Mathematics for Economists

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(ws)+β(A+Bln(s))).

The Örst order condition

1

ws(^1 )+βB

1

s=^0

s+βB(ws)

(ws)s

= 0

βB(ws)=s

s= βB

1 +Bβ

w,)c(w)= w

1 +Bβ