February 9, 2008 GLOPE-TCER Joint Junior Workshop 1 Interregional Mixed Duopoly, Location and...

February 9, 2008February 9, 2008 GLOPE-TCER Joint Junior WorkshopGLOPE-TCER Joint Junior Workshop 11

Interregional Mixed Duopoly, Interregional Mixed Duopoly, Location and WelfareLocation and Welfare

Tomohiro Inoue*, Yoshio Kamijo and Yoshihiro TomaruTomohiro Inoue*, Yoshio Kamijo and Yoshihiro Tomaru*Graduate School of Economics, Waseda University*Graduate School of Economics, Waseda University

[email protected]@suou.waseda.jp


OutlineOutline MotivationMotivation ModelModel LiteratureLiterature PropositionProposition EquilibriumEquilibrium Comparison of Two EquilibriaComparison of Two Equilibria ExtensionExtension ConclusionConclusion Future ResearchFuture Research


1. Motivation1. Motivation What is the effect of What is the effect of a local public firma local public firm on outside regions? on outside regions?

mixed duopoly: marketmixed duopoly: market in which a public firm competes with a in which a public firm competes with a private firmprivate firm

Most of studies analyze the market within Most of studies analyze the market within a single regiona single region..

↓↓A market across two regionsA market across two regions

The locations of local public firms have crucial effects on The locations of local public firms have crucial effects on the residents of outside regions.the residents of outside regions. e.g.e.g., public transportation, public hospital, public transportation, public hospital

↓↓Spatial modelSpatial model


2. Model (1/2)2. Model (1/2) Hotelling-type linear city [0, 1]Hotelling-type linear city [0, 1]

Consumers are uniformly distributed.Consumers are uniformly distributed. Two firms (A & B) locate in the city and produce a Two firms (A & B) locate in the city and produce a

homogeneous good.homogeneous good. Production costs of both firms are normalized to zero.Production costs of both firms are normalized to zero.

Each consumer purchases Each consumer purchases one unitone unit of the good from the of the good from the firm with firm with lower full pricelower full price.. full price = mill price (product price) + quadratic transportation full price = mill price (product price) + quadratic transportation

cost fromcost from the firm tothe firm to each consumereach consumer

Divide the city into two symmetric regions.Divide the city into two symmetric regions. Region 1: [0, 1/2), Region 2: [1/2, 1]Region 1: [0, 1/2), Region 2: [1/2, 1]

Firm A: local public firm of Region 1Firm A: local public firm of Region 1 Firm A maximizes the local welfare of Region 1 (LW1).Firm A maximizes the local welfare of Region 1 (LW1). LW1 = profit of Firm A – burden on the residents of Region 1LW1 = profit of Firm A – burden on the residents of Region 1

Firm B: private firmFirm B: private firm Firm B maximizes profit.Firm B maximizes profit.

Two-stage game: 1st. location, 2nd. priceTwo-stage game: 1st. location, 2nd. price


2. Model (2/2)2. Model (2/2)

00 1/21/2 11

Region 1Region 1 Region 2Region 2

full prices paid by the residentsfull prices paid by the residents


ExampleExample

Customers of Firm B

00 1/21/2 11

PPAA

PPBB

aa bbxx

full pricefull price

Customers of Firm A


3. Literature (1/3)3. Literature (1/3)Hotelling-type duopoly, quadratic transportation costHotelling-type duopoly, quadratic transportation cost d’Aspremont et al. (1979) d’Aspremont et al. (1979) – private duopoly– private duopoly

Firms avoid severe price competition.Firms avoid severe price competition.

The price competition becomes severe as the firms approach The price competition becomes severe as the firms approach each other.each other.

00 11x (= 1/2)x (= 1/2)


3. Literature (2/3)3. Literature (2/3) Cremer et al. (1991), Matsumura and Matsushima (2004) Cremer et al. (1991), Matsumura and Matsushima (2004)

– mixed duopoly (– mixed duopoly (state-ownedstate-owned public firm and private firm) public firm and private firm) State-owned firm maximizes social welfare of the whole city.State-owned firm maximizes social welfare of the whole city. Social welfare is maximized.Social welfare is maximized.

