If bitcoin is generated 6*25 coins per hour (average) *$315 = $47,100. Plus some fees, maybe, so let's call it $50,000. If people collectively are paying more than $50k per hour in electricity, than miners at the margin begin to fall off. Even at a basal state cost of $0.05 per kWh that's $50,000 per hour / 0.05 $/kWh = 1,000,000 kW or 1,000 MW. This doesn't include the cost of hardware deprecation, and uses a very conservative rate for power.
So how much is 1,000 MW? The world produced about 22,000 TWh last year and there's 8765.76 hours in a typical year, so the average electrical output is 2.5098 TW or 2,509,800 MW. Bitcoin is therefore 1,000 / 2,509,800 = 0.0357% of the total. Again, this may be high if the global average rate for power is higher than $0.05 but to a first approximation it's close enough.
The inevitable arms race to increase hash/W is irrelevant. From a microeconomic standpoint that just serves to distribute the coins to the players, and further from a macroeconomic point of view the amount of money spent on power will almost nearly match the current price, with some latency adjustment period and some caveats for people who voluntarily lose money, steal power, etc (I would assume these are small because they will eventually correct over a reasonable time period).
If this theory holds then does it put an upper limit on the price of bitcoin? If Bitcoin was currently worth 100x at $31,500 per coin right now it would logically mean 3.57% of the grid is being used to service bitcoin mining, and 3.5% would have a significant impact; power starts to become a scarce resource that needs to be allocated efficiently (i.e., cost increases). At $31,500 per coin BTC has a fully diluted market cap of $655B which would make it about the size of Apple. It is not beyond the stretch of imagination that a crypto-protocol, with all of it's payment processing functionality, brings that kind of value to the market (e.g., it's not like $5T or something to high of a percent of global GDP to be a credible theory). The price can go beyond this as it just serves to reward miners with more advanced hashing equipment (higher hash/W) or simply increase the profit margin of miners (which would then collectively go into advancements in technology), so round and around we go.
Basically, I have no point. But it's interesting to think about.
thanks for sharing your calculation.
but you forgive a point...
0.05 $/kWh it is not possible in a large amount of nations...
in eu we have 0.25euro /kWh
so electricity cost is 5 times more, without considering change who is EUR/USD --> 1,24!!!
so your calculation is restrictive