Von Neumann facets and the dynamic stability of perfect foresight equilibrium paths in neo-classical trade models
The author analyses the stability properties of a perfect foresight equilibrium path in time-phased trade models with neo-classical production functions. The model covers a finite number of countries and goods, the latter distinguished between produced and primary goods. Some of the produced goods are traded internationally, the other goods are non-tradeable. Production functions are of neoclassical type and both produced and primary goods are used as inputs. There is a representative consumer in each country maximising his discounted utility sum. In such a general framework it turns out that von Neumann facets may not be trivial. In a first step it is shown that, under standard assumptions, the input coefficients, consumption activities, and prices on a perfect foresight equilibrium path are Lyapunov stable and can be approximated by their stationary values. This result does not necessarily hold for production activities and the capital stock. Secondly, conditions for trivial von Neumann facets are examined. It appears that the exclusion of constant returns to scale or independence of technologies is not a necessary condition to ensure triviality, in which case the modified golden rule state is Lyapunov stable, too. Under stronger assumptions concerning the curvature of the utility function and the input coefficient functions even asymptotic stability is shown. Finally, the case of non-trivial von Neumann facets is analyzed and conditions for both Lyapunov and asymptotic stability of the perfect foresight equilibrium path are imposed on technologies and utility functions.
scientific article; zbMATH DE number 4130151
scientific article