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On the Economic Interpretation of Imprimitive Leontiev-vonNeumann-Sraffa Matrices: Cyclical Input-Output Relationships


  • Ennio Bilancini



Starting from the known results of Perron (1907) and Frobenius (1912) I apply graph theory to give an economically intuitive characterization of imprimitivity. Such property implies cyclical vertical relationships among groups of industries which, either directly or indirectly, use each others’ products as inputs. More precisely, if the index of imprimitivity is h, then industries may be sorted in h groups such that i) each group produces the inputs of one and only one other group and ii) there is no direct flow of commodities between industries of the same group. A sufficient condition for primitivity is provided which offers some reasons to expect non-basic industries to have more vertical cyclical flows than basic ones.

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  • Ennio Bilancini, 2006. "On the Economic Interpretation of Imprimitive Leontiev-vonNeumann-Sraffa Matrices: Cyclical Input-Output Relationships," Department of Economics University of Siena 475, Department of Economics, University of Siena.
  • Handle: RePEc:usi:wpaper:475

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    JEL classification:

    • C67 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Input-Output Models
    • L16 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Industrial Organization and Macroeconomics; Macroeconomic Industrial Structure

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