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The Singular Value Decomposition of a Technology Matrix

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  • Eric O'N. Fisher

Abstract

This paper is the first application of the singular value decomposition in general equilibrium theory. Every technology matrix can be decomposed into three parts: (1) a definition of composite commodities; (2) a definition of composite factors; and (3) a simple map of composite factor prices into composite goods prices. This technique gives an orthogonal decomposition of the price space into two complementary subspaces: (1) vectors that generate the price cone; and (2) a basis that describe the flats on the production possibility frontier. This decomposition can be used easily to compute Rybczynski effects.

Suggested Citation

  • Eric O'N. Fisher, 2014. "The Singular Value Decomposition of a Technology Matrix," CESifo Working Paper Series 4566, CESifo.
    • Handle: RePEc:ces:ceswps:_4566
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    References listed on IDEAS

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    1. Kleibergen, Frank & Paap, Richard, 2006. "Generalized reduced rank tests using the singular value decomposition," Journal of Econometrics, Elsevier, vol. 133(1), pages 97-126, July.
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    4. Georg Schaur & Chong Xiang & Anya Savikhin, 2008. "Factor Uses and the Pattern of Specialization," Review of International Economics, Wiley Blackwell, vol. 16(2), pages 368-382, May.
    5. Ronald W. Jones, 2018. "The Structure of Simple General Equilibrium Models," World Scientific Book Chapters, in: International Trade Theory and Competitive Models Features, Values, and Criticisms, chapter 4, pages 61-84, World Scientific Publishing Co. Pte. Ltd..
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    7. Ethier, Wilfred J., 1984. "Higher dimensional issues in trade theory," Handbook of International Economics, in: R. W. Jones & P. B. Kenen (ed.), Handbook of International Economics, edition 1, volume 1, chapter 3, pages 131-184, Elsevier.
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    More about this item

    Keywords

    singular value decomposition; international trade; Rybezynski; Stolper-Samuelson;
    All these keywords.

    JEL classification:

    • F10 - International Economics - - Trade - - - General
    • D50 - Microeconomics - - General Equilibrium and Disequilibrium - - - General

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