Systems of Benevolent Utility Interdependence

Abstract

This paper concerns the logic of benevolently related utility functions. A paradox of 'superbenevolence' is examined and defanged. For a finite set of benevolent consumers, the theory of cominant diagnoal matrices is shown to be a powerful tool for the study of 'normal' benevolence. To treat intergenerational benevolence properly, the standard theory of dominant diagonal matrices has to be extended to denumerably infinite dominant diagonal matrices. We show that there is a nice extension that exactly serves our purposes. These results make it possible to generalize and clarify the results of Robert Barro and Miles Kimball on familial altruism. Questions of cardinality and uniqueness of representation are also resolved. Finally, some additional light is thrown on the problem of forward and backward intertemporal consistency which was discussed by Robert Pollak, John Burbridge and others.