A general analytical model of materials flow analysis (MFA) incorporating physical waste input-output is proposed that is fully consistent with the mass balance principle. Exploiting the triangular nature of the matrix of input coefficients, which is obtained by rearranging the ordering of sectors according to degrees of fabrication, the material composition matrix is derived, which gives the material composition of products. A formal mathematical definition of materials (or the objects, the flow of which is to be accounted for by MFA) is also introduced, which excludes the occurrence of double accounting in economy-wide MFAs involving diverse inputs. By using the model, monetary input-output (IO) tables can easily be converted into a physical material flow account (or physical input-output tables [PIOT]) of an arbitrary number of materials, and the material composition of a product can be decomposed into its input origin. The first point represents substantial saving in the otherwise prohibitive cost that is associated with independent compilation of PIOT. The proposed methodology is applied to Japanese IO data for the flow of 11 base metals and their scrap (available as e-supplement on the JIE Web site).
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