Endogenous timing in private and mixed duopolies with emission taxes

This paper examines an endogenous timing game in product differentiated duopolies under price competition when emission tax is imposed on environmental externality. We show that a simultaneous-move (sequential-move) outcome can be an equilibrium outcome in a private duopoly under significant (insignificant) environmental externality, but this result can be reversed in a mixed duopoly. We also show that when environmental externalities are significant, public leadership yields greater welfare than private leadership, and that public leadership is more robust than private leadership as an equilibrium outcome. Finally, we find that privatization can result in a public leader becoming a private leader, but this worsens welfare.     

The Optimal Privatization Policies under an International Mixed Duopoly

This paper explores the socially optimal privatization policies under the setting of international mixed duopoly. We find that partial privatization is socially optimal under Cournot competition and private leadership competition, whereas full nationalization is socially optimal under public leadership competition. Moreover, the equilibrium social welfare under private leadership competition is higher than that observed under Cournot competition and that observed under private leadership competition, which differs from the findings of Matsumura ( 2003b ). We also show that the endogenous timing game has a subgame perfect Nash equilibrium outcome, under which the government chooses a partial privatization policy, and private leadership competition emerges as the optimal output decision sequence of firms. An important policy implication from this paper is that the government should partially privatize the public firm and facilitate the emergence of private leadership competition in an international mixed market.     

Leadership and Privatisation in a Mixed Multi‐product Oligopoly: An Endogenous Timing Model

This paper examines both leadership choice and welfare consequences of privatisation in an endogenous timing mixed multi‐product oligopoly. It shows that a multi‐product firm undermines the welfare‐maximising efforts of a public firm by cross‐subsidising. The paper demonstrates that a unique subgame perfect Nash equilibrium emerges in a multi‐product market, in contrast to the multiple equilibria of a single‐product market. This unique equilibrium indicates that profit‐maximising private firms retain leadership while a welfare‐maximising public firm acts as a follower. Even on the off‐equilibrium path where the public firm acts as a leader, it rarely generates maximum social welfare. However, privatising the public firm usually harms social welfare and results in a different timing structure in equilibrium.     

Corporate social responsibility and strategic trade policy: An endogenous timing game and its policy implications

This study incorporates the corporate social responsibility (CSR) initiatives of a domestic firm and analyses strategic trade policy towards a foreign firm in a different market structure. We show that the tariff rate under a foreign (domestic) firm's leadership is lowest when the degree of CSR is large (small). We also show that the foreign firm's leadership yields the highest welfare when the degree of CSR is intermediate, while the domestic firm's leadership yields the highest welfare otherwise. In an endogenous‐timing game, we show that a simultaneous‐move outcome is the unique equilibrium when the degree of CSR is small; thus, it is never socially desirable. We also show that the domestic firm's leadership can be an equilibrium, which results in the highest welfare when the degree of CSR is large. Finally, when the degree of CSR is large, collusive behaviours between the domestic and foreign firms can increase welfare.     

University–firm competition in basic research: Simultaneous versus sequential moves

This paper studies the endogenous timing of moves in a game with competition in basic research between a university and a commercial firm. It examines the conditions under which the two entities end up investing in innovation at equilibrium, both under simultaneous and sequential moves. It argues that when the innovation process is not too costly, under any timing, the firm conducts research despite the opportunities for complete free-riding. The two sequential move games with either player as leader emerge as equilibrium endogenous timings, with both entities realizing higher profits in either outcome than in a simultaneous move game. Each entity also profits more by following than by leading. Finally, as a proxy for a welfare analysis, we compare the propensities for innovation across the three scenarios and find that university leadership yields a superior performance. This may be used as a selection criterion to choose the latter scenario as the unique outcome of endogenous timing.     

A MODEL OF ENDOGENOUS PAYOFF MOTIVES AND ENDOGENOUS TIMING IN A MIXED DUOPOLY*

A model of endogenous payoff motives and endogenous order of moves is analysed in a mixed duopoly. We find that, when a non‐negative price constraint is imposed on public and private firms' quantity choice, both firms always choose to be relative‐payoff‐maximisers, and both simultaneous move and sequential move can be sustained in equilibrium. In contrast, when non‐negative absolute profit constraint is imposed, public and private firms always choose to be absolute‐payoff‐maximisers, and only sequential move can be sustained in equilibrium.     

