Market Competition, R&D and Firm Profits in Asymmetric Oligopoly

Presentation on theme: "Market Competition, R&D and Firm Profits in Asymmetric Oligopoly"— Presentation transcript:

1 Market Competition, R&D and Firm Profits in Asymmetric Oligopoly
Joint work with Junichiro Ishida and Noriaki Matsushima Oligopoly Theory

2 Plan of the presentation
(1) Rough sketch of the model and results (2) Overview of related works (3) Motivation (4) Formal explanation of our model (5) Results and implications Oligopoly Theory

3 Rough sketch of the model
one efficient firm (firm 1), n-1 inefficient firms, quantity-setting competition (n ≧2) At the first stage firms engage in cost-reducing R&D. At the second stage firms faces Cournot competition. Oligopoly Theory

4 Results (1) The efficient firm's profit can be increasing in n,　whereas less efficient firm’s is always decreasing in n. 　 (2) R&D of the efficient firm can be increasing in n, whereas less efficient firm’s is always decreasing in n. (3) Total R&D investments can be the inverse U-shaped. (4) An increase in the number of firms can increase HHI and at the same time it can improve welfare Oligopoly Theory

5 競争と企業の利潤 競争が激しいほど企業の利潤が増える (1) 競争の結果独占になる
同質財のBertrand~2社で完全競争だから誰も参入しない←実際に参入するライバル企業が増えると利潤が増えるという結果ではない。 (2) 参入によって競争が緩くなる ・他の参入者が入ってこなくなる ・価格競争をゆるめるコミットをする誘因が増す。 ←企業数が増えると競争が緩くなるというストーリー。 Oligopoly Theory

6 競争と企業の利潤 (3) 川下企業数が増えるとinput priceが下がる ・川上から川下への所得のトランスファー
・２重マージンの問題をmitigateする ←元々非効率的な垂直的な取引関係が前提 Oligopoly Theory

7 競争と企業の利潤 私たちのストーリ 垂直的取引関係なし 企業数が増えると実際に競争は激しくなる。 費用格差＋内生的な費用
弱い企業は(シェアがゼロでなくても)じゃまにならない。 競争は強い企業の利潤を増やし弱い企業の利潤を減らす。 Oligopoly Theory

8 意図的に競争者を増やす 大手電気事業者→小規模PPS 大手ガス事業者→小規模ガス事業者 自動車メーカー(トヨタ、フォード)
→他社への技術供与・支援 新日鐵→住金、神戸製鋼 Oligopoly Theory

9 Two Views on Competition and R&D
Monopoly View ~ Monopoly stimulates innovation ・R&D investments are financed from monopoly profits ・Monopolists internalize the spillover effects of R&D ・R&D has economy of the scale Competition View ~ Competition stimulates innovation ・Replacement effect (Arrow ,1950) ・Competitive pressure disciplines the management Oligopoly Theory

10 Our View Asymmetric View
Intense competition stimulates stronger firm's R&D and reduces weaker firm's 競争は強い企業のR&Dを増やし、弱い企業の投資を減らす→強い者が更に強くなる Oligopoly Theory

11 Brander and Spencer (1983) Two stage Strategic R&D game
Cost-reducing R&D Cournot Competition No Spillovers Oligopoly Theory

12 Cournot Model Ｙ２ Reaction Curve of Firm 1 Reaction Curve of Firm 2 Y2C
Y１ Y1C Oligopoly Theory

13 Shift of Reaction Curve of Firm 1 through strategic R&D
Ｙ２ New Reaction Curve of Firm 1 Reaction Curve of Firm 2 Y2C Y1C Y１ Oligopoly Theory

14 Cost-Reducing Investments
Model Duopoly, homogeneous goods market First stage: Each firm i independently chooses Ii (R&D investment level), which affect its production costs. Second stage: After observing firms' production costs, firms face Cournot competition. Payoff: Π1=P(Y1+Y2)Y1-C1(I1)Y1-I1 Oligopoly Theory

15 backward induction Second stage ~ Cournot Competition
Y1 C (I1,I2), Y2C(I2,I1) Firm's output is increasing in its own investment and decreasing in the rival's investment. First stage ~ R&D Competition F.O.C. P'Y1 (∂Y1C/∂I1 + ∂Y2C/∂I1)+P ∂Y1C/∂I1 -C1'(I1)Y1- C1 ∂Y1C/∂I1 -1=0 Oligopoly Theory

16 First stage First Stage F.O.C.
P'Y1 (∂Y1C/∂I1 + ∂Y2C/∂I1)+P∂Y1C/∂I1 -C1'(I1)Y1- C1 ∂Y1C/∂I1 -1=0 P'Y1∂Y2C/∂I1 -C1'(I1)Y1-1=0 (envelope theorem) Cost-Minimizing Level -C1'(I1)Y1-1=0 Investment level exceeds cost minimizing level under strategic substitutes~ strategic effect Oligopoly Theory

17 Shifts of Reaction Curves
New Reaction Curve of Firm 1 Ｙ２ New Reaction Curve of Firm 2 Y2C Y１ Y1C Competition Reduces profits of Both firms Oligopoly Theory