3/43/41/41/400 11x (= 1/2)x (= 1/2)


3. Literature (3/3)3. Literature (3/3) Existing mixed duopoly model:Existing mixed duopoly model:

Public firm maximizes social welfare (= Public firm maximizes social welfare (= all firms’all firms’ profits – total profits – total burden on the residents of burden on the residents of thethe whole citywhole city).).

Our model:Our model: Local public firm maximizes local welfare (= Local public firm maximizes local welfare (= ownown profit – total profit – total

burden on the residents of burden on the residents of thethe left half of the cityleft half of the city).).

↓↓The right half of the city is The right half of the city is the outside region the outside region

for the local public firm.for the local public firm.↓↓

Equilibrium locations of both firms are not symmetric.Equilibrium locations of both firms are not symmetric.


4. Proposition4. Proposition Two subgame perfect equilibria (E1 & E2)Two subgame perfect equilibria (E1 & E2) E1: Local public firm locates on the E1: Local public firm locates on the leftleft of private firm. of private firm. E2: Local public firm locates on the E2: Local public firm locates on the rightright of private firm. of private firm.

E2 is payoff dominant. E2 is payoff dominant. E1 is more socially desirable than E2.E1 is more socially desirable than E2.

00 1/21/2 111/41/4

00 1/21/2 11

xx

xx

E1:E1:

E2:E2:

PublicPublic PrivatePrivate

PublicPublicPrivatePrivate

PPAA < P < PBB

PPAA > P > PBB

Local public firm locates at slightly right of point 1/4.Local public firm locates at slightly right of point 1/4. Local public firm sets lower price than private firm to get more Local public firm sets lower price than private firm to get more

demand of Region 2 (Pdemand of Region 2 (PAA < P < PBB).). Only the increase of the profit from Region 2 improves LW1.Only the increase of the profit from Region 2 improves LW1.

Local public firm of Region 1 supplies the outside region Local public firm of Region 1 supplies the outside region in addition to the inside region.in addition to the inside region.


5. Equilibrium: E15. Equilibrium: E1


00 1/21/2 111/41/4

Demand for public Demand for public firm’s productfirm’s product

Demand for private Demand for private firm’s productfirm’s product

xx

Local public firm locates at slightly left of the center.Local public firm locates at slightly left of the center. Local public firm Local public firm mainlymainly supplies the outside region. supplies the outside region.

Local public firm does not reduce its price to obtain more profits Local public firm does not reduce its price to obtain more profits from Region 2 (Pfrom Region 2 (PAA > P > PBB).).

Private firm gets more demand and earns more profit than in Private firm gets more demand and earns more profit than in E1.E1.


5. Equilibrium: E25. Equilibrium: E2

PublicPublicPrivatePrivate

00 1/21/2 111/41/4

Demand for private Demand for private firm’s productfirm’s product

Demand for public Demand for public firm’s productfirm’s product

xx


6. Comparison of Two Equilibria (1/2)6. Comparison of Two Equilibria (1/2)Differences:Differences: 1.1. In E2, both firms obtain higher payoffs than in E1.In E2, both firms obtain higher payoffs than in E1.

Both firms have high profits at the expense of consumer surplus Both firms have high profits at the expense of consumer surplus of Region 2.of Region 2.

Social welfare in E2 is lower than in E1.Social welfare in E2 is lower than in E1.

2.2. In E1, the total transportation cost of Region 2 is lower In E1, the total transportation cost of Region 2 is lower than in private duopoly. In E2, the cost is higher than in than in private duopoly. In E2, the cost is higher than in private duopoly.private duopoly.


6. Comparison of Two Equilibria (2/2)6. Comparison of Two Equilibria (2/2)Common points:Common points: 1.1.The total transportation cost of Region 1 is lower than in The total transportation cost of Region 1 is lower than in

private duopoly.private duopoly.2.2.The mill prices of both firms are lower than in private The mill prices of both firms are lower than in private

duopoly.duopoly. Local public firm has the incentive to reduce the burden of Local public firm has the incentive to reduce the burden of

Region 1.Region 1.

