[SkyMarshal]

>you should find that the value of each bitcoin mirrors the size of the economy that uses bitcoins in the long run.

Your equation is actually saying the opposite, that the value (P) of each bitcoin is inversely proportional to the size of the bitcoin economy (Q):

MV = PQ => (refactored) =>

(MV)/Q = P

Hence P ~ 1/Q.

Thinking about it more, I think you may have Q and M mixed up. From a supply/demand point of view, the greater supply of bitcoin (M), relative to demand at least, the lower the value (P).

If we assume aggregate demand can be approximated by overall size of the economy that uses bitcoin (Q), then

P ~ Q

and

P ~ 1/M

so

(QV)/M = P

hence

QV = MP

Right?