Totally agree with your reasoning on a conceptual level, but could you explain the product A*B in a little more detail?
Sure.
I'm starting with the assumption that Bitcoin is used for transactions, not as a long-term value store (though the formula allows a transition to a value store - B increases). I think that's an accurate description of people who currently want to use Bitcoin for purchases - they trade fiat in, go shopping, buy their product, and the seller trades back to fiat. The duration of "go shopping" is B, and the sum of everyone's daily "buy their product" is A.
A * B is the total value that needs to be stored in Bitcoins for this to occur. It's somewhat related to the market cap.
An example in a highly stable, steady-state market:
Let's say that someone is selling paper clips for USD$1-equivalent, and they sell 3 per day, and that's the entire BTC economy. A = $3 . The average buyer obtains coins, shops for two days, spends, the seller holds them for one day, sells back to fiat on an exchange. B = 3. There are 30 total BTC that have been mined. C = 30. There are 12 BTC out of active circulation: some are lost, some are hoarded, whatever; they're not in use. D = 12.
Each day you will see:
Buyer1 buys 6BTC at USD$0.50 (total USD$3.00)
Buyer2 holds 6BTC.
Buyer3 buys 3 paper clips for 6BTC.
Seller goes from 6BTC to 12BTC, then dumps 6BTC (yesterday's paperclip revenue) on the market for USD$0.50/BTC = USD$3.00.
Hoarder holds their 12BTC, same as always.
At the end of the day you have 12BTC between Buyer1 and Buyer2; Seller has 6 BTC, having sold his other 6 to Buyer1; Hoarder has 12 BTC; total 30 BTC. The price holds steady at $0.50/BTC, as predicted by the formula: ($3 * 3) / (30 - 12) = ($9 stored value) / (18 coins) = $0.50 per BTC. The cycle repeats each day.
So what happens if the numbers start changing?
Let's drop the price to $0.25/BTC. Seller raises his price to 4BTC/paperclip. Buyer3 still wants his paperclips today, and Buyer2 knows he wants some soon, so they go back to the market and bid against Buyer1 to get some more BTCs to complete their purchase. The price gets run up until it hits equilibrium again.
Let's raise the price to $1/BTC. Seller lowers his price to 1BTC/paperclip. If Seller is still dumping yesterday's revenues on the market, the price drops - more BTCs available, and buyers don't need as many, so supply+demand does its thing. If Seller instead decides to hold, B increases, and the price stabilizes higher. If he doesn't think it's stable long-term, he gradually trades out faster than his revenues come in - IE, B gradually decreases - and the market price gradually falls (along with his gradually raising his price BTC/paperclip).
Let's say there's a run on paperclips: Buyers now want 10BTC to buy 5 paperclips each (A=$5). The BTC are not available on the exchange, so the USD/BTC (and BTC/paperclip) runs up until the market stores enough value for the buyers. Assuming B remains at 3, the total value store required (A * B) is USD$15. Thus the fundamental price goes to ($5 * 3) / (30-12) = USD$0.83/BTC.
So what do I want? More A; that's your economy! And more B - with stable value people will hold their BTC longer before cycling them back to fiat, perhaps even going through several product purchases between exchanges to fiat.
D is currently large, but shrinking due to capitulation; the rate of shrink directly forces the market down. Fortunately there's a limited supply of D, and it will gradually become less of a factor.
My argument about the very low fundamental price comes down to B. With current volatility, buyers don't want to hold their coins very long at all. We just want to buy paperclips and leave the currency risk to the speculators. B is extremely short (days at best), and that's going to seriously limit the price floor.
Want to try some real numbers?
A = USD$10,000 per day
B = 3 days
C = 7,500,000
D = 90% (generous!) = 6,750,000
Pf = (10,000 * 3) / (7,500,000 - 6,750,000) = $0.04
Ouch. We won't actually hit that price, but figuring for a 10x cushion, $0.40 is completely plausible. On the other hand it'll go lower if merchants don't adopt Bitcoin and A goes down.
Work on A, people, and stop fantasizing about bouncebacks and rockets to the moon. It's not happening until the fundamentals improve.
