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 target a constant growth rate in 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. It is shown that an actual tax on the price of the bitcoin can be used to displace the electricity costs. Using data from March 2014 to January 2019, it is estimated that the difficulty adjustment mechanism resulted in net welfare losses to the miners and buyers of bitcoins of 373.8 million USD. Average initial tax rates of 35% and 347.5% would have fully displaced the electricity costs and maximized their reduction, respectively.

本文开发了一个比特币市场模型，将比特币视为一种可交易商品，其供应由比特币协议管理。矿工利用设备和电力来解决复杂的计算问题，第一个解决问题的矿工将获得比特币奖励。该协议调整问题的难度，以比特币供应量随时间的恒定增长率为目标。该模型表明，增加（减少）难度的效果就像政府对商品价格征收从价税（补贴）一样。然而，由于限制供应而产生的租金被浪费为电费。结果表明，可以使用对比特币价格征收的实际税来代替电费。使用 2014 年 3 月至 2019 年 1 月的数据，据估计，难度调整机制给矿工和比特币购买者带来了 3.738 亿美元的净福利损失。35% 和 347.5% 的平均初始税率将分别完全替代电力成本并最大限度地减少它们。