Modely vzniku a eliminace ekonomických regionálních disparit jako úlohy optimálního řízení

The paper deals with two issues related to the existence of regions and their economic development. While the first problem concerns the issue of the possible emergence of regional disparities, the second one solves the contrary, the possibility of reducing the existing regional disparities. Regional disparities are understood quite narrowly in this paper, covering just the area of the difference between the economic productivity of the regions. It is known that the objective of regional policy is the regional development aimed at increasingthe cohesion of regions and their competitiveness. As will be shown in the first model it is more efficient to allocate investment and concentrate economic activity in those regions that have higher productivity. In this way, regions with lower productivity may get behind those regions that have higher productivity. These regions will then become less competitive and in order to maintain cohesion of regions it would be useful to make some redistribution of income between more productive and less productive regions. To the possible differences in productivity between regions the government directs investment in infrastructure to less developed regions. The aim of suchefforts is to improve the equipment of the population of the given region, to improve the technological level of the region and to strengthen the competitiveness of that region. This is the reason why the second mathematical model, described in this paper, deals with income redistribution and regional investments in their infrastructure. Both models are formulated as optimal control problems in continuous time and Pontryagin maximum principle is used to locate optimal solutions finally.