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Greater openness to international trade affects both firms' innovation incentives and the markups that they can charge. In this paper, we show that considering the interaction between these two effects yields new insights. Building a two-sector dynamic general equilibrium model with endogenous innovation and endogenous markups, we find that lower trade costs lead to both lower markups and higher innovation effort of incumbent firms. These findings are consistent with firm-level empirical evidence from Spain, which shows that both export and import shocks tend to decrease within-firm markups and increase within-firm productivity. However, our model also suggests that innovation may dampen or amplify the usual pro-competitive effects of trade, depending on the initial level of concentration of the industry: while trade lowers static markups, it also increases domestic firms' incentives to escape competition by innovating if these firms are sufficiently dominant to start with. When this is the case, successful domestic innovators charge higher markups going forward; otherwise, markups are further depressed. These effects are absent in standard models of trade. In a calibrated version of the model, we show that the growth effects of trade shocks are under-estimated if the innovation-competition feedback is ignored.
