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Commonly used firm-based models of importing imply that firm productivity should have no effect on the allocation of expenditure across a common set of sourcing countries. Using French data, we show that this homotheticity property is soundly rejected: larger firms concentrate their import spending on their top varieties, holding the sourcing strategy fixed. To rationalize this finding, we propose a novel model of importing that features (i) a complementarity between firm productivity and input quality and (ii) heterogeneity across countries in their ability to produce high quality inputs. This model implies that large firms bias their spending towards countries with a comparative advantage in producing high quality inputs and hence generates a non-homothetic import demand system. We provide empirical support for this and other predictions of this theory.