Oligopoly Theory 3. Mixed Oligopoly in International Markets

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1 Oligopoly Theory 3. Mixed Oligopoly in International Markets
今日の講義の目的 （１）混合寡占の基本的な発想を理解する （２）国際競争と国内競争の構造の違いを理解する OT:Mixed Oligopolt

2 Outline of the Third Lecture
3-1 Overview (第２講の続き) Free Entry 3-2 Overview (第２講の続き) Multiple Public Enterprises 3-3 Overview (第２講の続き) Optimal Degree of Privatization and Market Competition 3-4 Overview (第２講の続き) Relative Performance and Market Competition 3-5 Overview (第２講の続き) Optimal Degree of Privatization and Relative Performance 3-6 Competition against Foreign Competitors 3-7 Optimal Degree of Privatization and Foreign Competition OT:Mixed Oligopolt

3 Matsumura and Kanda(2005) Long-run analysis on mixed oligopoly
(1) Cournot-type (quantity-setting competition, simultaneous-move, no product differentiation) (2) No restrictions on the cost differences between public and private firms. (3) The objective function of the public firm is the weight sum of social welfare and its own profits. U0= (1-α) W+ α π0 (4) General demand and general cost (increasing marginal costs). (5) Free entry of private firms. OT:Mixed Oligopolt

4 自由参入市場 政府がそれを作る場合、設立費用としてF0かかる。
（１）政府が公企業（企業０）を作るか否かを決める。 政府がそれを作る場合、設立費用としてF0かかる。 （２）政府は企業０に対する持ち株比率s∈ [0,1]を決め、間接的にαをコントロールする。 （３）各私企業はαを観察し、参入するか否かを決める。各私企業は同質的である。 （４）私企業数が確定した後、参入した企業はCournot競争。 OT:Mixed Oligopolt

5 （２）から始まる部分ゲーム （最適なαの分析）
αが与えられたもとで決まる内生変数： n（企業数）、q1（各私企業の生産量）、q0（公企業の生産量）、Ｑ（総生産量） これらの変数に関する比較静学 (a) q1、Ｑ ともにαと独立 (b) q0はαの減少関数。 (c) nはαの増加関数。 政府の持ち株比率sの増加は公企業の生産量を増加させ、参入企業数を減らすが、個別私企業の生産量と公・私企業の総生産量に影響を与えない。 OT:Mixed Oligopolt

6 Free entry equilibrium
P private firm's residual demand private firm's AC Y private firm's output OT:Mixed Oligopolt

7 an decrease in α P private firm's residual demand private firm's AC Y
Y private firm's output long run : reduction of the number of private firms OT:Mixed Oligopolt

8 Results α =0 is optimal.（公企業の生産量は適正である。） ←限界費用価格付けによって無駄な私企業の参入が抑えられるから。 OT:Mixed Oligopolt

9 Intuition α をほんの少し下げる。 (1) Qは不変→消費者余剰は不変
(2) q0が増加→ 公企業の限界費用・Δq0だけ費用増加。 (3) nが減少→私企業の平均費用・私企業の１社あたり生産量・Δnだけ費用増加 私企業の１社あたり生産量・Δn =Δq0 私企業平均費用＝価格＞公企業の限界費用 ⇒αの引き下げで生産費用が削減される。(Welfare-improving production substitution) OT:Mixed Oligopolt

10 公企業を設立すべきだったか ～公企業が黒字であれば公企業を参入させるべきだった。逆に赤字を生むような公企業は不要だった。
・企業０の設立が経済厚生を改善する必要十分条件はπ＞ 0である ～公企業が黒字であれば公企業を参入させるべきだった。逆に赤字を生むような公企業は不要だった。 ・公企業と私企業の生産性が同じなら公企業は超過利潤を得られる。 OT:Mixed Oligopolt

11 No Cost Difference P AC public firm's output MC Y
Y private firm's output Public firm obtains positive profits OT:Mixed Oligopolt

