Dynamic efficiency of Cournot and Bertrand competition: input versus output spillovers

We consider the efficiency of Cournot and Bertrand equilibria in a duopoly with substitutable goods where firms invest in process R&D that generates input spillovers. Under Cournot competition firms always invest more in R&D than under Bertrand competition. More importantly, Cournot competition yields lower prices than Bertrand competition when the R&D production process is efficient, when spillovers are substantial, and when goods are not too differentiated. The range of cases for which total surplus under Cournot competition exceeds that under Bertrand competition is even larger as competition over quantities always yields the largest producers’ surplus.     

Bertrand versus Cournot revisited

Summary. Bertrand criticized Cournot's analysis of the competitive process, arguing that firms should be seen as playing a strategy of setting price below competitors' prices (henceforth, the Bertrand strategy) instead of a strategy of accepting the price needed to sell an optimal quantity (the Cournot strategy). We characterize Nash equilibria in a generalized model in which firms choose among Cournot and Bertrand strategies. Best responses always exist in this model. For the duopoly case, we show that iterated best responses converge under mild assumptions on initial states either to Cournot equilibrium or to an equilibrium in which only one firm plays the Bertrand strategy with price equal to marginal cost and that firm has zero sales. Received: December 11, 1995; revised version October 2, 1996     

ENDOGENOUS TIMING AND STRATEGIC CHOICE: THE COURNOT‐BERTRAND MODEL

Cournot establishes a Nash equilibrium to a duopoly game under output competition; Bertrand finds a different Nash equilibrium under price competition. Both treat the strategic choice variable (output versus price) and the timing of play as exogenous. We investigate Cournot‐Bertrand models where one firm competes in output and the other competes in price in both static and dynamic settings. We also develop a general model where both the timing of play and the strategic choice variables are endogenous. Consistent with the conduct of Honda and Scion, we show that Cournot‐Bertrand behaviour can be a Nash equilibrium outcome.     

PRICE AND QUANTITY COMPETITION IN A UNIONISED MIXED DUOPOLY: THE CASES OF SUBSTITUTES AND COMPLEMENTS*

We investigate a differentiated mixed duopoly in which private and public firms can choose to strategically set prices or quantities when unions are present. For the case of a unionised mixed duopoly, there exists a dominant strategy only for the public firm that chooses Bertrand competition irrespective of whether the goods are substitutes or complements; there is no dominant strategy for a private firm. Thus, we show that regardless of the nature of goods, social welfare under Bertrand competition is always determined in equilibrium, wherein Bertrand competition entails higher social welfare than Cournot competition. Moreover, our main results hold irrespective of the nature of goods, with the exception that when a sufficiently large parameter of complements is employed, the ranking of a private firm's profit is not reversed, which is in contrast to the standard findings.     

Comparing Cournot and Bertrand equilibria in an asymmetric duopoly with product R&D

We compare the Cournot and Bertrand equilibria in an asymmetric duopoly with product R&D competition. If a firm’s marginal cost is lower than that of its rival, then this firm (its rival) is referred to as the more (less) efficient firm. Under each mode of competition, there are three types of equilibria: blockaded-entry, deterred-entry, and accommodated-entry. Moreover, the presence of R&D investment makes it harder for the less efficient firm to survive. Cournot competition entails a unique equilibrium, whereas Bertrand competition may yield two equilibria. It is harder for the less efficient firm to survive under Bertrand competition than under Cournot competition. Versus Cournot competition, Bertrand competition yields higher industry output, and it shifts production from the less efficient firm to the more efficient firm. This result, together with the known size effect, explains the following three findings. First, the more efficient firm has a normal output ranking, whereas the less efficient firm may demonstrate an output reversal. Second, the more efficient firm may demonstrate a R&D reversal, whereas the less efficient firm has a normal R&D ranking (its Cournot R&D effort exceeds its Bertrand R&D effort). Third, Bertrand competition is more welfare-efficient than Cournot competition.     

