Why the feminine? Does it refer to "on the cheap" or " cheaply"? To only give the words " The cheap" is a bit of a cheat.
I can't pull it up it may have been deleted because it is really odd. Sometimes, the contributors run out of idea. :-) I get a 404 so it must have been removed.
You're right, it could have been masculine and neutral also. Besides I think that it sounds unnatural in English also to say "the cheap''. Better ''the cheap one'', no?