Comparing Cournot and Bertrand Equilibria in an International Differentiated Duopoly with Process R&D Investment

Purpose - The purpose of this paper is to analyze and compare Cournot and Bertrand equilibria in an international duopoly model in which two firms compete in a third-country market with differentiated goods and process R&D for free trade and the subsidy regime. Design/Methodology/Approach - This study uses previous work by Haaland and Kind (2008) and constructs an international duopoly model. It consists of two stages where two governments simultaneously set the optimal process R&D subsidy or tax levels to maximize their countries’ respective social welfare in the first stage and each firm located in each country simultaneously chooses its R&D level and the quantity (in Cournot competition) or price (in Bertrand competition) in order to maximize its profits in the second stage. Findings - It is shown that (i) the equilibrium levels of the firm profit and social welfare under Cournot (Bertrand) competition are greater than those under Bertrand (Cournot) competition if the goods are substitutes (complements) for free trade; (ii) the equilibrium levels of the firm profit for the subsidy regime are always greater than those for free trade and the equilibrium levels of social welfare for free trade (the subsidy regime) are greater than those for the subsidy regime (free trade) if the goods are substitutes (complements); (iii) the equilibrium levels of firm profit for free trade are greater than those for the subsidy regime if the goods are sufficiently differentiated substitutes and complements but vice versa if the goods are sufficiently less differentiated substitutes and complements, while the equilibrium levels of social welfare for the subsidy regime are greater than those for free trade if the goods are sufficiently differentiated substitutes and sufficiently less differentiated complements but vice versa if the goods are sufficiently less differentiated substitutes and sufficiently differentiated complements except too close substitutes; and (iv) the result from the comparison of the equilibrium levels of social welfare for the subsidy regime is the same as that for free trade. Research Implications- The main finding is that the equilibrium level of R&D investment is higher under Bertrand competition than Cournot competition for free trade but its comparison between Cournot and Bertrand is ambiguous for the subsidy regime. However, the equilibrium level of social welfare is higher under Cournot (Bertrand) competition than Bertrand (Cournot) competition when the goods are substitutes (complements) for free trade and the subsidy regime. It implies that the equilibrium level of R&D investment changes from the absence of government intervention to the presence of government intervention but that of social welfare does not. Therefore, we can surely expect which type of competition is more efficient according to the type of goods.