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This paper offers a unified framework to explore both the static and dynamic welfare effects of trade and multinational production (MP) in the presence of firm-specific productivity heterogeneity. The model captures the dynamic effects by allowing for R&D spillovers between firms in a framework of Helpman et al. (2004) that generates endogenous growth without scale effects. We show that multinational presence improves average productivity by strengthening the selection process among heterogeneous firms, but leads to a lower growth rate of intermediate varieties along the transition path toward the new steady state. Thus the presence of multinationals has an ambiguous effect on overall welfare. We also compare the welfare implications of a change in trade cost in our model and in trade models without multinationals. We find that the gains from trade can be higher or lower than the gains obtained in the trade-only models, depending on the degree of firm heterogeneity, the size of trade and FDI costs, and the magnitude of technology spillover parameters. We further show that firm heterogeneity always magnifies average productivity, international spillovers and fixed costs of developing a new variety, which leads to ambiguous effects on overall welfare. Calibrating the model to the US economy suggests that aggregate welfare improves in response to a reduction in trade and FDI costs for empirically plausible parameter values.