Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/327701 
Authors: 
Year of Publication: 
2025
Series/Report no.: 
CESifo Working Paper No. 12091
Publisher: 
Munich Society for the Promotion of Economic Research - CESifo GmbH, Munich
Abstract: 
Recursive utility functions are often defined implicitly, as the solution of a functional equation known as the Koopmans recursion. As conditions for a unique solution can be demanding, a recent literature has tackled the problem of multiplicity, advocating that one focus attention on either the least or greatest solution, which possess a number of attractive properties. While a least solution can be shown to exist, I show that in the most general formulation of the problem, a greatest solution need not. The goal of the paper is to provide a sufficient condition for the existence of a greatest solution, which I term the weakly contractive property and which generalizes the usual contractive property sufficient for uniqueness.
Subjects: 
recursive utility
greatest and lowest fixed point
contractions
JEL: 
C6
D9
Document Type: 
Working Paper
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