Great article. It's well written and easy to understand.
Just a quick question... You take the estimated btc for the current 2 week period and divide it by the "common ratio". Why not the percent increase? (y2 - y1) / y1
Cheers!
Thanks for asking. The answer is a bit mathematical but I'll see if I can explain that supposing you have not seen a geometric series before.
I divide it by I(1 - common ratio) because of a mathematical result that coincides with my model, which I chose for its simplicity.
I say let us call this value of the 1st 2-week blocks total earnings... I dont know, how about B for bitcoin. Ok so
total earnings in first two week period = B
Then I
postulate it is sufficient to say therefore the total earnings in the following two weeks will be a certain fraction
r of last times:
total earnings in the 2nd fortnight = r * B [/center
(Note that a fortnight is 14 days. Bitcoin has given us reason to finally use this hilarious word).
I have furthermore supposed that the ratio of earnings between to fortnights is always r. This is equivalent to saying that the difficulty rises by the same fraction each time it increases. If you look at this chart:
you can obtain "r" by dividing the difficulty between steps. Is the ratio, r, between adjacent steps actually always the same? Not really. But it is loosely constant within each 4 or 5 steps - and 4 or 5 steps is 10 weeks which is actually about the useful life of a miner.
So then
3rd fortnight's earnings = r * (second fortnights earnings) = r*( r*B ) = r2 *B
and the 4th fortnight yields r^3 * B...and the nth fornight r^(n-1) * B which looks like
total bitcoins ever = 1st fortnight's + 2nd fortnights + 3rd fortnight's + ... = B + r * B + r2*B + r3*B + r4*B + ... on and on forever
and if you look at the last line of the proof given here
you will perhaps understand why I have said take the first fortnight's earnings and divide by (1-r).