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 Author Topic: Using economics to predict future difficulty changes  (Read 2325 times)
Fjordbit
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 June 20, 2011, 09:47:34 PM

(Crossposted from newbies, since I could only post there before)

Like many here, I'm trying to get a handle around the bitcoin economy, and where it is going. One of the important factors driving price is the difficulty level. This is an indication of how long it will take a computer or pool to find a block of bitcoins. The difficulty level is set every 2016 blocks to set the rate of finding this amount to be 2 weeks. Thus if there is more computing power coming online, the difficulty rate will increase.

This gives another comparison point: the cost of entry. Many people are seeing that bitcoin mining is profitable and are purchasing their own rigs. In fact, with a modest investment, someone can suddenly get a passive income of a few hundred dollars/month. However, it's actually not the case that you get dollars/month and instead you get btc/month.

Add into this that you can, through an exchange like Mt. Gox, instead purchase btc, there is an interesting equilibrium that can be found, showing the relationship between bitcoin trade price, MH/s price, and difficulty level.

I'm going to pick specific values, because it illustrates this much better. Let's assume that
Cost of a bitcoin = 17 USD
Cost of 1000 MH/s = 900 USD

Therefore 1000 MH/s is about 53 btc

At the current difficulty, 1000 MH/s gives about 1.3759203893 btc. So now what we try to figure out is at what difficulty change rate will this pay back 53btc? This isn't easy (I don't know the closed form for it), but it can be found by finding how much one would earn in this difficulty period, and then the next period, and so on and so forth. One key aspect is that you have to adjust the size of the period to the assumed difficulty change. Thus if you assume the difficulty change is 25%, then you have to adjust the period to be 11.2 days. When putting this into a spreadsheet and extending out several periods, it is easy to find the bounds of this.

In this case, we end up with an average change of around 36.2%. At that rate of change, purchasing the 1000 MH/s system will yield about 53 bitcoins over its lifetime.

Now this does simplify a lot out. For example, it doesn't take into consideration the cost of electricity, space, infrastructure, etc. For another, it assumes a perfectly barrier-less entry into bitmining which is close to true, but there are still capital requirements and risk management that can act as barriers.

However, 36.2% represents almost an upper bound when assessing the difficulty change (given the exchange rate stays the same).

So what can we draw from this?

If the rate of difficulty change goes above this amount and all other things stay equal, then it will stop making sense to purchase systems and instead it makes more sense to buy bitcoins. This will drive up the price of bitcoins, lowering the btc per MH/s cost for a mining rig. It is possible the difficulty could fall if people come offline, but this is doubtful as it will still make sense to run an existing system.

If the rate of difficulty change goes below this point and all other things stay equal, then it will stop making sense to buy bitcoins and instead it makes more sense to buy a system. With more people coming online, this will push up the difficulty level.

If the exchange rate of usd to btc goes up and all other things stay equal, then the btc cost of MH/s goes down, and it makes more sense to mine than buy. With more people coming online, this will push up the difficulty level.

If the exchange rate of usd to btc goes down and all other things stay equal, then the btc cost of MH/s goes down, and it makes more sense to buy than mine. This will slow the difficulty rate.

If the dollar cost of a mining rig goes down, it makes more sense to mine than buy. This could have the effect of lowering the btc exchange rate or increasing difficulty or both.

This is just the basic analysis for now. There are some more interesting things that come out of this equilibrium relationship that I'll post on if there's any interest.
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tsvekric
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 June 20, 2011, 10:41:28 PM

It is true that price determines difficulty, not the other way around.
But I think it makes more sense to only look at continuous costs (like electricity) since you're looking at a barrier to entry with the mining rig set up.  You might take this into consideration for average cost of keeping a mining rig (meaning price/lifespan of the rig) but I wouldn't look at it for just those to start.  People should only drop out of mining if they could make more money selling their GPUs used than they would by continuing to use them (minus the cost of electricity)
So difficulty will rise to the point at which your average bitminer is indifferent between continuing to mine or sell the rig, basically.
Justsomeforumuser
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 June 20, 2011, 11:58:39 PM

It is true that price determines difficulty, not the other way around.

