arXiv:2611.13131v1 Announce Type: new Abstract: A serious criticism of Bitcoin's Proof-of-Work is its enormous electricity consumption. Proof-of-Useful-Work (PoUW), introduced by Ball, Rosen, Sabin, and Vasudevan (2017), in which mining performs useful computations, was suggested as an alternative to reduce electricity expenditure, with matrix multiplication (MatMul) as a recent concrete instantiation by Komargodski and Weinstein (2026). Perhaps surprisingly, we show that switching to PoUW may increase the total electricity consumption, echoing Jevons' paradox. Intuitively, the PoUW mechanism acts as a subsidy that lowers the effective price of the useful work. Recall that demand is elastic if a discount of x percent in the price leads to an increase of more than x percent in the quantity demanded. If demand is elastic, the resulting increase in quantity demanded leads to a net increase in total electricity consumption; if inelastic, total electricity consumption decreases. Even then, the electricity consumption due to PoUW never vanishes, since the mining subsidy is spent on useful work that would not have been produced without the subsidy. This result is proved in a simple model with electricity-only costs, no PoUW overhead, and an unchanged mining subsidy. The analysis extends to less restrictive settings with adjusted thresholds.