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 $c(w)$ .