Oligopoly Theory 1

Privatization WavesPrivatization Waves

Joint work with Daisuke Joint work with Daisuke ShimizuShimizu

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) Explanation of mixed oligopoly(2) Explanation of mixed oligopoly(3) Overview of related works on mixed oligopoly(3) Overview of related works on mixed oligopoly(4) (4) Formal explanation of our modelFormal explanation of our model(5) Results and implications

Oligopoly Theory 3

Rough sketch of the Rough sketch of the modelmodel

・・ m state-owned public firms compete against m state-owned public firms compete against N-m private firms. N-m private firms.

・・ Each public firm maximizes welfare, while Each public firm maximizes welfare, while each private firm maximizes its own profits. each private firm maximizes its own profits.

・・ N firms face Cournot competition.N firms face Cournot competition.

Our main concerns: Relationship Our main concerns: Relationship between m and welfare (consumer between m and welfare (consumer surplus plus profits of all firms).surplus plus profits of all firms).

Oligopoly Theory 4

MotivationMotivationWe focus on the following situations We focus on the following situations (1) Large scale privatization program in (1) Large scale privatization program in

developing or former communist transitional developing or former communist transitional economieseconomies

(2) Sequential privatizations(2) Sequential privatizations←←There are so many public firms that the There are so many public firms that the

government cannot privatize all public firms at government cannot privatize all public firms at the same time.the same time.

Oligopoly Theory 5

ProblemProblemDose a privatization of a public firm more Dose a privatization of a public firm more

likely improve welfare when the number of likely improve welfare when the number of remaining public firms is large or small?remaining public firms is large or small?

If largeIf large, the success of earlier stages , the success of earlier stages privatizations does not guarantee the privatizations does not guarantee the success of subsequent privatizations.success of subsequent privatizations.

If smallIf small, the failure of earlier stages , the failure of earlier stages privatizations does not imply the failure of privatizations does not imply the failure of subsequent privatizations. subsequent privatizations.

Oligopoly Theory 6

Result 1Result 1

(1) W(m) is decreasing if the public firms are (1) W(m) is decreasing if the public firms are significantly less efficient than the private significantly less efficient than the private firms. (W is total social surplus, consumer firms. (W is total social surplus, consumer surplus + profits of firms. m is the number surplus + profits of firms. m is the number of public firms) of public firms)

If public firms are sufficiently less efficient If public firms are sufficiently less efficient than the private firms, privatization than the private firms, privatization improves welfare regardless of m and Nimproves welfare regardless of m and N

Oligopoly Theory 7

Result 1Result 1

W

m (the number of public firms)0

Oligopoly Theory 8

Result 2Result 2(2) W(m) is increasing if the cost difference (2) W(m) is increasing if the cost difference

between public firms and private firms are between public firms and private firms are sufficiently small sufficiently small andand the total number of the total number of firms N is small. firms N is small.

The government should The government should improve the improve the competitiveness of the marketcompetitiveness of the market before before privatizing the public firms. privatizing the public firms.

Oligopoly Theory 9

Result 2Result 2

W

m (the number of public firms)0

Oligopoly Theory 10

Result 3Result 3

(3) W(m) is U-shaped if the cost difference (3) W(m) is U-shaped if the cost difference between public firms and private firms are between public firms and private firms are sufficiently small and N (the total number sufficiently small and N (the total number of firms) is large. of firms) is large.

This is the most interesting caseThis is the most interesting case

Oligopoly Theory 11

Result 3Result 3

W

m (the number of public firms)0

Oligopoly Theory 12

Even if privatization does not Even if privatization does not improve welfare at the early improve welfare at the early

stages, it can eventually lead to a stages, it can eventually lead to a point such that privatizations after point such that privatizations after that point on are beneficial to the that point on are beneficial to the

societysociety W

m m1 0

Oligopoly Theory 13

Larger scale privatizationLarger scale privatization 　　programs eventually more likely programs eventually more likely end up with great successend up with great success

W

m m1 m2

m30

Oligopoly Theory 14

Welfare-gains of Welfare-gains of privatizations is acceleratingprivatizations is acceleratingW

m m1 m2m30

Oligopoly Theory 15

Mixed Oligopoly, Mixed Mixed Oligopoly, Mixed MarketMarket

State-owned public firms compete against State-owned public firms compete against private firmsprivate firms

Oligopoly Theory 16

Examples of mixed Examples of mixed oligopoly in Japanoligopoly in Japan

Banking: Postal Bank, DBJ, Iwate BankBanking: Postal Bank, DBJ, Iwate Bank

Housing Loan: the Public House Loan Corporation Housing Loan: the Public House Loan Corporation

Private Funds: DBJ, Industrial Revitalization Private Funds: DBJ, Industrial Revitalization Corporation of Japan Corporation of Japan

Life Insurance: Postal Life Insurance (Kampo)Life Insurance: Postal Life Insurance (Kampo)

Overnight Delivery: Japan PostOvernight Delivery: Japan Post

Energy: Public Gas Corps (Narashino, Fukui,...)Energy: Public Gas Corps (Narashino, Fukui,...)

