First-order risk aversion and non-differentiability

First-order risk aversion happens when the risk premium π a decision maker is willing to pay to avoid the lottery t·ε̃, E[ε̃] = 0, is proportional, for small t, to t. Equivalently, ∂π/∂t|_t=0+>0. We show that first-order risk aversion is equivalent to a certain non-differentiability of some of the local utility functions (Machina [7]).