It is hard to imagine a more important and difficult economic challenge than to define a policy that would shape society's welfare in an optimal way, both for the present day and for our future generations. This is precisely the challenge that Frank Ramsey took up nearly a century ago when he asked the question: “How much should a nation save?” In trying to answer it, he founded the theory of optimal growth.

It turns out that neither Ramsey nor subsequent theorists came up with a reasonable, convincing answer to that famous question. Ramsey's disappointment is palpable when the answer he reached – an “optimal” savings rate equal to 60% – was, in his own words “greatly in excess of that which anyone would suggest”, adding that the utility function he used was “put forward merely as an illustration”. Subsequent essays either remained in the realm of theory or produced the strangest results: some authors gave short shrift to excessive savings rates or, when they worried about those, they had recourse to utility functions that would hardly be recognizable by anybody, and even less by a whole society; or they resorted to changing the values and the very significance of the parameters they used. Despite such bold moves, they could never prevent at least one central variable of the economy from taking a time path that was never observed historically or that was simply unacceptable.

Until now, the main problem was to define a model that would lead to reasonable trajectories for all central variables of the economy: not only the savings rate, but the marginal productivity of capital, the growth rate of income per person or the capital–output ratio, to name a few.

In the first edition of this book, we started unveiling the reason for the failure of the theory to yield consistent, sensible results: we showed that it hinged on the systematic use of a strictly concave utility function. This second edition will show that whenever we try to modify the utility function to obtain a more acceptable savings rate, we inevitably induce trajectories for other central variables of the economy that either do not fit with the capabilities of the economy or are inconceivable.