I still disagree with that (if I have a cost to overcome, I won't sell a BTC under cost, thus however long and costly the BTC was to produce, this is how high I need to let price go up before selling).

But the major issue with BTC isn't this whole value etc logic, it's how much wealth transfer is sustainable within the system.

IMHO a single BTC holder can completely overload/-burden the market at the moment, and thus we don't have a lot of reserves.
If more and more people keep piling into mining, but put no other "real" money into BTC, yet keep cashing out, _SOMEONE_ has to pay them out. So that money reservoir is not unending.
So, if
Sum of (value of btc selling people wanting to get cashed out) > (people willing to put forward real world cash for BTC they do not have yet)
then it all goes to shit, because you will end up with oversupply.

Some will argue this is wonderful, because then they can buy BTC cheaply.
Yes, up until the point that you run out of whatever savings you have. Then even at 1\$ you can't buy anymore BTC.

And now what happens? Now the last people who would have put out money for BTC, the bargain buyers and speculators, too, have run out of money. This now creates a huge pile of one sided potential supply vs the odd drug consumer wanting to buy illegal drugs via silk road and friends, likely a hugely outlevered and outnumbered relationship.
And the guy could not care less whether he needs to purchase 1 BTC at 20\$ or 20 BTC at 1\$ to get the equivalent amount of dimebag from it, because the drug price will still correspond to the _real_ world currency prices, not a fixed BTC price.

So, now what you have is a dried up market with an oil tanker worth of BTC, and basically a straw sized siphon for anyone trying to get his oil or rather BTC out..

What I am saying is this is what you should really ask yourself about in terms of future and economy.
I am sure a good amount of "rig investors" will be off well, they will always have at least a machine with which to play the next "Crysis"; but the people who put actual money into the system, well...they will have bitcoins.
And that's about it. And yes, I know THEIR argument is "Hah, but BTC is everything, and I can get everything(read: cheese and crackers at BTC munchies or whatever), plus it's better than the guvvurmints n awl", but let's see them explain that to their dentist when their tooth hurts or the lawyer when their car gets crashed and they only have BTC to foot the bill etc.

It's a nice experiment though while it lasts.

Ho-Hum.
tsvekric
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 June 21, 2011, 12:38:53 AM

It is true that price determines difficulty, not the other way around.

I still disagree with that (if I have a cost to overcome, I won't sell a BTC under cost, thus however long and costly the BTC was to produce, this is how high I need to let price go up before selling).

That doesn't make sense.  Miners hoarding BTC would have such a small effect on the market comparatively.  If it suddenly costs \$1000 a day to mine 5 BTC on average, that doesn't make BTC rise to \$200 each.  Miners would WISH it would rise to that, but effectively no one will continue to mine because it is too costly, and they will only re-enter mining at a level that makes costly sense IE the difficulty will fall to match the appropriate price of 1BTC in USD.
The only way difficulty could affect price is if miners could mine at whatever rate - but we know that the bitcoin system adjusts to only allow 50BTC per 10 minutes to enter the supply.  Since miners DO NOT AFFECT SUPPLY (really, it doesn't matter if one dude is CPU mining at low difficulty or 1million miners are mining at an insanely high difficulty, the same supply is made!) they cannot affect price.

However, price affects how many people choose to enter (or exit) the mining, thus changing the difficulty.
Fjordbit
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 June 22, 2011, 07:12:27 AM

However, price affects how many people choose to enter (or exit) the mining, thus changing the difficulty.

Right, but if the price is too low to justify starting new mining (meaning buying equipment to mine) and people want to transact in btc, then they will have to buy it. This will put the price up. This is why I think these three, price to enter mining, price of a btc, and difficulty, are all related by an equilibrium.
cothoms
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 June 22, 2011, 05:48:11 PM

This is why I think these three, price to enter mining, price of a btc, and difficulty, are all related by an equilibrium.

