ИСТИНА

A few resource allocation problems in a two-sector model with the Cobb–Douglas production function and different functional costs are considered. The planning horizon may be finite or infinite. A constructive description of the optimal solution is proposed in each case. The problems solution is based on the Pontryagin maximum principle. The optimal solution may have a singular arc. In all cases the correspondent singular arc is described by an analytical way. Moreover, the singular trajectory is the same in all problems. The optimality of an extreme solution is proved using the theorem on the sufficient optimality conditions in terms of constructions of the maximum principles. One of the studied problems with different production functions is open to biological interpretation under the model of balanced growth of plants within a given limited time span.