Matematicheskoe modelirovanie optimal'nogo planirovaniya ekonomiki s uchetom nalogov s pomoshch'yu prikladnogo vychislitel'nogo paketa Maple

We consider a particular issue of optimal economic planning based on models of intersectoral balance which taxes are additionally introduced as one of the controlling factors. The analysis of describing applications of optimal control methods in economics for various models, as well as an overview of applied software for the development of economic and mathematical models and calculations. The mathematical apparatus used in solving the problem is considered in detail, the formulation of the modeling problem and the rules for calculating the mathematical model using the applied package of numerical and symbolic modeling Maple are described. The mathematical model of the macroeconomic system optimal planning as an optimal task for speed is given, the mathematical apparatus of the optimality conditions is highlighted, the dependence of the planning results on the influence of the taxation factor is established. The degree of economy optimization at its fastest transition from one state and its dependence on certain combinations in the combination of control functions, such as total costs, capital intensity, consumption functions, the amount of taxes collected and production capacity, etc., are investigated.