Oligopoly Theory 1

On patent licensing in spatial On patent licensing in spatial competition with endogenous competition with endogenous

location choicelocation choice

Joint work with Noriaki MatsushimaJoint work with Noriaki Matsushima

Oligopoly Theory 2

Plan of the presentationPlan of the presentation

(1) Rough sketch of the model and results(1) Rough sketch of the model and results

(2) Motivation(2) Motivation

(3) Overview of related works (3) Overview of related works

(4) (4) Formal explanation of our modelFormal explanation of our model

(5) Results and implications

Oligopoly Theory 3

Rough sketch of the modelRough sketch of the model

Hotelling Model. Mill Pricing, Location then Price Hotelling Model. Mill Pricing, Location then Price Model, Bertrand, Inelastic Demand, licenser has Model, Bertrand, Inelastic Demand, licenser has a 100% bargaining power. a 100% bargaining power.

(a) Exogenous R&D (a) Exogenous R&D

Firm 1 has a cost advantage, d, and can transfer Firm 1 has a cost advantage, d, and can transfer its technology through licensing contract. its technology through licensing contract.

Firm 2 is an inferior firm. Firm 2 is an inferior firm.

licensing contract → location choice → Bertrand licensing contract → location choice → Bertrand competitioncompetition

Oligopoly Theory 4

Rough sketch of the modelRough sketch of the model(b) Endogenous R&D (b) Endogenous R&D

R&D → licensing contract → location choice → R&D → licensing contract → location choice → Bertrand competitionBertrand competition

(b-1) Firm 1 engages in R&D, which yields a cost (b-1) Firm 1 engages in R&D, which yields a cost advantage advantage

(b-1-1) R&D increases the cost advantage, d.(b-1-1) R&D increases the cost advantage, d.

(b-1-2) R&D increases the probability of success. (b-1-2) R&D increases the probability of success.

(b-2) Both firms engages in R&D.(b-2) Both firms engages in R&D.

Oligopoly Theory 5

Results Results

(1) Firm 1 has an incentive of licensing (1) Firm 1 has an incentive of licensing (regardless of (regardless of

locations and bargaining power) locations and bargaining power)

(2) Maximal Differentiation (regardless of the (2) Maximal Differentiation (regardless of the level of licensing fee)level of licensing fee)

(3) Efficient Level of R&D. (3) Efficient Level of R&D.

Oligopoly Theory 6

Motivation (Matsumura)Motivation (Matsumura)

ある論文の誤りにたまたま気が付いた。ある論文の誤りにたまたま気が付いた。→→NoteNoteにするつもりだった。にするつもりだった。

Oligopoly Theory 7

Sappington (2005 AER)Sappington (2005 AER)

Hotelling Model. Mill Pricing, exogenous Hotelling Model. Mill Pricing, exogenous location(location( 内生化しても結果同じ）内生化しても結果同じ） , Bertrand, , Bertrand, Inelastic Demand, Firm 1 has essential facility Inelastic Demand, Firm 1 has essential facility and Firm 2 pays access charge to firm 1. and Firm 2 pays access charge to firm 1.

The rate of access charge, s, is given The rate of access charge, s, is given exogenously. exogenously.

ResultResult

Market share does not depend on s.Market share does not depend on s.

Firm 2's profit does not depend on s.Firm 2's profit does not depend on s.

Oligopoly Theory 8

Intuition Intuition Firm 2Firm 2 の限界費用＝通常の生産費用＋ｓの限界費用＝通常の生産費用＋ｓFirm 1Firm 1 の限界費用＝通常の生産費用＋機会費用の限界費用＝通常の生産費用＋機会費用Firm 1Firm 1 の機会費用：自分が価格を下げ企業２の顧の機会費用：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 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。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。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（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）業２は損失を被らない）

Oligopoly Theory 9

Poddar and Sinha (2004 Economic Poddar and Sinha (2004 Economic Record)Record)

Hotelling Model. Mill Pricing, Location then Price Hotelling Model. Mill Pricing, Location then Price Model, Bertrand, Inelastic Demand, Firm 1 and Model, Bertrand, Inelastic Demand, Firm 1 and Firm 2 produce products. Firm 0 has a patent, Firm 2 produce products. Firm 0 has a patent, which reduces marginal cost (c → c-d)which reduces marginal cost (c → c-d)

(a) Vertical Separation(a) Vertical Separation

Firm 0 licenses both firms, and obtains profit d.Firm 0 licenses both firms, and obtains profit d.

(b) Vertical Integration (Firm 1 is the licenser)(b) Vertical Integration (Firm 1 is the licenser)

Firm 1 obtains a larger market share but the Firm 1 obtains a larger market share but the additional profit is smaller than d .additional profit is smaller than d .

→→Vertical Integration reduces R&D. Vertical Integration reduces R&D.

Oligopoly Theory 10

Poddar and Sinha (2004 Economic Poddar and Sinha (2004 Economic Record)Record)

Mathematical Structure of (b) in Poddar and Sinha Mathematical Structure of (b) in Poddar and Sinha and Sappington is similar (the former is a special and Sappington is similar (the former is a special case of the latter), but two yields different case of the latter), but two yields different results. results.

