Firms' success in international markets depends on their product's quality, prices, markups, and marginal cost. However, causally identified empirical evidence for the effect of trade policies that address non-tariff barriers on these mechanisms is rare. To fill this gap, we exploit a quasi-natural experiment in Denmark and examine the effects of an export support policy aimed at reducing non-tariff barriers to trade. We find that export support raises firm-level exports within markets. However, export support does not affect prices, quality, markups, or marginal costs. Instead, the results support trade theory predicting that firms grow in export markets by shifting demand.