Age structured optimal control : an application to optimal human capital investment

Abstract

In this thesis we analyse macro level optimal control models concerning education policies. The individuals in the economy thereby are allowed to differ in age and skill, with age as a continuous variable and the skill level being influenced by the education, which the individuals receive. Using this framework we derive the social optimal age specific education rates and their development over time. We further examine the effects of combinations of different education types, the influence of demographic changes and the impact of varying production technologies represented by different elasticities of substitution and productivities of the workers. Our analysis shows, that a growing or decreasing population has a significant impact on the optimal education policies if workers are not perfectly substitutable. We also derive that the optimal age specific education rates strongly depend not only on the costs of different education types, but also on the productivities of workers of different skill levels. Further we introduce a more detailed educational structure and additional possibilities to upgrade skills. Our results indicate that under specific parameter constellations it is optimal to also utilize these augmented policy options.