user15: Some people keep evangelizing that Bitcoin transaction fees are much lower than in PayPal or with credit cards.
However, once nearly all 21 million bitcoins have been mined, the network will still have to be secured.
But "miners" can then no longer be rewarded by newly minted bitcoins. They will have to be rewarded by transaction fees.
I read that the market will find the equilibrium how much these transaction fees will be.
Are there any estimates or more concrete calculations about that? Is it even possible to foresee, as the "degree of network security" is a rather nebulous incentive for most (casual) users? Will they thus be enforced by the software? Will these fees better be absolute or relative to the amount of a single transfer?

user343: Most likely the fees asked for will be based on the transaction numbers. The miner's rig will need to be paid for (electricity, replacement parts, etc) for cost assumption is kind of hard to figure out until such a time as we know how many transactions will be going through once mining is complete.

user3441: In any P2P currency, there are only 3 choices, or combination of them.

You fund miners from savers.
You fund miners from spenders.
You let the government provide the mining. A public need so the economy doesn't stop.

1 is not available to Bitcoin long-term, because debasement is halving every four years.
2 penalizes economic activity, which is more important than burying money, ahem saving. Also it doesn't scale, unless it is uniform in the protocol. Gavin wrote making it uniform won't work in the market.
3 is thus the outcome for Bitcoin. (as designed by Satoshi)

user94: In theory, as deflation continues and mining blocks becomes more efficient, the transaction cost will approach .00000001BTC/ 1 Satoshi and will stop multiple times on its way down at the point slightly above where profitability reaches cost.  It is also possible that the transaction fee will approach zero.
The reason this happens is competition will drive the price down to the point that only the most efficient miners will be in business.  The price reduction is further amplified by the deflation in Bitcoin. We will find the exact stopping point from the most efficient miners who are willing to take the lowest profit margin.
This will also be a floating point because as transaction volume increases so will profitability allowing miners to further reduce their fee.
To further answer some of your questions:
1)Are there any estimates or more concrete calculations about that?
A: None that I can find.  My prediction is that transaction fees will have a multi-tier approach where the most efficient miners will offer "dual" processing fees one of which would be 0BTC.  The miners would split their processing power(a percentage based on profitability and a simple maximization problem) and include only transactions that met the highest payment tier would be included.
For example, if you include a 0 Satoshi fee you will only get 5% total processing power.  If you include a 1 Satoshi fee you will get 10% processing power.
2)Is it even possible to foresee, as the "degree of network security" is a rather nebulous incentive for most (casual) users? 
A: The degree of network security will be improved if users provide their own processing power but, this will not be necessary as mining will be profitable to the most efficient miners.
3) Will they thus be enforced by the software? 
A: Fees will be enforced by miners not including transaction with too low of a fee into the block chain.  This will cause a significant delay in the speed of your transaction. In the worst case scenario, where EVERYONE on the network requires a fee, you will have to mine your own block to get your transaction processed.
4)Will these fees better be absolute or relative to the amount of a single transfer?
A: A miner can choose to accept a transaction and include it into a block based upon any criteria that they see fit.  It will be interesting to see how miners choose to tier their pricing.

user307: There are a lot of unknowns because the network is so young and transaction volume is so low.  
Currently the block reward is worth about $13.1 million annually.  If fees stabilized at 0.1% of transaction volume (compare that to 3%+ for cc/debit/paypal) it would require a transaction volume of ~ $13 billion for fees to someday generate the same global revenue as current block rewards. To put that into perspective, credit & Debit cards have an annual transaction volume of ~ $2.5 trillion.  Paypal has ~ $80 billion in transactions per year so this level of transaction volume is certainly possible.
The larger issue is that under current protocol rules fees will never stabilize at 0.1% (or any other meaningful percentage) of transaction volume.  The reason is that currently there is no disincentive for a miner to exclude any paying transaction unless the block is already full of higher paying transactions.  A transaction can become a paying transaction by merely including 1 satoshi with every transaction which even on a 1 BTC transaction is only 0.0000001% not 0.1%.  For larger transactions it becomes infinitesimally small.
There is no method to create granularity because fees can be arbitrarily small and miners should logically not exclude a paying transaction.  The current transaction fee system is simply not viable once block rewards (subsidies) are removed.  
One way to look at it is the current network costs about $13 million per year to run or roughly $20 per block per TerraHash (TH).  That cost is paid via subisides but that isn't a viable long term strategy.  Someday it will need to be paid for with fees.  If the amount of fees collected are higher than the network will be larger/stronger.  If the amount collected is smaller then the network will be smaller/weaker.
Remember Moore's law doesn't make the network stronger.  As miner's hardware becomes more efficient so does attacker's hardware.  The network needs to generate sufficient fees to remain strong not just increase nominal hashing power due to efficiency gains.  The current transaction fee system doesn't achieve that goal.  It will need to be changed.

