Intertemporal separability in overlapping-generations models

In a pure exchange overlapping-generations model with many goods, but a single consumer with preferences separable between two periods of life, there are (generically) finitely many equilibria in which money has no value. If money has value, then (generically) there is at most one dimension of indeterminacy. This property does not generalize to a model with many consumers and general preferences. It is shown why a separable representative consumer implies such strong conclusions. It is also shown that the absence of income effects leads to similar results.