This paper presents a tractable formalization and an empirical investigation of the quality-complementarity hypothesis, the hypothesis that input quality and plant productivity are complementary in generating output quality. We embed this complementarity in a general-equilibrium trade model with heterogeneous, monopolistically competitive firms, extending Melitz (2003), and show that it generates distinctive implications for two simple, observable within-sector correlations − between output prices and plant size and between input prices and plant size− and for how those correlations vary across sectors. Using uniquely rich and representative data on the unit values of outputs and inputs of Colombian manufacturing plants, we then document three facts: (1) output prices are positively correlated with plant size within industries on average; (2) input prices are positively correlated with plant size within industries on average; and (3) both correlations are more positive in industries with more scope for quality differentiation, as measured by the advertising and R&D intensity of U.S. industries. The predicted and observed correlations between export status and input and output prices are similar to those for plant size. We present additional evidence that market power of either final-good producers or input suppliers does not fully explain the empirical patterns we observe. These findings are consistent with the predictions of our model and difficult to reconcile with alternative models that impose symmetry or homogeneity of either inputs or outputs. We interpret the results as broadly supportive of the quality-complementarity hypothesis.