Quote from: satmas on June 08, 2016, 12:41:29 PM

After July, the bock reward is reduced to 12.5. So that will just be 15% of the world power generation. After a few more halving, it will be even lower.

Correct and true! That is why I said "in this era"

So, in order to keep our power consumption under about 2% of world wide power production, we cannot/do not want the price to get to $500,000 before era 6, which is about 2033 or so.

Using my previously derived formula for the power consumption:

P = (6(50/2^e) + f)(x)(1 - g)/c [kW]

where:

x = exchange rate [USD/BTC]
e = era [0..32] (we are currently in era 1)
f = average fees per hour [BTC/hour]
c = cost of energy [USD/kWh]
g = average gross profit margin [unitless ratio]

we can look at the power consumption in each era assuming a price of $500,000 per BTC.

In order to make it simple I will make the following assumptions:

x = $500,000 per BTC
f = fees per hour will keep the coinbase above 6 BTC/hour (1 BTC/block) in all eras
c = $0.10 per kWh
g = 0.1 miner gross profit margin

Code:

Original target Subsidy Est Fees Power % of total world
Era starting year BTC/block BTC/hour GW power production
--- --------------- ----------- ---------- ----- ----------------
  0 2009 50.00000000 0.00000000 1,350 58.41%
  1 2013 25.00000000 0.00000000 675 29.20%
  2 2017 12.50000000 0.00000000 337 14.60%
  3 2021 6.25000000 0.00000000 169 7.30%
  4 2025 3.12500000 0.00000000 84 3.65%
  5 2029 1.56250000 0.00000000 42 1.83%
  6 2033 0.78125000 1.31250000 27 1.17%
  7 2037 0.39062500 3.65625000 27 1.17%
  8 2041 0.19531250 4.82812500 27 1.17%
  9 2045 0.09765625 5.41406250 27 1.17%

Of course this is a vast oversimplification since the values of the USD the price of electricity vary over time and it is very hard to predict miners fees over time and to know the average gross profit margin of mining.