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.     

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.     

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.     

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.     

Product differentiation, process R&D, and the nature of market competition

We investigate the relationship between process and product R&D and compare the incentives for both types of R&D under different modes of market competition (Bertrand versus Cournot). It is shown that: (i) process R&D investments increase with the degree of product differentiation and firms invest more in product R&D when they can do process R&D than when they cannot; (ii) Bertrand firms have a stronger incentive for product R&D whereas Cournot firms invest more in process R&D; and (iii) cooperation in product R&D promotes both types of R&D relative to competition whereas cooperation in both types of R&D discourages R&D relative to cooperation in just product R&D.     

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.     

BERTRAND Vs. COURNOT COMPETITION WITH UPSTREAM FIRM INVESTMENT

This paper compares Bertrand and Cournot competition in a vertical structure in which the upstream firm sets the input price and makes R&D investments. We show that from the downstream firms’ point of view, Cournot competition has the advantage of a more monopolistic effect, leading to the setting of a higher price, but has the disadvantage of inducing a lower incentive for the upstream firm to invest. On the other hand, Bertrand competition has the advantage of providing a greater incentive for the upstream firm to invest but has the disadvantage of a more competitive effect, leading to the setting of a lower price. Our main findings are as follows. First, R&D investment level is greater under Bertrand competition than under Cournot competition. Second, from the standpoint of the upstream firm and industry, Bertrand competition is more efficient than Cournot competition. Third, from the standpoint of the downstream firms, Bertrand competition is more efficient than Cournot when investment is sufficiently efficient and products are sufficiently differentiated.     

Multi-market interaction and decentralization of R&D decisions

In this paper, we analyse under what conditions it is profitable for a multi-divisional firm to encourage divisions to perform independent R&D, and when it is better to centralize R&D so that the level be chosen co-operatively. Under Bertrand competition, firms always centralize R&D decisions. Under Cournot competition, however, with divisions of the same firm producing substitute products, the strategic advantage of decentralizing R&D compensates the co-ordination loss when the degree of substitutability among the products is not too high; in all other cases (when products are very good substitutes or when divisions of the same firm produce complement goods) the pay-off to co-ordination is greater than the strategic advantage of decentralization. Social welfare is maximized when firms centralize R&D.     

Emission tax and optimal privatization in Cournot–Bertrand comparison

We compare a Cournot with a Bertrand duopoly in a differentiated mixed market when both emission tax and privatization policies are used together. We find that the optimal emission tax is always lower than the marginal environmental damage, and it is always lower under Cournot than under Bertrand. We also find that the optimal privatization is always a partial privatization, and it is always higher under Cournot than under Bertrand. The socially optimal combinations of emission tax and privatization will damage the environment most, but Cournot yields lower environmental damage and social welfare than those under Bertrand. Finally, we show that the environmental damage is non-monotone in the level of privatization under both Cournot and Bertrand competitions.     

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     

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.     

Stochastic innovation and product market organization

Summary This paper analyzes how different types of product market organization affect firms' R&D investments in a stochastic innovation framework. Product market competition determines payoffs to successful and unsuccessful firms. Restrictions on the research project success probability distribution are identified that yield an invariance result for expenditure per R&D project. The impact of the number of firms (n) on the amount of market R&D is shown to be sensitive to product market organization. For a major process innovation, firms undertake more R&D projects under Cournot product market competition than under Bertrand competition, forn sufficiently large. A numerical example is used to illustrate welfare tradeoffs.Tom Lyon, Herman Quirmbach, Ferenc Szidarovszky, Mark Walker and two anonymous referees gave us helpful comments and suggestions on prior versions of this paper. Lucy Atkinson provided expert research assistance on numerical computations. Special thanks to Ted Bergstrom who gave us valuable suggestions about the first proposition.     

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.     

Competition and innovation: an experimental investigation

The paper analyzes the effects of more intense competition on firms’ investments in process innovations. More intense competition corresponds to an increase in the number of firms or a switch from Cournot to Bertrand competition. We carry out experiments for two-stage games, where R&D investment choices are followed by product market competition. An increase in the number of firms from two to four reduces investments, whereas a switch from Cournot to Bertrand increases investments, even though theory predicts a negative effect in the four-player case. The results arise both in treatments in which both stages are implemented and in treatments in which only one stage is implemented. However, the positive effect of moving from Cournot to Bertrand competition is more pronounced in the former case.     

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.     

Technology adoption in a differentiated duopoly: Cournot versus Bertrand

This paper shows that the cost as well as the effectiveness of technology has a differential impact on technology adoption under two alternative modes of competition. If the cost of the technology is high, Bertrand competition provides a stronger incentive to adopt technology than Cournot competition unless the effectiveness of the technology is very low. On the contrary, if the cost of the technology is low, Cournot competition fares better than Bertrand competition in terms of technology adoption by firms. This demonstrates that the commonly subscribed assumption of ‘positive primary outputs’ restricts (inflates) the scope of higher degree of technology adoption under Bertrand (Cournot) competition. Moreover, in contrast to standard welfare ranking, it shows that Cournot competition leads to higher social welfare than Bertrand competition under certain situations.     

Price and quantity competition under free entry

This paper complements that of Cellini et al. (Cellini, R., Lambertini, L., Ottaviano, G. I. P., 2004. Welfare in a differentiated oligopoly with free entry: A cautionary note. Research in Economics, 58:125–33.), which shows that Cournot competition may generate higher welfare compared to Bertrand competition in an economy with free entry. Unlike them, we provide a more general proof for this result and show that Cournot competition generates higher welfare compared to Bertrand competition when the products are sufficiently differentiated. If the products are close substitutes, welfare is higher under Bertrand competition. We show that these qualitative results hold whether or not number of varieties increases market size. We also show when the active firms earn higher profits under Bertrand competition compared to Cournot competition.     

Product R&D Investment Policies in an International Duopoly

This study analyzes the optimal product R&D investment policies of a developed and a developing country in an international Cournot duopoly where firms from these two countries compete through endogenous quality–quantity decisions. We explore a new international trade model by using demand functions derived from utility functions. We find that the optimal product R&D investment policies for both countries are subsidies. This study counters a finding that used Hotelling‐type demand functions and it partially modifies another result that adopted the same demand functions but with an international Bertrand duopoly.     

Bertrand versus Cournot competition in a downstream mixed oligopoly with foreign ownership

Focusing on foreign ownership in the private firm, we examine the Cournot-Bertrand comparison in a mixed oligopolistic market with vertical market structure. We have found that if public and private firms were charged with uniform price for their inputs, then Cournot-Bertrand ranking in market outcomes confirms those obtained by Ghosh and Mitra (2010). This implies that under uniform pricing in the upstream sector, the vertical market structure does not have substantial influences on Cournot-Bertrand ranking. However, if discriminatory pricing is adopted, firm's profits, output, and social welfare are often reversed to those obtained from uniform pricing in the upstream sector. Given the closeness of products, if the share of foreign ownership is sufficiently low, social welfare in Cournot competition can exceed that of Bertrand competition, contrasting with the standard welfare ranking that Bertrand welfare is strictly higher than Cournot. This implies that Cournot competition can be more socially desirable than Bertrand in mixed oligopoly with vertical market structure if discriminatory pricing scheme is adopted by foreign upstream monopolists.