In a steady-state system, the price of a monetary asset is given by the "quantity theory of money", which states that:
P x Q = M x V, where
P is the price of the goods, Q is the amount of goods bought by the monetary asset, M is the amount of monetary asset in circulation, and V is the average velocity (the number of times per year that a given bitcoin is used to buy something).
Dump the velocity. and you are good to go. It has to be liquid, the owner needs to know that he can easily get rid of the bitcoins, actual trades are not needed.
You cannot ignore the velocity. If everybody would pay their bills the same day they get the money, instead of waiting to the end of the month, the same amount of trading would require 1/30 as much currency in circulation. If the currency it bitcoin, the smaller demand would imply a lower value per BTC.
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If you have money, change your mind to having a car instead; someone else having a car, but prefers holding money, then the two switched roles, and no change in demand for money or cars happened. So it depends on the seller, does he have the same wish to hold money as the buyer before he decided to buy?
One has to use consistent quantities Q, V, M and P of course.
So in your example, if you include the car in Q, then you have to include the money transfer in V. Of course, if two people exchange something, you might think that that doesn't influence anything. That would be correct if they were going to exchange,
no matter what happens. If I'm going to exchange my car with my father, who gives me money he has under his matrass instead, then this might not influence the price of cars on the car market.
However, that is not the case in general.
I will make a decision to buy a car, or to buy something else, or to hold my money, based upon several criteria, like the price of the car, my projections of getting money in the future and so on. And it are these decisions which determine demand and offer, and settle prices. If I think I will get money next month, I might consider buying a car. If I think I will not get much money next month, I might reconsider buying that car. The person supposed to give me some money next month (my employer) will have to get that money from somewhere. Maybe by selling goods. The price he will get from his goods will depend on how much money people are willing to give. And so on.
So, exchanges, or better, the arbitration between different possible exchanges (or not), determine offer and demand, and hence price. So they are not "neutral to price" except if there is no choice and they are going to happen no matter what.