This article provides a theoretical model of firm dynamics that replicates the export elasticity values estimated in the empirical literature, and the heterogeneous response of firms. The analysis of alternative versions of the model allows for a decomposition of the contributions of the different mechanisms (distribution costs, imported intermediate inputs, gradual growth of foreign demand, and market access costs in foreign/domestic currency). Distribution costs represent the most important factor to replicate elasticity estimations. Furthermore, distribution costs allow the model to replicate the heterogeneous response of exports to exchange rate movements by decreasing the demand elasticity of more productive firms.