Mathematics for Economists

InÖnite cake eating problem

By the Bellman equation

V(w) = max

c 2 [ 0 ,w]

(u(c)+βV(wc))=

= max

s 2 [ 0 ,w]

(u(ws)+βV(s)).

The condition on optimality is

u^0 (c)=βV^0 (wc)

or

u^0 (ws)=βV^0 (s).

How we can calculateV^0 (u)?