When a shikigami is working in agreement with its master's will, it partakes of its master's power. (C.f. Bohemian Archive in Japanese Red. "By following my will, Ran can obtain power equal to my level.") Thus, when Ran is operating purely in accordance with Yukari, her own (huge) power is combined with Yukari's (obscene) power. They are here united in purpose, so we have Lunatic Phantasm Ran.
(My personal headcanon holds that Ran was the most powerful bakegitsune/kyuubi alive when Yukari bound her -- possibly Tamamo-no-mae herself, though I won't insist on that. Yukari wouldn't have settled for less. Their battle probably broke Lemuria.)