Broadcasting: NHK Broadcasting: NHK

Oligopoly Theory 17

Examples of mixed Examples of mixed oligopoly in other oligopoly in other

countriescountriesBanking: Postal Banks (New Zealand, U.K., GermanBanking: Postal Banks (New Zealand, U.K., Germany,...) y,...)

Automobiles: Renault, VWAutomobiles: Renault, VWMedicine: Public Institute in BrazilMedicine: Public Institute in BrazilNational Defense, Aviation: EADS, Airbus National Defense, Aviation: EADS, Airbus Airline: National airlines (Swiss, Belgian, France,...)Airline: National airlines (Swiss, Belgian, France,...)Overnight Delivery: USSP Overnight Delivery: USSP Energy: Electricite de France, Gas de FranceEnergy: Electricite de France, Gas de FranceBroadcasting: BBC Broadcasting: BBC

Oligopoly Theory 18

Differences between Differences between public and private firmspublic and private firms

(1)Public firms are less efficient than private firms. (1)Public firms are less efficient than private firms.

→→Many empirical works do not support this view Many empirical works do not support this view (and many other papers do support this view). (and many other papers do support this view).

(2) Difference of objective function (2) Difference of objective function

→→Private firms maximize their own profits, whereas Private firms maximize their own profits, whereas public firms might care about social welfare. public firms might care about social welfare.

Oligopoly Theory 19

Classical discussions of Classical discussions of public firmspublic firms

Why do public firms exist? Why do public firms exist?

(1) Natural monopoly (1) Natural monopoly

(a) Public firm monopoly (a) Public firm monopoly

(b) Regulated private firm monopoly(b) Regulated private firm monopoly

Oligopoly Theory 20

Natural MonopolyNatural Monopoly

P

Ｙ

AC

D

0

Oligopoly Theory 21

Classical discussions of Classical discussions of public firms(2)public firms(2)

Why do public firms exist? Why do public firms exist? (2) Unprofitable market (2) Unprofitable market

(a) Public firm monopoly(a) Public firm monopoly

(b) Private firm monopoly with subsidy (b) Private firm monopoly with subsidy (compensation of deficit from public (compensation of deficit from public funds)funds)

Oligopoly Theory 22

Non-Profitable MarketNon-Profitable Market

P

Y

AC

D

0

Oligopoly Theory 23

Classical discussions on state-Classical discussions on state-owned public firmsowned public firms

→→Public firm is the monopolist Public firm is the monopolist

In real economies, public firms are In real economies, public firms are not always monopolists. not always monopolists.

Public firms do not always face Public firms do not always face significant economy of scale, significant economy of scale, which guarantees monopoly by which guarantees monopoly by the public firmthe public firm

Oligopoly Theory 24

Problem(1)Problem(1)(1) How to provide incentives for welfare (1) How to provide incentives for welfare

maximization? maximization?

→ → This is the central issue for the public This is the central issue for the public firm's monopolyfirm's monopoly

Oligopoly Theory 25

Problem(2)Problem(2)(2) Is the welfare-maximizing behavior by the (2) Is the welfare-maximizing behavior by the

public firm efficient?public firm efficient?

→→This problem never appears in the public This problem never appears in the public firm's monopoly.firm's monopoly.

This question makes sense in mixed oligopoly This question makes sense in mixed oligopoly because welfare-maximizing behavior by because welfare-maximizing behavior by the public firm might worsen welfare the public firm might worsen welfare through strategic interaction between through strategic interaction between public and private firms. public and private firms.

→→This is the central issue of mixed oligopoly This is the central issue of mixed oligopoly

Oligopoly Theory 26

Issues of mixed oligopolyIssues of mixed oligopoly

・ Is welfare-maximizing behavior by the public firm desirable in mixed oligopoly ?・ What distortion does welfare-maximizing behavior by the public firm yield ?

