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Minimizing the Dependency Ratio in a Population with Below-Replacement Fertility through Immigrationтезисы доклада
- Авторы: Simon C., Feichtinger G., Belyakov A.O.
- Сборник: International Conference on Operations Research, August 30 to September 2, 2011
- Тезисы
- Год издания: 2011
- Место издания: ETH Zurich, Institute for Operations Research Zurich, Switzerland
- Аннотация: Many industrialized countries face fertility rates below the replacement level, combined with mortality decline, 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. A low dependency ratio indicates that there are proportionally more adults of working age that can support the young and old. In this paper we find the age-specific immigration pattern that minimizes the dependency ratio in a stationary population through immigration. We consider two different scenarios. First, we fix the total number of people who immigrate to the country. Alternatively, we prescribe the total size of the receiving country's population. For both cases we set up optimal control models and make use of Pontryagin’s maximum principle. We show that the optimal immigration profile in both setups is of bang-bang type switching from one age-specific limit for immigration to the other. For the first scenario we prove that additional to younger ages the optimal immigration profile also equals the age-specific upper bound for immigration for ages on every interval arbitrarily small and containing the upper age limit. The optimal solution of the second model formulation equals the upper bound for immigration on at the most two separate intervals to the left of the retirement age and is on the lower bound elsewhere. For either case we provide numerical results for the optimal immigration profile and for the resulting age-structure of the population, as well as for the dependency ratio.
- Добавил в систему: Беляков Антон Олегович