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.     

HORIZONTAL MERGERS IN A DIFFERENTIATED COURNOT OLIGOPOLY

Using a standard differentiated goods quantity competition setting, we show three facts about horizontal two‐firm mergers that are not true for a homogeneous goods Cournot market. First, merger of two firms is profitable for the merging firms provided that goods are sufficiently distant substitutes. Second, merging of two firms can lead to more two‐firm mergers. Third, an initially non‐profitable two‐firm merger can occur in anticipation of subsequent mergers. These facts imply that mergers are more likely to occur in differentiated goods markets than in homogeneous goods markets.     

ON THE SUSTAINABILITY OF COLLUSION IN A DIFFERENTIATED OLIGOPOLY WITH A CARTEL AND A FRINGE

We discuss the effects of the existence of non‐colluding (fringe) firms on cartel sustainability. We obtain, using trigger strategies, that with product differentiation collusion is always more easily sustained when firms compete in prices than when firms compete in quantities. This is true basically because (i) price competition is more intense than quantity competition, and (ii) fringe firms exacerbate the fact that cartel firms have more incentives to deviate from the agreement under quantity competition. This result reverses previous findings where, in the absence of fringe firms, product differentiation plays a crucial role in determining the effectiveness of price or quantity competition in sustaining collusion.     

WELFARE ENHANCING COORDINATION IN CONSUMER COOPERATIVES UNDER MIXED OLIGOPOLY

The recent globalization of world economies has led the retail markets of developed countries towards increasing levels of integration and strategic interdependence. A non negligible share of retail and food markets is currently served by co‐operative societies. Consistently with this trend, the consumer cooperatives have recently experienced increasing levels of integration. The main aim of this paper is to study the welfare effects of coordination among consumer cooperatives competing in quantities in a mixed oligopoly against profit‐maximizing firms. We show that, in absence of agency problems, under increasing or constant returns to scale a higher output coordination of the consumer cooperatives does not affect the total welfare as long as a nonnegative profit constraint holds in these firms. On the other hand, under decreasing returns to scale, the consumer cooperatives contribute more to social welfare when acting on behalf of all consumers. This is because, by coordinating consumers’ preferences, these firms can reduce their market output, thus helping the market to come closer to the first best. All together these results seem to provide an argument in favour of the recent process of integration involving consumer cooperatives in many developed countries.     

A continuum of commitment

We examine a generic three-stage game for two players with alternating moves, where the first player can choose the level of adjustment cost to be paid in the last period to modify the action she announced in the first period. In the resulting continuum of commitment options, convexifying the choice between first-mover and second-mover advantage in pure strategies, we characterize when an intermediate adjustment-cost level is chosen in equilibrium. We show that the wastefulness of the adjustment cost may be in the players’ best interest, improving both of their individual net payoffs over making any fraction of the adjustment cost a side-payment from the first to the second player.     

INSUFFICIENT ENTRY OF EMPLOYEE‐CONTROLLED FIRMS IN A FREE‐ENTRY OLIGOPOLY

This study is a theoretical examination of whether employee‐controlled firms (ECFs) enter a free‐entry oligopolistic market excessively or insufficiently, from the viewpoint of welfare maximization. The excess entry theorem is well known in oligopoly theory. According to this theorem, a greater number of profit‐maximizing firms enter a free‐entry oligopolistic market than is optimal for welfare maximization. We demonstrate the possibility that insufficient entry arises when ECFs compete in a free‐entry market. In particular, we show that if both the demand and cost functions are convex, insufficient ECF entry necessarily occurs. Our results suggest that competition among firms seeking purposes other than profit might lead to insufficient entry because differences in competing firms’ objectives affect the intensity of market competition.     

THE SCOPE FOR NON‐PROFIT OBJECTIVES IN A MIXED OLIGOPOLY UNDER INTERNATIONAL COMPETITION

We ask how the scope for non‐profit objectives in a state‐owned enterprise (SOE) in a mixed oligopoly changes because of competition from firms in another country. There is no change if costs and demand are given, unless the trade partner is a low‐cost country. However, the scope for non‐profit objectives is limited by the country's relative size if wages are market‐clearing and if workers and firms are stationary, because of reduced competitiveness caused by higher real wage rates. The total surplus is then not affected by the actions of the SOE. International trade does not otherwise reduce the scope for its non‐profit objectives if workers and firms are mobile, but productivity differences might require restrictions in order to avoid a complete relocation of the workforce in either country.     

ENDOGENOUS TIMING IN A MIXED DUOPOLY WITH ENDOGENOUS VERTICAL DIFFERENTIATION

We consider a game of endogenous timing with observable delay in a mixed duopoly with endogenous vertical differentiation in the context of sequential quality and price choice. We find that a simultaneous play in the first opportunity at each stage turns out to be the unique subgame perfect Nash equilibrium, which contrasts with the endogenous timing in a purely private duopoly.     

Coalition-proof supply function equilibria in oligopoly

In an industry where firms compete via supply functions, the set of equilibrium outcomes is large. If decreasing supply functions are ruled out, this set is reduced significantly, but remains large. Specifically, the set of prices that can be sustained by supply function equilibria is the interval between the competitive price and the Cournot price. In sharp contrast, when the number of firms is above a threshold we identify (e.g., three if demand is linear), only the Cournot outcome can be sustained by a coalition-proof supply function equilibrium.     