Oligopoly Theory 27

This paper's approachThis paper's approach (1) We do not make restrictions on the difference of production efficiency between public and private firms. (For the discussion of endogenous cost differences, see Nett (1994), Matsumura and Matsushima (2004). Ishibashi and Matsumura (2006).)(2) We assume that each private firm maximizes its own profits, public firm maximizes social welfare. （ For more general objective function, see Matsumura (1998).)

Oligopoly Theory 28

This paper's approachThis paper's approach (3) The number of firms is given exogenously. （ For endogenous number of private firms, see Anderson et al. (1997) , Matsumura and Kanda (2005), Fujiwara (2007). ） (4) Simultaneous-move game (For sequential or endogenous move game, see Pal (1998), Matsumura (2003a, 2003b), Lu (2006))

Oligopoly Theory 29

This paper's approachThis paper's approach (5) Homogeneous Products. (For the discussion of differentiated products, see Cremer et al. (1991), and Matsumura and Matsushima (2003, 2004).)(6) Competition between Public and Domestic Private firms (For the model with foreign private firms, see Fjell and Pal (1996) and Pal and White (1998).)(7) No Tax or subsidy Policy. (For this topic, see Mujumdar and Pal (1998).)

Oligopoly Theory 30

De Fraja and Delbono(1989)De Fraja and Delbono(1989)

(1) Cournot-type (quantity-setting competition, simultaneous-move, no product differentiation)(2) No cost difference between public and private firms. (3) Linear demand and quadratic cost function. (4) The private firm maximizes its own profits given outputs of other firms. (5) The public firm maximizes social welfare given outputs of other firms. →The public firm chooses its output level so that the price equals to its marginal cost.

Oligopoly Theory 31

ResultsResults Compare the pure economy (after the privatization) to the mixed economy (before the privatization)→Privatization of the public firm might improve welfare WP >WM or WP<WM.

Oligopoly Theory 32

IntuitionIntuition

(1) Privatization of the public firm reduces public firm's output q0

(2) Privatization increases private firm's output q1 →production substitution from the public firm to the private firm. (3) Privatization decreases total output q0

+q1 Effects (1) and (3) reduces welfare and effect (2) improves welfare. Effect (2) may be the strongest, leading to an improvement of welfare.

Oligopoly Theory 33

Production substitutionProduction substitution

q1

reaction curve

after privatization

reaction curve of the private firm

0

reaction curve before privatization

q0

Oligopoly Theory 34

More detailed explanation of intuitionMore detailed explanation of intuition

Privatization of the public firm reduces q0 and increases q1 (production substitution). Before Privatization p=c0' >c1' →Public firm's marginal cost is higher than private firm's → Production substitution from public to private economizes production costs →Welfare-improving →Privatization reduces total production level and so consumer surplus → Welfare-reducing It is possible that the former effect dominates the latter effect.

Oligopoly Theory 35

Contribution of De Fraja and Delbono(1989)Contribution of De Fraja and Delbono(1989)

(1) No cost difference between public and private firms → privatization does not improve production efficiency (2) Public firm's objection: welfare →No agency problem in the public firm (3) No additional policies by regulation, tax, or subsidy ⇒Ideal circumstances for the existence of public firm. Against assumptions for the advocators of privatizations. → Nevertheless, privatization might improve welfare

Oligopoly Theory 36

Assumptions of De Fraja and Delbono(1989)Assumptions of De Fraja and Delbono(1989)

Many researchers in this field believe that the assumptions above are plausible, but many other researchers (as well as I) make these assumptions for strategic purposes.(1) Even without cost differences, privatization improves welfare. →If public firm is less efficient, much more.(2) Even without any agency problem in the public firm, privatization improves welfare. →If public firm has agency problem, much more.

Oligopoly Theory 37

Assumptions of single public firmAssumptions 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 (because substantial public firms remain after the privatization of several firms). →Existing works cannot analyze these markets effectively.

Oligopoly Theory 38

Examples of economies with Examples of economies with multiple public firmsmultiple public firms

(1) Former communist transitional (1) Former communist transitional countriescountries

(examples) Russia, Many of Eastern and (examples) Russia, Many of Eastern and Central European countries, China, Central European countries, China, Vietnam, Mongolia... Vietnam, Mongolia...

(2) Developing and emerging countries (2) Developing and emerging countries

(examples) Brazil, India, Iran, Indonesia, (examples) Brazil, India, Iran, Indonesia, Thailand, Korea, Chinese Taipei...Thailand, Korea, Chinese Taipei...

