikawa Kokubunji Kunitachi

  4. Delivered Pricing Model (Shipping Model, Spatial Price Discrimination Model) Hokkaido Tohoku Kanto Tokai Kansai Kyusyu

  5. Delivered Pricing (Shipping) Models

  6. Consider a symmetric duopoly. Transport cost is proportional to both distance and output quantity (linear transport cost). In the first stage, each firm chooses its location independently. In the second stage, each firm chooses its output independently. Each point has an independent market, and the demand function is linear demand function, P=A-Y. No consumer's arbitrage. Production cost is normalized as zero. A is sufficiently large. Hamilton et al (1989), Anderson and Neven (1991) Spatial Cournot Model

  7. Properties of Spatial Cournot Model Market overlap ~ Two firms supply for all markets Market share depends on the locations of the two firms.

  8. the location of firm 1 Equilibrium Location the location of firm 2 ０ １ Two firms agglomerate at the central points. similar result in . Anderson and Neven (1991).

  9. Location and Transport Costs A slight increase of x1 ０ １ The area for which the relocation increases the transport cost of firm 1 The area for which the relocation decreases the transport cost of firm 1

  10. Consider a symmetric duopoly. Transport cost is proportional to both distance and output quantity (linear transport cost). In the first stage, each firm chooses its location independently on the circle. In the second stage, each firm chooses its output independently. Each point has an independent market, and the demand function is linear demand function, P=A-Y. No consumer's arbitrage. Production cost is normalized as zero. A is sufficiently large. Pal (1998) Spatial Cournot with Circular-City

  11. Equilibrium Location Without loss of generality. we assume x1=0 Consider the best reply for firm 2.

  12. Location and Transport Costs the area for which the relocation of firm 2 increases transport cost An increase of x2 the area for which the relocation of firm 2 decreases transport cost

  13. Equilibrium Location the output of firm 2 is small The location minimizing the transport cost of firm 2. the output of firm 2 is large

  14. Equilibrium Location Maximal distance is the unique pure strategy equilibrium location pattern as long as the transport cost is strictly increasing (Matsumura and Shimizu 2006). the equilibrium location of firm 2

  15. Equilibrium Location Equidistant Location Pattern

  16. Equilibrium Location Partial Agglomeration ～Matsushima (2001)

  17. Equilibrium Location a continuum of equilibria exists ～Shimizu and Matsumura (2003), Gupta et al (2004)

  18. Equilibrium Location Under non-liner transport cost

  19. Equilibrium Location in Under non-linear transport cost ~ Matsumura and Matsushima (2012)

  20. Equilibrium Location a continuum of equilibria exists In all equilibria, CS and PS, and so TS are the same.

  21. Equilibrium Location in Under non-liner transport cost, dispersion equilibrium yields larger PS and TS and smaller CS than partial agglomeration equilibrium (Proposition 1). Price dispersion yields larger CS.

  22. CS P Pa Pb D Pb Pa 0 Y

  23. Equilibrium Location in Free Entry ~ Under non-liner transport cost, dispersion equilibrium yields larger number of entering firms. Thus CS can be larger than that in partial agglomeration equilibrium. (Proposition 2)

  24. mixed strategy equilibria under quadratic transport cost (Shopping, Bertrand) the locations of firm 1 the locations of firm 2 non-maximal differentiation, Ishida and Matsushima, 2004.

  25. mixed strategy equilibria (Shopping, Cournot) the locations of firm 1 （no-linear transport cost) the locations of firm 2

  26. mixed strategy equilibria (linear transport cost) a continuum of equilibria exists～Matsumura and Shimizu (2008)

  27. 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 except for duopoly.

  28. General Model (1) α 1 0 It costs α to transport from 0 to 1. The transport cost from 0 to 0.9 is min(0.9t, α+0.1t). If α＝０, this model is a circular-city model. If α >t, this model is a linear-city model.

  29. General Model (2) market size α 0 market size 1 1/2 If α=0, this model is a linear-city model. If α=1, this model is a circular-city model.

  30. General Model (3) It costs α to across this point 0 1/2 If α=0, this model is a circular-city model. If α>1, it is a linear-city model. (essentially the same model as (1)).

  31. Application In the mill pricing (shopping) location-price models, both linear-city and circular-city models yield maximal differentiation. delivered pricing model (shipping model) →linear-city model and circular-city model yield different location patterns~ We discuss this shipping model.

  32. Location-Quantity Model 0 3/4 1/4 Firm 1 Firm 2 α=0 1/2 Firm 1 α =1 Firm 2

  33. Results ・The equilibrium locations are symmetric. ・The equilibrium location pattern is discontinuous with respect to α (A jump takes place). ・Multiple equilibria exist. Abina et al (OT 2012)

  34. Results the equilibrium location of firm 1 the same outcome as the linear-city model 1/2 1/4 0 α Ebina, Matsumura and Shimizu (2011)

  35. Intuition Why discontinuous (jump)? Why multiple equilibria？ ←strategic complementarity Suppose that firm 1 relocate form 0 to 1/2. It increases the incentive for central location of firm 2. ～Matsumura (2004)

  36. ComplementarityMatsumura (2004) Firm 2 Firm 1 1 0 1/2

  37. ComplementarityMatsumura (2004) Firm 1 Firm 2 1 0 1/2 Central location by firm 1 increases the value of market 0 and decreases that of market 1 for firm 2→it increases the incentive for central location by firm 2.

More Related