Mixed ownership in a mixed duopoly with differentiated products

We determine optimal privatization in a symmetric differentiated duopoly when the public firms do not bear the full cost of production and hence their objective functions differ from the government’s objective function. In the social optimum firms will generally have mixed ownership, and it will depend on the type of uncovered cost, the degree of substitutability of the two products and the output decision rule of the partially public firms. Different types of mixed duopoly emerge, ranging from both firms being partially privatized, to one being fully privatized. We also derive an optimal tax-subsidy scheme as a substitute for privatization.      

Employee ownership and internal governance

This paper is designed to counter Oliver Williamson's hypothetical ‘Peer Group’ model of organization with a discussion of three prosperous populations of employee-owned firms: worked-owned scavenger companies, taxi cooperatives, and professional partnerships such as the large law firm. It will be shown here that these firms are formed, endure and prevail over their competition for reasons that Williamson, more than anyone else, has taught us to appreciate. In particular, this paper will argue that the metering problems and human asset considerations that are so prominently featured in Williamson's work are crucial for understanding the success of these firms.     

Profit-sharing in a unionized cournot duopoly

The main purpose of this paper is to analyze when it is optimal for firms in a unionized duopoly to introduce profit-sharing. It is shown that a firm only prefers a profit-sharing system if its own union does not have “too much” bargaining power, and if the union in the other firm does not have “too much” bargaining power. However, if a firm introduces profit-sharing, the employment increases, and the price in the goods market decreases. Hence, even if it is not in the own interest of a firm to introduce profit-sharing, it may be in the interest of the society.     

Unilateral production restrictions in a dynamic duopoly

This paper examines a dynamic game of exploitation of a productive asset by a duopoly. A closed-loop Nash equilibrium of the game is constructed and used to analyze the effects of a unilateral production restriction. Surprisingly, such unilateral action may result in a decrease of the long-run asset's stock. We also exhibit production restrictions that can result simultaneously in an increase of the asset's stock and the long-run profits of the firm that is being imposed the production restriction. Moreover, a unilateral decrease of the production of one firm can induce its rival to also decrease its production.     

Optimal pollution taxation in a Cournot duopoly

It is well known that the optimal pollution tax in a competitive industry is equal to the marginal damage inflicted by the pollution. It has also been shown that the optimal pollution tax on a monopoly is less than the marginal damage. In this paper, I derive the optimal pollution tax for a Cournot duopoly. If firms have different production costs, the optimal tax rate may exceed the marginal damage. This is so because the tax may be an effective instrument for allocating production from the less to the more efficient firm. It is also shown that, if one firm has a positive most preferred pollution tax, the sum of consumer and producer surpluses will be declining in the tax at this level.     

Trade liberalization in a differentiated duopoly reconsidered

Constructing a model of differentiated Cournot duopoly, we consider welfare effects of trade liberalization (i.e. reductions in transport costs). We examine both multilateral trade (i.e. the firms in both countries export bilaterally) and unilateral trade, under which foreign entry is possible but the home firm cannot export. Some new results on trade gains under differentiated oligopoly are proved and their implications are discussed.     

Sick pay reforms and health status in a unionised labour market

We theoretically analyse the effects of sick pay and employees' health on collective bargaining, assuming that individuals determine absence optimally. If sick pay is set by the government and not paid for by firms, it induces the trade union to lower wages. This mitigates the positive impact on absence. Moreover, a union may oppose higher sick pay if it reduces labour supply sufficiently. Better employee health tends to foster wage demands. If the union determines both wages and sick pay, we identify situations in which it will substitute wages for sick pay because adverse absence effects can be mitigated.     

Price discrimination and price dispersion in a duopoly

This paper analyses the problem of price discrimination in a market where consumers have heterogeneous preferences both over a horizontal parameter (brand) and a vertical one (quality). Discriminatory contracts are characterized for different market structures. It is shown that price dispersion, i.e. the observed range of prices for each class of customers, increases almost everywhere as competition is introduced in the market.     

Commitment and price competition in a dynamic differentiated-product duopoly

This paper characterizes linear Markov-perfect equilibrium in a duopolistic environment where firms engage in dynamic price competition. Firms have constant (but potentially different) marginal costs and produce differentiated products. We show that, for the case of linear demand, dynamically stable Markov-perfect equilibrium prices are strictly higher than one-shot Nash equilibrium prices, but lower than fully collusive (monopoly) prices. We provide closed-form solutions for the Markov-perfect equilibrium prices which, in principle, can be estimated given data on firm demand and costs. Our results suggest that static two-stage models of price commitment are on reasonably solid ground in that they might be viewed as a reduced form for more complicated dynamic models.     

