The purpose of this paper is to investigate the relationship between the risk aversion function and the demand functions. Two hypotheses about risk aversion are studied: risk aversion independent of prices, and risk aversion constant on each indifference locus. The implications of these hypotheses for the utility and demand functions are then considered; in addition, the derivation of the risk aversion function from the demand functions is examined. The cases of constant (absolute and relative) risk aversion, and the problems raised by the choice of numeraire, are also dealt with.