GENEVA — European automakers are having a tough time moving their $15,000 models off the lot these days. But selling a $200,000 car seems to be getting easier and easier.

While Europe’s mass-market carmakers are still struggling in their home market, some builders of high-performance supercars — which are on gleaming display at the Geneva Motor Show, ending on March 16 — are selling their models faster than they can build them. The number of competitors is proliferating, as entrepreneurial shops and big car companies alike seek profits from the world’s wealthiest people.

A case in point is McLaren Automotive, a sister company of the British Formula One racecar builder. The automaker said at the Geneva show that it made its first profit in 2013. That is just three years after it began selling its debut model, a turbocharged V8 with a lightweight carbon fiber body that can hit 60 miles per hour in three seconds. Starting price: about $275,000.

“The market is getting more crowded,” Mike Flewitt, chief executive of McLaren Automotive, said as the company’s newest model, the $360,000 650S, rotated slowly on a display stand a few feet away. “But the world is growing.”