This feat of longevity is a delight to her family, and the 114-year-old is sure to be celebrating with, among others, her 60-year-old grandson, Takeshi. But for the rest of Japan there is something chilling about Mrs Koyama’s achievement: who is going to foot the bill if everyone starts to live that long? In the world’s fastest-ageing industrialised society that fear is not so outlandish. A new report from the population division of the UN Department of Economic and Social Affairs projects that, by 2050, 15 per cent of Japanese will be more than 80 years old. Life expectancy in Japan — 85 for women and 78 for men — is higher than in Britain, Europe and the US by more than four years, and still rising.

But the real ageing problem is only partially to do with Mrs Koyama and her silver cohorts. Japan would be perfectly capable of supporting its elderly, and the 20 million octogenarians implied by the UN report, if the ranks of under-20s were swelling as fast as the ranks of over-65s. But they are not.

The true crisis — a time bomb that could cripple the world’s second largest economy — is 500 miles away in Tokyo, the most densely populated metropolis on Earth, where fertility rates are the lowest in Japan, at 0.99 children per woman of child bearing age.

Economists have produced a wide range of views on how serious the problem is now and could become. Few doubt that Japan is facing a crisis of fearsome proportions. They range from the apocalyptic prediction by Japan’s National Institute of Population that, at current rates of fertility, the Japanese will be extinct by the year 3387, to the more immediate concern of the International Monetary Fund that Japanese welfare costs could surge so fast that Japan’s economy never properly achieves recovery.

Although the ageing problem has previously been seen as a slow-burner, the sense of impending crisis has finally hit home. A flurry of panic-stricken proposals aimed at encouraging the Japanese to start reproducing has recently emerged. The Government’s main hope rests in the belief that children born in the second baby boom of the 1970s will hit childbearing age over the next five years. A white paper on the subject in December, which political analysts say smacks audibly of desperation and has been dubbed the “Angel Plan”, recommends a range of ideas from providing proper paternity leave to building more nurseries.

Many academics have pointed out that the demographic situation in Japan is merely a more rapidly developed version of what is already happening in Europe. The only major difference is that higher immigration levels dull many of the effects that Japan is feeling.

A few analysts are coming round to the contrary view that Japan’s demographics may become a stimulus for growth. The great majority of Japan’s 25 million over-65s have around £50,000 in savings, and 81 per cent do not have any debts. Donald Skinner, an Asia economist, says that for companies providing healthcare, travel, electronic devices, and a range of other services “this is a huge business opportunity”.

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