FIRST-ORDER RISK-AVERSION AND NON-DIFFERENTIABILITY

First-order risk aversion happens when the risk premium pi a decision maker is willing to pay to avoid the lottery t .<(epsilon)over tilde>, E[<(epsilon)over tilde>] = 0, is proportional, for small t, to t. Equ ivalently, partial derivative pi/partial derivative t\(t=0+) > 0. We s how that first-order risk aversion is equivalent to a certain non-diff erentiability of some of the local utility functions (Machina [7]).