InÖnite cake eating problem
By the Bellman equation
V(w) = max
c 2 [ 0 ,w]
(u(c)+βV(w c))=
= max
s 2 [ 0 ,w]
(u(w s)+βV(s)).
The condition on optimality is
u^0 (c)=βV^0 (w c)
or
u^0 (w s)=βV^0 (s).
How we can calculateV^0 (u)?
By the Bellman equation
V(w) = max
c 2 [ 0 ,w]
(u(c)+βV(w c))=
= max
s 2 [ 0 ,w]
(u(w s)+βV(s)).
The condition on optimality is
u^0 (c)=βV^0 (w c)
or
u^0 (w s)=βV^0 (s).
How we can calculateV^0 (u)?