On patent licensing in spatial competition with

							      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                                    4
                      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                                    5
                   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                            6
                   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                                  7
                   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               8
                   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                                     9
                   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.

Oligopoly Theory                                       10
          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                            11
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                                  12
 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                          13
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                                 14
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                                  15
                    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                16
                    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                                   17
                    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                                   18
                    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                                      19
                    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                                     20
                    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                                    21
                    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                                    22