Innovation,licensing, and price vs. quantity competition

In this paper, we develop a differentiated duopoly model with endogenous cost-reducing R&D and review the argument on welfare effect of price and quantity competition in the presence of technology licensing. We show that, with licensing, the standard conclusion on duopoly (Singh and Vives, 1984) is completely reversed. Cournot competition induces lower R&D investment than Bertrand competition does. Moreover, Cournot competition leads to lower prices, lower industry profit, higher consumer surplus and higher social welfare than Bertrand competition.     

Maximum-revenue tariffs versus free trade

Welfare with the maximum-revenue tariff is compared to free-trade welfare under Cournot duopoly with differentiated products; under Bertrand duopoly with differentiated products; and under perfect competition in the case of a large country able to affect its terms of trade. Under Cournot duopoly and Bertrand duopoly, assuming linear demands and constant marginal costs, welfare with the maximum-revenue tariff is always higher than free-trade welfare. Under perfect competition, assuming linear demand and supply, welfare with the maximum-revenue tariff will be higher than free-trade welfare if the country has sufficient market power.     

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.     

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.     

REALIZED COST‐BASED SUBSIDIES FOR STRATEGIC R&D INVESTMENTS WITH EX ANTE AND EX POST ASYMMETRIES*

We discuss stochastic cost‐reducing R&D investments and examine efficient subsidies. We discuss a two‐stage duopoly model in which each firm chooses R&D levels (innovation size and probability of success) in the first stage and competes à la Cournot in the second stage. We find that simple subsidies depending on the realized cost differences induce the efficient levels of R&D with respect to the innovation size and probability of success by two firms regardless of ex ante and ex post asymmetries between the two firms.     

TO REGULATE OR TO DEREGULATE? THE ROLE OF DOWNSTREAM COMPETITION IN UPSTREAM MONOPOLY VERTICALLY LINKED MARKETS

This paper attempts to cast light to the effect of monopoly regulation in Cournot markets compared to its effect in Bertrand markets. To this purpose, we use a simple model of a vertically linked market, where an upstream regulated natural monopoly is trading via two‐part tariff contracts with a downstream duopoly. Combining our results to those of the existing literature on deregulated markets, we argue that when the downstream competition is in prices, efficiency dictates regulating the monopoly with a marginal cost based pricing scheme. However, this type of regulation leads to significant welfare loss, when the downstream market is characterized by Cournot competition.     

POLITICAL ECONOMY OF STRATEGIC EXPORT POLICY IN A DIFFERENTIATED DUOPOLY*

This paper investigates the effect of a home firm's lobbying on a strategic export policy in a third market with a differentiated duopoly. We focus on its effect on domestic welfare under Bertrand and Cournot competition. Regardless of the mode of competition, the strategic export policy cannot improve domestic welfare in the presence of lobbying if the degree of product differentiation is high or the government is overly concerned with political contribution relative to domestic welfare. Moreover, for the same degree of product differentiation, the lobbying‐induced export policy is more likely to deteriorate domestic welfare relative to free trade under Cournot competition.     

Collusion in Differentiated Duopolies with Quadratic Costs

The analysis of collusion in infinitely repeated duopoly games has generally assumed that marginal cost is constant, but this note uses quadratic costs (linear marginal costs) to compare the sustainability of collusion under Bertrand and Cournot duopoly with differentiated products. It is shown that when marginal costs are sufficiently increasing in output, then it is always easier to sustain collusion under Cournot duopoly than under Bertrand duopoly for any degree of product substitutability.     

A note on merger in mixed duopoly: Bertrand versus Cournot

In this note we analyze the incentives to merge in a mixed duopoly if firms compete in prices or quantities. Our model framework mainly follows Barcena-Ruiz and Garzon (J Econ 80:27–42, 2003) who set up the model with quantity competition. We extend their analysis by analyzing the case of competition in prices. Further we compare the incentives to merge with Bertrand and Cournot competition. Comparing quantity with price competition we can show that a merger is more likely with Cournot competition than with Bertrand competition.     

