Product vs process innovation under budget constraint

This paper develops a theoretical model of strategic R&D investment under a hard budget constraint. Two symmetric firms must choose between product and process innovation, where the former increases product quality and the latter reduces marginal costs. We show that the equilibrium depends on the effectiveness of product innovation. When quality improvements are sufficiently effective, both firms converge on product innovation; when they are weaker, no dominant strategies exist and the game admits mixed-strategy equilibria as well as asymmetric pure-strategy equilibria. In contrast, social welfare is always maximized under an asymmetric allocation, with one firm innovating in product and the other in process. This divergence highlights a coordination failure that justifies policy intervention. To address this inefficiency, we propose a targeted ex-ante subsidy scheme that restores the socially optimal asymmetric outcome as a unique pure-strategy Nash equilibrium. We also compare welfare maximization with total R&D investment as alternative policy objectives and show that the two may diverge, particularly when product innovation becomes highly effective. These findings offer important insights for the design of innovation policies in environments characterized by strategic interaction and resource constraints.