Studying a Modified Ramsey Model with Variable Production Flexibility

摘要

A one-dimensional nonlinear problem of optimal control on an infinite planning horizon is considered that is a modification of Ramsey's model for endogenous economic growth with the Cobb-Douglas production function. The model is innovative in its consideration of variable production flexibility, a parameter of the Cobb-Douglas function. As the first step in the study, the problem is considered for piecewise-smooth and piecewise-constant flexibility functions. Optimal solutions are constructed on the basis of a special integral representation of the functional and are unique for each type of flexibility function. The optimal solutions include singular modes. The final results can be used to estimate the effect of uncertainty in a Ramsey problem with constant parameters.