Strategic Cost Reduction and Cost Revelation

Strategic cost reduction requires cost transparency. When unilateral cost revelation is feasible, strategic cost reduction indeed arises as equilibrium. If it is not feasible, however, credible revelation has to be organized, possibly by a trade association. Then, firms face a prisoners' dilemma: in Cournot duopoly, cost revelation arises as an equilibrium, but hurts firms; in Bertrand duopoly, cost concealing is the equilibrium, while firms would be better off with cost revelation. Since cost revelation is socially desirable (undesirable) in Cournot (Bertrand) competition, it should be encouraged (discouraged).     

THE PUZZLING DIVERGENCE OF RENTS AND USER COSTS, 1980–2004

This paper demonstrates that, in the context of U.S. housing data, rents and ex ante user costs diverge markedly—in both growth rates and levels—for extended periods of time, a seeming failure of arbitrage and a puzzle from the perspective of standard capital theory. The tremendous volatility of even appropriately‐smoothed ex ante annual user cost measures implies that such measures are unsuitable for inclusion in official price statistics. The divergence holds not only at the aggregate level, but at the metropolitan‐market level as well, and is robust across different house price and rent measures. But transactions costs matter: the large persistent divergences did not imply the presence of unexploited profit opportunities. In particular, even though detached housing is readily moved between owner and renter markets, and the detached‐unit rental market is surprisingly thick, transactions costs would have prevented risk‐neutral investors from earning expected profits by buying a property to rent out for a year, and would have prevented risk‐neutral homeowners from earning expected profits by selling their homes and becoming renters for a year. Finally, computing implied appreciation as a residual yields a house price forecast with huge errors; but either longer‐horizon or no‐real‐capital‐gains forecasts—which turn out to have similar forecast errors—imply a far less divergent user cost measure which might ultimately be useful for official price statistics. Some conjectures are offered.     

OPTIMUM-WELFARE AND MAXIMUM-REVENUE TARIFFS UNDER BERTRAND DUOPOLY

This article derives the maximum‐revenue tariff and the optimum‐welfare tariff under Bertrand duopoly with differentiated products. It is shown that both tariffs are lower under Bertrand duopoly than under Cournot duopoly. Also, the optimum‐welfare tariff may exceed the maximum‐revenue tariff under both Bertrand duopoly and Cournot duopoly. This result is more likely the lower the costs of the home firm relative to the costs of the foreign firm, and the greater the degree of product substitutability. Also, it is shown that the optimum‐welfare tariff is less likely to exceed the maximum‐revenue tariff under Bertrand duopoly than under Cournot duopoly.     

Product differentiation and the gains from trade under Bertrand duopoly

Abstract.  In the literature on the welfare effects of free trade under imperfect competition, one important case seems to have been overlooked, and that is the Bertrand duopoly model with differentiated products. Although many authors have analysed the welfare effects of free trade under Cournot duopoly and demonstrated the possibility of losses from trade, there has been no thorough analysis of the welfare effects of free trade under Bertrand duopoly. In this article we present a thorough analysis of the welfare effects of free trade under Bertrand duopoly with differentiated products, and it is shown that there are always gains from trade. JEL Classification: F12     

Licensing under vertical product differentiation: Price vs. quantity competition

This paper develops a duopoly model of vertical product differentiation where two domestic firms incur variable costs of quality development. These domestic firms can purchase a superior foreign technology through licensing. Outcomes between Bertrand and Cournot competition are compared. We find that licensing raises domestic welfare, and domestic welfare is higher in Bertrand than in Cournot competition regardless of whether or not domestic firms engage in licensing. Non-exclusive licensing is also found to benefit the domestic country more than exclusive licensing.