Titanium isn't particularly expensive in itself, but one of its biggest uses is in aerospace,especially titanium bar for aerospace, and those titanium and titanium alloys are refined to very high levels of purity which pushes up the cost.However,is it possible to build a car with a titanium frame?
There is no particular value in using titanuim for a complete car body structure. It isn't very light weight, it doesn't absorb any energy after a crash by deforming plastically like steel or aluminum, and it's hard to fabricate. You can't press sheets of it into complex shapes, and you can't weld it without taking precautions to stop it catching fire.Titanium is useful for small highly stressed components, and for fashion gimmicks like titanium steering wheels.
Titanium for a car frame gives more strength and safety but expect higher cost than an ordinary framing.If you want a stiffer and lighter car body structure than steel plate, composite materials or carbon fibre are better options.