Mathematics for Economists

Production saving model

We can get the same equation with dynamic programing. By the Bellman

equation

Vt(kt) = max

ct 2 [ 0 ,kt]

βtU(ct)+Vt+ 1 (kt+ 1 )

=

= max

ct 2 [ 0 ,kt]

βtU(ct)+Vt+ 1 (f(kt)ct)

VT+ 1 = 0.

Assuming that no corner solution appears derivation by the control

parameterctby Fermatís principle

βtU^0 (ct)+Vt^0 + 1 (f(kt)ct)( 1 )= 0 ,

βtU^0 (ct)=Vt^0 + 1 (f(kt)ct)=Vt^0 + 1 (kt+ 1 ).