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.
