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Singular value decomposition of a technology matrix
Author(s) -
Fisher Eric O'N.
Publication year - 2014
Publication title -
international journal of economic theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.351
H-Index - 11
eISSN - 1742-7363
pISSN - 1742-7355
DOI - 10.1111/ijet.12026
Subject(s) - singular value decomposition , linear subspace , decomposition , matrix (chemical analysis) , basis (linear algebra) , mathematics , space (punctuation) , simple (philosophy) , value (mathematics) , matrix decomposition , mathematical optimization , computer science , pure mathematics , algorithm , statistics , geometry , eigenvalues and eigenvectors , physics , ecology , philosophy , materials science , epistemology , quantum mechanics , composite material , biology , operating system
This paper is the first application of the singular value decomposition (SVD) in general equilibrium theory. Every technology matrix can be decomposed into three parts: a definition of composite commodities; a definition of composite factors; and 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: vectors that generate the price cone; and a basis that describe the flats on the production possibility frontier. This decomposition can be used easily to compute Rybczynski effects.