Mathematics for Economists

Dynamic programming

In this case the value of the goal function is

r

w

k+ 1 +

s

k



w

w

k+ 1



=

r

w

k+ 1 +

s

k



w(k+ (^1) )w
k+ 1



=

=

r

w

k+ 1 +

s

k^2 w

k+ 1 =(^1 +k)

r

w

k+ 1 =

p

1 +k

p

w.

But we should also checkc=0 andc=w.Ifc=0 then

p

kw<

p

1 +k

p

w,

ifc=w then p

w<

p

1 +k

p

w

so

VT 1 (w)=

p

1 +k

p

w