This paper defines the concept of simple strategy and introduces three kinds of simple strategies: wealth-invariant, scale-invariant and "wealthier-accept more". For three commonly used utility function families: CARA, CRRA and DARA equivalent characterizations are obtained in terms of the corresponding simple strategy, in terms of the buying and selling price properties, and in terms of the utility function properties as expressed by Cauchy functional equations. Moreover, an extension of famous Pratt (1964) theorem is proved which involves buying price for a lottery as an alternative measure of comparative risk aversion. Additionally a number of propositions on both selling and buying price for a lottery and CRRA utility class are proved.