1. February 9, 2008 GLOPE-TCER Joint Junior Workshop 1 Interregional Mixed Duopoly, Location and Welfare Tomohiro Inoue*, Yoshio Kamijo and Yoshihiro Tomaru *Graduate School of Economics, Waseda University tomo-ino@suou.waseda.jp

2. February 9, 2008 GLOPE-TCER Joint Junior Workshop 2 Outline  Motivation  Model  Literature  Proposition  Equilibrium  Comparison of Two Equilibria  Extension  Conclusion  Future Research

3. February 9, 2008 GLOPE-TCER Joint Junior Workshop 3 1. Motivation  What is the effect of a local public firm on outside regions?  mixed duopoly: market in which a public firm competes with a private firm  Most of studies analyze the market within a single region. ↓ A market across two regions  The locations of local public firms have crucial effects on the residents of outside regions.  e.g., public transportation, public hospital ↓ Spatial model

4. February 9, 2008 GLOPE-TCER Joint Junior Workshop 4 2. Model (1/2)  Hotelling-type linear city [0, 1]  Consumers are uniformly distributed.  Two firms (A & B) locate in the city and produce a homogeneous good.  Production costs of both firms are normalized to zero.  Each consumer purchases one unit of the good from the firm with lower full price.  full price = mill price (product price) + quadratic transportation cost from the firm to each consumer

5.  Divide the city into two symmetric regions.  Region 1: [0, 1/2), Region 2: [1/2, 1]  Firm A: local public firm of Region 1  Firm A maximizes the local welfare of Region 1 (LW1).  LW1 = profit of Firm A – burden on the residents of Region 1  Firm B: private firm  Firm B maximizes profit.  Two-stage game: 1st. location, 2nd. price February 9, 2008 GLOPE-TCER Joint Junior Workshop 5 2. Model (2/2) 0 1/2 1 Region 1 Region 2 full prices paid by the residents

6. February 9, 2008 GLOPE-TCER Joint Junior Workshop 6 Example Customers of Firm B 0 1/2 1 PAPAPAPA PBPBPBPB a b x full price Customers of Firm A

7. February 9, 2008 GLOPE-TCER Joint Junior Workshop 7 3. Literature (1/3) Hotelling-type duopoly, quadratic transportation cost  d’Aspremont et al. (1979) – private duopoly  Firms avoid severe price competition.  The price competition becomes severe as the firms approach each other. 01 x (= 1/2)

8. February 9, 2008 GLOPE-TCER Joint Junior Workshop 8 3. Literature (2/3)  Cremer et al. (1991), Matsumura and Matsushima (2004) – mixed duopoly (state-owned public firm and private firm)  State-owned firm maximizes social welfare of the whole city.  Social welfare is maximized. 3/4 1/4 01 x (= 1/2)

9. February 9, 2008 GLOPE-TCER Joint Junior Workshop 9 3. Literature (3/3)  Existing mixed duopoly model:  Public firm maximizes social welfare (= all firms’ profits – total burden on the residents of the whole city).  Our model:  Local public firm maximizes local welfare (= own profit – total burden on the residents of the left half of the city). ↓ The right half of the city is the outside region for the local public firm. ↓ Equilibrium locations of both firms are not symmetric.

10. February 9, 2008 GLOPE-TCER Joint Junior Workshop 10 4. Proposition  Two subgame perfect equilibria (E1 & E2)  E1: Local public firm locates on the left of private firm.  E2: Local public firm locates on the right of private firm.  E2 is payoff dominant.  E1 is more socially desirable than E2. 0 1/2 1 1/4 0 1/2 1 x x E1: E2: Public Private PublicPrivate P A < P B P A > P B

