Optimal control of a nonlinear model of economic growth

A nonlinear control model of a flrm describing the change of pro- duction and accumulated R&D investment is investigated. An optimal control problem with R&D investment rate as a control parameter is solved. Optimal dynamics of economic growth of a flrm versus the current cost of innovation is studied. It is analytically determined that dependent on the model parameters, the optimal control must be of one of the following types : a) piecewise con- stant with at most two switchings, b) piecewise constant with two switching and containing a singular arc. The intervals on which switching from regu- lar to singular arcs occur are found numerically. Finally, optimal investment strategies and production activities are compared with econometric data of an actual flrm.