The Singular Value Decomposition of a Technology Matrix - Eric O'N. Fisher (Center for Economic Studies and ifo Institute (CESifo), 2014)
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.
Keywords: F10; D50; 330; singular value decomposition; international trade; Rybezynski; Stolper-Samuelson