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

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  • Edward J. Balistreri
  • David G. Tarr

Abstract

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.

Suggested Citation

  • Edward J. Balistreri & David G. Tarr, 2019. "Mathematics of the Armington, Krugman and Melitz Models with Multiple Sectors and Heterogeneous Regions, with Detailed Derivations," Center for Agricultural and Rural Development (CARD) Publications 19-wp596, Center for Agricultural and Rural Development (CARD) at Iowa State University.
    • Handle: RePEc:ias:cpaper:19-wp596
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    References listed on IDEAS

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    1. Andrew B. Bernard & Jonathan Eaton & J. Bradford Jensen & Samuel Kortum, 2003. "Plants and Productivity in International Trade," American Economic Review, American Economic Association, vol. 93(4), pages 1268-1290, September.
    2. James Markusen & Thomas F. Rutherford & David Tarr, 2017. "Trade and direct investment in producer services and the domestic market for expertise," World Scientific Book Chapters, in: Trade Policies for Development and Transition, chapter 19, pages 439-458, World Scientific Publishing Co. Pte. Ltd..
    3. Krugman, Paul, 1980. "Scale Economies, Product Differentiation, and the Pattern of Trade," American Economic Review, American Economic Association, vol. 70(5), pages 950-959, December.
    4. Balistreri, Edward J. & Rutherford, Thomas F., 2013. "Computing General Equilibrium Theories of Monopolistic Competition and Heterogeneous Firms," Handbook of Computable General Equilibrium Modeling, in: Peter B. Dixon & Dale Jorgenson (ed.), Handbook of Computable General Equilibrium Modeling, edition 1, volume 1, chapter 0, pages 1513-1570, Elsevier.
    5. Costinot, Arnaud & Rodríguez-Clare, Andrés, 2014. "Trade Theory with Numbers: Quantifying the Consequences of Globalization," Handbook of International Economics, in: Gopinath, G. & Helpman, . & Rogoff, K. (ed.), Handbook of International Economics, edition 1, volume 4, chapter 0, pages 197-261, Elsevier.
    6. Marc J. Melitz, 2003. "The Impact of Trade on Intra-Industry Reallocations and Aggregate Industry Productivity," Econometrica, Econometric Society, vol. 71(6), pages 1695-1725, November.
    7. Robert C. Feenstra, 2010. "Measuring the gains from trade under monopolistic competition," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 43(1), pages 1-28, February.
    8. Balistreri, Edward J. & Hillberry, Russell H., 2007. "Structural estimation and the border puzzle," Journal of International Economics, Elsevier, vol. 72(2), pages 451-463, July.
    9. Balistreri,Edward Jay & Tarr,David G., 2018. "Comparison of Welfare Gains in the Armington, Krugman and Melitz Models : Insights from a Structural Gravity Approach," Policy Research Working Paper Series 8570, The World Bank.
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