Please show me where I'm wrong!
Here's a few nitpicks with your assumptions/reasoning, that do change the results a bit:
1. The monetary base is about 1.2 trillion dollars
http://research.stlouisfed.org/fred2/series/MBCURRCIR?cid=124. This is a much better approximation than M2, because most of what goes into M2 (and M1 for that matter) is actually the value of outstanding bank loans. Bitcoin will not replace loans, so it can't "soak up" that value. So you're overestimating future BTC value (assuming it replaces USD entirely) by 10x.
That alone brings down energy consumption to less than 1% of the world's total. Other effects may come into play depending on the nature of bitcoin's behaviour as money (but I can only speculate whether it will drive value up or down).
2. Then your steady state formula assumes equal energy efficiency for all miners. And therefore you assume all miners are at the edge of profitability. Realistically only a small fraction of miners will ever be at that point, as long as energy efficiency increases over time.
Example: Assume 50% of mining hardware 1GH/Joule and 50% is 10GH/Joule, and 1GH/Joule is the breakeven point. Then energy consumption of the network is only 55% of what the everyone-has-the-same-efficiency model would predict. This can be even more drastic (10%/90% split). In other words, real energy consumption can only be equal to or lower than what your model predicts.
Yes, energy efficiency doesn't matter in a steady state world, because eventually enough hardware is brought online to make everyone uniformly efficient, and competition drives revenues down to electrical cost.
But as long as Moore's law holds, there will be significant
increases in energy efficiency every year. Which means each year it's profitable to bring new hardware online that outclasses the existing stuff, and takes a while to drop down to near-zero profitability. This keeps electrical usage down by driving the least efficient miners out of the market on a regular basis.
Moreover it introduces the need for mining investments to pay back their fixed costs in a relatively short time (less than a decade), which means that mining cost is mostly dominated by fixed hardware costs, rather than electricity, as long as hardware efficiency keeps increasing.
I honestly don't know what the adjusted formula should look like.
This doesn't change the total amount of
money Bitcoin mining will consume, but it does change what portion of it is spent as electricity, versus hiring electrical engineers, or making chips.
3. Subsidy halving means that, if Bitcoin mining is as competitive as you model, miners can't expect to make money for more than four years before needing to throw out their hardware and start again. This means that they will not get into mining unless they expect they can make a net profit in that short time.
Disclaimer: Obviously we're both speculating, no one really knows the economics of mining well enough to actually make good projections right now.
