¹²A small technicality: Absolute prudence of value functions is inﬁnite at kink points in the consumption function, so if both $c(m)$ and $ˆc(m )$ had a kink point at exactly the same $m$ , the comparison of prudence would not yield a well-deﬁned answer. Under these circumstances we will say that $Aˆ(m ) ≥ A (m )$ if the decline in the MPC is greater for $ˆc(m )$ at $m$ than for $c(m )$ .