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Looking for nonnegative solutions of a Leontief dynamic model

Authors
Journal
Linear Algebra and its Applications
0024-3795
Publisher
Elsevier
Publication Date
Volume
364
Identifiers
DOI: 10.1016/s0024-3795(02)00569-4

Abstract

Abstract 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 b⩾0.In this paper, using properties about nonnegatives matrices, we present sufficient conditions in order that the Leontief price model (I+F)p(k+1)=[1+r(k)]Fp(k)+Gp 0(k+1)a 0, where F=( I− A T) −1 B T and G=( I− A T) −1, have nonnegative solutions.

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