Quality and Welfare in a Mixed Duopoly with Regulated Prices: The Case of a Public and a Private Hospital

Abstract. Hospital markets are often characterized by price regulation and the existence of different ownership types. Using a Hotelling framework, this paper analyses the effect of heterogeneous objectives of hospitals on quality differentiation, profits and overall welfare in a price‐regulated duopoly with exogenous symmetric locations. In contrast to other studies on mixed duopolies, this paper shows that, in this framework, privatization of the public hospital may increase overall welfare. This holds if the public hospital is similar to the private hospital or less efficient and competition is low. The main driving force is the single‐regulated price which induces under‐provision (over‐provision) of quality of the more (less) efficient hospital compared with the first best. However, if the public hospital is sufficiently more efficient and competition is fierce, a mixed duopoly outperforms both a private and a public duopoly due to an equilibrium price below (above) the price of the private (public) duopoly. This medium price discourages over‐provision of quality of the less efficient hospital and – together with the non‐profit objective – encourages an increase in quality of the more efficient public hospital.     

Mixed duopoly,privatization, and subsidization with excess burden of taxation

We investigate optimal tax‐subsidy policies in mixed and private oligopolies with excess burden of taxation. We compare the optimal subsidies and the resulting welfare levels among four regimes: mixed and private Cournot duopolies and Stackelberg competition with public and private leaderships. We show that, in contrast to the existing works on the privatization neutrality theorem, privatization affects resulting welfare.     

PRIVATISATION AND TIMING IN A MIXED OLIGOPOLY WITH BOTH FOREIGN AND DOMESTIC FIRMS*

This paper models a mixed oligopoly with both a domestic and a foreign private firm and examines the resulting timing in the quantity setting game. We demonstrate that with a single simultaneous pre‐game delay stage, the resulting endogenous timing has either the public firm leading or the two private firms leading. An alternative characterisation of the pre‐game stage results in the single timing in which the two private firms lead and the public firm follows. For all timings that emerge endogenously, we show that privatisation will always lower domestic welfare but its influence on global welfare is ambiguous.     

Choosing Price or Quantity? The Role of Delegation and Network Externalities in a Mixed Duopoly

This paper considers a differentiated goods managerial mixed duopoly composed of one social welfare‐maximising public firm and one profit‐maximising private firm. We model the firm choice of the strategic contract. We find that when the strength of network effects is sufficiently strong, the price competition can become the unique equilibrium market structure. Furthermore, we show that there exists an area of the degree of product differentiation and the strength of network effects such that the situation wherein the public firm chooses its price contract whereas the private firm chooses its quantity contract can become the unique equilibrium structure.     

Variety‐Controlling Public Policy Under Addiction and Saturation

This paper constructs a tractable general equilibrium model for investigating the dissimilar effects of addiction and saturation on consumption and public policy. By introducing an industry‐specific intertemporal consumption externality, we provide clear analytical results that a lump‐sum subsidy for firms can increase welfare in the presence of a negative externality (saturation). A tax can accomplish the same given a positive externality (addiction). Unlike existing studies of cultural goods, these results are not based on assumptions concerning exogenous different preferences across groups, but rather on conventional monopolistic competition and consumption habit formation models in macroeconomics.     

Endogenous timing game in a mixed duopoly with partial foreign ownership and asymmetric increasing marginal costs

This study examines a timing game in a mixed duopoly wherein public and private firms compete by taking account of the increasing marginal cost of both firms, as well as partial foreign ownership of the private firm. This study finds that if the private firm has a strong cost advantage over the public firm, public leadership is a risk dominant equilibrium irrespective of foreign ownership ratio. This result means that the cost difference between the public and private firms matters in selecting the risk-dominant equilibrium of the timing game. Additionally, if the private firm has only a weak cost advantage over the public firm, then private leadership (public leadership) is the risk dominant equilibrium if the foreign ownership ratio is (not) small.     

Endogenous timing in tax competition: The effect of asymmetric information

This study explores the effects of asymmetric information on endogenous leadership in a simple tax competition environment. The study models a two-country economy where one country is informed about its own and opponent's productivity of private goods, while the other country only knows its productivity. The results show that each type of informed country has an incentive to pretend to be the other type, which leads to a Stackelberg outcome endogenously, while the simultaneous move is the unique outcome under complete information. Under the Stackelberg outcome, the uninformed country moves first and the informed country moves second. Moreover, ex-post social welfare under asymmetric information can become larger than that under complete information, because the uninformed country chooses a less aggressive tax rate under asymmetric information. These results depend on the type of uncertainty, and capital ownership and share.     

