A novel approach to stochastic input-output modeling

An approach to input-output modeling is proposed in which the inner consumption and the final demand are random. The main aspects of its novelty are: (a) the economy is allowed to be nonproductive with a certain probability K is an element of [0,1); (b) the economy can be open, which means that import of the corresponding commodities is included in the model. In this approach, the production-and-import plan is set to be feasible if the probability of not satisfying the final demand does not exceed a certain value alpha is an element of (0,1). Then the problem of finding optimal plans consists in minimizing the production and import costs on the set of feasible plans. The solvability of this problem and properties of the solutions are studied and a concrete example of the stochastic input-output model is analyzed.