A modification of the approach to the analysis of the input-output balance is proposed. Instead of the assumption of V.V. Leontief on the constancy of the rates of costs of production factors, a more realistic assumption in modern conditions is used about the constancy of the proportions of intersectoral cash flows. An algorithm for solving the inverse problem is proposed, which allows us to identify a nonlinear input-output balance model with a utility function and Cobb-Douglas production functions according to the data from a symmetric input-output table. Based on the use of the Young transform and Fenchel duality, a technology is developed for analyzing intersectoral relationships using this model. The technology is tested on data from Russian economic statistics.
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