12 Brandao and Castro (2007) ～公企業を民営化すると経済厚生が改善することも悪化することもある。
・民営化後の参入規制を考える。企業数を最適に設定 ～公企業を民営化すると経済厚生が改善することも悪化することもある。 OT:Mixed Oligopolt

13 Matsumura and Shimizu (forthcoming)
(1) Cournot-type (quantity-setting competition, simultaneous-move) (2) No restrictions on the cost differences between public and private firms. (3) Linear demand and quadratic costs (4) m public firms, N-m private firms. OT:Mixed Oligopolt

14 Assumptions of single public firm
Most existing works consider models with single public firm. If this single public firm is privatized, the market becomes pure market economy. Considering desirable reform of the economic system in former communist transitional countries, this is not a plausible assumption. In reality numerous public firms exist in such countries and it is politically impossible to privatize all of the public firms at the same time. Considering large scale privatization program in traditional mixed economies, one privatization does not yield pure market economy. OT:Mixed Oligopolt

15 Examples of economies with multiple public firms
(1) Former communist transitional countries (examples) Russia, Many of Eastern and Central European countries, China, Vietnam, Mongolia... (2) Developing and emerging countries (examples) Brazil, India, Iran, Indonesia, Thailand, Korea, Chinese Taipei... OT:Mixed Oligopolt

16 Examples of economies with multiple public firms
(3) Successful privatization programs in developed countries (examples) UK, Japan, Germany, Australia, NZ (4) Traditional mixed economies in developed countries (examples) Japan, France, Germany, Korea OT:Mixed Oligopolt

17 Why did existing works consider models with single public firm?
If no cost differences between public and private firms exists, obviously N=m yields the first best outcome. →Full nationalization of the economy (complete communist economy) yields the first best. → It is nonsense to discuss mixed oligopoly under such assumptions. But the result （complete communist economy yields the first best） is so unrealistic and implausible. OT:Mixed Oligopolt

18 The assumption of no cost difference between public and private firms
(1) Strategic assumption. (Even if no cost difference, privatization can improve welfare.) →Much more if cost difference exits. (2) Realistic assumption. (In mixed market, the public firm faces tough competition with private firms. If the public firm is extremely less efficient than private firms, it would not be able to survive.) OT:Mixed Oligopolt

19 The assumption of no cost difference between public and private firms
If m=N (pure planned economy), no competitive pressure exists and the assumption of no cost difference is not plausible. →Restricting attentions to single public firm and avoiding the nonsense result that the first best is achieved by pure nationalized economy. OT:Mixed Oligopolt

20 This paper's approach Suppose that the economy has 100 firms and 25 of them are public firms. Then the number of public firms becomes 24,23,22,... by privatization. What happens in the process of this privatization? We believe that it is worth discussing this problem. We dare to deviate from the traditional single public firm model. OT:Mixed Oligopolt

21 Notations N: Number of total firms m: Number of public firms
qi: Firm i's output Ci(qi) : Firm i's production cost p(Q): demand function Q: Total output πi: Firm i's profit CS: Consumer surplus W: social surplus OT:Mixed Oligopolt

22 The Model Players: identical m public firms,
identical N-m private firms. Payoff: Welfare (Public firm), Its own profits (Each private firm). All firms simultaneously choose their outputs（Cournot competition）. Linear demand: p=A-Q. Quadratic costs: c=0.5α(qi)２ +K (public firm), c=0.5β(qi)２ +K (private firm), α≧β OT:Mixed Oligopolt

23 Proposition 1 If α>(β+1)2 /(β+2), then W* is decreasing in m.
If cost difference between public and private firms is sufficiently large, privatization of a public firm always improves welfare regardless of N and m. →This is because privatization improves production efficiency OT:Mixed Oligopolt

24 Proposition 1（the case where public firms are extremely inefficient）
m (the number of public firms) OT:Mixed Oligopolt

