Implicitly additive utility and the nature of optimal economic growth

The solution of an optimization problem frequently depends only on the constraint set and on the indifference set through the optimum. This observation is spelled out and applied to the problem of optimal economic growth. The validity of the turnpike property of optimal growth plans is investigated when the intertemporal utility function is not additive, but has the property that each of its indifference sets is also an indifference set for some other utility function which is additive and has a constant rate of discount. A characterization is provided for such utility functions, which are called implicitly additive.