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.