This paper is concerned with the effect of increases in risk on optima
l decision variables. for the class of linear payoffs. We show that fo
r this class of payoffs one can extend the class of admissible increas
es in risk and obtain the desirable comparative statics properties. We
propose the definition of a ''relatively weak increase in risk'' and
apply it to the case of the competitive firm with constant marginal co
sts, the standard portfolio model and the coinsurance problem.