I'm not looking for anything based upon historical data
So we can make up anything we want?
I guess that would be par for conventional BTC economic analysis.
I honestly don't think that there's enough of a bitcoin economy to base it upon that.
Indeed.
More so, I'm looking for the math/econ approach to how the value would be affected based upon payment and transaction volume.
Just do it like the Keynesians: reach a conclusion, put a few closed forms behind it, and proclaim to the faithful how true it is even after discredited by true economists.
0.5 BTC is too high a price for that.
Predicting the future Bitcoin supply curve is trivial. Predicting the future demand curve is less so and using historical trends would largely be useless - we don't have enough of a history of cryptocurrency, IMO. For that reason, I'll take a theoretical analysis since it's the only one that I would feel comfortable with.