There is a large and rapidly growing empirical literature that has documented that a reduction in international trade costs can have a substantial impact on individual firms decisions to produce, export, and engage in research and development to improve the cost or quality of existing products. Motivated by these observations, we build a simple general equilibrium model of these decisions, and we use this model to examine the question: do considerations of the impact of a reduction in trade costs on heterogeneous firms decisions to produce, export, and innovate, lead to new answers to the macroeconomic question of the impact of a reduction in trade costs on aggregate productivity and welfare? Our answer is largely, no.
For the last several decades, research in international trade has modeled comparative advantage as an attribute of the firm. We follow this approach, and model firms as producing differentiated products that are traded subject to both a fixed and a marginal cost of exporting. Our model of innovation builds on Grilichesm(1979) knowledge capital model of firm productivity. Each firm has a stock of a firm specific factor that determines its current profit opportunities. Our model includes two forms of innovation: innovation to increase the stock of this firm specific factor in an existing firm q process innovation, and innovation to create new firms with a new initial stock of the firm specific factor q product innovation.