On patent licensing in spatial competition with endogenous location choice

1. On patent licensing in spatial competition with endogenous location choice Joint work with Noriaki Matsushima

2. 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

3. 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

4. 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.

5. 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.

6. 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。

7. 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.

8. 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）

9. 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.

10. 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 price-competition.

11. 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

12. 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.

13. 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！！

14. 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.

15. 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

16. 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

17. 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.

18. 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.

19. 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.

20. 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).

21. 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.

22. 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