The "Saddlepoint Property" and the Structure of Dynamic Heterogeneous Capital Good Models

Abstract

The topological properties of dynamic heterogeneous capital good models are examined, and it is found that the savings hypothesis crucially influences the dimension of the manifold consisting of the locus of backward solutions from stationary equilibrium. If not all capital gains are saved, the convergent manifold is generally of higher dimension than it is if no income from capital gains is spent on consumption. Accordingly, the characteristic equation for the associated linear system near stationary equilibrium may have more than half its roots with negative real parts, and thus in general the model does not possess a "regular saddlepoint property."