Minimizing the dependency ratio in a population with below-replacement fertility through immigration

Many industrialized countries face fertility rates below replacement level, combined with declining mortality especially in older ages. Consequently, the populations of these countries have started to age. One important indicator of age structures is the dependency ratio which is the ratio of the nonworking age population to the working age population. In this work we find the age-specific immigration profile that minimizes the dependency ratio in a stationary population with below-replacement fertility. It is assumed that the number of immigrants per age is limited. We consider two alternative policies. In the first one, we fix the total number of people who annually immigrate to a country. In the second one, we prescribe the size of the receiving country's population. For both cases we provide numerical results for the optimal immigration profile, for the resulting age structure of the population, as well as for the dependency ratio.