user50: It's impossible to say for sure right now, because according to Gavin, Bitcoin's transaction fee structure will be redesigned at some point:

bitcoin's fee structure isn't right either, and fixing it to create a market between miners and clients is high on the TODO list


user351: I read that the market will find the equilibrium how much these transaction fees will be.
It will not.  This is perhaps the biggest flaw in Bitcoin at the moment: once mining rewards end there is no direct linkage between the amount of hashpower needed to secure the network and the incentive to mine.
True, there is a limit on the blocksize, so if the transaction volume in a block window (approximately 10 minutes) exceeds the block size you can expect a miniature "auction" where transactions fight for space in the block by bidding up the minimum transaction fee needed to get in.  However this isn't really a closed-loop adjustment: the maximum blocksize is an arbitrarily chosen number, and there's no reason to believe the maximum blocksize is small enough to ensure that transaction fees are high enough to incent enough miners to mine to keep the system secure.  Unlike the difficulty and the USD/BTC exchange rate it does not respond to market activity.  It also has the negative side effect of capping the worldwide Bitcoin transaction throughput since other parts of the protocol rely on the assumption that blocks are created -- in the long run -- no more than once every ten minutes.
Compare this to the current situation with mining rewards: the more valuable a bitcoin is the more incentive there is for somebody to try to overwhelm the "good guys" by gaining 50%+1 hashpower.  However, the more valuable a bitcoin is the more miners will mine!  It isn't perfect, but the important point is that the demand for security increases the incentive to mine.  Note that although the difficulty will go up, that simply ensures that the reward granted every ten minutes is an approximately constant number of BTC -- the number of terahashes/sec fighting over that amount of BTC is free to respond to changes in their changing value (as measured in terms of all other goods in the world, including other currencies).
As the mining reward is reduced this "direct coupling" between the network's need for security and the incentive to mine becomes progressively more diluted.
I worry a lot about what will happen to Bitcoin once we decouple those two forces.  I think the developers ought to at least come up with a story on how this will be solved so people can start testing it.

15: <p>Some people keep evangelizing that Bitcoin transaction fees are much lower than in PayPal or with credit cards.</p>

<p>However, once nearly all 21 million bitcoins have been mined, the network will still have to be secured.</p>

<p>But "miners" can then no longer be rewarded by newly minted bitcoins. They will have to be rewarded by transaction fees.</p>

<p>I read that the market will find the equilibrium how much these transaction fees will be.</p>

<p>Are there any estimates or more concrete calculations about that? Is it even possible to foresee, as the "degree of network security" is a rather nebulous incentive for most (casual) users? Will they thus be enforced by the software? Will these fees better be absolute or relative to the amount of a single transfer?</p>
 343: <p>Most likely the fees asked for will be based on the transaction numbers. The miner's rig will need to be paid for (electricity, replacement parts, etc) for cost assumption is kind of hard to figure out until such a time as we know how many transactions will be going through once mining is complete.</p>
 3441: <p>In any P2P currency, there are only 3 choices, or combination of them.</p>

<ol>
<li>You fund miners from savers.</li>
<li>You fund miners from spenders.</li>
<li>You let the government provide the mining. A public need so the economy doesn't stop.</li>
</ol>

<p>1 is not available to Bitcoin long-term, because debasement is halving every four years.</p>

<p>2 penalizes economic activity, which is more important than burying money, ahem saving. Also <strong>it doesn't scale</strong>, unless it is uniform in the protocol. Gavin wrote making it uniform won't work in the market.</p>

<p>3 is thus the outcome for Bitcoin. (<a href="https://bitcoin.stackexchange.com/questions/8671/any-counter-proof-that-satoshi-nakamoto-did-not-design-a-ponzi-scheme-on-purpose">as designed by Satoshi</a>)</p>
 94: <p>In theory, as deflation continues and mining blocks becomes more efficient, the transaction cost will approach .00000001BTC/ 1 Satoshi and will stop multiple times on its way down at the point slightly above where profitability reaches cost.  It is also possible that the transaction fee will approach zero.</p>

<p>The reason this happens is competition will drive the price down to the point that only the most efficient miners will be in business.  The price reduction is further amplified by the deflation in Bitcoin. We will find the exact stopping point from the most efficient miners who are willing to take the lowest profit margin.</p>

<p>This will also be a floating point because as transaction volume increases so will profitability allowing miners to further reduce their fee.</p>

<p>To further answer some of your questions:</p>

<p>1)Are there any estimates or more concrete calculations about that?
A: None that I can find.  My prediction is that transaction fees will have a multi-tier approach where the most efficient miners will offer "dual" processing fees one of which would be 0BTC.  The miners would split their processing power(a percentage based on profitability and a simple maximization problem) and include only transactions that met the highest payment tier would be included.</p>

<p>For example, if you include a 0 Satoshi fee you will only get 5% total processing power.  If you include a 1 Satoshi fee you will get 10% processing power.</p>

