By Costas Arkolakis, Svetlana Demidova, Peter J. Klenow, and Andrés Rodríguez-Clare* quantities, and hence contribute little to welfare. We refer to this effect as the effect of “curvature” in weakening the variety gains from trade. In Section III we relate this result to recent models of firm-level heterogeneity and derive a simple formula that shows the effect of curvature. These results do not take into account the effect of trade liberalization on domestic variety. But it seems reasonable to think that an increase in import competition would cause a decline in domestic variety as domestic firms exit. In fact, the evidence does suggest that trade liberalization leads to exit by domestic firms (James Tybout 2003). Consistent with this, domestic variety is endogenous in most recent models and falls with a decline in trade costs. 1 In Section IV we present a model with firm-level increasing returns, differentiated goods, monopolistic competition, endogenous variety, and free entry to show that, as in Richard E. Baldwin and Rikard Forslid (2004), total variety (domestic plus imported) can either increase, decrease, or remain constant with trade liberalization. More importantly, the gains from trade do not depend on what happens to total variety. In fact, we find that the real wage is ultimately dependent on the ratio of imports to total expenditure with an elasticity that is the same across a range of models. We will argue that, conditional on the estimated elasticities of trade with respect to trade costs, the implications of models with increasing returns, endogenous variety, free or restricted entry, and heterogeneity (or not) across firms have exactly the same implications for welfare gains from trade liberalization as traditional models. 2 In our view,