In the last two years, the phrase "10 billion" has come to stand for a supposed demographic crisis. In 2011, the UN projected that there will be 10 billion people living on the planet in 2100, and this has been perceived as unsustainable. In Britain, Stephen Emmott has come to be most closely associated with the figure because of the play he performed, or rather the vivid lecture he gave, at the Royal Court theatre, in London, last year. The Guardian's Michael Billington called it "one of the most disturbing evenings" he had ever spent in a theatre: "Emmott uses an array of statistics to reinforce his argument that the current global population of seven billion will grow to 10 billion, maybe more, by the end of the century … We are facing a crisis with ecosystems being destroyed, the atmosphere polluted, temperatures rising and a billion people facing water shortage." (Emmott's book expanding on the lecture is due next month.)

I regard the figure of 10 billion differently: it isn't simply an indication of crisis or, in Emmott's words "an unprecedented planetary emergency". It is even one of hope – because what it means is that the world's population is increasing more slowly than it used to.

Because of this slowdown, 10 billion is the most we can expect to ever be: there are not too many of us and there will not be too many of us. But there is another vital issue: what matters is planning for a world in which we are squeezing ever more tightly into cities and where – for a few generations – more will be old than are young.

What 10 billion actually represents is a slowdown in population growth rates to peak at that number. The slowdown began shortly after 1971. Quite why it began then no one knows. That year, worldwide, population grew by 2.1% in a single year, more than it ever had before and more than it ever would again.

One reason we are unsure why the slowdown began when it did is that hardly anyone was looking back then. It is only in the light of four decades of near continuous fertility decline that it has become clear when the turning point was. And the causes? We don't really know. In Europe and North America the postwar baby boom tailed off. In China the one-child policy had not yet started, so it wasn't that. Across much of the planet far better access to contraception was spreading, but quite why 1971 was the year that growth reached its peak we may never pin down. The population has carried on growing since then, but less each year than the year before – and the increase has been more the result of better health and fewer deaths than of more births.

Back in 1968, all the talk was of the population bomb. In 1970, Ansley Coale, a demographer at Princeton, predicted that, at the then current rates of growth, the number of people in just over a dozen centuries' time would be too many to even fit on the surface of the Earth. That is what compound growth of 2.1% a year results in if it continues unabated. No wonder there was no sense of the beginning of a slowdown: the experts were still saying that the end was nigh.

But people began to have fewer children in the 1970s. The power that women had to limit births increased. The need to have more offspring to secure an old age free of poverty diminished. A human population explosion that had been under way for 120 years came to an end. Again, I am referring not to the growth in the number of people but the growth of the rate of increase. Population levels will continue to rise for many decades. But the acceleration ended more than 40 years ago. And we should not be panicking about 10 billion.

But why did the population explosion begin when it did, just after 1851? It might have been due to the disruption of most of the world's traditional societies, all with their own population control traditions. No one back then could have known because no one was counting all the people. The theory I prefer is that following a few "favourable seasons", the rise in a species number can be astonishing. "We have better evidence on this subject than mere theoretical calculations," Charles Darwin wrote, "namely, the numerous recorded cases of the astonishingly rapid increase of various animals in a state of nature, when circumstances have been favourable to them during two or three following seasons. Still more striking is the evidence from our domestic animals of many kinds." He was writing just as those favourable seasons were beginning for humans worldwide.

I am far from advocating waste and profligacy or cheerleading for an unbridled capitalism. Until now, the growth in population and the growth in capitalism have gone hand in hand. Markets made more than was needed because more consumers were arriving each year. It is not hard to make a profit when there are more people clamouring to buy your products, clothes, food, gadgets, haircuts and university degrees. For decades it was thought to have been geographical expansion that made continual growth economically possible. Then, when the entire world was embraced within global markets, it was thought to be the increased speed at which goods were traded that kept capitalism working, time triumphing over space. The simple reality of there being more consumers born every year than those who were dying has been largely ignored. But that is about to end – there will soon be fewer young consumers.

Do not be frightened that our population is forecast to rise to 10 billion – it may not, and even if it does there is more than enough to go round. It is only the richest billion who are consuming too much and, just as most of us do not emulate the most affluent of a century ago, there is no need to believe people in a century's time will have the playthings the rich have today.

That the world's population will settle at or around 10 billion is good news. (The change that we should really prepare for is the population decline that will occur after 10 billion is reached.) One of the best possible outcomes of the slowdown might be that the way in which we now produce and consume too much will become impossible without ever-growing numbers of young people to make up the market. Your great grandchild could be living in better, calmer, less polluting and less profit-obsessed times than you.