[wizzwizz4]

You can pay A for B, which you then pay for C. B is the price of C, and A is B's price. If A has a low value, then B is cheap, and thus a cheap price.

Pretty much all money can be bought for very slightly more money. Thus, a price can be cheap.

[huhtenberg]

"Cheap X" means "an X that costs less".

"Cheap price" literally means "a price that costs less".

You can certainly say that, but it makes no sense.

[wizzwizz4]

I've just demonstrated that it makes sense. But, really, that's irrelevant. You're telling me that a particular arrangement of 26 symbols “makes sense”, but another “doesn't”, even though both convey the intended meaning perfectly well – as evidenced by your critique describing the intended meaning?