Oligopoly Theory 39

Examples of economies with Examples of economies with multiple public firmsmultiple public firms

(3) Successful privatization programs in (3) Successful privatization programs in developed countries developed countries

(examples) UK, Japan, Germany, Australia, (examples) UK, Japan, Germany, Australia, NZNZ

(4) Traditional mixed economies in (4) Traditional mixed economies in developed countries developed countries

(examples) Japan, France, Germany, Korea(examples) Japan, France, Germany, Korea

Oligopoly Theory 40

Why did existing works consider Why did existing works consider models with single public firm?models with single public firm? If no cost differences between public and private If no cost differences between public and private

firms exists, obviously N=m yields the first best firms exists, obviously N=m yields the first best outcome. outcome.

→→Full nationalization of the economy (complete Full nationalization of the economy (complete communist economy) yields the first best.communist economy) yields the first best.

→ → It is nonsense to discuss mixed oligopoly under It is nonsense to discuss mixed oligopoly under such assumptions.such assumptions.

But the result But the result （（ complete communist economy complete communist economy yields the first bestyields the first best ） ） is so unrealistic and is so unrealistic and implausible.implausible.

Oligopoly Theory 41

The assumption of no cost The assumption of no cost difference between public and difference between public and

private firmsprivate firms

(1) Strategic assumption. (Even if no cost (1) Strategic assumption. (Even if no cost difference, privatization can improve welfare.)difference, privatization can improve welfare.)

→→Much more if cost difference exits.Much more if cost difference exits.

(2) Realistic assumption. (In mixed market, the (2) Realistic assumption. (In mixed market, the public firm faces tough competition with private public firm faces tough competition with private firms. If the public firm is extremely less efficient firms. If the public firm is extremely less efficient than private firms, it would not be able to than private firms, it would not be able to survive.)survive.)

Oligopoly Theory 42

The assumption of no cost The assumption of no cost difference between public and difference between public and

private firmsprivate firms

If m=N (pure planned economy), no competitive pIf m=N (pure planned economy), no competitive pressure exists and the assumption of no cost dressure exists and the assumption of no cost difference is not plausible.ifference is not plausible.

→→Restricting attentions to single public firm and Restricting attentions to single public firm and avoiding the nonsense result that the first best avoiding the nonsense result that the first best is achieved by pure nationalized economy.is achieved by pure nationalized economy.

Oligopoly Theory 43

This paper's approachThis paper's approach

Suppose that the economy has 100 firms and 25 Suppose that the economy has 100 firms and 25 of them are public firms. of them are public firms.

Then the number of public firms becomes Then the number of public firms becomes 24,23,22,... by privatization. 24,23,22,... by privatization.

What happens in the process of this privatization? What happens in the process of this privatization?

We believe that it is worth discussing this We believe that it is worth discussing this problem. problem.

We dare to deviate from the traditional single We dare to deviate from the traditional single public firm model. public firm model.

Oligopoly Theory 44

NotationsNotationsN: Number of total firms m: Number of public firms qi: Firm i's outputCi(qi) : Firm i's production costp(Q): demand function Q: Total output πi: Firm i's profitCS: Consumer surplus W: social surplus

Oligopoly Theory 45

The ModelThe 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

Oligopoly Theory 46

Why quadratic costsWhy quadratic costs ？？Constant marginal cost yields problems Constant marginal cost yields problems

If marginal costs are constant and no cost If marginal costs are constant and no cost differences exists, the public firm's monopoly differences exists, the public firm's monopoly yields the first best.yields the first best.

→ → It is nonsense to discuss mixed oligopoly in It is nonsense to discuss mixed oligopoly in such a circumstance.such a circumstance.

Oligopoly Theory 47

How to avoid this How to avoid this problem?problem? (1) Using constant marginal costs and assuming (1) Using constant marginal costs and assuming

cost differences between public and private cost differences between public and private firms. Mujumdar and Pal (1998)firms. Mujumdar and Pal (1998) 、、 Pal (1998), Pal (1998), Matsumura (2003) Matsumura (2003)

(2) Using increasing marginal costs. De Fraja and (2) Using increasing marginal costs. De Fraja and Delbono (1989), Fjell and Pal (1996),Matsumura Delbono (1989), Fjell and Pal (1996),Matsumura and Kanda (2005), This paper. and Kanda (2005), This paper.

(3) Dropping the assumption of homogenous (3) Dropping the assumption of homogenous goods. Cremer et al. (1992), Anderson et al. goods. Cremer et al. (1992), Anderson et al. (1997), Matsumura and Matsushima (1997), Matsumura and Matsushima (2003,2004), Matsushima and Matsumura (2003,2004), Matsushima and Matsumura (2003,2006).(2003,2006).

