Deriving the Armington, Krugman and Melitz models of trade

This paper shows how the Armington, Krugman and Melitz models of international trade are all specialized versions of a basic model. It is inspired by Balistreri and Rutherford (2012) who set out stylized versions of three models: Armington (1969); Krugman (1980); and Melitz (2003). In their exposition, Balsitreri and Rutherford develop each model separately. This paper draws out connections between the three models by developing them sequentially as special cases of a common basic model. We derive the Armington model by imposing strong assumptions on the basic model. We relax some of these assumptions to derive the Krugman model and make further relaxations to derive the Melitz model.