Oligopoly Theory (14) Mixed Oligopoly

Oligopoly Theory (14) Mixed Oligopoly Aim of this lecture (1) To understand the concept of mixed oligopoly. (2) To understand the result that welfaremaximizing behavior by a public firm can yield suboptimal outcome. Oligopoly Theory 1

Plan of the presentation (1) Mixed Oligopoly (2) Classical Discussion of Public Enterprises (3) Welfare-Improving Privatization (4) Three Typical Model Formulations of Mixed Oligopoly (5) Partial Privatization (6) International Competition (7) Endogenous Competition Structure (8) Multiple Public Enterprises (9) Privatization Neutrality Theorem (10) Other topics Oligopoly Theory 2

Mixed Oligopoly, Mixed Market State-owned public firms compete against private firms Oligopoly Theory 3

Examples of mixed oligopoly in Japan Banking: Postal Bank, DBJ, Iwate Bank Housing Loan: the Public House Loan Corporation Private Funds: DBJ, Industrial Revitalization Corporation of Japan Life Insurance: Postal Life Insurance (Kampo) Overnight Delivery: Japan Post Energy: Public Gas Corps (Narashino, Fukui,...) Broadcasting: NHK Oligopoly Theory 4

Examples of mixed oligopoly in other countries Banking: Postal Banks (New Zealand, U.K., Germany,...) Automobiles: Renault, VW Medicine: Public Institute in Brazil Defense, Aviation: EADS, Airbus Airline: airlines (Swiss, Belgian, France,...) Overnight Delivery: USSP Energy: Electricite de France, Gas de France Broadcasting: BBC Oligopoly Theory 5

Differences between public and private firms (1)Public firms are less efficient than private firms. Many empirical works do not support this view (and many other papers do support this view). (2) Difference of objective function Private firms maximize their own profits, whereas public firms might care about social welfare. Oligopoly Theory 6

Classical discussions of public firms Why do public firms exist? (1) Natural monopoly (a) Public firm monopoly (b) Regulated private firm monopoly Oligopoly Theory 7

Natural Monopoly P D AC 0 Y Oligopoly Theory 8

Classical discussions of public firms(2) (2) Unprofitable market (a) Public firm monopoly Why do public firms exist? (b) Private firm monopoly with subsidy (compensation of deficit from public funds) Oligopoly Theory 9

Non-Profitable Market P AC D 0 Y Oligopoly Theory 10

Classical discussions on stateowned public firms Public firm is the monopolist In real economies, public firms are not always monopolists. Public firms do not always face significant economy of scale, which guarantees monopoly by the public firm. Oligopoly Theory 11

Problem(1) (1) How to provide incentives for welfare maximization? This is the central issue for the public firm's monopoly If we assume that the public firm is a welfaremaximizer under the monopoly, it is absolutely obvious that the first best is achieved by definition. No unsolved research problem exists. Thus, researchers never assume that the public firm is a welfare maximizer when they consider monopoly situations. Oligopoly Theory 12

Problem(2) (2) Is the welfare-maximizing behavior by the public firm efficient? This problem never appears in the public firm's monopoly. This question makes sense in mixed oligopolies because welfare-maximizing behavior by the public firm might worsen welfare through strategic interaction between public and private firms. This is the central issue of mixed oligopolies. Oligopoly Theory 13

Issues 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 14

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 15

Results Compare the pure economy (after the privatization) to the mixed economy (before the privatization) Privatization of the public firm might improve welfare W P >W M or W P <W M. W P >W M more likely takes place when the number of private firms are large. Oligopoly Theory 16

Intuition (1) Privatization of the public firm reduces public firm's output q 0 (2) Privatization increases each private firm's output q 1 production substitution from the public firm to the private firms. (3) Privatization decreases total output q 0 +nq 1. Effects (1) and (3) reduce welfare and effect (2) improves welfare. Effect (2) may be the strongest, leading to an improvement of welfare. (2) is stronger and (3) is weaker when m is larger Privatization morel likely improves welfare when n is larger. Oligopoly Theory 17

Production substitution q 1 reaction curve before privatization reaction curve of the private firm 0 reaction curve after privatization q 0 Oligopoly Theory 18

More detailed explanation of intuition Privatization of the public firm reduces q 0 and increases q 1 (production substitution). Before Privatization p=c 0 ' >c 1 ' 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 19

