What's the Difficulty? Understanding and Incentivizing Bitcoin's Difficulty Adjustment Mechanism

Abstract

This paper develops a model of the bitcoin market that views the bitcoin as a tradeable commodity whose supply is managed by the Bitcoin protocol. Miners utilize equipment and electricity to solve complex computational problems and the first miner to solve a problem is rewarded with bitcoins. The protocol adjusts the difficulty of the problem to regulate the supply of bitcoins over time. The model demonstrates that an increase (decrease) in the difficulty works in effect like a government's placing an ad valorem tax (subsidy) on the price of a commodity. The rents that would have arisen from limiting supply, however, are wasted as electricity costs that benefit neither a government nor the miners. Ironically, while the bitcoin is esteemed for its nongovernmental design, its system of supply management is far less efficient than if a government were to regulate the quantity of bitcoins by imposing a tax on its price. I show that an actual tax on the price of the bitcoin can incentivize the protocol to minimize the electricity costs it induces and I characterize the cost-minimizing tax. Using data from March 2014 to January 2019, I estimate that the difficulty adjustment mechanism resulted in net social welfare losses of 351.6 million USD and an average initial tax of 119.5% would have minimized the electricity costs during this time period.