A Harrod modell strukturális stabilitása (Structural stability of the Harrod model)

In this study it is shown that the nontrivial hyperbolic fixed point of a nonlinear dynamical system, which is formulated by means of the adaptive expectations, corresponds to the unstable equilibrium of Harrod. We prove that this nonlinear dynamical (in the sense of Harrod) model is structurally stable under suitable economic conditions. In the case of structural stability, small changes of the functions (C1-perturbations of the vector field) describing the expected and the true time variation of the capital coefficients do not influence the qualitative properties of the endogenous variables, that is, although the trajectories may slightly change, their structure is the same as that of the unperturbed one, and therefore these models are suitable for long-time predictions. In this situation the critique of Lucas or Engel is not valid. There is no topological conjugacy between the perturbed and unperturbed models; the change of the growth rate between two levels may require different times for the perturbed and unperturbed models.

Endogenous choice of decision variables

In this paper we allow the firms to choose their prices and quantities simultaneously. Quantities are produced in advance and their common sales price is determined by the market. Firms offer their “residual capacities” at their announced prices and the corresponding demand will be served to order. If all firms have small capacities, we obtain the Bertrand solution; while if at least one firm has a sufficiently large capacity, the Cournot outcome and a model of price leadership could emerge.