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.