STOCHASTIC

TWO-PERIOD CONSUMPTION MODELS
AND PORTFOLIO REVISION
JOURNAL OF ECONOMIC THEORY 5, 308-335 (1972)
Consumption Decisions under Uncertainty*
JACQUES H. DREZE
Center for Operations Research and Econometrics,
Unirersite Catholiqite de Louvain, Louvain, Belgium
AND
FRANCO MODIGLIANI
Massachussets Institute of Technology, Cambridge, Massachusetts 02139
Received May 15, 1970
INTRODUCTION
This paper deals with three issues related to consumption decisions
under uncertainty, namely, (i) the determinants of risk aversion for future
consumption; (ii) the impact of uncertainty about future resources on
current consumption and (iii) the separability of consumption decisions
and portfolio choices. These issues are discussed in the context of a simple
model introduced, together with our assumptions, in Section 1. The first
issue is motivated and treated in Section 2, the conclusions of which are
summarized in Proposition 2.5. The other two issues are treated in Section
3 under the assumption that there exist perfect markets for risks,
and in Section 4 under the converse assumption.
Some technical results needed in the text are collected in Appendices A,
B and C; a simple graphical illustration of our major result, Theorem 3.3,
is given in Appendix D. 1
* The research underlying this paper was initiated while the authors were both
affiliated with the Graduate School of Industrial Administration, Carnegie-Mellon
University; the 6upport of that institution, and at a later stage of the Sloan School of
Management, Massachussets Institute of Technology, is gratefully acknowledged.
The authors also wish to thank Albert Ando and Ralph Beals for their helpful assistance
at an early stage of this work, as well as Louis Gevers, Agnar Sandmo and Joseph
Stiglitz for their critical reading of the final manuscript.
1 An earlier summary version of this paper, written in French, has appeared in the
Cahiers du Seminaire d'Econometrie [5].
Copyright © 1972 by Academic Press, Inc.
All rights of reproduction in any form reserved.
TWO-PERIOD CONSUMPTION MODELS AND PORTFOLIO REVISION 459