The Carbon Effect of Flexible Computing Loads: A Distribution-Free Theory of Dispatch, Investment, and Optimal Contracts

Abstract

Bitcoin mining and AI training are among the fastest-growing electricity demands, and both are flexible loads, ramping up when power is plentiful and off when scarce. Whether that flexibility warms the grid or helps clean it is still unsettled, since careful studies reach opposite conclusions for the same technology in different regions. The catch is that a flexible load pulls carbon two ways at once. It keeps fossil plants running in idle hours, which raises emissions, and it funds new renewable capacity, which lowers them. This study solves dispatch and long-run investment together to identify when such loads cut carbon and the contract that does so. We find the equilibrium cutoffs are distribution-free, pure ratios of prices and costs for every demand shape. The load enters down to (phi)₁ = Cₘ/(R−p), and the net carbon change collapses to a single closed-form functional, (delta) = Phi(F). Under an unconstrained run-whenever-profitable rule, a load large enough to matter always raises emissions. Under a surplus-only contract that runs computing only on otherwise-wasted renewable power, dispatch becomes carbon-optimal. The same cutoffs carry over to a competitive market of third-party miners, where fossil planning separates entirely from the load. Across eight demand distributions the load raises profit and cuts blackout risk in sixteen of sixteen cases, and carbon falls only in a bounded cheap-renewable regime. These findings establish when, and in which market, flexible computing can decarbonize the power grid, in a form robust to the regional heterogeneity that causes previous estimates to disagree.