On Continuity of the Utility Function in Intertemporal Allocation Models: An Example.

A standard model of intertemporal allocation (described by a technology set and a welfare function defined on consumption) can be reduced to one described by a technology set and a utility function defined on this set. The authors present an example to show that even when the welfare function is concave, monotone, and continuous, the utility function can be discontinuous. They also provide sufficient conditions on the technology set and the welfare function under which the utility function is continuous. Their results indicate that the common practice of assuming continuity of the utility function is more restrictive than might be apparent. Copyright 1989 by Economics Department of the University of Pennsylvania and the Osaka University Institute of Social and Economic Research Association.