Unions, government's preference, and privatization

By introducing the government's preference for tax revenues into the theoretical framework of unionized mixed oligopolies, this study investigates the efficiency of privatization. The results are twofold. First, regardless of the government's preference for tax revenues and the number of private firms, the government and the public firm do not always have an incentive to privatize the public firm even if the government places lesser emphasis on the tax revenues than on social welfare. Second, social welfare increases with an increased number of private firms regardless of the government's preference for tax revenues and decreases with the government's preference for tax revenues regardless of the number of private firms. Hence, the government can use tax more efficiently as a commitment device to control the union's wage demand so as to maintain lower wage level under unionized mixed oligopoly.     

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.     

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.     

The Cournot-Bertrand profit differential: A reversal result in a differentiated duopoly with wage bargaining

This paper compares Cournot and Bertrand equilibria in a downstream differentiated duopoly in which the input price (wage) paid by each downstream firm is the outcome of a strategic bargain with its upstream supplier (labor union). We show that the standard result that Cournot equilibrium profits exceed those under Bertrand competition - when the differentiated duopoly game is played in imperfect substitutes - is reversible. Whether equilibrium profits are higher under Cournot or Bertrand competition is shown to depend upon the nature of the upstream agents’ preferences and on the distribution of bargaining power over the input price. We find that the standard result holds unless unions are both powerful and place considerable weight on the wage argument in their utility function.     

STRATEGIC INVESTMENT IN A LABOUR‐MANAGED DUOPOLY

Developing a Cournot two‐stage game model with strategic capital interaction, we compare two different kinds of equilibrium in a labour‐managed (LM) duopoly. An LM firm's reaction function is negatively sloped when capital and output are simultaneously determined, while the slope of its reaction function in the second stage changes in sign depending on the magnitude of its labour‐expansion elasticity. Hence, whether the LM firms employ more capital and produce greater output at the equilibria in the two‐stage game model than at the equilibria resulting from the simultaneous selection of capital and output depends on the magnitude of their labour‐expansion elasticity.     

FARSIGHTED COALITIONAL STABILITY OF A PRICE LEADERSHIP CARTEL

This paper analyzes the farsighted behaviour of firms that form a dominant price leadership cartel. We consider stability concepts such as the farsighted core, the farsighted stable sets, and the largest consistent set. We show that: (i) the farsighted core is either an empty set or a singleton set of the grand cartel; (ii) any Pareto efficient cartel is itself a farsighted stable set; and (iii) the set of cartels in which fringe firms enjoy higher profits than the firms in the minimal Pareto efficient cartel is the largest consistent set.     

Comparative statics for oligopoly: A generalized result

We perform comparative statics for a general model of asymmetric oligopoly and derive a concise formula for the response of one firm to a marginal change in its rival’s strategic variable, taking into account the responses of all other firms. We obtain the conditions under which the sign of this response coincides with that of the mixed second-order partial derivative of the firm’s payoff function. We then propose a distinction between gross and net strategic relationships (i.e., strategic substitute and complement).     

Undesirable competition

We show that the entry of private profit-maximising firms makes the consumers worse off compared to having a nationalised monopoly. Such entry increases the nationalised firm’s profit, industry profit, and social welfare, at the expense of the consumers. Our result is important for competition policy.     

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.     

The codetermined firm in a Cournot duopoly: A stability analysis

This paper aims to study the stability issue in a Cournot duopoly with codetermined firms. We show that when both firms codetermine employment together with decentralised employees' representatives, a rise in wages acts as an economic (de)stabiliser when the wage is fairly (high) low, while under profit maximisation a rise in wages always acts as a stabilising device because the parametric stability region monotonically increases with the wage in such a case. Moreover, a rise in the union's bargaining power has a de-stabilising effect, except when the wage is low and the firm power is already high. Therefore, under codetermination a change either in the wage or firm power in the Nash bargaining plays an ambiguous role on stability. We also show with numerical simulations that complex dynamics can also occur.     

Competing auctions with endogenous quantities

Two sellers decide on their discrete supply of a homogenous good. There is a finite number of buyers with unit demand and privately known valuations. In the first model, there is a centralized market place where a uniform auction takes place. In the second, there are two distinct auction sites, each with one seller, and buyers decide where to bid. Using the theory of potential games, we show that in the one-site auction model there is always an equilibrium in pure-strategies. In contrast, if the distribution of buyers values has an increasing failure rate, and if the marginal cost of production is relatively low, there is no pure-strategy equilibrium where both sellers make positive profits in the competing sites model. We also identify conditions under which an equilibrium with a unique active site exists. We deal with the finite and discrete models by using several results about order statistics developed by Richard Barlow and Frank Proschan [R. Barlow, F. Proschan, Mathematical Theory of Reliability, Wiley, New York, 1965; R. Barlow, F. Proschan, Inequalities for linear combinations of order statistics from restricted families, Ann. Math. Statist. 37 (1966) 1593-1601; R. Barlow, F. Proschan, Statistical Theory of Reliability and Life Testing, McArdle Press, Silver Spring, 1975].