The "Saddlepoint Property" and the Structure of Dynamic Heterogeneous Capital Good Models
Date
1973-01
Authors
Burmeister, Edwin
Caton, Christopher
Dobell, Rod
Ross, Stephen
Journal Title
Journal ISSN
Volume Title
Publisher
The Econometric Society
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."
Description
An
earlier
version
of
this
paper
was
presented
at
the
Second
World
Congress
of
the
Econometric
Society,
Cambridge,
England,
September
8-14,
1970.
Keywords
butterfly theorem, dual stability, complex systems, optimization, asset pricing, saddlepoint property, heterogeneous capital good models
Citation
Burmeister, E. et al. Econometrica, Vol. 41, No. 1 (Jan., 1973), pp. 79-95