OWNERSHIP VERSUS TIMING OF THE GAME

This study examines the impact of timing of the game on the welfare gains of privatisation in the presence of strategic trade policy. We argue that only if the public enterprise acts as a Cournot player will it generate an additional distortion that could outweigh the distortion caused by the oligopolistic behaviour of private firms. But with a first-mover advantage it can serve as an effective regulatory device comparable with a production subsidy. We further show that, in the presence of strategic trade policy, Cournot assumptions are inconsistent with the firms' preferences over the timing of the game. As public Stackelberg leadership is a subgame Nash equilibrium of the extended game with endogenous order of moves, we conclude that it is the timing of the game rather than firms' ownership structure which is responsible for the inefficiency of an international mixed market found by earlier studies.     

Price or Quantity? A New Irrelevance Result for Mixed Markets

Earlier studies for mixed markets have established a series of so‐called irrelevance results. While previous results relate to the attainment of the first‐best allocation for welfare, we provide a new irrelevance result in terms of the choice of strategic variable in the product market. We show that regardless of whether a public or private firm is the market leader, the leader always chooses the price contract whereas the follower is indifferent between the price contract and the quantity contract. The identity of the leader and the follower firm is therefore irrelevant for the equilibrium mode of competition. Implications for economic models in mixed market settings emerge, which are also discussed.     

PRICE AND QUANTITY COMPETITION IN A UNIONISED MIXED DUOPOLY: THE CASES OF SUBSTITUTES AND COMPLEMENTS*

We investigate a differentiated mixed duopoly in which private and public firms can choose to strategically set prices or quantities when unions are present. For the case of a unionised mixed duopoly, there exists a dominant strategy only for the public firm that chooses Bertrand competition irrespective of whether the goods are substitutes or complements; there is no dominant strategy for a private firm. Thus, we show that regardless of the nature of goods, social welfare under Bertrand competition is always determined in equilibrium, wherein Bertrand competition entails higher social welfare than Cournot competition. Moreover, our main results hold irrespective of the nature of goods, with the exception that when a sufficiently large parameter of complements is employed, the ranking of a private firm's profit is not reversed, which is in contrast to the standard findings.     

Service Quality,Competition, and Regulatory Policies in the Postal Sector

This paper presents a simple model which illustrates the possible policy- and welfare-implications of endogenous product selection in the postal sector. The cost of a unit of mail depends on its "quality" (e.g., speed of delivery) and on the type and location of the addressee (firms, urban households, and rural households). Senders have inelastic demands and differ in their willingness to pay for quality. Addressees are passive but their utility may affect social welfare. Two operators play a two-stage game, first choosing qualities and then prices. We first show that the equilibrium with two private (profit maximizing) operators results in an inefficient provision of quality. Then, we consider the mixed (Nash) equilibrium with one private and one (welfare maximizing) public operator. If the budget constraint of the public firm is not binding, this equilibrium is shown to be first-best efficient even if social welfare accounts for the utility of addressees. If the budget constraint is binding, the mixed equilibrium is not efficient but yields a higher level of welfare than the private equilibrium. Finally, we study the impact of minimum quality standards within our setting.     

Optimal pollution control in a mixed oligopoly with research spillovers

We study optimal pollution abatement under a mixed oligopoly when firms engage in emissions‐reducing research and development (R&D) with imperfect appropriation. The regulator uses a tax to curb emissions. Results show that in a mixed oligopoly, the public firm has positive emissions reduction in equilibrium; however, emissions reductions of the private firm could be positive or zero. Under certain conditions, the optimal pollution tax is positive; otherwise, the tax reverts to a subsidy. Comparing mixed and private duopolies, privatisation leads to reductions in R&D and output, but to an increase in overall emissions, so privatisation tends to make the environment worse.     

What role should public enterprises play in free-entry markets?

We investigate a desirable role of public enterprise in mixed oligopoly in free-entry markets. We compare the following three cases: (a) a public firm produces before private firms (public leadership), (b) all firms produce simultaneously (Cournot), (c) a public firm produces after private firms (private leadership). We find that private leadership is best and public leadership is worst, in contrast to the cases without entries and exits of private firms. We also investigate the welfare implication of privatization. We find that some important results shown by existing works do not hold under private leadership.     

QUALITY DIFFERENTIATION,WELFARE, AND THE MODE OF COMPETITION IN A VERTICALLY DIFFERENTIATED PRODUCT MARKET: A NOTE*

We analyse the implications of quality differences in a vertically differentiated product market for social welfare by employing an endogenous quality choice model. We find that in of Bertrand and Cournot duopolies, the degree of quality differentiation at equilibrium in an unregulated market is larger or smaller, respectively, than that of the socially second‐best optimum. This implies that a reduction in quality difference, respectively, increases or decreases social welfare in the case of Bertrand or Cournot duopolies.