Production saving model

We can also consider the problem as a KuhnñTucker problem

T

∑

t= 0

βtU(ct)! max

ct+kt+ 1 f(kt)  0 ,

ct,kt  0

If we assume that ifx>0 thenf(x)>0 then Slaterís condition holds

The Lagrange function is

L =

T

∑

t= 0

βtU(ct)+∑

t

λt(ct+kt+ 1 f(kt))

∑

t

μtct∑

t

νtkt.