Mr. Rapa recently applied for work at warehouses, in security, and at commercial kitchens. As of late July, he expected to gain none of these positions given the deteriorating economy.

“Tourists are not coming as they were before,” he said.

At Hestaland, a farm outside the town of Borgarnes that leads mostly American visitors on trail rides atop handsome Icelandic horses, the guesthouse has vacancies. “It used to be sold out all the time in July and August,” the owner, Gudmar Petursson, said. “Now, quite a lot, we have rooms.”

At Lake Myvatn, where tourists soak in natural hot springs and gape at pits of boiling mud, demand for local accommodation has plunged. Thuridur Helgadottir, 54, manager at Vogar Travel Service, has dropped prices by as much as half. She plans to shut down for four months this winter, a quieter season.

Yet beneath the concerns about Iceland’s economy, some harbor a sense that a dip in tourism may be healthy; a needed respite for an overwhelmed island.

“When the people who are coming are more about getting Instagram posts, and everyone goes to the same spots, then it’s overcrowded,” said Hordur Mio Olafsson, 32, whose family business leads tourists through lava caves near Húsafell. “What people are seeking here is pristine nature in this strange country in the North Atlantic, full of mystery. Now, we have a chance to do things properly.”