# Bitcoin: Difficulty per Issuance - A PoW Pricing Model

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The fact we are worrying about people dumping coins suggests we haven’t determined an accurate value yet. (dwdollar on 6 February 2010)

Every Bitcoin has a value. The key is finding it and tracking it.

Bitcoin’s consensus is based on a set of rules:

[1] Whenever someone finds proof-of-work to generate a block, they get some new coins [2] The PoW difficulty is adjusted every two weeks [3] The coins given per block is cut in half every 4 years

So — people do PoW to create new coins and sell them. What price do those who work for Bitcoin’s consensus need?

The very first BTC / USD exchange rate, published on 5 October 2009 on New Liberty Standard (NLS) was \$0.00764 per Bitcoin. They calculated this exchange rate using a formula based on:

The average amount of electricity required to run a computer with high CPU, multiplied by the average residential cost of electricity, divided by the number of bitcoins generated by the computer. (NLS on 5 October 2009)

As you can see, in the early days price was determined not by buying and selling activity, but by the cost of electricity and the mining output. A lot has happened in the mining industry since then: ASICs, immersion cooling and above all, a global hunt for cheap energy. But one thing has not changed — at least a lower price limit should be given by the production costs, unless Bitcoin retains its value for other reasons.

Today, the calculation of production costs is more complex, partly due to global access to energy. Instead of calculating the true cost of production, we consider the difficulty D. Difficulty is the current estimated number of hashes required to mine a block (denoted in raw hashes). This quantity is proportional to the energy consumption and the energy efficiency and reflects the demand. We use difficulty to estimate production costs. As mining becomes more efficient over time, hash rate becomes cheaper. Therefore we add a damping coefficient k and a scaling factor a (the cost per unit of adjusted difficulty). To get the value per coin, we divide by the issuance I.

We get the values for a and k by fitting the function to price. For this we use the lows of the last two halving cycles, deep in the bear market when only the most efficient mining was profitable.

The damping coefficient is k = 0.41. Statistically, this means that doubling the difficulty increases the estimated production cost by ~33%. We use a moving average for the difficulty and look at a 180 day period. For the upper bands we use the 1.41 and 2 multiples. The formula used is:

Is a continuation of the efficiency trend conceivable for the future? Possibly. Right now we are seeing electricity costs close to zero with Flared Gas in North America. And why the big difference before 2015? PoW mining was in its infancy. It’s been a business ever since.

Multiplying the formula by two equals the cost of production after the next halving (assuming constant difficulty). We are currently below that level.

In this article, we have proposed a pricing model based on difficulty to estimate production costs. Unlike S2F, it is demand sensitive. Production costs should remain the lower limit for a PoW system with demand. For any additional value that might be priced in going forward, I quote Satoshi:

The central bank must be trusted not to debase the currency, but the history of fiat currencies is full of breaches of that trust. Banks must be trusted to hold our money and transfer it electronically, but they lend it out in waves of credit bubbles with barely a fraction in reserve. We have to trust them with our privacy, trust them not to let identity thieves drain our accounts. Their massive overhead costs make micropayments impossible. (Satoshi on 11 February 2009)