Income and Substitution Effects of Increases in Risk when Payoffs are Linear in the Random Variable

Abstract

Payoff functions that are linear in the random variable arise in a wide variety of decision models under uncertainty. The decomposition of the effect of increased risk on decisions into income and substitution terms for such models has received much attention in the literature. This paper provides a Hicks-Slutsky decomposition of the effect of Rothschild-Stiglitz increases in risk on the optimal decision. Two measures of aversion to additional risk are introduced. Their behavior is shown to control the signs of the income and substitution effects.