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

49 Pages Posted: 3 Feb 2020 Last revised: 17 Sep 2020

See all articles by Edward J. Balistreri

Edward J. Balistreri

Iowa State University

David G. Tarr

International Trade Analysis

Date Written: August 19, 2020

Abstract

We provide detailed textbook style mathematical derivations of an extended version of the heterogenous firms model of Melitz (2003), as well as the Armington (1969) and Krugman (1980) models. Our model of heterogeneous firms extends the model of Melitz (2003) by allowing multiple sectors, intermediates, heterogeneous regions based on data, labor-leisure choice, initial heterogeneous tariffs as well as iceberg trade costs, multiple factors of production and the possibility of sector-specific inputs. Balistreri and Tarr (2019) apply these models to data where they assess the relative welfare impacts of trade cost reductions. We hope this will be a clear roadmap for understanding and constructing modern multi-sector, multi-region international trade models that must be fitted to data.

Keywords: heterogeneous firms, heterogeneous regions, gains from the new trade theory, intermediates, labor-leisure choice

JEL Classification: F12, F13, C65, C68, D58

Suggested Citation

Balistreri, Edward J. and Tarr, David G., Mathematics of the Armington, Krugman and Melitz Models with Multiple Sectors and Heterogeneous Regions, With Detailed Derivations (August 19, 2020). Available at SSRN: https://ssrn.com/abstract=3517390 or http://dx.doi.org/10.2139/ssrn.3517390

Edward J. Balistreri

Iowa State University ( email )

260 Heady Hall
Ames, IA 50011
United States
3032531674 (Phone)

David G. Tarr (Contact Author)

International Trade Analysis ( email )

7901 Hispanola Avenue
Apt. 1102
North Bay Village, FL 33141
United States
5712242796 (Phone)

HOME PAGE: http://https://sites.google.com/site/davidgtarr/

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