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 after privatization. Ideal circumstances for the existence of public firm. Against assumptions for the advocators of privatizations. Nevertheless, privatization might improve welfare Oligopoly Theory 20

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 21

Why quadratic costs? Constant marginal cost yields problems If marginal costs are constant and no cost differences exists, the public firm's monopoly yields the first best. It is nonsense to discuss mixed oligopolies in such a circumstance. Oligopoly Theory 22

How to avoid this problem? (1) Using constant marginal costs and assuming cost differences between public and private firms. Mujumdar and Pal (1998),Pal (1998),Matsumura (2003a),Matsumura and Ogawa (2010) First best is achieved by the marginal cost pricing of the private firm. The private leadership yields the second best where only private firms produce and the price is equal to the marginal cost of the public firm. It is the equilibrium in the observable delay game. Oligopoly Theory 23

How to avoid this problem? (2) Using increasing marginal costs. De Fraja and Delbono (1989),Fjell and Pal (1996), White (1996), Matsumura and Kanda (2005), Heywood and Ye (2009a), Wang et al. (2009). If there is no cost difference between public and private firms, at the first best all firms choose the same output level. It is not always achieved in mixed oligopoly since public and private firms have different objectives. Oligopoly Theory 24

How to avoid this problem? (3) Dropping the assumption of homogenous goods. Monopolistic competition: Anderson et al. (1997), Matsumura et al. (2009) Linear demand (quadratic utility function) with product differentiation: Fujiwara (2007), Matsumura and Ogawa (2012), Haraguchi and Matsumura (2014,2016) Mill pricing location model: Cremer et al. (1992), Matsumura and Matsushima (2003,2004), Inoue et al. (2008) Delivered pricing location model: Matsushima and Matsumura (2003,2006), Heywood and Ye (2009b) Oligopoly Theory 25

How to avoid this problem? More general Costs : Matsumura (1998, 2003b), Kiyono and Tomaru (2013) Discuss both (1) and (2): Matsumura and Okamura (2015). Discuss both (2) and (3): Matsumura and Shimizu (2010) Oligopoly Theory 26

Partial Privatization De Fraja and Delbono: The public sector holds whole shares in the firm (nationalization) or the private sector holds whole shares in the firm (privatization) In the real world, we observe many firms with mixture ownership (partial privatization) NTT, JT, JP, Iwate Bank, Hokuriku Electric Power Company, VW, Renault Oligopoly Theory 27

Matsumura (1998) (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. (Partial Privatization) U 0 = (1-θ) W + θπ 0 (4) General demand and general costs. The government chooses s and s affects θ. After observing θ firms compete in the product market. Oligopoly Theory 28

Results θ =0 is optimal only if it yields public monopoly. If we allow partial privatization, no privatization (full nationalization) never becomes optimal. Oligopoly Theory 29

Intuition (1) Suppose that θ =0. A slight increase of θ from 0 reduces public firm's output q 0. Since p=c 0 when θ =0, this effect is negligible (second order) envelope theorem (2) An increasing in θ increases private firm's output q 1. Since p>c 1 ', this effect is nonnegligible (first order) (2) dominates (1). Oligopoly Theory 30

Partial Privatization Free Entry: Matsumura and Kanda (2005), Wang et al. (2010) Product Differentiation: Fujiwara (2007) Spatial Model: Lu and Poddar (2007) Environmental Policy: Kato (2006), Ohori (2006) Anti-Trust: Barcena-Ruiz and Garzon (2003) Labour Market: Beladi and Chao (2006) Subsidization: Tomaru (2006) Endogenous Timing: Matsumura and Ogawa (2010), Barcena-Ruiz and Garzon (2010) Oligopoly Theory 31

Optimal degree of privatization If we adopt partial privatization approach, we can investigate the optimal degree of privatization (optimal degree of θ. Optimal degree of privatization depends on (i) the number of private firms (ii) the degree of foreign penetration (iii) cost difference between public and private firms (iv) existence of other policy instruments such as taxsubsidy policy and shadow cost of public funding (vi) Competition structure (free entry, role of public firm and so on) Oligopoly Theory 32

