This study establishes a third‐country trade model where firms from developing and developed countries invest into product R&D under their governments' subsidisation policies to analyse firms' quality–price choices and governments' optimal product R&D investment policies. We show that a rise in the developing (developed) country's product R&D subsidy makes firms' quality–price competition more (less) intense and that the governments' optimal product R&D policies, depending on the features of their quality and demand functions, can both be subsidies even under Bertrand price competition, contrary to the findings of previous studies.