An optimization model of the economic growth under presence of structural changes

Abstract

The paper investigates economic growth models with non-smooth production functions. The non-smoothness of a production function can be caused, for example, by structural changes in the economy of a region (or a country). Another possible reason is the self-adjustment property of the model, which implies that estimated parameters of the production function may change after the econometric analysis conducted for statistical data augmented with data of new periods. Application of the Pontryagin maximum principle leads to analysis of the Hamiltonian system that includes derivatives of the production function, therefore, the smoothness property of the production function is important for this application. The paper proposes the technique that makes the production function differentiable and, under some additional assumptions, does not affect the qualitative behavior of optimal solutions. Theoretical results are supported by the numerical example.