18 企業数が増えたら？ 企業数が増える→投資の誘因が増える？減る？
Cost-minimizing Level: 企業数が増える→ｎが増えると１社当たりの生産量減る→ R&D減る 戦略効果(1):ｎが増えると自分の投資がライバルの生産量を減らす効果は大きくなる(ライバル企業数が増えるから)→ 戦略効果強まる 戦略効果(2):ライバルの生産量が減り価格が上がる利益は自分の生産量に比例→ｎが増えると１社当たりの生産量減る→ 戦略効果弱まる 通常の対象的な寡占では最初と最後の効果が効いて競争が激しくなるとR&Dが減る Oligopoly Theory

19 企業間にAsymmetryがあると Low Cost Firm(競争力のある企業) n-1 High Cost Firms(その他弱い企業)
⇒ｎが増えると投資が増えることがありえる。 →費用差が拡大し、ますます投資の誘因の格差が生まれる。 ⇒この効果が更に強いとLow Cost Firm の利潤がｎの増加に伴い増加する可能性すら出てくる。 競争が激しくなると強い企業はより強くなり、弱い企業はより弱くなる Oligopoly Theory

20 Notations Firm 1: Low Cost Firm, Firm 2,3,...,n : High Cost Firms
qi : Firm i's output, Q: Total output ci=(zi-xi) Firm i's marginal cost z1 < z2=z3=...=zn=1/2 xi: Firm i's R&D, I=γxi2: R&D costs P(Q)=1-Q: demand function πi: Firm i's gross profit, Пi: Firm i's net profit, zL : z1がこれ以上小さくなると企業１の独占になるinitialな費用格差 superscript E denote the equilibrium values Oligopoly Theory

21 The Model Two stage strategic commitment R&D
First stage R&D competition Second Stage Cournot Competition Oligopoly Theory

22 Assumption γ≧1 ←The second order condition in the first stage
Oligopoly Theory

23 Proposition 1 (i) There exists some nonempty interval
Zx:=(zL, zLx) such that x1E is increasing in n if and only if zL ∈ Zx ; (ii) xiE, i ≠ 1, is decreasing in n. →An increase in n increases low cost firm's R&D investment when the initial cost difference z1 - z2 is large, whereas it always reduces high cost firm's R&D investment . Oligopoly Theory

24 Proposition 3 (i) There exists some nonempty interval
ZP:=(zL, zLP) such that Π1E is increasing in n if and only if zL ∈ ZP ; (ii) ΠiE, i ≠ 1, is decreasing in n. → An increase in n increases low cost firm's profit when the initial cost difference z1 - z2 is large, whereas it always reduces high cost firm's profit. Oligopoly Theory

25 Proposition 5 (ii) ZP ⊂ Zx
→企業数の増加によってLow Cost FirmのR&Dが増加するのは、利潤が増加するための必要条件だが十分条件ではない。 Oligopoly Theory

26 Proposition 6 (ii) PE is increasing in n.
→An increase in n always accerarates competition and improves consumer surplus. Oligopoly Theory

27 Proposition 7 (i) There exists some nonempty interval
ZQ:=(zL, zLQ) such that QE-1 is decreasing in n if and only if zL ∈ ZQ ; (ii) ZP ⊂ ZQ ⊂ Zx. → An increase in n can reduces total output of high cost firms and it is a nesesary condition for increasing of profit of the low cost firm and a sufficient condition for increasing R&D by the low cost firm. Oligopoly Theory

28 Remarks ・x12+nx22 can be non-monotone. (Inverse U-shaped)
・An increase in n can increase HHI and it improves welfare. Oligopoly Theory

29 Welfare 費用格差が大きくγが比較的小さいときには企業数の増加に伴いwelfareが改善する傾向
→企業数の増加に伴い効率的な企業の利潤が増えやすい状況では総余剰も増加する傾向 Oligopoly Theory

30 Welfareに影響を与える４つの効果 (1) 企業数が増えるとマージンが下がって経済厚生が上がる～Cournotの極限定理の世界
(2) R&Dに関する規模の経済性のため、企業数が増えると経済厚生が下がる～重複投資 (3) 企業数が増えるとより効率的な企業のシェアが下がり、生産効率性が悪化～welfare-reducing production substitution (4) nの増加が生産性格差を拡大させ、経済厚生を改善(Lahiri and Ono (1998)の応用) γが小さいと(2)の効果が出にくくなり、(4)の効果が出やすくなる Oligopoly Theory

31 Summary 競争によって強い企業はますます強くなる
(1)　企業数の増加に伴って効率的な企業の投資が促進されることがあるが、非効率的企業の投資は必ず減少する。この結果競争の激化に伴い投資格差がひろがって費用格差も大きくなり、また効率的企業のマーケットシェアは増加することがある。この現象は費用格差が大きいほど起こりやすい。 (2)　企業数の増加に伴って効率的な企業の利潤が増加することがあるが、非効率的企業の利潤は必ず減少する。この現象は費用格差が大きいほど起こりやすい。 Oligopoly Theory