Production saving model
βt ^1 U^0 (ct 1 ) = βtU^0 (ct)f^0 (kt)
U^0 (ct 1 ) = βU^0 (ct)f^0 (kt)
U^0 (f(kt 1 ) kt) = βU^0 (f(kt) kt+ 1 )f^0 (kt)
βt ^1 U^0 (ct 1 ) = βtU^0 (ct)f^0 (kt)
U^0 (ct 1 ) = βU^0 (ct)f^0 (kt)
U^0 (f(kt 1 ) kt) = βU^0 (f(kt) kt+ 1 )f^0 (kt)