Leontief Model: How to Make the Economics Productive

The Leontief input-output model describes the inter-industry retationships with Linear a[gebraic toots. The productivity of economics is expressed in terms of the Perron eigenvalue of the consumption matrix. Suppose for each sector of economics, we have severaltypes of technotogies to organize production, We need to make a choice for each sector to make the whote economics productive. Mathematicatl.y, this is equivatent to minimizing the spectraI radius over a speciaI set of nonnegative matrices. This probtem is notoriuosty hard. Nevertheless, in most cases it can be efficientty sotved by the so-catted spectral simptex method Some interesting relations of this probtem to other areas of mathematics such as combinatorics and functionaI analysis wit[ atso be discussed.

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