25 Proposition 2 If α<(β+1)2 /(β+2) and
then W* is non-decreasing in m and strictly increasing if m>0 or (1) is satisfied with strict inequality. OT:Mixed Oligopolt

26 Proposition 2（cost difference between public and private firm is small and the market is not sufficiently competitive） W m (the number of public firms) OT:Mixed Oligopolt

27 Proposition 3 If α<(β+1)2 /(β+2) and (1) is not satisfied, then
(i) W* is decreasing in m for [0, mMIN) is minimized at mMIN and increasing in m for ( mMIN, N] where mMIN≡α [N(β2 –αβ-1)+(β+1)3- α(β+1)(β+2)] /(β+1-α){αβ- (β+1)2} ∈[0,N] (ii) W* is convex with respect to m for [0, mMIN) OT:Mixed Oligopolt

28 Proposition 3:cost difference between public and private firms is small and the market is sufficiently competitive W m mMIN OT:Mixed Oligopolt

29 ・Larger scale privatization program eventually more likely ends up with great success ・Failures at early stages do not imply the failure of the whole privatization program W mMIN m2’ m1 m2 OT:Mixed Oligopolt

30 Welfare-gains of privatizations are accelerating
m m3 m2 m0 m1 mMIN OT:Mixed Oligopolt

31 Intuition Suppose that m public firms and N-m private firms exist. Suppose that one public firm is privatized. →Production substitutions from the privatized firm to m-1 public firm and to N-m private firms take place. →The former production substitution reduces welfare and the latter improves welfare. →The latter becomes stronger when m is smaller and N is larger. OT:Mixed Oligopolt

32 Summary (1) Failures at early stages do not imply the failure of the whole privatization program (except for highly concentrated markets) → We should evaluate privatization program from the long term viewpoint. (2) Smaller size privatization programs more likely fail. (3) Welfare-gains of privatizations are larger, the latter stage of privatization program is. →Once we reach the critical stage, the privatization automatically proceeds with larger support. (4) Similar results are obtained under constant marginal cost if we introduce product differentiation. OT:Mixed Oligopolt

33 Optimal Degree of Privatization
One Public Firm, m Private firms. The public firm's objective is U0= (1-α) W+ απ0 No cost difference between public and private firms. Linear demand and quadratic cost function. The private firm maximizes its own profits given outputs of other firms. Exactly the same as in De Fraja and Delbono (1989) except for the objective of the public firm. In the first stage the government chooses α. The government's objective is W. In the second stage firms face Cournot competition. OT:Mixed Oligopolt

34 Second Stage Equilibrium output of the public firm is (increasing, decreasing) in α. Equilibrium output of the each private firm is (increasing, decreasing) in α. OT:Mixed Oligopolt

35 First Stage Equilibrium level of α is (increasing, decreasing) in m.
OT:Mixed Oligopolt

36 Relative Performance OT:Mixed Oligopolt

37 相対利潤 各企業が自社の利潤ではなくライバルとの相対利潤を最大化したら？（利潤の差を最大化） →よりaggressiveに生産する
OT:Mixed Oligopolt

38 均衡 最大化の一階条件 P+P'Y1-C1' -P'Y2=0
→symmetricな均衡(Y1=Y2)では価格＝限界費用となる（完全競争の世界） ⇒数量競争の文脈で、寡占市場でも激しい競争になる典型例 この状態がevolutionary stable (Vega-Redondo, 1997) OT:Mixed Oligopolt

39 相対利潤 U1=π1-απ2 α=1 完全競争 α=0 Cournot α=-1 Collusion
完全競争からカルテルまで競争度を連続的に表現可能 応用例 カルテルの安定性はαに関して単調減少 R&Dの水準はαに関して非単調ーU字型 プロセスイノベーションとプロダクトイノベーションの選択に影響 製品差別化の程度はαに関して単調減少 自由参入市場の企業数と価格はαに関して単調減少 αが十分大きい・小さいときMulti-Storeが均衡に OT:Mixed Oligopolt

