Profits and competition under alternative technologies in a unionized duopoly with product differentiation

This paper aims at investigating if the conventional wisdom (i.e. an increase of competition linked to a decrease in the degree of product differentiation always reduces firms׳ profits) can be reversed in a unionized duopoly model. We show that a decrease in the degree of product differentiation may affect wages, hence profits, differently, depending on both the firms׳ production technology and the mode of competition in the product market. Specifically, under constant returns to labour, the “reversal result” can apply under both Cournot and Bertrand competition, but it is more likely when firms compete in quantities. By contrast, under decreasing returns, profits can increase with competition but only if firms compete in prices.     

The cournot duopoly model reconsidered in the presence of costly communication and enforcement agreements

Recently I proposed a general notion of equilibrium for n-person games which is based on mutual threats and promises (responses), and which leads, in general, to a determinate solution with respect to the order of choice moves. The nature of the solution set in our model is a function of the action sets, the payoff functions, and the cost of ‘communication and enforcement of agreements’ (C&E). The main concern of this paper is to show that the Cournot duopoly solution, for the case of a linear demand function facing two identical firms, can be regenerated by our solution concept under a certain assumption about a high cost C&E. On the other hand, it is shown that under a relatively low cost of C&E the Cournot/Nash solution does not belong to our solution set, because it is Pareto inferior for both duopolists relative to some solutions in our set, among them, the standard monopoly solution.     

Free entry and stability in a cournot model

In a Cournot model for a single homogeneous good, we study simultaneously two stability properties of a Cournot equilibrium: the stability of a continuous quantity adjustment process with a fixed number of firms and the stability relative to entry. Under usual assumptions, we show that these two properties are consistent—i.e., there exists an equilibrium that is stable in both senses—and determine quite sharply the number of active firms.     

Spatial dispersion in cournot competition

This paper considers the spatial model used by Anderson and Neven (1991) to study firms' decisions on locations without restricting the consumers' reservation price. We note that the pattern of locations varies as the reservation price for a fixed transportation rate decreases. For a high enough reservation price, we find Anderson and Neven (1991)'s result where firms group at the center of the market and serve all consumers. As the reservation price falls, firms start to move away from each other, increasing the quantities shipped to the consumers close to their locations.     

Open Innovation in a dynamic Cournot duopoly

In recent years Open Innovation (OI) processes have been receiving growing attention from the empirical and theoretical economic literature, where a debate is taking place on the aspects of complementarity or substitutability between internal R&D and OI spillover. By means of a differential game approach, we analyze the case of substitutability in an OI setup in a Cournot duopoly where knowledge spillovers are endogenously determined via the R&D process. The game produces multiple steady states, allowing for an asymmetric solution where a firm may trade off the R&D investment against information absorption from the rival. The technical analysis and the numerical simulations point out that the firm which commits to a higher level of OI absorption produces a smaller output and enjoys higher profits than its rival.     

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.     

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.     

Employee share ownership in a unionised duopoly

Profit sharing schemes have been analysed assuming Cournot competition and decentralised wage negotiations, and it has been found that firms share profits in equilibrium. This paper analyses a different remuneration system: employee share ownership. We find that whether firms choose to share ownership or not depends on both the type of competition in the product market and the way in which workers organise to negotiate wages. If wage setting is decentralised, under duopolistic Cournot competition both firms share ownership. If wage setting is centralised, only one firm shares ownership if the degree to which goods are substitutes takes an intermediate value; otherwise, the two firms share ownership. In this case, if the union sets the same wage for all workers neither firm shares ownership. Therefore, centralised wage setting discourages share ownership. Finally, under Bertrand competition neither firm shares ownership regardless of how workers are organised to negotiate wages.     

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.     

Optimal research for cournot oligopolists

An oligopolistic industry faces uncertain demand. Firms can conduct research prior to production, obtaining private data that is informative of the unknown parameters of demand. Firm strategies thus consist of a level of research and a subsequent production strategy based on their research findings. We characterize the Bayes equilibrium of such a model when demand is linear, with unknown intercept, and the information structure has linear conditional expectations. We compare the solution to an efficiency standard, finding inefficiencies even in the competitive limit.     

Regulating a duopoly by a Pretend-but-Perform Mechanism

In a linear duopoly, participants are required to declare their costs under a Pretend—but—Perform Mechanism (PPM) which enforces accordance of performance with pretended (declared) cost.Specifically, under the PPM, each firm's output in reaction to rival output is to maximize profit according to declared cost. Compared with the Cournot solution before PPM Regulation, Nash implementation of the PPM induces a Cournot solution, among the make—believe firms, giving greater industry output and efficiency along with increased consumer surplus even after compensating the duopolists for decreased profits, except in a trivial case which — educatively — thruthful declarations are confined.     

Profitable parallel trade in unionized markets

Why do producers often accept parallel trade in some markets such as automobiles, clothing, toys and consumer electronics? This paper points to a new factor, viz., the wage reducing effect of parallel trade in unionized markets, which may make parallel trading beneficial to a manufacturer. The benefit of parallel trade disappears in our analysis when such factor is removed.     

Feasibility of predatory pricing in a capacity-constrained duopoly

Predatory pricing is feasible only if the minimax profit of the prey is strictly smaller than the expected profit in the corresponding Bertrand-Nash equilibrium. We completely characterize the conditions for feasibility of predatory pricing in Kreps and Scheinkman's model of capacity-constrained duopoly. The predator must have a capacity larger than that of the prey, and also larger than the Cournot capacity. Surprisingly, predatory pricing may be infeasible not only if the prey is too large but also if it is too small.     

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.     

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.     

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.     

Employee Profit-sharing and Labor Extraction in a Classical Model of Distribution and Growth

This article sets out a classical model of economic growth in which the distribution of income features the possibility of profit-sharing with workers, as firms choose periodically between two labor-extraction compensation strategies. Workers are homogeneous with regard to labor power, and firms choose to compensate them with either only a conventional wage or a share of profits on top of this conventional wage. Empirical evidence shows that labor productivity (i.e. labor extraction) in profit-sharing firms is higher than labor productivity in non-sharing firms. The frequency distribution of labor-extraction employee compensation strategies and labor productivity across firms is time-variant, being driven by satisficing imitation dynamics from which we derive two significant results. First, heterogeneity in labor-extraction compensation strategies across firms, and hence earnings inequality across workers can be a stable long-run equilibrium outcome. Second, although convergence to a long-run equilibrium may occur with either a falling or increasing proportion of profit-sharing firms, the share of net profits in income and the rates of net profit, capital accumulation and economic growth nevertheless all converge to the highest possible long-run equilibrium values.