Oligopoly Theory 48

Proposition 1Proposition 1If α>(β+1)If α>(β+1)2 2 /(β+2), then W* is decreasing in /(β+2), then W* is decreasing in

m.m.

If cost difference between public and private If cost difference between public and private firms is sufficiently large, privatization of a firms is sufficiently large, privatization of a public firm always improves welfare public firm always improves welfare regardless of N and m.regardless of N and m.

→→This is because privatization improves This is because privatization improves production efficiencyproduction efficiency

Oligopoly Theory 49

Proposition 1Proposition 1 （（ the case the case where public firms are where public firms are extremely inefficientextremely inefficient ））

W

m (the number of public firms)0

Oligopoly Theory 50

Proposition 2Proposition 2

If α<(β+1)If α<(β+1)22 /(β+2) and /(β+2) and

N ≦((β+1)N ≦((β+1)2 2 -α(β+1) (β+2))/(1-β-α(β+1) (β+2))/(1-β22+αβ) (1)+αβ) (1)

then W* is non-decreasing in m and then W* is non-decreasing in m and strictly strictly

increasing if m>0 or (1) is satisfied increasing if m>0 or (1) is satisfied with strict inequalitywith strict inequality..

Oligopoly Theory 51

Proposition 2Proposition 2 （（ cost difference cost difference between public and private between public and private

firm is small firm is small andand the market is the market is notnot sufficiently competitive sufficiently competitive ））W

m (the number of public firms)0

Oligopoly Theory 52

Proposition 3Proposition 3If α<(β+1)If α<(β+1)22 /(β+2) and (1) is not satisfied, then /(β+2) and (1) is not satisfied, then (i) W* is decreasing in m for [0, m(i) W* is decreasing in m for [0, mMINMIN) ) is minimized at mis minimized at mMINMIN and increasing in m and increasing in m for ( mfor ( mMIN, MIN, N] where N] where mmMINMIN≡α [N(β≡α [N(β2 2 –αβ-1)+(β+1)–αβ-1)+(β+1)33- α(β+1)(β+2)]- α(β+1)(β+2)]/(β+1-α){αβ- (β+1)/(β+1-α){αβ- (β+1)22} ∈[0,N]} ∈[0,N](ii) W* is (ii) W* is convexconvex with respect to m for with respect to m for [0, m[0, mMINMIN) )

Oligopoly Theory 53

Proposition 3Proposition 3 （（ cost difference cost difference between public and private between public and private

firm is small firm is small andand the market is the market is sufficiently competitivesufficiently competitive

W

m 0

mmMINMIN

Oligopoly Theory 54

・・ Larger scale privatization program Larger scale privatization program eventually more likely ends up with great eventually more likely ends up with great successsuccess・・ Failures at early stages do not imply the Failures at early stages do not imply the failure of the whole privatization programfailure of the whole privatization program

W

m1m2m2’

0mmMINMIN

Oligopoly Theory 55

Welfare-gains of Welfare-gains of privatizations are privatizations are

acceleratingacceleratingW

m1m2

m0m3mmmMINMIN

Oligopoly Theory 56

IntuitionIntuitionSuppose that m public firms and N-m private Suppose that m public firms and N-m private

firms exist. Suppose that one public firm is firms exist. Suppose that one public firm is privatized. privatized.

→→Production substitutions from the privatized Production substitutions from the privatized firm to firm to m-1m-1 public firm and to public firm and to N-mN-m private private firms take place.firms take place.

→→The former production substitution reduces The former production substitution reduces welfare and the latter improves welfare.welfare and the latter improves welfare.

→→The latter becomes stronger when The latter becomes stronger when mm is is smaller and smaller and NN is larger. is larger.

Oligopoly Theory 57

SummarySummary(1) Failures at early stages do not imply the failure (1) Failures at early stages do not imply the failure

of the whole privatization program (except for of the whole privatization program (except for highly concentrated markets).highly concentrated markets).

→→We should evaluate privatization program from We should evaluate privatization program from the long term viewpoint. the long term viewpoint.

(2) Smaller size privatization programs more likely (2) Smaller size privatization programs more likely fail.fail.

(3) Welfare-gains of privatizations are larger, the (3) Welfare-gains of privatizations are larger, the latter stage of privatization program is. latter stage of privatization program is.

→ →Once we reach the critical stage, the Once we reach the critical stage, the privatization automatically proceeds with larger privatization automatically proceeds with larger support. support.