Optimal degree of privatization Suppose that firms face Cournot competition. Optimal degree of privatization is increasing in the number of private firms. (Han and Ogawa, 2007, Lin and Matsumura, 2012, Matsumura and Okamura, 2015). It is decreasing in the foreign penetration in product markets in the short run (Han and Ogawa, 2007, Lin and Matsumura, 2012), and the result is inversed in the long run (free entry markets). The latter result is robust because it does not depend on the strategic substitutability in product markets (Cato and Matsumura, 2013). Oligopoly Theory 33

Optimal degree of privatization and the number of firms The number of firms is larger. (1) Marginal cost of each private firm is smaller when marginal cost is increasing. (2) Price-cost margin is smaller. An increase in θ reduces the total output (welfare loss) and induces welfare-improving production substitution. The welfare loss is less significant because of (2) and welfare gain is more significant because of (1). Both increase the optimal degree of privatization. Oligopoly Theory 34

Optimal degree of privatization and the toughness of competition Consider a relative-profit-maximization approach. α is larger (the competition is tougher). (1) Marginal cost of each private firm is larger when marginal cost is increasing. (2) Price-cost margin is smaller. An increase in θ reduces the total output (welfare loss) and induces welfare-improving production substitution. The welfare loss is less significant because of (2) and welfare gain is less significant because of (1). Oligopoly Theory 35

Optimal degree of privatization and the toughness of competition When marginal cost is constant, only (2) matters. The optimal degree of privatization is increasing in α. When the marginal cost is increasing, (1) and (2) has different effects. When the production cost is quadratic, (1) dominates (2). The optimal degree of privatization is decreasing in α. The two popular models yield the opposite policy implications. (Matsumura and Okamura, 2015.) Oligopoly Theory 36

Foreign Competitors Public firm maximizes domestic welfare The public firm's behavior is dependent on whether its rivals are domestic or foreign If the rivals are foreign, the public firm becomes more aggressive. Fjell and Pal (1996) De Fraja and Delbono (1989) Pal and White (1998) Strategic Trade Policy Mukherjee and Suetrong (2009) FDI Chang (2005), Chao and Yu (2006), Fujiwara (2006) partial privatization version Cato and Matsumura (2015) Strategic Trade Policy at Free Entry Markets. Oligopoly Theory 37

Optimal degree of privatization and foreign ownership share in private firms The foreign ownership share in private firms is larger, a lower price benefits for domestic welfare more. An increase in θ reduces the total output (welfare loss) and induces welfare-improving production substitution. Welfare loss effect becomes more significant The optimal degree of privatization is decreasing in the foreign ownership share in private firms. Oligopoly Theory 38

Optimal degree of privatization and foreign ownership share in privatized firms ~ Lin and Matsumura (2012) The foreign ownership share in the privatized firm is larger, the privatized firm becomes more aggressive after privatization. Expecting this aggressive behavior, the stock price of the former public firm falls, resulting in a welfare loss. Thus, the government chooses a larger degree of privatization sells more when foreign ownership in the privatized firm is larger. The optimal degree of privatization is decreasing in the expected foreign ownership share in privatized firm. Oligopoly Theory 39

Free Entry Equilibrium In the first stage, the government chooses the degree of privatization. In the second stage, each private firm chooses whether or to enter the market. In the third stage, all firms face Cournot cometition. Consider the subgame starting at the beginning of the second stage. The equilibrium price is independent of θ. Oligopoly Theory 40

Long-Run Equilibrium under Cournot Competition AC>MC P>MR MC AC D 0 MR D equilibrium output of each firm Oligopoly Theory 41

Free Entry Equilibrium Welfare = CS+ profit of the public firm (privatized firm). CS is independent of θ. Price is independent of θ. Only the public firm s profit matters. Because the price is constant, marginal cost pricing is the best. When the private firms are domestic, θ=1 is optimal. Matsumura and Kanda (2005). The optimal degree of privatization is increasing in the foreign ownership share in private firms. Cato and Matsumura (2013). Oligopoly Theory 42

Ex ante and ex post privatization Ex ante privatization ~ The same time structure as Matsumura and Kanda (2005). Ex post privatization In the first stage, each private firm chooses whether or to enter the market. In the second stage, the government chooses the degree of privatization. In the third stage, all firms face Cournot cometition. Question: The equilibrium price of the ex ante privatization is (higher than, lower than, the same as) that in the ex post privatization model. Oligopoly Theory 43

