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.     

Location of public and private firms under endogenous timing of choices

This paper studies the choices of locations in a mixed duopoly when production costs are endogenously determined and the public firm maximizes a weighted sum of social surplus and its profits. We find that the locations of the two firms are decided simultaneously when the weight of the public firm’s profits in its objective function is high enough. When this is not the case we find that one firm (not always the public firm but sometimes also the private one) behaves as a leader in the choice of location and location decisions are made sequentially. Moreover, in equilibrium, the production cost of the public firm is never higher than that of the private firm.     

Endogenous Timing in Mixed Duopolies With Externality

We investigate endogenous timing in a mixed duopoly with a negative externality. We find that quantity (price) competition yields a simultaneous‐move (sequential‐move) outcome under a significant negative externality. These results indicate that mixed duopolies yield the same results as private duopolies under a significant negative externality, which is in sharp contrast to the results in mixed duopolies without a negative externality. Unless the negative externality is insignificant, public leadership yields greater welfare than private leadership, and public leadership is more robust than the private leadership as equilibrium. If optimal environmental tax policy is introduced, however, private leadership yields the greatest welfare and this an equilibrium outcome in the endogenous timing game under quantity competition.     

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.     

Endogenous Timing in a Mixed Duopoly: Price Competition

The endogenous order of moves is analyzed in a mixed duopoly for differentiated goods, where firms choose whether to set prices sequentially or simultaneously. It is shown that, in contrast to the private duopoly where firms set prices sequentially, in the mixed duopoly firms choose prices simultaneously. Moreover, the result obtained in the mixed duopoly under price competition differs from the one under quantity competition, since in the latter case decisions are taken sequentially.      

Media Plurality: Private versus Mixed Duopolies

In this paper, we analyze the level of media plurality in a market with two private news firms (private duopoly) and in a market with a private news firm and a public news firm (mixed duopoly). In the private duopoly news firms maximize profits. In the mixed duopoly, the private news firm maximizes profits, while the public news firm maximizes social welfare. We show that, in spite of the public news firm maximizing social welfare, neither media plurality nor social welfare needs to be higher under the mixed duopoly compared with the private duopoly. This will depend on the relation between the costs of adapting news to readers' political preferences, the intensity of the readers' political preferences, and the size of the advertising market.     

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.     

ENDOGENOUS TIMING IN A MIXED DUOPOLY AND PRIVATE DUOPOLY –‘CAPACITY‐THEN‐QUANTITY’ GAME: THE LINEAR DEMAND CASE*

We consider a game of endogenous timing of sequential choice of capacity and quantity with observable delay in a mixed duopoly and a private duopoly. In mixed duopoly, we find that a simultaneous play at the capacity stage or at the quantity stage can never be supported as subgame perfect Nash equilibrium (SPNE); whereas a simultaneous play at each stage turns out to be the unique SPNE in a private duopoly. In mixed duopoly there is multiplicity of equilibria and all SPNEs require sequentiality at the capacity as well as quantity stage.     

ON THE ROBUSTNESS OF PRIVATE LEADERSHIP IN MIXED DUOPOLY

We investigate a mixed duopoly where a state‐owned public enterprise competes against a profit‐maximising private enterprise. We analyse whether private leadership or public leadership is robust in the observable delay game. We find that private leadership is always risk dominant. We also investigate how ownership structure in a public firm affects the equilibrium distribution of roles. We find that the roles are as follows: (1) Cournot, when the degree of privatisation is low, (2) private leadership, when it is middle, (3) both private leadership and public leadership, when it is high. The result implies that private leadership is again more robust.     

Duopoly models with a joint capacity constraint

The paper proposes a two-stage mixed duopoly model of exhaustible resource market where at the first stage the government decides on the degree of privatization of public firm and at the second stage the public and private firms decide simultaneously on the two-period extraction paths. It is demonstrated that if the two firms have symmetric technologies with increasing marginal extraction costs and the same resource stocks, then neither full nationalization of any of the two firms nor full privatization will be socially desirable. It is shown that the presence of a semi-public firm improves intertemporal allocation of the fixed resource stock. Thus, partial privatization is optimal even under exogenously fixed total outputs of each firm. For asymmetric cost case, when the public firm is less efficient than the private firm, we derive the conditions under which full nationalization or full privatization is optimal.     

