Mixed duopoly, cross-ownership and partial privatization

This paper investigates the effects of cross-ownership on optimal privatization, and vice-versa, in mixed duopoly. It shows that cross-ownership is profitable to the private firm only if the level of privatization of the public firm is sufficiently high. In equilibrium, cross-ownership does not take place even if there is partial privatization. However, the possibility of cross-ownership significantly limits the socially optimal level of privatization in most of the situations. Moreover, it demonstrates that full nationalization is socially optimal, in case of sufficiently convex identical cost functions and homogeneous goods. These results have strong implications to both divestment and competition policies.     

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.     

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.     

PRIVATIZATION AND EFFICIENCY GAIN IN AN INTERNATIONAL MIXED OLIGOPOLY WITH ASYMMETRIC COSTS*

This paper examines two policy instruments, privatization of the domestic public firm and imposition of a tariff on foreign private firms in an international mixed oligopolistic model with asymmetric costs. It first demonstrates that different orders of moves of firms will imply different government decisions on optimal tariff and on privatization policy. Following Hamilton and Slutsky (1990 ), this paper then uses an extended game to discuss endogenous roles. It indicates that the efficiency gain that highlights the importance of foreign competition is crucial in determining the welfare improving privatization policy. Moreover, the endogenous equilibria are associated with different government decisions on privatization.     

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.     

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.     

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.     

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.     

Lack of commitment to future privatization policies may lead to worst welfare outcome

We investigate the welfare consequences of a lack of commitment to future privatization policies. The government implements a privatization policy after the competition structure is determined by the entry of private firms. We find that in an equilibrium, the government fully privatizes (nationalizes) a public firm if private firms expect that the government fully privatizes (nationalizes) the public firm. This is because an increase in the number of firms entering a market increases the government's incentive to privatize the public firm, which mitigates future competition and stimulates entries. The full-privatization equilibrium is the worst privatization policy among all possible (either equilibrium or non-equilibrium) privatization policies for welfare because it causes excessive market entry of private firms. Partial commitment of a minimal public ownership share may mitigate this problem.     

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.     

Optimal manipulation rules in a mixed oligopoly

We study the optimal manipulation rules of a public firm’s objective function in a mixed oligopoly with imperfect product substitutability. We start with a baseline duopoly model and compare the solutions under quantity and price competition, and the way they are affected by product substitutability. This allows us to show that partial privatization, strategic delegation and other specific government’s commitments on the objective function of the public management can be looked at as special cases of these optimal rules, and to evaluate the viability of these policies under the two modes of competition. In this framework, we also discuss the equivalence between manipulation of the objective function and Stackelberg leadership. Since optimal manipulation rules change as new dimensions are added, we also derive the optimal rules under oligopoly, quadratic costs, and competition of international firms. This fairly general unified framework allows to discuss the impact of these factors on the government’s implementation policies of the optimal manipulation rules.     

WELFARE ANALYSIS OF PRIVATIZATION IN A MIXED MARKET WITH BARGAINING

The author analyzes the welfare effects of privatization in a mixed duopoly model in which the wage rate for the privatized firm is determined by Nash bargaining beforehand. The evaluations are based on three-stage privatization frameworks respectively under two regimes: Cournot competition and a public firm acting as a Stackelberg leader. The author finds that the optimal degrees of privatization from the viewpoint of social welfare may be different for various types of competition. The article also shows that even optimal privatization set by a welfare-maximization government may not guarantee welfare improvement, owing to the interference of wage bargaining. (JEL D60, D78, L32, L33 )     

Mixed duopoly: Differential game approach

This study formulates a dynamic mixed oligopoly model, in which a state‐owned public firm competes against a private firm over multiple periods. We adopt a differential game formulated by Fershtman and Kamien [Econometrica 55 (1987), pp. 1151–1164] and investigate how the dynamic competition affects the optimal privatization policy. We characterize the open‐loop Nash equilibrium (OLNE) and Markov‐perfect Nash equilibrium (MPNE). We show that in the MPNE, an increase in the degree of privatization has a nonmonotonic effect on the price, increasing it in a wide range of parameter spaces, which is in sharp contrast to the result in the OLNE or static analyses. We also find that the optimal degree of privatization is higher in the MPNE than that in the OLNE and static equilibrium. These results suggest that intertemporal strategic behavior changes the optimal privatization policy.     

