Standard Work on cost-of-living indexes uses nonstochastic price. Baye (1985) and Reinsdorf (1994a), however, describe Konus indexes that allow prices to be random. However, when the utility level is determined by an indirect utility function, these indexes may violate an identity axiom and allow utility to increase when the cost-of-living index increases. As an alternative, a new Konus index is described that does not violate the above-mentioned identity axiom and ranks price regimes in the opposite order as indirect utility functions. In addition, it provides a natural way to introduce risk aversion into cost-of-living indexes.