We introduce asymmetric product differentiation in a model characterized by a linear demand system, endogenous markups and heterogeneous firms (as in Melitz-Ottaviano [2008]). In particular, a single industry is divided into a number of market segments, each characterized by a different degree of horizontal product differentiation. Such a setup allows us to explain, within a single theoretical framework, the non-linear relations between firm productivity, size and exporting behavior that have been documented by the empirical literature. The theoretical results are tested empirically by examining the performance of French wine producers operating in market segments characterized by different levels of horizontal product differentiation. Such segments are identified using the official classification of French wines based upon the controlled denomination of origin, i.e., the Appellation d'Origine Contrôlée (AOC) system.