Transcript Interregional Mixed Duopoly, Location and Welfare

Interregional Mixed Duopoly,
Location and Welfare
Tomohiro Inoue*, Yoshio Kamijo and Yoshihiro Tomaru
*Graduate School of Economics, Waseda University
[email protected]
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Outline
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Motivation
Model
Literature
Proposition
Equilibrium
Comparison of Two Equilibria
Extension
Conclusion
Future Research
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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
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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
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2. Model (2/2)
 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
full prices paid by the residents
 Firm B maximizes profit.
 Two-stage game: 1st. location, 2nd. price
Region 1
0
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Region 2
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Example
full price
Customers of Firm B
Customers of Firm A
PB
PA
0
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a
1/2
x
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1
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3. Literature (1/3)
Hotelling-type duopoly, quadratic transportation cost
 d’Aspremont et al. (1979) – private duopoly
 Firms avoid severe price competition.
0
x (= 1/2)
1
 The price competition becomes severe as the firms approach
each other.
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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.
0
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1/4
x (= 1/2)
3/4
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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.
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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.
Private
Public
PA < PB
E1:
0
1/2
1/4
Private
x
1
Public
PA > PB
E2:
0
x
1/2
1
 E2 is payoff dominant.
 E1 is more socially desirable than E2.
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5. Equilibrium: E1
 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 (PA < PB).
 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.
Demand for public
firm’s product
Demand for private
firm’s product
Private
Public
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5. Equilibrium: E2
 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 (PA > PB).
 Private firm gets more demand and earns more profit than in E1.
Demand for public
firm’s product
Demand for private
firm’s product
Private
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Public
1/4
x
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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.
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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.
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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.
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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.
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7. Extension (3/3)
Demand for public firm's product
Private
Public
Case I:
Private
Public
Basic (E1):
Public
Private
Case II:
Note: This is the case where public firm locates on the left of private firm.
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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.
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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.
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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.
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