Published by: Oxford University Press

 

In recent notes 1 Terence Ryan and Kenneth Arrow present con- ditions on a utility function U for returns in X= [O,oo) and on a probability distribution over X, which imply that expected utility is finite without simultaneously requiring U to be bounded above. Ryan's comment was motivated by the fact that if expected utilities represent a preference relation on a suitably large set of probability distributions over X then U must be bounded, whereas some attrac- tive functional forms that might serve as utility functions on X are not bounded above.