Bitcoin Forum

Hello all,

I'm currently reading the paper: Cryptocurrency value formation: An empirical study leading to a cost of production model for valuing bitcoin by A. Hayes. At page 1316 and further you will find some formulas that he uses to calculate the fundamental value. I would like to replicate his finding using todays figures (he calculated it around april 2016), and see whether or Bitcoin's price equal the outcome of the formula.

The expected number of bitcoins expected to be produced per day can be calculated as follows:
BTC/day = [(β · ρ)/(δ · 2^32)] · sec(hr) · hr(day) (1)
where β is the block reward (at 2016 25 BTC/block) , ρ is the hashing power employed by a miner, and δ is the difficulty (which is expressed in units of GH/block). The constant sechr is the number of seconds in an hour (3600), while hrday is the number of hours in a day (24).

Hayes sets ρ = 1000 GH/s
The cost of mining per day, E(day) can be expressed as follows:
E(day) = (price per kWh · hrday · W per GH/s)(ρ/1000 GH/s) (3)

Assuming that the bitcoin market is a competitive market, the marginal product of mining should be equal to its marginal cost, so that the $/BTC (equilibrium) price level is given by the ratio of (cost/day) / (BTC/day):
p = E(day)/(BTC/day) (4)

Other assumptions: average electricity cost: 0.13 cents KW/H. Average energy efficiency 0.40W per GH. Mining difficulty 166,851,513,283

Yields for a 1 TH/s  (1000 GH/s) mining rig approximately: (0.13*24*0.40)*(1000 /1000) = $1.248/day. (3)
Equation (1) yields 0.00301 BTC/day. and (4) (1.248 $/day)/(0.00301 BTC/day) = $414.62/ BTC.

My question:
1. what would be a good approximation of the average hash power employed by a miner currently. And what about the average energy efficiency? Are there any sources that can give an indication?

If I hold all else constant but adjust the mining difficulty to 3511060552899 and the block reward to 12.5 I find a value of 17.425 which does not come close to the current value.

Probably somewhere in the neighborhood of 12TH per machine, 0.1J/GH efficiency. A lot of the network is powered by industrial miners paying between 2 and 6 cents per kilowatt-hour.

I'd go with those numbers except use $0.10/kwh - since that is a typical home users power - and also a number that scales easily.

The problem with the author is he disregarded Bitcoin's decentralization and the "competitiveness or lottery" of the mining system which can't be measured based on a single miner or the average.

Bitcoin doesn't have an "operational cost", you'll need it if you want to "mine" for profit (not to help the blockchain but the blockchain benefits from you). And that expenses wasn't directly used for generating bitcoins in the network, literally, the Bitcoin blockchain can generate the same number of coins everyday using a single Pentium I computer.

The Price is pure speculation, it's 0 if no one uses it, $1+ if used and $20,000 when hyped.

A miner can have a 1TH of mining power, but the competition is too tough that by computing his chance, it will be decimals percentage.
A miner with a 1TH of mining power can join a pool which could secure his "wagered" Bitcoins at a standard rate. Now you need a different formula for pool miners.

The expected number of Bitcoins produced per day in total (which must be considered to the formula) is:
12.5 is the current block reward, 24 hours per day and 6 (six "10 minutes" per hour).
1,800BTC.

The difficulty always changes depending on the total Hashrate of the previous block.
That is to maintain an average of 10 minutes per block.