Saddlepoint Stability and a Regular Economy: An Example

Abstract

Unlike theoretical physics and other physical sciences, many problems in economic theory are not subject to eventual empirical verification, and much of modern economic theory is totally abstract and void of even simple numerical examples. Perhaps this fact reflects the pedestrian nature of concrete examples. Yet sometimes it is important to make certain that sufficient conditions for a theorem, do not leave us with vacuous results. The technology analyzed in this paper provides definitive examples for two separate economic problems: (1) the question of the asymptotic or turnpike of an optimally controlled economy, and (2) the question of excluding the paradoxical consumption behavior known to exist from the literature associated with the Cambridge controversy in capital theory. With regard to (1), we calculate the characteristic roots of the linearization around