Flexible Computing Loads, Power Purchase Agreements, and Carbon: A Contract-theoretic Analysis of Bitcoin Mining as Grid-adjacent Demand Response

Abstract

Bitcoin miners consume roughly 0.5% of global electricity and, unlike most industrial loads, can curtail consumption on subsecond timescales. I develop a contract-theoretic model of a vertically-integrated utility that jointly chooses fossil, renewable, and flexible-computing-load (FCL) capacities and then dispatches against stochastic residual demand. Under the maintained assumptions of the model I derive sufficient conditions under which introducing an FCL weakly reduces expected carbon emissions in equilibrium, with strict reduction on the interior event. I sign the comparative statics of the equilibrium carbon functional Ψ(F; θ) with respect to seven primitives and verify each sign numerically across eight residual-demand distributions, confirming five distribution-free signs and two shape-sensitive ones. On the Pareto tail I obtain a closed-form distributionally robust characterization: the worst-case tail index shifts from 2.50 to 2.10 as the Wasserstein-1 ambiguity radius grows, and the price of robustness is bounded by 0.125 units of expected profit in the tested grid. I calibrate the model to the June 2021 power purchase agreement between Cipher Mining's Odessa facility and Luminant ET Services (Vistra Corp), a 200 MW fixed-price contract with curtailment rights extending through July 2027, and show that publicly disclosed curtailment events during the summer 2022 ERCOT scarcity episodes are broadly consistent with the model's carbon-optimal dispatch rule.