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.     

Quantity competition vs. price competition under optimal subsidy in a mixed oligopoly

This paper reconsiders the literature on the irrelevance of privatization in mixed markets within which both quantity and price competition are investigated under product differentiation. By allowing for partially privatization of a state-controlled firm, we explore competition under different timings of firms' moves and derive the conditions under which an optimal subsidy allows to achieve maximum efficiency. We show that, irrespective of the mode of competition, while the ownership of the controlled firm is irrelevant when firms play simultaneously, it matters when firms compete sequentially, requiring the leader to be publicly-owned for an optimal subsidy to restore the first-best. The paper also focuses on the extent to which a subsidy is needed to attain the social optimum in the considered scenarios, providing an ordering which highlights the subsidy equivalence between Cournot (Bertrand) private leadership and simultaneous Bertrand (Cournot) under duopoly, and the dominance of the former in oligopoly.     

The competition of investments for endogenous transportation costs in a spatial model

This paper proposes a two-stage spatial duopoly model to explore how the firms improve the value of product by service enhancement. In the model, we assume that the higher service ability means lower transportation cost. The results show that when two private firms participate in competition, no firm tends to invest more under the profit-maximizing objection. But when one is a public firm, the private firm may participate in competition with better service and higher price relative to the public one.     

Partial privatization in mixed duopoly with price and quality competition

We analyze price and quality competition in a mixed duopoly in which a profit-maximizing private firm competes against a state-owned public firm. We first show that the welfare-maximizing public firm provides a lower quality product than the private firm when they are equally efficient. In order to maximize social welfare, government manipulates the objective of the public firm that is given by a convex combination of profits and social welfare. It is demonstrated that an optimal incentive of the public firm is welfare maximization under the absence of quality competition, but it is neither welfare maximization nor profit maximization under the presence of quality competition. The result supports a completely mixed objective between welfare and profit maximizations or partial privatization of the public firm.      

Emission tax and optimal privatization in Cournot–Bertrand comparison

We compare a Cournot with a Bertrand duopoly in a differentiated mixed market when both emission tax and privatization policies are used together. We find that the optimal emission tax is always lower than the marginal environmental damage, and it is always lower under Cournot than under Bertrand. We also find that the optimal privatization is always a partial privatization, and it is always higher under Cournot than under Bertrand. The socially optimal combinations of emission tax and privatization will damage the environment most, but Cournot yields lower environmental damage and social welfare than those under Bertrand. Finally, we show that the environmental damage is non-monotone in the level of privatization under both Cournot and Bertrand competitions.     

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.     

Optimal degree of privatization and the environmental problem

We determine the optimal degree of privatization in a mixed duopoly when the environmental problem exists. With regard to the ownership of the private firms, we analyze two cases: (h) the private firm is owned by domestic private investors and (f) it is owned by foreign private investors. A comparison of the two cases presents the following results. Partial privatization is always desirable in (h), and the optimal degree of privatization is independent of the degree of environmental damage. However, in (f), whether partial privatization is desirable or not depends on the degree of environmental damage: there are cases where full privatization or full nationalization is optimal.     

How do Markets Manage Water Resources? An Experiment

We experimentally test how a private monopoly, a duopoly and a public utility allocate water of differing qualities to households and farmers. Most of our results are in line with the theoretical predictions. Overexploitation of the resources is observed independently of the market structure. Stock depletion for the public utility is the fastest, followed by the private duopoly and private monopoly. On the positive aspects of centralized public management, we find that the average quality to price ratio offered by the public monopoly is substantially higher than that offered by the private monopoly or duopoly.     

Consumer surplus and the reform of network industries: a primer

Starting from an industry where production is provided by a public monopolist, we observe the effects of a sequence of reforms within the network industry on consumer surplus. Using a simple comparative statics framework, we find the indifference conditions for the consumer surplus under the following regimes: a public monopoly, an unregulated private monopoly, a regulated private monopoly, a vertically disintegrated monopoly, a duopoly and a liberalized market. The results are determined by the relative size of the x-inefficiencies of the public monopolist, allocative inefficiencies of the private monopoly, the cost of unbundling and the costs related to establishing a competitive market.     

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.