The open Leontiev–Ford model

This article deals with an open Leontiev–Ford model that describes a linear economics. It is assumed that this economics produces $m$ commodities and $n$ damages; under these assumptions the model is a underdetermined linear system of $m+n$ equations with $m+2n$ unknowns. The results of the article are the producity criterium, theorems about conditions under which the system can compensate the whole damage and theorems about conditions under which the final damage consists of a given part of the whole damage and so on. Formally, these results are theorems about the existence (for the system under consideration) of nonnegative solutions with special properties.