Private Leadership, Public Leadership Consider a duopoly model with quantity competition under strategic substitutes. Consider two Stackelberg models. One is Public Leadership (the public firm is the Stackelberg Leader) and the other is Private Leadership (the public firm is the Stackelberg follower). Oligopoly Theory 44

Private Leadership The public firm plays a passive role as a potential competitor of the private firm. The public firm supplies only when the private firm's supply is insufficient. ~ Public firm plays a complementarity role of the private sector. This role is intensively discussed in Canada and in Japan (when Koizumi was prime minister) Oligopoly Theory 45

Public Leadership The public firm leads the private sector, a positive role. Question: The public firm produces (less, more) under public leadership than under simultaneous production of public and private firms. Oligopoly Theory 46

Free Entry Version of Public Leadership In the first stage, each private firm chooses whether or to enter the market. In the second stage, one public firm produces and then all private firms produce simultaneously (Public leadership). Question: The equilibrium price of the public leadership is (higher than, lower than, the same as) that in the Cournot model. Oligopoly Theory 47

Free Entry Version of Public Leadership In the first stage, each private firm chooses whether or to enter the market. In the second stage, one public firm produces and then all private firms produce simultaneously (Public leadership). Private firms are domestic. Question: The total social surplus under the public leadership is (larger than, smaller than, the same as) that under the Cournot competition. Oligopoly Theory 48

Free Entry Version of Private Leadership In the first stage, each private firm chooses whether or to enter the market. In the second stage, all private firms produce simultaneously, and then, one public firm produces (Private leadership) Question: The equilibrium price of the private leadership is (higher than, lower than, the same as) that in the Cournot model. Oligopoly Theory 49

Endogenous Role Consider the observable delay game. There are two possible time periods for output choice. In the first stage, firm i simultaneously chooses whether it likes to be the leader (ti=l) or the follower (ti=f). If two players' choices are consistent, i.e., one chooses to be the leader and the other does to be the follower, they get the equilibrium payoffs of a agreed timing Stackelberg. Otherwise, they receive the equilibrium payoffs in Cournot. Oligopoly Theory 50

Desirable Role, Endogenous Role Quantity Competition. Pal (1998): When the private firm is domestic, the private leadership is better than the public leadership and it is an equilibrium in the observable delay game. It is a unique equilibrium if the number of private firm is larger than 3. In a mixed duopoly, both private leadership and public leadership constitute equilibria, but the former is risk dominant (Matsumura and Ogawa 2012). Matsumura (2003a): In the two production-period model, only the robust equilibrium is private leadership. Oligopoly Theory 51

Desirable Role, Endogenous Role Quantity Competition. Matsumura (2003b): When the private firm is foreign, the public leadership is better than the private leadership and it is an equilibrium in the observable delay game. Oligopoly Theory 52

Endogenous Price-Quantity Choice Matsumura and Ogawa (2012) investigate price-quantity choice in a mixed duopoly, using the model of Singh and Vives (1984). choosing a price contract is a dominant strategy for both firms, resulting in Bertrand competition in mixed duopolies, in contrast to the results in private duopolies. Bertrand yields larger profit in the private firm and greater welfare than Cournot. These results hold true even if the private firm is owned by foreign investors (Haraguchi and Matsumura 2014) but not in an oligopoly (Haraguchi and Matsumura 2016). Oligopoly Theory 53

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. Oligopoly Theory 54

Assumptions of single public firm 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 55

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, recently developed, and emerging countries (examples) Brazil, India, Iran, Indonesia, Thailand, Korea, Taiwan... Oligopoly Theory 56

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 Oligopoly Theory 57

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. Oligopoly Theory 58

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.) Oligopoly Theory 59

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. Oligopoly Theory 60

Approach of Matsumura and Shimizu (2010) 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. Oligopoly Theory 61

Matsumura and Shimizu (2010) m state-owned public firms compete against N-m private firms. N firms face Cournot competition. Each public firm maximizes welfare, while each private firm maximizes its own profits. Quadratic costs: C = 0.5θ(q i ) 2 + K (public firm), C = 0.5β(q i ) 2 + K (private firm), θ β Main concerns: Relationship between m and welfare. Oligopoly Theory 62

