On the Existence of Non-Negative Solution to the Cauchy Problem in Dynamic Economic Models

Abstract

The paper is devoted to the study of dynamic models of economic processes, which are described by systems of linear differential equations for the existence of a non-negative solution to the Cauchy problem on a segment under the condition of non-negativity of the initial condition. The Leontief model of intersectoral balance, as well as the Evans-Samuelson model of a market economy, were studied. The conditions under which the Cauchy problem has a non-negative solution on the interval [0,T] are obtained.