11.  Local public firm locates at slightly right of point 1/4.  Local public firm sets lower price than private firm to get more demand of Region 2 (P A < P B ).  Only the increase of the profit from Region 2 improves LW1.  Local public firm of Region 1 supplies the outside region in addition to the inside region. February 9, 2008 GLOPE-TCER Joint Junior Workshop 11 5. Equilibrium: E1 Public Private 0 1/2 1 1/4 Demand for public firm’s product Demand for private firm’s product x

12.  Local public firm locates at slightly left of the center.  Local public firm mainly supplies the outside region.  Local public firm does not reduce its price to obtain more profits from Region 2 (P A > P B ).  Private firm gets more demand and earns more profit than in E1. February 9, 2008 GLOPE-TCER Joint Junior Workshop 12 5. Equilibrium: E2 Public Private 0 1/2 1 1/4 Demand for private firm’s product Demand for public firm’s product x

13. February 9, 2008 GLOPE-TCER Joint Junior Workshop 13 6. Comparison of Two Equilibria (1/2) Differences: 1. In E2, both firms obtain higher payoffs than in E1.  Both firms have high profits at the expense of consumer surplus of Region 2.  Social welfare in E2 is lower than in E1. 2. In E1, the total transportation cost of Region 2 is lower than in private duopoly. In E2, the cost is higher than in private duopoly.

14. February 9, 2008 GLOPE-TCER Joint Junior Workshop 14 6. Comparison of Two Equilibria (2/2) Common points: 1. The total transportation cost of Region 1 is lower than in private duopoly. 2. The mill prices of both firms are lower than in private duopoly.  Local public firm has the incentive to reduce the burden of Region 1. 3. Social welfare is lower than in mixed duopoly with a state-owned firm.

15. February 9, 2008 GLOPE-TCER Joint Junior Workshop 15 7. Extension (1/3) Change in the local public firm’s objective function  Case I: Local public firm also takes account of the profit of private firm.  Local public firm does not behave aggressively in the competition. ↓  The demand for the public firm's product is smaller than in the basic model.  Both firms set higher prices to get higher profits.

16. February 9, 2008 GLOPE-TCER Joint Junior Workshop 16 7. Extension (2/3)  Case II: Local public firm also takes account of the burden of the residents of Region 2. = state-owned public firm and foreign-owned private firm  Public firm behaves aggressively to prevent (foreign) private firm from charging high price on the residents. ↓  The demand for the public firm's product is larger than in the basic model.  Both firms set lower prices.

17. February 9, 2008 GLOPE-TCER Joint Junior Workshop 17 7. Extension (3/3) Case I: Basic (E1): Case II: Note: This is the case where public firm locates on the left of private firm. Public Private Public Private Public Private Demand for public firm's product

18. February 9, 2008 GLOPE-TCER Joint Junior Workshop 18 8. Conclusion  Two subgame perfect equilibria  E2 is a payoff dominant equilibrium.  E1 is more socially desirable than E2.  The burden on the residents of Region 2 is very high in E2.  Local public firm reduces the mill prices of both firms compared to in private duopoly.  Local public firm may increase the transportation cost of the outside region compared to in private duopoly (E2).  If local public firm takes account of the profit of private firm, consumer surplus of the outside region decreases.

19. February 9, 2008 GLOPE-TCER Joint Junior Workshop 19 9. Future Research  Asymmetric regions  The size differences of regions can affect the behavior of local public firm.  Quantity-setting duopoly  Most of the studies on mixed duopoly consider quantity competition.

20. February 9, 2008 GLOPE-TCER Joint Junior Workshop 20 Reference  d’Aspremont C., Gabszewicz J. J., Thisse J.-F. (1979), On Hotelling’s ‘stability in competition’, Econometrica, 47, 1145-1150.  Cremer H., Marchand M., Thisse J.-F. (1991), Mixed oligopoly with differentiated products, International Journal of Industrial Organization, 9, 43-53.  Matsumura T., Matsushima N. (2004), Endogenous cost differentials between public and private enterprises: A mixed duopoly approach, Economica, 71, 671-688.