14A small technicality: Absolute prudence of value functions is infinite at kink points in the consumption function, so if both c(w)  and ˆc(w)  had a kink point at exactly the same w  , the comparison of prudence would not yield a well-defined answer. Under these circumstances we will say that  ˆ
A (w ) ≥ A (w )  if the decline in the MPC is greater for ˆc(w)  at w  than for c(w)  .