The relationship between bitcoin price and difficulty

This is a guest post by nanotube of bitcoin-otc, the leading over-the-counter bitcoin exchange. –Brock

One sees a lot of discussion about the relationship between bitcoin price and difficulty. It is often remarked on IRC and forums, when a difficulty jump is expected, that there’s an expected concomitant jump in the price forthcoming. In this post, we’ll dispel some frequently-heard misconceptions.

There is a long-run feedback cycle between difficulty and price. If price goes up, that makes mining more lucrative, and people buy new hardware to capitalize on that. As hashing power increases as a result, however, there’s actually a temporary increase in the daily bitcoin production, thereby causing an increase in the supply. This occurs because difficulty only adjusts every 2016 blocks, so as mining power increases it takes difficulty some time to catch up – and in the meantime, blocks are produced more frequently than once per 10 minutes target rate. Thus, unless new interest in bitcoin materializes in the form of more buyers, it is in fact not unreasonable to expect a bit of a price decline, due to the increasing supply. In the longer term, higher difficulty increases the security of the network, causing more confidence and an increase in demand, thereby causing increase in price, and we see the cycle begin anew. The primary effect, however, is the high price drawing new miners in, rather than new mining capacity drawing the buyers in.

This is more clearly seen when we look at what must happen in order for difficulty to decrease. If price declines far enough to make marginal mining unprofitable, we may see a decrease in mining power as marginally-profitable miners exit. The decrease in mining power may cause the marginal investor to lose confidence in the security of the bitcoin network and sell, thereby causing further mining power decrease, etc., in a similar cycle as above, but going the other way. Note, however, that until price declines to the point of making mining unprofitable for a segment of marginally-profitable miners, mining power will not exit the the network, since a rational miner will keep mining as long as the revenue exceeds the costs. Here we can clearly see that the first-order effect is the change in the price, rather than a change in mining power, and that the feedback from mining power to price is secondary.

Another side point bears discussion, and that is the idea that events the occurrence of which is known in advance, will be reflected in the price of the affected goods, due to investors/speculators trading activity in anticipation thereof. Specifically, consider the folly of people who expect immediate price increases with a difficulty change upwards. The fact that the difficulty will change, and a fairly accurate estimate of future difficulty, is available for all to see, days in advance. Thus, anyone who thinks that this should affect the price, would have already made his bets on that happening, by buying some bitcoins on the market, thus causing the price to increase. By the time the actual change in difficulty occurs, everyone who was going to make that bet has made it already, and thus there’s not going to be any new demand on that very day due to that change.

I hope this gives the reader a better idea of the price-difficulty relationship in the bitcoin system.