Production saving model

AssT =kT+ 1 /f(kT)= 0 ,

sT 1 = αβ

1 +αβ

which implies with backward induction that

sT 2 = αβ

1 +αβ 1 +αβαβ

= αβ(^1 +αβ)

1 +αβ+αβ( 1 +αβ)αβ

=

= αβ+(αβ)

2

1 +αβ+(αβ)^2

sTt =

t

∑

s= 1

(αβ)s

1 +

t

∑

s= 1

(αβ)s