Mathematics for Economists

Production saving model

Hence

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

Hence

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

which is the same Euler equation for the production saving model.