Partial Privatization,Foreign Competition,and Optimum Tariff*

Using a simple international mixed oligopoly model with one public and one or more foreign firms, this paper examines the effect of partial privatization or foreign competition on optimum tariffs and finds that foreign competition lowers the optimal tariff rate but partial privatization raises it. This result implies that trade liberalization is welfare improving if a country opens up its economy by allowing foreign competition. However, the liberalization policy is not desirable when the country only partially or completely privatizes its publicly‐owned enterprises.     

ALTERNATIVE STRATEGIES OF A PUBLIC ENTERPRISE IN OLIGOPOLY REVISITED: AN EXTENSION TO STACKELBERG COMPETITION

This paper revisits De Fraja and Delbono (1989), which is the seminal paper on mixed oligopoly, in order to pay more attention to Stackelberg competition. First, we show that, even in Cournot competition, if the number of private firms is sufficiently small, privatization necessarily reduces social welfare. Second, we demonstrate that when a public firm is a Stackelberg leader before and after privatization, privatization necessarily reduces welfare irrespective of the number of private firms. Moreover, we show that even when a public firm remains a follower, privatization reduces welfare if the number of private firms is relatively small.     

Do cost efficiency gap and foreign competitors matter concerning optimal privatization policy at the free entry market?

In this paper, we demonstrate that in contrast to the case with exogenous number of foreign private firms, partial privatization is always the best policy for the public firm in long-run equilibrium, which casts doubt on the robust result in Matsumura and Kanda (J Econ 84(1):27–48, 2005) who argued that welfare-maximizing behavior by the public firm is always optimal in mixed markets. Critical cost gap determines that long-run degree of privatization is larger than the short-run one. In particular, regarding the scenario wherein one public firm competes with domestic private firms and foreign private firms, equilibrium price is lower than marginal cost of public firm instead of being equivalent to marginal cost of the public firm, and that public firm’s outputs, profit, and social welfare is the smallest in the concerned mixed oligopoly models.     

On the Neutrality of Profit Taxation in a Mixed Oligopoly

This paper investigates the neutrality of profit taxation in a mixed oligopoly where one (partially) public firm competes with private firms. We find that the neutrality of a profit tax is robust under a general cost and a general demand function as long as the degree of privatization is endogenously determined. This result is also true when product heterogeneity is considered under both Cournot and Bertrand competition. By contrast, if the degree of privatization is exogenously given, the profit tax neutrality holds only in the cases where the public firm is fully privatized or fully state-owned; otherwise, the neutrality breaks down.     

Public investment,the rate of return,and optimal fiscal policy in a stochastically growing economy

This study examines the optimal fiscal policy in a stochastic endogenous growth model with private and public capital. The government is willing to actualize a socially optimal equilibrium using a lump-sum tax and government debt linked to public investments, subject to the budget constraint under the golden rule of public finance. A socially optimal fiscal policy states that a deterministic rate of return on government bonds sets the marginal product of public capital. Moreover, public investments optimally adjust the ratio of private capital to public capital to equate the rates of return on such capital. The presence of stochastic disturbances results in a disparity between the optimal marginal products of the two types of capital, as reported in previous empirical studies. This disparity significantly affects the socially optimal growth rate in response to investment risk.     

PRICE AND QUANTITY COMPETITION WITH ASYMMETRIC COSTS IN A MIXED DUOPOLY: A TECHNICAL NOTE

We consider a mixed duopoly in which private and public firms can choose to strategically set prices or quantities when the public firm is less efficient than the private firm. Thus, even with cost asymmetry, we obtain exactly the same result (i.e., Bertrand competition) of Matsumura and Ogawa (2012) if Singh and Vives’ (1984) assumption of positive primary outputs holds. However, compared to endogenous determination of the type of contract without cost asymmetry, our main finding is that in the wider range of cost asymmetry, different type(s) of equilibrium related to or not related to the limit‐pricing strategy of the private firm can be sustained. Thus, when considering an implication on privatization, we may overestimate the welfare gain of privatization because Cournot competition takes place after privatization even though cost asymmetry exists between firms. While the result of Matsumura and Ogawa (2012) holds true if the goods are complements, we find the novel results in the case of substitutes.     

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.