Proposition 6.C1: Suppose a decision-maker is an expected utility maximizer with a utility function u(o)on amounts of money-then the following properties are equivalent (1 the decision maker is risk averse (2)u(is concave (3)C(F, u)<xdF(x)for all F () (4)I(x,G,u)>0 for all X, e AWG Definition 6.C 3: Given a twice differentiable utility function u( ), the arrow pratt coefficient of absolute risk aversion at X is defined as rA(, u) u (X The coefficient of relative risk aversion isProposition 6.C.1: Suppose a decision-maker is an expected utility maximizer with a utility function u(.) on amounts of money– then the following properties are equivalent: (1) the decision maker is risk averse (2) u(.) is concave (3) c(F,u)  xdFx for all F(.) (4) x, ,u  0 for all x,  MWG Definition 6.C.3: Given a twice differentiable utility function u(.), the arrow pratt coefficient of absolute risk aversion at x is defined as rAx, u   ux u x The coefficient of relative risk aversion is x ux u x