The long-term impact of trade with firm heterogeneity

After the emergence and development of heterogeneous firm trade models, some (most notably Arkolakis, Costinot and Rodriguez-Clare 2012, ACR) have argue that a family of these models (e.g. a Melitz-type model with Pareto distributed firms) do not add to the evaluation of welfare effects of freer trade. In this paper we expand that model in two directions: we introduce a very simple growth mechanism and we allow for asymmetric countries. Introducing simple dynamics in the heterogeneous firm model adds new static and dynamic effects to the well-known decrease in prices that increases welfare in the static model. The constant level of nominal expenditure is affected as firm selection changes the average value of firms which modifies consumers' resource constraint. The growth rate of real consumption is also affected by firm selection since greater average efficiency means a larger amount of resources are required to create a new variety. Country asymmetry yields differentiated results between countries. We provide a welfare formula comparable to that in ACR to show how the new mechanisms can interplay in our model and highlight the effects of firm heterogeneity in this context. In all cases net welfare results depend on parameter values which highlights how much welfare evaluations depend on region's characteristics.