InÖnite cake eating problem
Example
Solve the problem ifu(c)=lnc.
In this case we guess thatV(w)=A+Blnw.Hence
A+Blnw= max
s 2 [ 0 ,w]
(ln(w s)+β(A+Bln(s))).
The Örst order condition
1
w s( ^1 )+βB
1
s=^0
s+βB(w s)
(w s)s
= 0
βB(w s)=s
s= βB
1 +Bβ
w,)c(w)= w
1 +Bβ