Two Estimands, One Identity: Equilibrium-Implied Electricity Demand from Bitcoin Mining at Coin Prices of $1-$10 Million

Estimates of Bitcoin mining's electricity use disagree by an order of magnitude, and are usually read as uncertainty about one quantity. They are not. The engineering literature estimates electricity from observed hashpower and an assumed fleet-efficiency distribution; the expenditure literature computes the electricity revenue implies, given a tariff and cost decomposition.

We show the two coincide if and only if revenue equals total economic cost, and away from that locus stand in the exact ratio E R /E H = R/C. In one miner's filings the same electricity expenditure reproduces under all five disclosed cost denominators while R/C ranges from 0.61 to 1.72, so the reported spread is a range of cost concepts not of electricity. Chain data cannot close the gap: observed hashpower and revenue place one restriction on three unknowns, and the deficiency does not fall with length.

Replacing the assumed coordinates with disclosed ones, we assemble tariffs and cost shares from filings, screen them against the hardware record, and evaluate the schedule at coin prices of one to ten million dollars. The surface is exactly linear in price; under the constant-share baseline it steps down on each halving. At one million dollars a coin the implied electricity in 2027 is 2,247 TWh, about 6.6 per cent of projected world generation; the requirement, not a forecast, is the informative object.

The single most valuable disclosure would be the effective economic life of a mining fleet, which no filing reports and would narrow the capital-cost uncertainty.