Does international trade produce convergence?

In spite of increasing globalization around the world, the effects of international trade on economic growth are not very clear. I consider an endogenous economic growth model in an open economy with the Home Market Effect (HME) and non-homothetic preferences in order to identify some determinants of the different results in this relationship. The model shows how trade between similar countries leads to convergence in economic growth when knowledge spillovers are present, while trade between very asymmetric countries produces divergence and may become trade in a poverty or growth trap. The results for welfare move in the same direction as economic growth since convergence implies increases in welfare for both countries, while divergence leads to increases in welfare for the largest country and the opposite for its commercial partner in the absence of knowledge spillovers. International trade does not implicate greater welfare as is usual in a static context under CES preferences.