Efficiency of Cryptocurrencies 
For the distribution of preference shocks in evaluates the efficiency of Bitcoin
as a means of payment relative to a cash system. All computations are for our benchmark model
with the same preference parameters, but using different payments systems: cash, Bitcoin, optimal
reward structure for Bitcoin. Besides mining costs, we report two measures of the welfare cost.
The first measure gives the fraction of consumption people are willing to sacrifice in order to use
cash under the Friedman rule which implies zero welfare costs. The second one computes the
inflation rate with traditional cash so that people are indifferent between such system and the
cryptocurrency.
The current Bitcoin design is very inefficient, generating a welfare loss of 1.4% relative to an efficient
cash system.27 The main source for this inefficiency is the large mining cost, which is estimated to
be 360 mn USD per year. This translates into people being willing to accept a cash system with
an inflation rate of 230% before being better off using Bitcoin as a means of payment.
For comparison, a cash system with a 2% money growth rate generates a relatively small welfare cost of 0.003%.
chose ε so that the average size of transactions equals the one observed in these payments systems,
$38.29 and $6.5mn respectively. This is driven by data limitations. Double-spending incentives
however increase with transaction size and, hence, we assume that the largest transactions in the
debit card and Fedwire systems are 100 times and 5 times the average trade size.
Table 5.4 confirms that the welfare losses in a retail payment system are much smaller than in a
large-value one. In terms of the consumption equivalent measure, the welfare loss in a larger-value
system is 0.006% of consumption, which is about 10 times larger than that in a retail system. A
large-value system incurs a huge mining cost of 22 bn USD, which is over 5000 times of that in
the retail system. In the last row, we also derive the required transaction fee of a cash system (at
2% inflation) so that people are indifferent between such system and the cryptocurrency. When
a cryptocurrency is used for retail transactions, the equivalent transaction fee is a negligible 0.02
cents per transfer. For the large-value system, the corresponding fee becomes a very large $392.
The basic intuition follows directly from the double spending constraint we have derived in our
theoretical model. As the transaction size is smaller in the retail system, the incentives to double
spend are also smaller. Furthermore, mining is a public good so that the rewards from money
growth can support a large transaction volume. This implies that confirmation lags can be shorter
and one needs to induce less mining effort to dwarf double spending. Consequently, money growth
can also be smaller in a retail system, making a cryptocurrency system less costly due to inflation.
This implies that a cryptocurrency works best when the volume of transactions is larger relative to
the individual transaction size. As a result, a cryptocurrency tends to be much more efficient for
conducting retail payments.
The transaction fee measures in the last row of the table allow us to also evaluate whether cryptocurrencies can be a viable alternative to currenct payment systems. The interchange fee in the
current debit card system is about 23 cents per transfer, while the service fee for Fedwire is 82 cents
per transfer.29 This suggests that a well-functioning cryptocurrency system can potentially challenge current debit card systems by offering users a competitive transaction fee with large enough
transaction volumes.
This comparison – especially for retail payments systems – needs to be interpreted with caution.
First, we do not consider certain private costs of running a cryptocurrency system. Examples
are costs for data storage, network communication and software such as wallets to operate the
system. Second, while the mining cost is a deadweight loss to society, part of the fees collected by
retail and large value payment systems are profits earned by the providers so that operating costs
tend to be lower than reflected in those fees. Finally, the above comparison does not take into
account an important technical limitation of cryptocurrencies. Bitcoin and other implementations
of cryptocurrencies face tight limits to their scalability. Unless one can address this issue by
changing limits on block size and latency due to network speed, such systems will not be able to
handle a large volume of transactions as required by modern retail payment systems.