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.     

A Mixed Duopoly With Switching Costs

We examine the effects of switching costs in a two‐period Hotelling‐type model where a profit‐maximising private firm competes with a welfare‐maximising public firm. We show that, in contrast with the case in which both firms are private, where switching costs raise prices in both periods, in the mixed duopoly they raise prices in the second period but reduce them in the first period. Moreover, the first‐period price reduction is of such magnitude that switching costs reduce firms’ profits and raise consumer welfare. We also find that switching costs affect the consequences of privatisation in favour of firms and against consumers.     

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.     

Endogenous Choice of Strategic Contracts in a Mixed Duopoly with Bargaining Over Managerial Delegation Contracts

We revisit the endogenous choice problem of strategic contracts for the public firm and the private firm in a managerial mixed duopoly with differentiated goods. We consider the situation wherein the managerial delegation contracts are determined by maximising social welfare within the public firm, which is equal to the objective function of its owner, and through bargaining over the content of managerial delegation contracts between the owner and manager within the private firm. We show that, in equilibrium, when the manager of the private firm has high bargaining power relative to that of the owner, the public firm chooses a price contract, while the private firm chooses a quantity contract. However, there is no equilibrium market structure under the pure strategic contract class when the manager has sufficiently low bargaining power relative to that of the owner.     

LOCATION OF PUBLIC FIRM IN THE PRESENCE OF MULTINATIONAL FIRM: A MIXED DUOPOLY APPROACH*

By incorporating a multinational private firm into the mixed duopoly model with Hotelling‐type spatial competition, we show that the private firm's nationality is a matter of the public firm's location. As the share of foreign capital increases in the private (multinational) firm, the public firm moves to a central place. The effects of price regulation and sequential location choice are also discussed.     

Stackelberg Mixed Duopoly with a Foreign Competitor

We investigate Stackelberg mixed duopoly models where a state‐owned public firm and a foreign private firm compete. We examine a desirable role (either leader or follower) of the public firm. We also consider endogenous roles by adopting the observable delay game of Hamilton and Slutsky (1990). We find that, in contrast to Pal (1998) discussing a case of domestic competitors, the public firm should be the leader and that it becomes the leader in the endogenous role game. We also find that in contrast to Ono (1990) eliminating a foreign firm does not improve domestic welfare in mixed oligopolies.     

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.     

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.     

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.      

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.     

Mixed Oligopoly at Free Entry Markets

We investigate the optimal behavior of a public firm in a mixed market involving private firms and one public firm. Existing works show that welfare-maximizing behavior by the public firm is suboptimal when the number of firms is given exogenously. We allow free entry of private firms and find that, in contrast to the case with the fixed number of firms, welfare-maximizing behavior by the public firm is always optimal in mixed markets. Furthermore, we find that mixed markets are better than pure markets involving no public firm if and only if the public firm earns nonnegative profits.     

Mixed Oligopoly and Environmental Policy

We show in this paper that when there are both public and private firms in product markets (a mixed oligopoly) the decision whether to privatize a public firm interacts with the environmental policy of governments. Therefore, the outcome of the decision whether to privatize a public firm may be different if the government internalizes the environmental damage than if the government ignores it. When the government sets a tax to protect the environment, the tax is lower in the mixed oligopoly than in the private one even though the environmental damage is greater. In the mixed oligopoly the marginal cost of the public firm is lower than the market price.     

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.     

Price control and privatization in a mixed duopoly with a public social enterprise

We explore the issue of the optimal degree of privatization for a public firm that does not need to care about its rival’s profit completely. We find that the optimal privatization of a public social enterprise under exogenous price control depends on the level of the regulated price. Namely, when the regulated price is low (medium, high), the optimal privatization is partial privatization (complete privatization, completely public owned). If the price control is optimized by maximizing social welfare, then the optimal privatization is complete privatization. For the case of the traditionally defined public firm, its optimal privatization is completely public owned when the price control is exogenously given. If the price control is endogenously determined, then privatization policy is redundant.     

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.     

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.     

Organizational Structure and the Choice of Price versus Quantity in a Mixed Duopoly

We consider the choice of price/quantity of a public and a private firm in a mixed differentiated duopoly. First, we study the way in which the strategic choice of the market variable is affected by different given organizational structures (managerial or entrepreneurial) of the public and the private firm. Second, we investigate how the price/quantity choice interacts with the endogenous choice of the organizational structure, thus determining a subgame perfect equilibrium at which firms choose to behave as price‐setters and to adopt a managerial structure.     

Incentive Regulation of Prices When Costs are Sunk

We present a model featuring irreversible investment, economies of scale, uncertain future demand and capital prices, and a regulator who sets the firm’s output price according to the cost structure of a hypothetical replacement firm. We show that a replacement firm has a fundamental cost advantage over the regulated firm: it can better exploit the economies of scale because it has not had to confront the historical uncertainties faced by the regulated firm. We show that setting prices so low that a replacement firm is just willing to participate is insufficient to allow the regulated firm to expect to break even whenever it has to invest. Thus, unless the regulator is willing to incur costly monitoring to ensure the firm invests, revenue must be allowed in excess of that required for a replacement firm to participate. This contrasts with much of the existing literature, which argues that the market value of a regulated firm should equal the cost of replacing its existing assets. We also obtain a closed-form solution for the regulated firm’s output price when this price is set at discrete intervals. In contrast to rate of return regulation, we find that resetting the regulated price more frequently can increase the risk faced by the firm’s owners, and that this is reflected in a higher output price and a higher weighted-average cost of capital.     

R&D competition between public and private sectors

We investigate a mixed market where a welfare-maximizing public research institute competes against profit-maximizing private firms. We investigate R&D competition by using a standard model of patent races where each firm chooses both its innovation size and R&D expenditure. We find that the innovation size (R&D expenditure) chosen by the public institute is too small (too large) from the viewpoint of social welfare, respectively, and so the government should control the public institute appropriately. We also discuss the welfare implications of privatization of public research institutes.     

Price-cost markups in UK industry

This article tests for the presence of monopolistic price markups across UK industrial sectors by testing for a non-zero covariance between the Solow residual and various instruments. This restriction derives from profit maximising conditions for a representative imperfectly competitive firm under the assumption of constant returns to scale. We find evidence of significant markups in the Manufacturing and Services sectors which together account for more than 90% of total employment within the UK.