Product Diversification, Entry

On patent licensing in spatial
competition with endogenous
location choice
Joint work with Noriaki Matsushima
Oligopoly Theory
1
Plan of the presentation
(1) Rough sketch of the model and results
(2) Motivation
(3) Overview of related works
(4) Formal explanation of our model
(5) Results and implications
Oligopoly Theory
2
Rough sketch of the model
Hotelling Model. Mill Pricing, Location then Price
Model, Bertrand, Inelastic Demand, licenser has
a 100% bargaining power.
(a) Exogenous R&D
Firm 1 has a cost advantage, d, and can transfer
its technology through licensing contract.
Firm 2 is an inferior firm.
licensing contract → location choice → Bertrand
competition
Oligopoly Theory
3
Rough sketch of the model
(b) Endogenous R&D
R&D → licensing contract → location choice →
Bertrand competition
(b-1) Firm 1 engages in R&D, which yields a cost
advantage
(b-1-1) R&D increases the cost advantage, d.
(b-1-2) R&D increases the probability of success.
(b-2) Both firms engages in R&D.
Oligopoly Theory
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Results
(1) Firm 1 has an incentive of licensing (regardless of
locations and bargaining power)
(2) Maximal Differentiation (regardless of the level of
licensing fee)
(3) Efficient Level of R&D.
Oligopoly Theory
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Motivation (Matsumura)
ある論文の誤りにたまたま気が付いた。
→Noteにするつもりだった。
Oligopoly Theory
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Sappington (2005 AER)
Hotelling Model. Mill Pricing, exogenous
location(内生化しても結果同じ）, Bertrand,
Inelastic Demand, Firm 1 has essential facility
and Firm 2 pays access charge to firm 1.
The rate of access charge, s, is given exogenously.
Result
Market share does not depend on s.
Firm 2's profit does not depend on s.
Oligopoly Theory
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Intuition
Firm 2の限界費用＝通常の生産費用＋ｓ
Firm 1の限界費用＝通常の生産費用＋機会費用
Firm 1の機会費用：自分が価格を下げ企業２の顧
客を１人奪うと接続料収入がｓだけ下がる
⇒両企業の限界費用がｓ上がるだけで、両企業の
費用格差は生まれない。
⇒接続料の引き上げは価格を上げるだけ。
（消費者が被害を受け企業１が利益を受けるが企
業２は損失を被らない）
Oligopoly Theory
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Poddar and Sinha (2004
Economic Record)
Hotelling Model. Mill Pricing, Location then Price
Model, Bertrand, Inelastic Demand, Firm 1 and
Firm 2 produce products. Firm 0 has a patent,
which reduces marginal cost (c → c-d)
(a) Vertical Separation
Firm 0 licenses both firms, and obtains profit d.
(b) Vertical Integration (Firm 1 is the licenser)
Firm 1 obtains a larger market share but the
additional profit is smaller than d .
→Vertical Integration reduces R&D.
Oligopoly Theory
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Poddar and Sinha (2004
Economic Record)
Mathematical Structure of (b) in Poddar and Sinha
and Sappington is similar (the former is a special
case of the latter), but two yields different results.
Either the former and the latter must be wrong.
Obviously, the former is wrong.
Poddar and Sinha (2007) did not include revenue
from licensing fee when they consider pricecompetition.
Oligopoly Theory
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Motivation (Matsushima)
昔すごく面白い論文を書いたのに(Matsushima and
Matsumura ``Cost Uncertainty and Spatial
Agglomeration''、審査にさんざん手間取ってる
間に追い抜かれてしまった。
悔しくてしょうがない
→このネタで再挑戦
Oligopoly Theory
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Matsumura and Matsushima (2004
Economica)
Hotelling Model. Mill Pricing, Location then Price
Model, Bertrand, Inelastic Demand, Firm 1 is a
public firm and firm 2 is a private firm.
R&D → location choice → Bertrand competition
Results
Location pattern is efficient
Firm 2 engages in excessive R&D, resulting in a
cost difference between public and private firms.
Privatization yields insufficient R&D, but can be
welfare-improving.
Oligopoly Theory
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Cost Difference in Private Duopoly
R&D → location choice → Bertrand competition
benchmarkとして民営化後の均衡を分析
on pathでは同じ投資量だとしても投資量が違うoff
pathも分析する必要がある。
松島:費用格差が十分に大きいと両企業が端に集まる
松村:これは明らかに均衡ではない。
松島:均衡の必要条件を満たし立地パターンはこれし
かない
松村:純粋戦略均衡は存在しない→おもしろいじゃな
いか！！
Oligopoly Theory
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Matsumura and Matsushima (2008
Annals of Regional Science)
Hotelling Model. Mill Pricing, Location then Price
Model, Bertrand, Inelastic Demand, Firm 1 has a
cost advantage.
Results
The cost differences is sufficiently high, no pure
strategy equilibrium exists. In this case both
firms edges of the linear city with equal
probability.
Oligopoly Theory
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Matsushima and Matsumura (2007,
国民経済雑誌)
費用構造が決まってから立地が決まるの？立地の
方が先なのが現実的なのでは？
location choice → Nature chooses Cost Structure
→Bertrand competition
⇒Central Agglomeration
Oligopoly Theory
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Notations
T: Transport Costs (quadratic)
xi: Firm i's location
pi : Firm i's price
r: license fee (per unit)
πi: Firm i's profit
W: social surplus
d: cost advantage of lisencer
Oligopoly Theory
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The Model
Players: Firm 1 (licenser) , Firm 2 (licensee)
Payoff: Its own profits
First, Firm 1 undertakes R&D. If it succeeds,
its cost becomes c-d. Otherwise its cost is c.
Firm 2's cost is c.
Second, license fee s is determined.
If firm 2 accept the offer, its cost becomes c-d.
Third, both firms simultaneously choose their
locations.
Forth, price-setting competition.
Oligopoly Theory
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Fourth stage
Under licensing contract (0≦s≦d),
s does not affect the market share of both firms.
The equilibrium price is const +s.
Firm 2's profit is not depends on s and
Firm 1's profit is const + s.
Without licensing contract,
competition under cost asymmetries
lower price, lower market share of firm 2.
Oligopoly Theory
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Third Stage
Under licensing contract (0≦s≦d),
Maximal Differentiation.
←Equilibrium Location without Cost Asymmetries
Without licensing contract,
competition under cost asymmetries
maximal differentiation or firm 1 chooses a location
closer to the central point.
Oligopoly Theory
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Second Stage
Rejecting licensing contract accelerates
competition and reducing both firms' profit.
The level of firm 2's profit does not depend on s,
while an increase in s increases firm1's profit.
→There is no conflict of interest between lisencers
and licensee.
Naturally, s=d. ←100% bargaining power of firm 1
(Assumption).
Oligopoly Theory
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First stage
Social gain of the reduction of production cost is d.
Private gain of the reduction of production cost is d.
→Socially efficient Investment.
Oligopoly Theory
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Summary
(1) Efficient R&D investments whether or not the
inventor is an outsider.
(2) Strong incentives of licensing for both licenser and
licensee
(3) Cost asymmetries disappear under licensing.
(4) Maximal Differentiation
Oligopoly Theory
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