Mathematics for Economists

Cake eating problem

IfT=3 then by the Euler equations

1

c 1 =β

1

c 2 =β

21

c 3

and the resource equation is

c 1 +c 2 +c 3 =w 1

This implies that

c 1 =

w 1

1 +β+β^2

,c 2

βw 1

1 +β+β^2

,c 3 =

β^2 w 1

1 +β+β^2

The value function is

V 1 =lnc 1 +βlnc 2 +β^2 lnc 3 =A 3 +B 3 lnw 1.