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.
We derive a new formula for the optimal uniform tariff in a small-country, heterogeneous-firm model with roundabout production and a nontraded good. Tariffs are applied on imported intermediate inputs. First-best policy requires that markups on domestic intermediate inputs are offset by subsidies. In a second-best setting where such subsidies are not used, roundabout production and the monopoly distortion in the traded sector create strong incentives to lower the optimal tariff on imported inputs. In a quantitative version of our two-sector small open economy, we find that the optimal tariff is lowered under nearly all parameter values considered, and can be negative.