We propose a dynamic industry equilibrium model for Bitcoin electricity consumption to investigate Bitcoin miners’ optimal entry and exit with technology innovation. Using average operating costs to approximate the true operating costs, we overcome the difficulty of strong path dependency incurred by the interaction among entry, exit, and technology innovation. The model is formulated as a singular stochastic control problem, whose value function satisfies a variational inequality with gradient constraints. The model can capture the upside and downside co-movements of miners’ computing power, electricity consumption, and mining revenue. The model predicts that the Bitcoin electricity consumption will not grow indefinitely and the ratio of Bitcoin electricity consumption to the miners’ revenue fluctuates within a certain range. This work is jointly with Steven Kou, Shuaijie Qian, and Ling Qin.

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