Children and teenagers in the world’s developed countries have a more than 50 per cent chance of living past 100. By the early 2100s, in other words, “being a centenarian will no longer be a rarity. In fact, it will be the norm”.

That from Lynda Gratton and Andrew Scott’s book, The 100-Year Life: Living and Working in an Age of Longevity, which has received well-deserved attention this summer for its thoughtfully optimistic take on careers and lives in a world full of old people.

Gratton and Scott’s core idea is that we will have to move on from the three-stage life of education, career and retirement to four and five-stage trajectories with multiple, if often related, careers of differing intensities — with time off for recharging and retraining in between, before finally easing into retirement in our late eighties.

The book can be a bit jargony in spots, but the concepts really do resonate.

I watched the movie Jason Bourne right after finishing it and kept thinking that the Central Intelligence Agency needed to be more open to Bourne using a “recharging or recreating transition” to prepare for a lower-intensity, post-assassin “portfolio stage”.

I also found myself getting legitimately excited about the careers I might yet have.

Still, it is hard to read the book, or just think about the consequences of 100-year lifespans, without some dread.

The most obvious worry is how to finance retirement. I have occasionally defended old-style pension plans as more efficient and fair than employee-managed replacements, but in the world that Gratton and Scott describe they really do not make much sense.

People trying to manage several career transitions are better off with an account that they can tap from time to time, then keep building up into their eighties, than a pension that kicks in at a preset age.

And pension systems that offer a guaranteed income from age 60 or 65, or even 70, are simply going to go broke without significant changes as 100-year-olds become the norm.

Which brings me to the other big worry: Gratton and Scott are both professors — she is a psychologist who teaches “management practice” and he is an economist — at the highly rated London Business School, and developed the ideas in the book while teaching them to students there; a pretty rarefied group. As Gratton and Scott put it:

“One of the audiences for whom this book was written are those who benefit from high levels of education and income, and possess some market power in the workplace with their employer and an array of choices and options.

“Not everyone will be so fortunate.”

Not to mention that those with high levels of education and income are much more likely to live past 100 than other folks. And while in most of the world such life-expectancy inequality is on the decline, in the United States it has been increasing since at least 2001.

So while raising the retirement age for pensions makes obvious sense as lifespans grow longer, it also obviously shortchanges those who do not live as long.

And while transitioning from career to career over six decades of working life sounds like great fun for London Business School graduates, less-educated workers in low-wage jobs may see it as switching from one form of drudgery to another — “the blight of endless work”, Gratton and Scott call it.

Even worse than endless work may be endless idleness, as technological and economic change wipes out certain job categories, and those who cannot find work sit at home watching television.

Gratton and Scott have some ideas for addressing these issues, mainly along the lines of governments should do something. Pension systems could be retained for those with low incomes even as they are dismantled for the rest. Investments in education and healthcare could reduce lifespan disparities. Income supplements could enable low-wage workers to slow down or to take time off for “recharging and recreating”.

But no, this is not going to be easy. All the challenges that rising economic inequality already poses for developed countries are just going to get more challenging as most people start living past 100.

•Justin Fox is a Bloomberg View columnist writing about business