The german mathematician David Hilbert once imagined a hotel with an infinite number of rooms. Even if all of the rooms were occupied, he pointed out, the hotel could accommodate a new arrival, simply by asking each guest to move into the room next door. One guest would move into a second guest’s room, freeing up a spot for the new arrival. The second guest would move into a third guest’s room, and so on. With an infinite number of rooms, the sequence would never end.
For years, China’s property developers operated along similar lines. They would sell flats far in advance of building them. The money raised for these flats was supposedly reserved for building them, just as each room in Hilbert’s hotel was supposedly reserved for an existing guest. But developers would instead use the money for other purposes, such as buying land. When the time came to pay for construction, they would sell more unbuilt flats and use that money instead. Just as Hilbert’s hotel accommodated each guest in the room next door, China’s property developers built each pre-sold flat with the money from the next pre-sale. As long as there were always new buyers, the sequence could go on.