<p>2)Is it even possible to foresee, as the "degree of network security" is a rather nebulous incentive for most (casual) users? 
A: The degree of network security will be improved if users provide their own processing power but, this will not be necessary as mining will be profitable to the most efficient miners.</p>

<p>3) Will they thus be enforced by the software? 
A: Fees will be enforced by miners not including transaction with too low of a fee into the block chain.  This will cause a significant delay in the speed of your transaction. In the worst case scenario, where EVERYONE on the network requires a fee, you will have to mine your own block to get your transaction processed.</p>

<p>4)Will these fees better be absolute or relative to the amount of a single transfer?
A: A miner can choose to accept a transaction and include it into a block based upon any criteria that they see fit.  It will be interesting to see how miners choose to tier their pricing.</p>
 307: <p>There are a lot of unknowns because the network is so young and transaction volume is so low.  </p>

<p>Currently the block reward is worth about $13.1 million annually.  If fees stabilized at 0.1% of transaction volume (compare that to 3%+ for cc/debit/paypal) it would require a transaction volume of ~ $13 billion for fees to someday generate the same global revenue as current block rewards. To put that into perspective, credit &amp; Debit cards have an annual transaction volume of ~ $2.5 trillion.  Paypal has ~ $80 billion in transactions per year so this level of transaction volume is certainly possible.</p>

<p>The larger issue is that under current protocol rules fees will never stabilize at 0.1% (or any other meaningful percentage) of transaction volume.  The reason is that currently there is no disincentive for a miner to exclude any paying transaction unless the block is already full of higher paying transactions.  A transaction can become a paying transaction by merely including 1 satoshi with every transaction which even on a 1 BTC transaction is only 0.0000001% not 0.1%.  For larger transactions it becomes infinitesimally small.</p>

<p>There is no method to create granularity because fees can be arbitrarily small and miners should logically not exclude a paying transaction.  The current transaction fee system is simply not viable once block rewards (subsidies) are removed.  </p>

<p>One way to look at it is the current network costs about $13 million per year to run or roughly $20 per block per TerraHash (TH).  That cost is paid via subisides but that isn't a viable long term strategy.  Someday it will need to be paid for with fees.  If the amount of fees collected are higher than the network will be larger/stronger.  If the amount collected is smaller then the network will be smaller/weaker.</p>

<p>Remember Moore's law doesn't make the network stronger.  As miner's hardware becomes more efficient so does attacker's hardware.  The network needs to generate sufficient fees to remain strong not just increase nominal hashing power due to efficiency gains.  The current transaction fee system doesn't achieve that goal.  It will need to be changed.</p>
 50: <p>It's impossible to say for sure right now, because <a href="https://bitcointalk.org/index.php?topic=41345.msg507159#msg507159">according to Gavin</a>, Bitcoin's transaction fee structure will be redesigned at some point:</p>

<blockquote>
  <p>bitcoin's fee structure isn't right either, and fixing it to create a market between miners and clients is high on the TODO list</p>
</blockquote>
 351: <p><em>I read that the market will find the equilibrium how much these transaction fees will be.</em></p>

<p><strong>It will not.</strong>  This is perhaps the biggest flaw in Bitcoin at the moment: once mining rewards end there is no direct linkage between the amount of hashpower needed to secure the network and the incentive to mine.</p>

<p>True, there is a limit on the blocksize, so if the transaction volume in a block window (approximately 10 minutes) exceeds the block size you can expect a miniature "auction" where transactions fight for space in the block by bidding up the minimum transaction fee needed to get in.  However this isn't really a closed-loop adjustment: the maximum blocksize is an arbitrarily chosen number, and <strong>there's no reason to believe the maximum blocksize is small enough to ensure that transaction fees are high enough to incent enough miners to mine to keep the system secure</strong>.  Unlike the difficulty and the USD/BTC exchange rate it does not respond to market activity.  It also has the negative side effect of capping the worldwide Bitcoin transaction throughput since other parts of the protocol rely on the assumption that blocks are created -- in the long run -- no more than once every ten minutes.</p>

<p>Compare this to the current situation with mining rewards: the more valuable a bitcoin is the more incentive there is for somebody to try to overwhelm the "good guys" by gaining 50%+1 hashpower.  However, the more valuable a bitcoin is the more miners will mine!  It isn't perfect, but <strong>the important point is that the demand for security increases the incentive to mine</strong>.  Note that although the difficulty will go up, that simply ensures that the reward granted every ten minutes is an approximately constant number of BTC -- the number of terahashes/sec fighting over that amount of BTC is free to respond to changes in their changing value (as measured in terms of all other goods in the world, including other currencies).</p>

<p><strong>As the mining reward is reduced this "direct coupling" between the network's need for security and the incentive to mine becomes progressively more diluted.</strong></p>

<p>I worry a lot about what will happen to Bitcoin once we decouple those two forces.  I think the developers ought to at least come up with a story on how this will be solved so people can start testing it.</p>
