The “power-society-economy” model with a slightly corrupt discrete hierarchy

For the “power-society-economy” discrete chain model in the case of a slightly corrupt hierarchy the problem of finding the distribution of power, maximizing per capita consumption in steady state is considered. This problem reduces to finding the maximum of a nonlinear function of many variables with a small parameter and linear constraints. With the help of the asymptotic expansion of the objective function has constructed a linear programming problem to determine the terms of the asymptotic of the first order. The obtained extreme problems lead to an approximate stationary distribution of power maximizing per capita consumption. An illustrative example is given.