The fall in the savings rate observed in most OECD countries in recent years propounds the perennial question of optimal savings, and foremost the problem of defining an optimality criterion. For nearly eighty years – since Frank Ramsey's seminal contribution (1928) – the fundamental problem of optimal savings policy has been to find the time path of capital accumulation maximizing, over a finite or an infinite horizon, the sum of discounted utility flows pertaining to consumption.

The Ramsey problem was a problem in the theory of optimal growth; unfortunately however, it remained in the realm of theory. No serious attempt to compare an optimal strategy of investment to the amounts actually invested in a given nation was ever carried out. In our opinion, this is due to the fact that the optimal paths resulting from the differential equations governing the motion of the economy were simply inapplicable because they implied unrealistic policies, in particular exceedingly high savings rates.

We hold that a fundamental reason for such a lack of applicability of the traditional model is the use of an arbitrary utility function. However, the idea of introducing a concave utility function cannot be dismissed outright because it has considerable intuitive appeal. Indeed, one could well envision (as many writers did) a benevolent planner for whom adding one more unit to consumption when total consumption is low has more value for society than when total consumption is high, and who therefore would have a bias toward giving more consumption to poorer generations; hence, one could feel well justified to use a concave utility function. But the outcome of those models is, as we will see, exactly the contrary of what intuition would dictate. A few warning lights had been flashed in the sixties: in a two-sector model, Goodwin (1961) had obtained “optimal” savings rate in excess of 60%; and Stoléru (1970), in the only numerical solution of the Ramsey problem ever given, was led to savings rates in the order of 90%.