Looking for nonnegative solutions of a Leontief dynamic model Original Research Article

Let A be an n×n nonnegative real matrix. We know that A is Γ-monotone if it has a nonnegative Γ-inverse. Moreover if A has an appropriate generalized inverse, then we can obtain nonnegative solutions for the linear system Ax=b, where bgreater-or-equal, slanted0.In this paper, using properties about nonnegatives matrices, we present sufficient conditions in order that the Leontief price modelimage(I+F)p(k+1)=[1+r(k)]Fp(k)+Gp0(k+1)a0,where F=(I−AT)−1BT and G=(I−AT)−1, have nonnegative solutions.