H. Hayakawa et S. Ishizawa, THE FUNDAMENTAL PRINCIPLE OF INTERTEMPORAL OPTIMIZATION - CONSUMER-BEHAVIOR UNDER RECURSIVE PREFERENCES, Economics letters, 41(3), 1993, pp. 273-280
This paper shows that a simple principle, expressible by a single equa
tion, runs through intertemporal consumer behavior: the effect of any
given variations of consumption on the utility must be balanced agains
t the effect of such variations on subsequent stocks of assets. The fo
rmer is measured by the directional marginal utility and the latter by
the directional marginal value of assets; the implicit utility price
of assets, necessary to convert the latter into utility units, is then
determined in reference to the maximized value of the utility functio
nal. It is this equation that is implied by Pontryagin's maximum princ
iple.