Mathematics for Economists

Cake eating problem

The value function is

V 1 (w 1 ) = lnc 1 +βlnc 2 =ln

1

1 +βw^1 +βln

β

1 +βw^1 =

= ln^1

1 +β

+lnw 1 +βlnw 1 +βln β

1 +β

$

$ A 2 +B 2 lnw 1.