No doubt these three play into the equilibrium equation, but there are other factors as well.  Additionally, it's going to be impossible to accurately weight on any one of these factors; for now, we are only able to speak in very broad generics.
tsvekric
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 June 22, 2011, 06:26:52 PM

However, price affects how many people choose to enter (or exit) the mining, thus changing the difficulty.

Right, but if the price is too low to justify starting new mining (meaning buying equipment to mine) and people want to transact in btc, then they will have to buy it. This will put the price up. This is why I think these three, price to enter mining, price of a btc, and difficulty, are all related by an equilibrium.

Well, if someone is looking to spend in BTC and they choose to acquire it via mining, then that one less block (or part of the block) in the supply side of the market for currency exchange, which effectively makes the price go up (or not go down as much) all else equal.  If they instead let someone else mine it and buy that 50BTC, theoretically the price should go up about the same (or not go down about the same), assuming everyone's preferences for BTC and USD are the same in both situations.  Again, it does not affect price.

Price is the intersection of quantity demanded and quantity supplied.  In your situation that quantity does not change.  If price to mine jumped up to 100x the price it would not change the quantity demanded or supplied for BTC, just shifts where people spend their money to acquire it (assuming difficulty adjusts fast enough, which is the only lagging factor than can affect price because it means more (or less) than 6 blocks an hour on average are being created)
Fjordbit
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 June 23, 2011, 12:03:21 AM

Well, if someone is looking to spend in BTC and they choose to acquire it via mining, then that one less block (or part of the block) in the supply side of the market for currency exchange, which effectively makes the price go up (or not go down as much) all else equal.  If they instead let someone else mine it and buy that 50BTC, theoretically the price should go up about the same (or not go down about the same), assuming everyone's preferences for BTC and USD are the same in both situations.  Again, it does not affect price.

It's not true that btc supply is limited. If we stuck to 6 block an hour then there wouldn't be difficulty increases. But actually, that doesn't matter even assuming supply of btc is fixed and the demand of btc is fixed. The actions of the person determine the equilibrium

Again, the three are related through the equilibrium. Assume someone wants to transact in bitcoin but they have none. If it is cheaper to mine than buy (e.g btc at \$200), they will invest in mining but this will push the difficulty up. Everyone acting together pushes the difficulty up until mining is at parody with buying.

If it is cheaper to buy than mine (e.g. btc at \$5), then the person will have to buy bitcoins which drives the price up.

Price is the intersection of quantity demanded and quantity supplied.  In your situation that quantity does not change.  If price to mine jumped up to 100x the price it would not change the quantity demanded or supplied for BTC, just shifts where people spend their money to acquire it (assuming difficulty adjusts fast enough, which is the only lagging factor than can affect price because it means more (or less) than 6 blocks an hour on average are being created)

Something to note is that there is a bit of a difference in demand in these two scenarios. People don't have a demand for btc, they have a demand for the transaction. Let's say they want to use btc to buy a spot troy oz of silver (\$36.25). In the first case they need .18 btc, in the second case they need 7.25 btc. Even though the real demand is the same, the nominal demand for btc is higher when the price is lower (this is an econ forum, I hope that is obvious).

It seems like you are treating btc like a thing and not a currency. You can't eat, sleep in, or fuck a btc. You use btc to eat, sleep, and fuck.
minor_miner
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 June 23, 2011, 11:35:39 PM

Something to note is that there is a bit of a difference in demand in these two scenarios. People don't have a demand for btc, they have a demand for the transaction. Let's say they want to use btc to buy a spot troy oz of silver (\$36.25). In the first case they need .18 btc, in the second case they need 7.25 btc. Even though the real demand is the same, the nominal demand for btc is higher when the price is lower (this is an econ forum, I hope that is obvious).

Point taken and it makes perfectly sense.

But what does that imply?
iopq
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 June 24, 2011, 10:31:14 AM

You use btc to eat, sleep, and fuck.
I would like links to these merchants
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