40 相対利潤・相対評価の正当化 （１）CEOの市場での評価 （２）evolutionary approach
（３）ねたみ、利他主義（実験経済学・経済心理学の成果） （４）Fershtman and Judd (1987)の応用 （５）政治学の分野への応用 （６）ステータスの議論 OT:Mixed Oligopolt

41 Conjectural Variation
自社が１単位生産量を増やすとｒだけ市場全体の全体の生産量が増えると仮定して各企業が行動する。 Cournotならr=1。 Conjectural Variation Model~Cournotを特殊ケースとして含む一般的モデル（？） でもr=1以外のケースは意味あるのか？ OT:Mixed Oligopolt

42 Conjectural Variation Modelの解
Duopoly, 同質財市場、限界費用一定で両企業の限界費用は同じ（ｃ） 企業１の一階条件 P+P'rＹ1 =c ２階条件は満たされているものとする 均衡の導出 P+P'rＹ1 =c、P+P'rＹ2 =cの連立方程式を解く OT:Mixed Oligopolt

43 Conjectural Variation Model
企業１の生産量の変化は企業２の生産量も変化させる →企業１の生産量を見てから企業２が生産量を決めるのでないとおかしい 企業２の生産量の変化は企業１の生産量も変化させる →企業２の生産量を見てから企業１が生産量を決めるのでないとおかしい ⇒静学的なモデルとしては論理的に破綻している OT:Mixed Oligopolt

44 論理的に破綻しているのになぜConjectural Variation Modelが使われるのか？
（１）an unmodeled dynamic model ～動学的なinteractionを考えている →もしそうなら動学モデルを作るのが筋 （２）市場の競争度を表現 OT:Mixed Oligopolt

45 Conjectural Variation Modelの解
CV Modelでの企業１の一階条件　P+P'rＹ1 =c Cournot Model での企業１の一階条件 P+P'Ｙ1 =c　ｒ＝１に対応 Bertrand Model~完全競争モデルでの一階条件 P =c　ｒ＝０に対応 Joint Profit Maximization(カルテル）での一階条件 P+P'(Ｙ1+Ｙ2) =c　ｒ＝２に対応 それぞれ競争度の違うモデルに対応。ｒが小さいほど競争が激しい。競争度を特定化しないでモデル化できる。 ～実証系の論文で特にadvantageがある。 OT:Mixed Oligopolt

46 相対利潤アプローチのadvantage (1) 静学的モデルとして破綻していない（コンシステントなモデル）。
(2) Cournot, Bertrand, Collusionの３つの間の競争状態に対してもちゃんとしたfoundationがある。 (3) 静学的な文脈ではより現実的（おそらく賛否両論ある） OT:Mixed Oligopolt

47 Relative Profit Approach: Mixed Oligopoly
Vi=πi-α(他社の利潤） 私企業は上記の相対利潤を、公企業はU0= (1-θ) W+ θπ0を最大化。 私企業数はｍ。需要・費用関数等はDe Fraja and Delbono (1989)と同じ。 In the first stage the government chooses θ. The government's objective is W. In the second stage firms face Cournot competition. OT:Mixed Oligopolt

48 Second Stage Equilibrium output of the public firm is (increasing, decreasing) in θ. Equilibrium output of the each private firm is (increasing, decreasing) in θ. Equilibrium output of the public firm is (increasing, decreasing) in α. Equilibrium output of the each private firm is (increasing, decreasing) in α. OT:Mixed Oligopolt

