Bitcoin Hash Rate Follows Price or Price Follows Hash Rate?

It’s intuitive to me that the Bitcoin hash rate movements are anchored to price, not the other way around. The price moves and the hash rate naturally follows due to market forces. But sometimes we see the hash rate moving first. Why is that? The Hash rate moving first is mathematically equal to new demand. I’ll explain why this is the case here.

The first thing that needs to be appreciated is what causes the Bitcoin price to be where it is in the first place. This article elaborates. It has nothing to do with hash rate directly.

It would also be helpful to understand how to calculate mining profitability, explained here.

Take this scenario to illustrate:

Imagine you are a miner with 10% of the world’s hash rate. The bitcoin price is $40k. The network allows the production of 900 bitcoin per day currently. Because you have 10% of the hash rate, your mining rigs earn you 10% of 900 = 90 bitcoin a day ($3600k). For this example, all the electricity you consume costs you $3200k ($3.2 million), or 80 bitcoin if you sell at the current price. Your profit is $3600k – $3200k = $400k, or 10 bitcoin per day.

Imagine now that Elon Musk decides to buy 10 more billion dollars worth of bitcoin and the price moves to $80k. This has nothing to do with the hash rate, just supply and demand.

Now, at that instant of price increase, you still produce 90 bitcoin per day (income increased to $7200k. And your electricity cost is unchanged, $3200k (this cost is now 40 bitcoin, not 80 bitcoin). You are making a huge profit, $4000k per day, or 50 bitcoin per day.

No doubt, other miners will seek this profit and join the network. This causes hash rate to go up, blocks to be produced faster, difficulty is adjusted, blocks then return to every 10 minutes. The world hash rate has gone up, and you now have, for example, 5% of the world’s share of hash power.

You now only earn 45 bitcoin per day (5% of 900). Your electricity costs are unchanged at $3200k (40 bitcoin compared to 80 before) because you haven’t added or removed any mining rigs. Your profit is 5 bitcoin per day, or $400k – Exactly what it was before in dollars.

So what happened in summary? The price went up. Miners joined in. You earn fewer bitcoin for your efforts, but in dollar terms, your profit is unchanged, because your access to cheap electricity is unchanged and you remained competitive. The world hash rate went up in response to a price increase. Hash rate followed price. This is all rational.

Now consider the alternative (price follows hash rate), which SEEMS irrational:

Let’s say again that the price is 40k. You have the same mining set-up, and now, you double your contribution to the world network.

You had 10%. You now have 18.18% (The math… 10h is yours, the world has 100h; double yours is now 20h; the world now has 10h more, 110h. Your fraction is 20h/110h=0.18181818).

Before any difficulty adjustment, MORE than 900 bitcoin a day are produced. You earn the original 90 bitcoin per day, plus another 90 bitcoin a day because you doubled your own hash rate, and find blocks twice as fast. Your profit has doubled because your income has doubled and your costs have doubled. That math is simple. It’s like you doubled the size of your business in every department. Naturally, you can expect profit to double, with simplistic logic.

But the difficulty then adjusts…

18.18% of the hash power gives you 900×0.1818= 163.6 bitcoin, not 180 bitcoin as you were initially getting.

Your electricity cost doubled (I’m ignoring capital expenditure for simplicity)

You now spend $6400k – the actual price of electricity is assumed to be stable, only the total cost has doubled.

Your profit is (163.6 bitcoin x 40k) minus $6400k electricity costs = 6544k – 6400k = 144k.

Previously the profit was $400k, and now it’s $144k. That’s a disaster, and irrational… if you want dollar profits.

But if we look at bitcoin earnings, not dollars…

Previously, bitcoin was being accumulated at 90 per day, well below cost. Now, 163.6 bitcoin are being accumulated, again, below cost, just not as cheaply.

A miner that is bullish on bitcoin will want to accumulate bitcoin. 163.6 bitcoin is better than 90 bitcoin. And so, it is rational for such a miner to increase production, sacrificing profit in dollars, until the equilibrium point where bitcoin is being accumulated at the market rate. After that, the only reason to increase further and pay above market rate is to accumulate KYC-free bitcoin, and some people do that. Ignoring that motive, a miner will find a sweet spot that matches his/her desire for dollar profit, and bitcoin accumulation, and the hash rate will be higher the more he/she wants to accumulate bitcoin – up to a point where it becomes irrational to increase further.

We see hash rate move before price sometimes. This can indicate miners are becoming more bullish, and are willing to sacrifice dollar profits to accumulate more bitcoin.

However, there is a limit to this. Hash rate is still anchored to price. If the price was to 10x, hash rate follows due to rational market participation of miners.

But if instead, it is hash rate to 10x first, it indicated miners are increasing hash power and sacrificing dollar profits to get more bitcoin. This suggests they are unwilling to sell newly mined bitcoin, causing a supply shock, and price follows. In reality, miners in this scenario are behaving like buyers, not pure miners. A sacrifice of a dollar profit by a miner is equivalent to new demand, mathematically.

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