The microeconomics of new trade models

International trade can increase product market competition and hence be pro-competitive. Is this feature captured in new trade models? I study this question in a setting with firm heterogeneity à la Melitz, under any productivity distribution and standard demands (e.g., demands from an additively separable utility, linear, translog, logit). My results indicate that better export opportunities are pro-competitive: they reduce the domestic firms' markups and induce the exit of the least productive domestic firms. But, surprisingly, tougher import competition is completely offset by a reduction in the mass of domestic incumbents, leaving the competitive environment unaffected. Thus, it does not impact the prices, quantities, or survival productivity cut-off of domestic firms. Consistent with previous studies, I also find that a reduction in import trade costs under two large countries and two-way trade always decreases competition. I show that this outcome can be rationalized as capturing worse export conditions exclusively.