Production saving model
To calculateVt^0 + 1 (kt+ 1 )we want to use the envelope theorem. The
parametric goal function is
g(kt+ 1 ,ct+ 1 ) = βt+^1 U(ct+ 1 )+Vt+ 2 (kt+ 2 )=
= βt+^1 U(ct+ 1 )+Vt+ 2 (f(kt+ 1 ) ct+ 1 ).
In the second case di§erentiating by the state parameterkt+ 1
Vt^0 + 2 (f(kt+ 1 ) ct+ 1 )f^0 (kt+ 1 )
which is again hopeless as it expressesVt^0 + 1 withVt^0 + 2 , in the Örst case
kt+ 1 is not in the formula.