Toward exploring the location-scale condition: a constant relative risk aversion location-scale objective function

Abstract

A constant relative risk aversion (CRRA) location-scale function is derived, analysed, and demonstrated for modelling choice under uncertainty. The function contributes to further exploration of the location-scale condition in agricultural economics risk research. Such analysis has been infrequent in recent research because the well-known linear mean-variance function implicitly assumes constant absolute risk aversion (CARA). Examples demonstrate that the CARA meanvariance function produces substantially different results than the CRRA locationscale function. Further, the CRRA location-scale function produces results similar to direct expected utility maximisation with a CRRA utility function and normally distributed returns.