Optimal immigration age-patterns in populations of fixed size

Due to a low birth rate many countries need immigration to sustain a given population size. The resulting model consists of specific non-standard age-structured control systems on an infinite horizon. This paper investigates the question of optimal choice of the immigration age-profile within certain bounds. The main qualitative result is that under certain conditions the optimal control (the immigration age-profile) is time-invariant, although a dynamic framework is used. This makes it possible to give a detailed description of the optimal immigration policy and to obtain numerical solutions for the Austrian case. The analysis requires a number of new results obtained in the paper: a new type of transversality condition for the adjoint equation involved in the optimality conditions, generic conditions for well-posedness of the problem and appropriate stability conditions.