Dynamic programming

3. It gives us the induction hypothesis:

VTt =

p

1 +k+k^2 +.. .+kt

p

w

σTt =

w

1 +k+k^2 +.. .+kt

The only thing we should show is to prove this hypothesis:

VT(t+ (^1) )(w)= max
c 2 [ 0 ,w]
p
c+VTt(k(wc))

= max
c 2 [ 0 ,w]
p
c+
p
1 +k+k^2 +.. .+kt
q
k(wc)



.