Mathematics for Economists

Production saving model

Again we rewrite the value function and introduce a new control

parameterkt+ 2 =f(kt+ 1 )ct+ 1

Vt+ 1 (kt+ 1 ) = c max

t+ 12 [^0 ,kt+ 1 ]

βt+^1 U(ct+ 1 )+Vt+ 2 (kt+ 2 )

=

= max

kt+ 22 [ 0 ,f(kt+ 1 )]

βt+^1 U(f(kt+ 1 )kt+ 2 )+Vt+ 2 (kt+ 2 )

Di§erentiating the parametric goal function by the parameterkt+ 1 the

second termís derivative is zero

Vt^0 + 1 (kt+ 1 )=βt+^1 U^0 (f(kt+ 1 )kt+ 2 )f^0 (kt+ 1 ).