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.

This study derives non-cooperative and cooperative optimal product research and development (R&D) policies of a country with a high-quality firm and a country with a low-quality firm in the presence of technology spillover under Cournot and Bertrand competitions in an international duopoly. When the respective governments determine their R&D policies non-cooperatively, optimal policies for both countries involve an R&D tax (subsidy) if spillover is large (small). When the governments choose their R&D policies cooperatively, a tax is always optimal for the country with low-quality firm and a subsidy (tax) is optimal for the country with high-quality firm if spillover is large (small). In addition, we show that the non-cooperative optimal product R&D Policy is tax for a wider range of spillover effects under Cournot competition, compared to the case of Bertrand competition.

This study clarifies how governments' industrial policies affect the firm's R&D choice when firms simultaneously conduct both costreducing process and qualityimproving product R&D. We found the following results. Under Cournot competition, while output increases when quality improves and/or the production cost decreases, output decreases as the proportion of product R&D becomes higher compared to that of process R&D. Under Bertrand competition, whether prices become higher or lower depends on the degree of fraction of investment in two types of R&D. If firms only conduct one of the two kinds of R&D, this effect does not exist. A government always subsidizes its domestic firm's R&D investments.