Foundation of the Small Open Economy Model with Product Differentiation

We derive a small open economy (SOE) as the limit of an economy as the number or size of its trading partners goes to infinity and trade costs also go to infinity. We obtain this limit in the Armington, Eaton-Kortum, Krugman, and Melitz models. In all cases, the trade of the SOE with the foreign countries approaches a finite limit, and the domestic expenditure share for the SOE approaches a limit that is not zero or unity. The foreign countries can be either infinitely many SOEs, or alternatively, one or many large countries with domestic expenditure shares that approach unity. We illustrate the usefulness of this framework by obtaining a formula for the optimal tariff in the SOE -- depending on the elasticity of domestic wages with respect to the tariff -- that is consistent with all models.