On the Economic Interpretation of Imprimitive Leontiev-vonNeumann-Sraffa Matrices: Cyclical Input-Output Relationships
AbstractStarting 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.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoPaper provided by Department of Economics, University of Siena in its series Department of Economics University of Siena with number 475.
Date of creation: Mar 2006
Date of revision:
Find related papers by 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
This paper has been announced in the following NEP Reports:
- NEP-ALL-2006-04-01 (All new papers)
You can help add them by filling out this form.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Fabrizio Becatti).
If references are entirely missing, you can add them using this form.