Input-output models, directed graphs and flows in networks

Abstract

This article demonstrates that a dual pair of input-output price and quantity models, taken together, constitutes a composite network flow model. The network flow model has become a dominant analytical tool within the fields of operations analysis and electrical engineering, and the aim of the article is to enable input-output users within non-standard applications to take advantage of the large body of literature within these disciplines. Through a simple example it is shown that the solution of a dual pair of input-output models is a special case of the general problem of finding a minimum cost circulation in a transportation network. Second, it is shown that the common method of determining quantities and prices in input-output models is identical to the classical node method for determination of currents and voltages in an electrical network. The theory of transportation networks offers well developed methods for analysis of capacity constraints on the network flows, while the theory of electrical networks supplies methods for analysis of models with price sensitivities and for dynamic analysis. In addition, the elegant symmetry of currents and voltages in electrical networks contributes significantly to a better understanding of the logical relationship between price and quantity models.