TOKYO — Japan is caught in a demographic squeeze unprecedented among developed countries: a ballooning number of elderly, coupled with a decline in the overall population that is causing communities to wither and markets to vanish.

If the country is to maintain its vitality, new ideas are needed to combat the problem — and quickly.

Mount Hakodate, on the northern island of Hokkaido, is renowned for its view of the surrounding bay and city, especially at dusk. Tourists often gasp when they see the lights of the city below, and those of the squid fishermen out for their nightly catch.

But will there be anyone left to admire the scene in future years? In April, the central government designated Hakodate as a depopulated area, the first city with a population of around 300,000 or more in Japan to earn that distinction. The population of Hakodate has dropped to 270,000 from 340,000 in 1985, qualifying it for state support offered to localities whose populations drop by around 20% or more.

The fall is especially steep in the center of the city. The central government forecasts Hakodate’s population will fall to 170,000 by 2040. The city […]