We use customs data for Irish firms to show that in successful episodes of export market entry, there are statistically and economically significant post-entry dynamics of quantities, but not of markups. To match these moments, we structurally estimate a model where firms can invest in future customer base through two channels: by selling more today, and by spending on marketing and advertising. Our estimates suggest that customer base is insensitive to lagged sales, so firms have no incentive to engage in dynamic pricing to accumulate customers. Instead, investment in customer base through marketing and advertising explains the dynamics of quantities. The ratio of advertising and marketing expenditures to sales implied by the model is consistent with data from other sources. Our estimated model generates long run export responses to permanent tariff changes that are bigger than short run responses, as well as responses that are increasing in the expected persistence of tariff shocks, contributing to our understanding of the International Elasticity Puzzle.