According to tradition, Japanese schoolchildren preparing for entrance exams are encouraged to live by the exhausting credo of yontougoraku — “sleep four hours, pass; sleep five hours, fail.”

In other words, at an early stage in people’s lives, Japanese society transmits the message that sleep has intrinsically less worth than wakefulness and is a commodity that can — and should — be traded for something more valuable.

“Sleep debt” has become a national focus, but it remains unclear whether managers see this as anything more sinister than just the cost of business.

However, a small company in Tokyo called Crazy, an upmarket wedding-planning boutique, has taken an unexpectedly bold stand and decided to reward sleep. It will pay its staff a bonus if they prove they sleep longer each night. If they are able to keep up a steady pace of extended slumber and manage to get at least six hours on all weekday nights, workers can accumulate the equivalent of 64,000 yen ($562) a year.

I’m deeply concerned that nowadays Japanese people are less able to make a rational judgment because of sleep shortage. Jun Kohyama, neurologist

It is a radical experiment in incentives and productivity. Kazuhiko Moriyama, its architect and Crazy’s CEO, passionately believes it should become a model for companies across the country. Japan will surely become weaker, he declares, banging his fist on the table, if a worker’s right to sleep is permanently abused. The declaration seems all the more strident given the rather gentle part of the service sector in which Moriyama works.

The nature of his business, he says, is irrelevant. “We want to show that companies of all types need to be better,” Moriyama says. “We are a creative industry and we are creating a new business standard.”

Emerging technology and its availability at a reasonable price, he acknowledges, have played a key part in the sleep payment idea and other health-enhancing innovations introduced at Crazy. Where once a manager might infer fatigue by the dark circles under employees’ eyes, it can now be accurately deduced from the output of their smartphones. The sleeping habits of staff at Crazy will be (optionally) monitored by an app that draws data from sensors embedded in their mattresses.

Crazy is not the only company to have spotted this. Japan’s producers of medical devices have begun to approach the country’s “sleep debt” as a business opportunity. Several companies, including Teijin, have produced sleep monitoring devices capable of uploading data to companies and, in theory, giving managers the information they need to send overworked staff home to bed.

Since April, Hitachi has been working on a service whereby large companies pay for the administration of a system that tracks employees’ physical activity and sleep.

Investment bank Morgan Stanley produced a heavyweight report on the future of the Japanese economy in September in which it detailed more than 100 unlisted but extremely promising technology startups. Several had business models centered on the thesis that Japanese companies would come under ever-greater pressure to invest in the well-being of their staff. That pressure, the report suggested, would increase significantly as demographics impel Japan’s workforce to shrink and companies fight to attract and retain talent.

O Inc., one of the companies identified by Morgan Stanley, was started by an entrepreneur who had seen colleagues taking extended sick leave or quitting because of sleep deprivation. Junya Tanimoto, the company’s founder, says there were many similar cases across corporate Japan but no services to tackle the problem seriously. Employees’ sleep patterns, now that they can be more accurately monitored, have become a critical indicator of broader problems within a company, Tanimoto adds.

In sociological terms, say experts, the simple cash-for-sleep equation at the heart of Moriyama’s scheme could not have come at a more critical time.

To an extent that has now officially alarmed the Ministry of Health, Labor and Welfare, the “sleep is expendable” attitude has underpinned decades of evolution of the Japanese workplace — most particularly in the culture that coerces the workforce to toil far beyond their contractual duties in unpaid, undeclared overtime.

In 2014, in what was seen as overdue and a statement of the obvious, the Health Ministry published a hefty document offering the corporate world “guidance” on the importance of sleep.

The statistics that underpinned the government report, which in some cases were from surveys conducted over a decade earlier, showed a number of alarming features of Japanese sleep patterns, including the finding that more than 30 percent of adults drink alcohol to sleep. More recent statistics showed more than 71 percent of Japanese adult men sleeping fewer than seven hours a night. Such findings should have sounded a louder alarm, says Jun Kohyama, a neurologist in the Japanese Society of Sleep Research.

“Japanese people have a mentality that working hard, sacrificing sleeping hours is a good thing,” he says, “but without enough sleeping hours, your brain cannot function well. I’m deeply concerned that nowadays Japanese people are less able to make a rational judgment because of sleep shortage.”

An attempt by analysts at Goldman Sachs in early 2017 to quantify the overwork and sleep-deprivation problem estimated that the average Japanese worker does about 200 hours a year of unpaid overtime. The good news, concluded the report, was that the situation placed Japan in a strong position to benefit — in terms of marginal labor productivity — from any policies that reduced working hours and increased, for example, sleep.

Media headlines blare the most extreme effects of this culture — namely the dozens of karoshi deaths every year ascribed to overwork. But the everyday expression of the problem, say academic experts, is no less fearsome.

A 2009 study by Rand Corp., which set out to quantify the cost of insufficient sleep, suggested that Japan lost an estimated $138 billion a year through higher mortality risk and productivity losses associated with sleep shortage. Japan was by no means the only country suffering an economic hit — deficient sleep was calculated to cost the U.S. economy $411 billion a year — but the sleep deficit blow to Japan was, by some margin, the largest as a percentage of gross domestic product at 2.92 percent.