Cost-based access regulation and collusion in a differentiated duopoly

This paper revisits the conventional doctrine that “it is easier to collude among equals”, applied in the context of vertically related markets. In a differentiated duopoly model, we study how cost-based access price regulation may hinder the sustainability of tacit collusion.     

Strategic managerial incentives in a two-period Cournot duopoly

This paper examines the nature of optimal managerial incentives in the context of a duopoly marked by competition between the firm's managers in a dynamic production environment. If the marginal cost of production falls moderately over time or remains unchanged, there exists an equilibrium where one owner requires her manager to maximize profit, whereas the rival-owner requires her manager to maximize sales revenue. The profit-maximizing manager turns his firm into a Stackelberg-leader, while the sales-revenue-maximizing manager turns his firm into a Stackelberg-follower. Further, the profit-maximizing manager may generate a larger firm profit relative to the sales-revenue-maximizing manager.     

Licensing to a durable-good duopoly in patent litigation

Incorporating patent litigation into a durable-good duopoly model, we revisit the optimal licensing contract on a cost-reducing innovation. We find that both the optimal licensing contract and the innovator's licensing revenue are closely related to the patent's strength, i.e., the probability it would be found valid if tested in court. It is shown that, for a relatively weak patent (patent's strength is low), it's optimal for the innovator to charge the royalty rate as high as possible coupled with a negative fixed fee. But for a relatively strong patent (patent's strength is high), contract involving the combination of a medium level royalty rate and a positive fixed fee is optimal. We also discuss how the patent's strength affects the social welfare of a patent. Finally we present two policy suggestions that may alleviate the social welfare loss raised by the licensing of weak patents.     

Sequencing R&D decisions in a two-period duopoly with spillovers

Summary. We compare simultaneous versus sequential moves in R&;D decisions within an asymmetric R&;D/Cournot model with linear demand (for differentiated products), general R&;D costs, and spillovers. Simultaneous play and sequential play (with and without a specified leader) can emerge as appropriate formulations, depending on the ratios of spillover rate over demand cross-slope, but not on R&;D efficiency. When at least one ratio is above 1/2, a sequential solution mitigates competition and leads to higher profits for each firm, and to higher social welfare. When uniquely specified, the stronger firm emerges as the R&;D first-mover.     

Optimal privatization in a mixed duopoly with consistent conjectures

We show that partially privatizing a public firm alters underlying conjectures, in turn, changing the optimal degree of privatization. The consistent conjectures equilibrium (CCE) generates substantially greater optimal privatization than does any conjecture shared between the firms including the standard Cournot–Nash equilibrium (CNE). Yet, when the private rival is foreign, the CCE generates substantially less privatization than the CNE. The optimal extent of privatization with a domestic rival exceeds that with a foreign rival in the CCE as well as in the CNE.     

Strategic incentives in dynamic duopoly

We compare steady states of open loop and locally stable Markov perfect equilibria (MPE) in a general symmetric differential game duopoly model with costs of adjustment. Strategic incentives at the MPE depend on whether an increase in the state variable of a firm hurts or helps the rival and on whether at the MPE there is intertemporal strategic substitutability or complementarity. A full characterization is provided in the linear-quadratic case. Then with price competition and costly production adjustment, static strategic complementarity turns into intertemporal strategic substitutability and the MPE steady-state outcome is more competitive than static Bertrand competition.     

Stackelberg leadership in a dynamic duopoly with stochastic capital accumulation

I propose a dynamic duopoly model where firms enter simultaneously but compete hierarchically á la Stackelberg at each instant over time. They accumulate capacity through costly investment, with capital accumulation dynamics being affected by an additive shock the mean and variance of which are known. The main findings are the following. First, the Stackelberg game is uncontrollable by the leader; hence, it is time consistent. Second, the leader invests more than the follower; as a result, in the steady state, the leader’s capacity and profits are larger than the follower’s. Therefore, the present analysis does not confirm Gibrat’s Law, since the individual growth rate is determined by the timing of moves.JEL Classification: C61, C73, D43, D92, L13Financial support within the project The post-entry performance of firms: technology, growth and survival lead by Enrico Santarelli, co-financed by the University of Bologna and MIUR, is gratefully acknowledged. I thank Uwe Cantner, Roberto Cellini, Roberto Golinelli, Helen Louri, Enrico Santarelli, Antonello Scurcu, Peter Thompson, two anonymous referees and the audience at the final workshop of the project (Bologna, November 22-23, 2002) for useful comments and discussion. The usual disclaimer applies.