3.3.Social welfare is lower than in mixed duopoly with a Social welfare is lower than in mixed duopoly with a state-owned firm.state-owned firm.


7. Extension (1/3)7. Extension (1/3)Change in the local public firm’s objective functionChange in the local public firm’s objective function

Case I: Local public firm also takes account of Case I: Local public firm also takes account of the profit the profit of private firmof private firm.. Local public firm does not behave aggressively in the Local public firm does not behave aggressively in the

competition.competition.

↓↓ The demand for the public firm's product is smaller than in the The demand for the public firm's product is smaller than in the

basic model.basic model. Both firms set higher prices to get higher profits.Both firms set higher prices to get higher profits.


7. Extension (2/3)7. Extension (2/3) Case II: Local public firm also takes account of Case II: Local public firm also takes account of the the

burden of the residents of Region 2burden of the residents of Region 2..= state-owned public firm and foreign-owned private firm= state-owned public firm and foreign-owned private firm Public firm behaves aggressively to prevent (foreign) private Public firm behaves aggressively to prevent (foreign) private

firm from charging high price on the residents.firm from charging high price on the residents.

↓↓ The demand for the public firm's product is larger than in the The demand for the public firm's product is larger than in the

basic model.basic model. Both firms set lower prices.Both firms set lower prices.


7. Extension (3/3)7. Extension (3/3)

Case I:Case I:

Basic (E1):Basic (E1):

Case II:Case II:

Note: This is the case where public firm locates on the Note: This is the case where public firm locates on the leftleft of private firm. of private firm.




Demand for public firm's productDemand for public firm's product


8. Conclusion8. Conclusion Two subgame perfect equilibriaTwo subgame perfect equilibria

E2 is a payoff dominant equilibrium.E2 is a payoff dominant equilibrium. E1 is more socially desirable than E2.E1 is more socially desirable than E2.

The burden on the residents of Region 2 is very high in E2.The burden on the residents of Region 2 is very high in E2.

Local public firm reduces the mill prices of both firms Local public firm reduces the mill prices of both firms compared to in private duopoly.compared to in private duopoly. Local public firm may increase the transportation cost of the Local public firm may increase the transportation cost of the

outside region compared to in private duopoly (E2).outside region compared to in private duopoly (E2). If local public firm takes account of the profit of private If local public firm takes account of the profit of private

firm, consumer surplus of the outside region decreases.firm, consumer surplus of the outside region decreases.


9. Future Research9. Future Research Asymmetric regionsAsymmetric regions

The size differences of regions can affect the behavior of local The size differences of regions can affect the behavior of local public firm.public firm.

Quantity-setting duopolyQuantity-setting duopoly Most of the studies on mixed duopoly consider quantity Most of the studies on mixed duopoly consider quantity

competition.competition.


ReferenceReference d’Aspremont C., Gabszewicz J. J., Thisse J.-F. (1979), On d’Aspremont C., Gabszewicz J. J., Thisse J.-F. (1979), On

Hotelling’s ‘stability in competition’, Hotelling’s ‘stability in competition’, EconometricaEconometrica, 47, 1145-1150., 47, 1145-1150.

Cremer H., Marchand M., Thisse J.-F. (1991), Mixed oligopoly with Cremer H., Marchand M., Thisse J.-F. (1991), Mixed oligopoly with differentiated products, differentiated products, International Journal of Industrial International Journal of Industrial OrganizationOrganization, 9, 43-53., 9, 43-53.

Matsumura T., Matsushima N. (2004), Endogenous cost Matsumura T., Matsushima N. (2004), Endogenous cost differentials between public and private enterprises: A mixed differentials between public and private enterprises: A mixed duopoly approach, duopoly approach, EconomicaEconomica, 71, 671-688., 71, 671-688.

February 9, 2008 GLOPE-TCER Joint Junior Workshop 1 Interregional Mixed Duopoly, Location and...

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