Either the former and the latter must be wrong.Either the former and the latter must be wrong.

Obviously, the former is wrong. Obviously, the former is wrong.

Poddar and Sinha (2007) did not include revenue Poddar and Sinha (2007) did not include revenue from licensing fee when they consider price-from licensing fee when they consider price-competition. competition.

Oligopoly Theory 11

Motivation Motivation (Matsushima)(Matsushima)

昔すごく面白い論文を書いたのに昔すごく面白い論文を書いたのに (Matsushima (Matsushima and Matsumura ``Cost Uncertainty and and Matsumura ``Cost Uncertainty and Spatial Agglomeration''Spatial Agglomeration'' 、審査にさんざん手、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。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悔しくてしょうがない→→このネタで再挑戦このネタで再挑戦

Oligopoly Theory 12

Matsumura and Matsushima (2004 Matsumura and Matsushima (2004 Economica)Economica)

Hotelling Model. Mill Pricing, Location then Price Hotelling Model. Mill Pricing, Location then Price Model, Bertrand, Inelastic Demand, Firm 1 is a Model, Bertrand, Inelastic Demand, Firm 1 is a public firm and firm 2 is a private firm. public firm and firm 2 is a private firm.

R&D → location choice → Bertrand competitionR&D → location choice → Bertrand competition

ResultsResults

Location pattern is efficientLocation pattern is efficient

Firm 2 engages in excessive R&D, resulting in a Firm 2 engages in excessive R&D, resulting in a cost difference between public and private firms.cost difference between public and private firms.

Privatization yields insufficient R&D, but can be Privatization yields insufficient R&D, but can be welfare-improving.welfare-improving.

Oligopoly Theory 13

Cost Difference in Private DuopolyCost Difference in Private DuopolyR&D → location choice → Bertrand competitionR&D → location choice → Bertrand competition

benchmarkbenchmark として民営化後の均衡を分析として民営化後の均衡を分析on pathon path では同じ投資量だとしても投資量が違うでは同じ投資量だとしても投資量が違う off off

pathpathも分析する必要がある。も分析する必要がある。松島松島 ::費用格差が十分に大きいと両企業が端に集まる費用格差が十分に大きいと両企業が端に集まる松村松村 ::これは明らかに均衡ではない。これは明らかに均衡ではない。松島松島 ::均衡の必要条件を満たし立地パターンはこれし均衡の必要条件を満たし立地パターンはこれしかないかない松村松村 ::純粋戦略均衡は存在しない→おもしろいじゃな純粋戦略均衡は存在しない→おもしろいじゃないか！！いか！！

Oligopoly Theory 14

Matsumura and Matsushima (2008 Matsumura and Matsushima (2008 Annals of Regional Science)Annals of Regional Science)

Hotelling Model. Mill Pricing, Location then Price Hotelling Model. Mill Pricing, Location then Price Model, Bertrand, Inelastic Demand, Firm 1 has a Model, Bertrand, Inelastic Demand, Firm 1 has a cost advantage. cost advantage.

ResultsResults

The cost differences is sufficiently high, no pure The cost differences is sufficiently high, no pure strategy equilibrium exists. In this case both strategy equilibrium exists. In this case both firms edges of the linear city with equal firms edges of the linear city with equal probability.probability.

Oligopoly Theory 15

Matsushima and Matsumura Matsushima and Matsumura (2007, (2007, 国民経済雑誌国民経済雑誌 ))

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？方が先なのが現実的なのでは？

location choice → Nature chooses Cost Structure location choice → Nature chooses Cost Structure →Bertrand competition→Bertrand competition

⇒⇒Central AgglomerationCentral Agglomeration

Oligopoly Theory 16

NotationsNotationsT: Transport Costs (quadratic)xi: Firm i's location pi : Firm i's pricer: license fee (per unit) πi: Firm i's profitW: social surplusd: cost advantage of lisencer

Oligopoly Theory 17

The ModelThe 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 18

Fourth stageFourth 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 asymmetrieslower price, lower market share of firm 2.

Oligopoly Theory 19

Third StageThird Stage

Under licensing contract (0 s d), ≦ ≦Maximal Differentiation.←Equilibrium Location without Cost Asymmetries

Without licensing contract,competition under cost asymmetriesmaximal differentiation or firm 1 chooses a location closer to the central point.

Oligopoly Theory 20

Second StageSecond 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 21

First stageFirst 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 22

SummarySummary

(1) Efficient R&D investments whether or not (1) Efficient R&D investments whether or not the inventor is an outsider.the inventor is an outsider.

(2) Strong incentives of licensing for both (2) Strong incentives of licensing for both licenser and licenseelicenser and licensee

(3) Cost asymmetries disappear under (3) Cost asymmetries disappear under licensing. licensing.

(4) Maximal Differentiation (4) Maximal Differentiation