Mathematics for Economists

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.