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Their model shows an especially sharp decline for China, with its population expected to fall from 1.41 billion now to about 730 million in 2100. If that happens, the population pyramid would essentially flip. Instead of a base of young workers supporting a narrower band of retirees, China would have as many 85-year-olds as 18-year-olds.

China’s rust belt, in the northeast, saw its population drop by 1.2 percent in the past decade, according to census figures released on Tuesday. In 2016, Heilongjiang Province became the first in the country to have its pension system run out of money. In Hegang, a “ghost city” in the province that has lost almost 10 percent of its population since 2010, homes cost so little that people compare them to cabbage.

Many countries are beginning to accept the need to adapt, not just resist. South Korea is pushing for universities to merge. In Japan, where adult diapers now outsell ones for babies, municipalities have been consolidated as towns age and shrink. In Sweden, some cities have shifted resources from schools to elder care. And almost everywhere, older people are being asked to keep working. Germany, which previously raised its retirement age to 67, is now considering a bump to 69.

Going further than many other nations, Germany has also worked through a program of urban contraction: Demolitions have removed around 330,000 units from the housing stock since 2002.