It's the most obvious thing in the world to think of price in terms of quantities. After all, what else is price but quantitative? Well, for one thing price is symbolic. In fact, it is primarily symbolic. The quantitative dimension of price is only a secondary characteristic. So although the quantitative aspect of price can be said to "occupy space", it's qualitative aspect does not.
Forget about labor. Forget about value. What is money?
Let's just say that money is a symbol of a particular form of sovereignty. The central bank issues notes that are legal tender. Let's not worry about how many of those notes there are or how much they're worth. Is it the pictures on the notes that make them symbols of whatever they symbolize? Is it the numbers in the corner? Is it the quantity of notes issued or the change in that number from one day to the next? It is none of those things. It is faith -- faith that the issuer of the notes is acting as sovereign, as the supreme authority. So what "space" does that sovereignty occupy? What portion of the whole sovereignty is represented by each of the notes? The plain answer is that each note symbolizes the entire indivisible sovereignty because if sovereignty was divisible it wouldn't be sovereign.
So where does that leave price? Interestingly (or not), it leaves price in precisely the same morass of the whole ball of wax as the labor theory of value. For value, it is socially necessary labour time; for price, it is sovereignty. We could easily say that sovereignty = socially necessary labour time (after all, it's the wealth of _nations_) and thereby "solve" the transformation problem with a tautology. But we would have done so only for the qualities of price and value, not for their accidental and secondary quantities.
The Sandwichman