49 First Stage Equilibrium θ is (increasing, decreasing) in m.
OT:Mixed Oligopolt

50 First Stage Equilibrium θ is increasing in m.
Equilibrium θ is (increasing, decreasing) in α. OT:Mixed Oligopolt

51 競争相手が外国企業だったら？ 公企業の目的関数がdomestic welfareなら、ライバルの国籍と公企業の行動が関係している
Private Duopolyならライバルの国籍は関係なし 公企業の目的関数がdomestic welfareなら、ライバルの国籍と公企業の行動が関係している 問題：ライバルが外国企業なら公企業の最適生産量は増えるか減るか？（反応曲線がどうシフトするか？） ～ライバルの生産量ゼロならもちろん同じ。ライバルの生産量が正の範囲では？ OT:Mixed Oligopolt

52 公企業の反応曲線 ライバルが外国企業：P’’<0 Ｙ２ ライバルが外国企業 ：線形需要 ライバルが国内企業
Y１ OT:Mixed Oligopolt

53 Optimal Degree of Privatization
One Public Firm, m Private firms. mβ is foreign private firms, m(1-β) is domestic private firms. The public firm's objective is U0= (1-α) W+ απ0 No cost difference between public and private firms. Linear demand and quadratic cost function. The private firm maximizes its own profits given outputs of other firms. In the first stage the government chooses α. The government's objective is W. In the second stage firms face Cournot competition. OT:Mixed Oligopolt

54 Second Stage Equilibrium output of the public firm is (increasing, decreasing) in α. Equilibrium output of the each private firm is (increasing, decreasing) in α. Equilibrium output of the public firm is (increasing, decreasing) in β. Equilibrium output of the each private firm is (increasing, decreasing) in β. OT:Mixed Oligopolt

55 First Stage Equilibrium α is (increasing, decreasing) in m.
OT:Mixed Oligopolt

56 Lin and Matsumura (unpublished)
Players: government, firm 0 (public firm), mβ foreign private firms, m(1-β) domestic private firms, Payoffs: domestic welfare (government), Its own profits (private firms) α(its own profit)＋(1-α) domestic welfare (firm 0) (1) Government sells α shares at the price M= α π0e. Infinitesimal foreign investors purchase αγ at the price γM and domestic purchase at the price (1-γ)M . (2) Given α and M, firms faces Cournot competition. OT:Mixed Oligopolt

57 Second Stage Firm 0's payoff απ0 +(1-α) domestic welfare
=απ0+(1-α)(CS+(1-αγ)π0+m(1-β)π1+γM) q0S is decreasing in α and increasing in βand γ Privatization makes firm 0 less aggressive. An increase in the foreign presence makes firm 0 more aggressive. OT:Mixed Oligopolt

58 First stage The government's payoff domestic welfare
=CS+(1-αγ)π0+m(1-βγ)π1+γM =CS+π0+m(1-β)π1 Important Point: In the second stage, M is given exogenously, whereas in the first stage M depends on α, so it is endogenous. OT:Mixed Oligopolt

59 Results (i)α* is increasing in γ and (ii)α* is decreasing in β.
(i) An increase in foreign presence in the capital market for privatization increases the optimal degree of privatization Complementarity between privatization policy and open market policy (ii) An increase in foreign presence in product markets decreases the optimal degree of privatization Substitute between privatization policy and open market policy OT:Mixed Oligopolt

60 Intuition (ii) A decrease of α accelerates the competition, resulting in a lower price and lower outputs of foreign firms. →It reduces the rent obtained by the foreign firms. The government has a stronger incentive to commit to larger output when β is large. Exactly the same mechanism repeatedly appear in the world of strategic trade policy. OT:Mixed Oligopolt

61 Intuition (i) A decrease of α accelerates the competition, resulting in a lower price and lower profits of firm 0. This effect becomes stronger when γ is larger. →It reduces M. The government has a stronger incentive to commit to smaller output (larger output) when γ is larger. Time-inconsistency. The government want to restrict aggressive behavior of firm 0 before selling the stocks. After selling the stocks, it has incentive to expand the outputs of firm 0. Committing to a smaller output by a larger α. OT:Mixed Oligopolt