The real need, he added, is in the affordable range, which is subsidized by the state. Mr. Yuan said there were between seven million and eight million beds in the country. In July, China Economic Weekly magazine reported the government-run Beijing No. 1 Social Welfare Home, where a bed costs $110 to $570 a month, had a waiting list of more than 9,000.

Costs for government-financed places will be covered by a mixture of national and local government spending, with individuals’ pensions also contributing, Mr. Yuan said. He pointed out that the pension system was undergoing an overhaul, in part to cope with the challenge.

Whatever income group new old-age homes are designed to serve, the number of beds across China will have to rise fast, experts agree. That means more business — for somebody. Mr. Yuan did a quick calculation: 500 million old people paying 1,000 renminbi a month, comes to half a trillion renminbi a month.

How much foreign companies will be allowed to take part in that boom is unclear. Under the law, foreign providers of care for the elderly cannot run centers in China on their own but must find Chinese partners — a policy Mr. Yuan described as one of many that were “outdated” and “unreasonable.” Yanda is exploring cooperation deals with providers in the United States, Japan and Europe. Consulting contracts are also being signed with foreign businesses, from which Chinese companies can learn how to operate.

How to pay for this is equally unclear. By 2050, just 52 percent of the population will be of working age, Mr. Yuan said. Its members will need to support the 34 percent who are elderly and the 16 percent who are children. “How can China maintain its economic growth?” he asked.

In the meantime, governments are working on the infrastructure. In Beijing, the municipal government has decided it must earmark large areas of land for care for the elderly, in the same way land is designated for food markets or schools, The Beijing News reported in July.

The newspaper cited Chen Gang, the Communist Party secretary of the Chaoyang district of Beijing, as saying the city planned to allocate land along a highway circling the city’s suburbs for such facilities. “We’ll take that green, empty space and solve the problem of how to group old people together,” Mr. Chen said, according to the report.