Title
Necessity of the Transversality Condition for@Stochastic Models with CRRA Utility
Abstract
This paper shows that the standard transversality condition (STVC) is necessary
for optimality for stochastic models with constant-relative-risk-aversion
(CRRA) utility under general conditions. We consider an infinite-horizon
stochastic maximization problem that takes a general form of multi-sector
growth model with a single consumption good and CRRA utility. We
establish two results. The first result is that the STVC is necessary
in the case of logarithmic utility. The second result is that the
STVC is necessary in the case of non-logarithmic CRRA utility as long as
lifetime utility is finite at the optimum. These results apply to
various stochastic growth models, including real business cycle (RBC) models
with endogenous labor supply. Our results make it clear that there
is practically no issue about necessity of the STVC for stochastic models
with CRRA utility.
Takashi KAMIHIGASHI
Research Institute for Economics and Business
Administration
Kobe University
Rokkodai-cho, Nada-ku, Kobe
657-8501
Japan
Phone: (81) 78 803 7036
Fax:
(81) 78 803 7059