Mathematics of the Armington, Krugman and Melitz Models with Multiple Sectors and Heterogeneous Regions, with Detailed Derivations

Edward J. Balistreri, David G Tarr
November 2019  [19-WP 596]

In Balistreri and Tarr (2018), we numerically assess the relative welfare impacts of trade cost reductions in models based on Armington (1969), Krugman (1980) and Melitz (2003). In order to be able to apply these models to data, Balistreri and Tarr (2018) consider extended or general versions of these models to include: intermediates with data-based shares of inputs, labor-leisure choice, heterogeneous regions based on data, initial heterogeneous tariffs as well as iceberg costs, multiple factors of production and the possibility of sector-specific inputs. In this paper we provide detailed derivations of the equilibrium conditions of these models. We hope these derivations will be a clear roadmap for understanding and constructing modern multi-sector, multi-region international trade models that must be fitted to data.

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