The Method of Finding the Coefficients of a Dynamic Input-Output Model

In the paper a modification of the dynamic input-output model for a multibranch economics in the discrete and continuous forms is considered. Phase variables are annual production volumes in the branches of economics. The final product vector is divided into consumption and capital investments to the fixed assets of the branches. The latter depends on the production growth in respect to the previous period, which leads to difference equations. The main goal of the research is a comparative analysis of solutions of difference and differential equations with the same matrices. Besides, we determine the conditions on the system coefficients, which provide equality between the solutions of both systems in integer times. Under such conditions the algorithm is constructed to switch from discrete time model to continuous time model and back for any intervals of time in linear case.