Solution of the problem of optimal consumption and saving based on the maximum principle

The article deals with the problem of optimal control associated with the search for a consumption strategy in order to obtain the maximum total utility adjusted for inflation. Solution of the problem of saving optimization is carried out within the maximum principle for power and logarithmic utility functions of consumption. The problem under consideration admits an analytical solution depending on the relations between the parameters of a model. As a result, we have obtained optimal consumption programs (cash outflow) in terms of maximizing the utility functionality. The article describes the evolution of capital depending on the parameters of growth and inflation. We note that for the logarithmic utility fonction the optimal consumption for subjects with a low monetary resource contains zero segments (periods of "starvation") at the initial or final part of the planning interval.