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The Singular Value Decomposition of a Technology Matrix


  • Eric O'N. Fisher


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 Group Munich.
  • Handle: RePEc:ces:ceswps:_4566

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    References listed on IDEAS

    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.
    2. Ethier, Wilfred, 1974. "Some of the theorems of international trade with many goods and factors," Journal of International Economics, Elsevier, vol. 4(2), pages 199-206, May.
    3. Chang, Winston W. & Ethier, Wilfred J. & Kemp, Murray C., 1980. "The theorems of international trade with joint production," Journal of International Economics, Elsevier, vol. 10(3), pages 377-394, August.
    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, 1965. "The Structure of Simple General Equilibrium Models," Journal of Political Economy, University of Chicago Press, vol. 73, pages 557-557.
    6. John Romalis, 2004. "Factor Proportions and the Structure of Commodity Trade," American Economic Review, American Economic Association, vol. 94(1), pages 67-97, March.
    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.
    8. Harrigan, James, 1995. "Factor endowments and the international location of production: Econometric evidence for the OECD, 1970-1985," Journal of International Economics, Elsevier, vol. 39(1-2), pages 123-141, August.
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    More about this item


    singular value decomposition; international trade; Rybezynski; Stolper-Samuelson;

    JEL classification:

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

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