Non-renewable resources in an open dynamic Leontief model

In this paper we study a generalisation of the dynamic Leontief input–output model. We extend the standard dynamic Leontief model with the balance equation of non-renewable resources. Obviously the non-renewable stocks will decrease exploiting primary resources. In this study we examine the controllability of this extended model taking the consumption as control parameter. We suppose a balanced growth path both for consumption and production, and we examine how long these scare resources will cover the inputs of production and how the lifetime of the system depends on the balanced growth rate and on the consumption, as well. To these investigations we use the classic results of the control theory and the eigenvalue problems of the linear algebra.