Result 1 (1) W(m) is decreasing if the public firms are significantly less efficient than the private firms. (W is total social surplus, consumer surplus + profits of firms. m is the number of public firms) If public firms are sufficiently less efficient than the private firms, privatization improves welfare regardless of m and N Oligopoly Theory 63

Result 1 W 0 m (the number of public firms) Oligopoly Theory 64

Result 2 (2) W(m) is increasing if the cost difference between public firms and private firms are sufficiently small and the total number of firms N is small. The government should improve the competitiveness of the market before privatizing the public firms. Oligopoly Theory 65

Result 2 W 0 m (the number of public firms) Oligopoly Theory 66

Result 3 (3) W(m) is U-shaped if the cost difference between public firms and private firms are sufficiently small and N (the total number of firms) is large. This is the most interesting case Oligopoly Theory 67

Result 3 W 0 m (the number of public firms) Oligopoly Theory 68

Even if privatization does not improve welfare at the early stages, it can eventually lead to a point such that privatizations after that point on are beneficial to the society W 0 m 1 m Oligopoly Theory 69

Larger scale privatization programs eventually more likely end up with great success W 0 m 3 m 2 m 1 Oligopoly Theory 70 m

Welfare-gains of privatizations is W accelerating 0 m 3 m 2 m 1 m Oligopoly Theory 71

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. Oligopoly Theory 72

Implications (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 at the latter stage of privatization program. Once we reach the critical stage, the privatization automatically proceeds with larger support. Oligopoly Theory 73

Privatization Neutrality Theorem Privatization Neutrality Theorem: Privatization does not matter under optimal subsidy policy. It implies that if the optimal subsidy policy is adopted, discussing mixed oligopoly or privatization policy does not make sense. Most of the results in mixed oligopoly literature have quite limited implications and importance if this theorem is really robust. Distractive Result, Disaster for researchers in this field. Oligopoly Theory 74

Intuition behind PNT Suppose that all firms are symmetric. Consider the private oligopoly. The first best is achieved when P=c i ' (price =marginal cost) ~ all firms choose the same output level It is achieved by the production subsidy s*. Oligopoly Theory 75

Intuition behind PNT Suppose that one firm is nationalized. Suppose that all of remaining firms do not change their output. The nationalized firm, which is welfare-maximizer, never changes its output. All remaining private firms obviously have no incentive to change their outputs. s* yields the first best outcome in the mixed oligopoly. Oligopoly Theory 76

Condition for PNT When I explain the intuition behind PNT, I do not use any of (1) Private firms are profit maximizers (2) Homogeneous product market, (3) Single public firm and so on. All we use is the condition that the first best is achieved at the symmetric equilibrium, the first best is achieved by the simple unit subsidy, and the pubic firm is welfare maximizer. Oligopoly Theory 77

White(1996) Introducing subsidy policy into the Cournot-type model of De Fraja and Delbono (1989). The government chooses unit subsidy s so as to maximize resulting welfare Results: Privatization affects neither optimal subsidy rate nor resulting welfare Privatization does not matter under optimal subsidy policy (Irrelevance Results) Oligopoly Theory 78

Subsequent works Poyago-Theotoky (2001): public firms' leadership; Myles (2002):general demand and cost functions; Tomaru (2006): partial privatization approach; Hashimzade et al. (2007): product differentiation; Kato and Tomaru (2007): various payoff functions of private firms. Irrelevance result (especially irrelevance result on welfare) is quite robust. General formulation and general result Matsumura and Okumura (2013) Oligopoly Theory 79

Exception Fjell and Heywood (2004): Privatization is relevant under asymmetric order of moves among private firms. Oligopoly Theory 80

Robustness of PNT Privatization Neutrality Theorem is far from robust: (1) PNT obviously does not hold when there is cost difference between public and private firms. (2) PNT does not hold unless all firms are domestic.~ Matsumura and Tomaru (2012) (3) PNT does not hold at free entry markets ~Cato and Matsumura (2013) (4) If there is an excess burden of taxation, PNT does not hold. ~Matsumura and Tomaru (2013) (5) PNT does not hold if firms control two or more independent variables Oligopoly Theory 81

Other Topics (1) R&D Competition, Cost-Reducing Investment, Quality-Improving Investment, Patent Race, Strategic Contracting, and so on. (2) Spatial Competition (3) Relationship between Financial and Product Markets Oligopoly Theory 82