It was Europe’s deadliest ever import. A particularly virulent form of the bubonic plague travelled westwards from China across the steppes of Asia and ended up at Black Sea ports. As far as can be established, rats carrying diseased fleas were on ships that set sail from the Crimea to Mediterranean ports. Between 1348 and 1350, the Black Death killed at least a third of Europe’s population, with mortality rates as high as 60% in some parts of the continent.

Europe has not since witnessed anything remotely like the depopulation of the mid-14th century. It took hundreds of years in some regions for the population to regain its pre-Black Death level and the economic effects were profound. A shortage of labour meant wages went up. Land was left untilled and fell in price. The gap between landowners and workers narrowed. Incentives to develop labour-saving devices meant productivity rose.

Roll the clock forward 670 years and there are those who think the world is about to discover what it is like to have a falling population, even though the projections seem completely out of whack with United Nations forecasts that a global total already well on its way to 8 billion will keep on rising to about 10 billion by the middle of the century and more than 11 billion by 2100.

It has been the prospect of an ever-rising population that has given rise to fears for the future of the planet. Past improvements in agricultural productivity – the so-called green revolution – have meant that up until now it has been possible to meet a growing demand for food. But at some point, it is argued, the pessimism of Thomas Malthus will be vindicated because population growth will outstrip the world’s supply potential. And it will be a Malthusian crisis with a twist, because attempts to feed and meet the other demands of more and more people will cause irreversible environmental damage. That’s why many of those most worried about climate change also argue for a rethink of one of the few economic ideas accepted by political parties of both left and right: that growth is good.

Despite attempts to develop alternative ways of assessing well-being, the great god of gross domestic product still reigns supreme. When the UK grew by 0.6% in the third quarter of 2018 it was seen as much better news than when, in the final three months of the year, the pace of expansion slowed to 0.2%. More growth means more people in work, which in turn means more spending power, more taxes and more public spending. For at least 200 years, governments have been grappling with the problems of growth: how to build more schools, hospitals, roads and railways for an expanding population.

But what would happen if populations started to fall, not in the dramatic way that occurred at the time of the Black Death but slowly and steadily over many decades? What if the UN’s central forecast for population growth is too high and that the rest of the 21st century will see life expectancy continue to rise and fertility rates continue to decline?

That’s the thesis of a new book, Empty Planet by Darrell Bricker and John Ibbotson, in which they say many countries are already being forced to grapple with the problems caused by a falling population. Bulgaria has a low birth rate of 1.5 births per woman, the toughest of lines against immigration and its population has fallen by almost 2 million in 30 years, to just over 7 million. Spain, where the fertility rate is even lower at 1.3, has appointed a sex tsar to see what can be done to prevent the population – currently just over 46 million – from falling by 5.6 million by 2080. Poland has closed hundreds of schools because there not enough children to fill them. Fewer Italian babies were born in 2015 than in any year since the country was unified in 1861. Germany’s ageing population was a key factor in Angela Merkel’s decision to accept a million Syrian refugees in 2015.

But, say Bricker and Ibbotson, it is not just Europe. The same trend applies to Japan and will soon apply to China, thanks to the one-child policy imposed by Beijing 40 years ago. India’s birthrate has also dropped, as has Brazil’s. Two factors lie behind falling birthrates – more people living in cities and the empowerment of women – and they apply to the developing as well as the developed world.

If the authors of Empty Planet are right, the world by the middle of the century could be a lot cleaner than anybody currently dares expect. The threat that the oceans will be sucked dry of fish will be smaller, the chances of limiting the rise in global temperatures will be greater. Just as in the second half of the 14th century, wages will go up and land will become less valuable. House prices will become more affordable.

But a world of smaller family units would be greyer and probably lonelier. If developed countries wanted to maintain growth rates at anything like their current levels, they would have to welcome immigration from the one part of the world where the population will keep growing, Africa, and change the welfare system to make it more attractive to have babies. Both go against the current grain of policy. More than that, fewer and fewer young people would be expected to pay for the healthcare and pensions of an ageing population. Houses would be for living in rather than a nest egg for retirement. It would all require quite a mindset change.

• Empty Planet by Darrell Bricker and John Ibbitson, published by Little Brown