# Last edited on 2017-01-20 00:56:53 by stolfilocal
# Analysis of fees in an unlimited capacity scenario

> If the total reward for mining a block, including mining transactions, was zero, only charitable miners would exist.  Therefore as the block reward is halved down to zero, Bitcoin needs the total transaction fees to increase to a level where they're paying for a suitable amount of "security".

No question about that.

> But how do you get people to pay 83 cents per transaction if there is no fee market?

You set the minimum fee to 83 cents, and ignore transactions that pay less than that.

> Bitcoin today has $15k / 10 minutes worth of security. If we want the same security

Why do you want the same security?

That number was not a design parameter, or means anything.  It is the result of the price being 850 USD/BTC and the reward being 12.5 BTC/block.  

> How do you stop a miner from accepting a 50c fee?

How does Coca-Cola stop another company from charging $0.25 for a can of cola?

You are approaching the issue from a totally wrong angle.  

The block size limit should be many times larger (20x or more) than the average block size, so that it does affect the network's normal operation, even at peak demand times, and can be ignored by users and miners alike.  That ensures "next-block" confirmation for all transactions that pay a known minimum fee, practically eliminates the risk of spam attacks, minimizes the cost for users, AND maximizes the revenue of miners.

To start the discussion, assume that all miners agree on the minimum fee rate F (satoshis per byte), that they all have a fixed cost A (satoshis per day) and a marginal cost B (satoshis per byte); and ignore periodic variations of demand.  This would be equivalent to a monopoly market, with a single supplier and single price.

For each value of F there will be a demand D(F) (in bytes/day), that depends on the bitcoin economy, not on the network. The total profit of the miners will be P(F) = (F - B) x D(F) - A (satoshis per day).  

If miners set the fee F near zero, D(F) would be huge but P(F) will be negative.  If they set F too high, the demand will be zero so P(F) will again be negative.  Somewhere in between there is an optimum fee value F = Fopt that makes P(F) maximum.  

If that maximum is negative or near zero, then bitcoin mining is not worth it, because there is not enough demand; and bitcoin is dead.  Otherwise the miners will set the minimum fee at that level, and stick to it.  

Imposing an arbitrary capacity limit Dmax (by a small block size limit) would be pointless if Dmax > D(Fopt).  If Dmax < D(Fopt), all the bad things of the "fee market" will occur -- users pay more than Fopt but have to wait longer, fees and delays are unpredictable, spam attacks become cheap and easy, growth stops -- AND the miners will make LESS profit, because F > Fopt means P(F) < P(Fopt).  

Moreover, because of all those bad effects of the "fee market", the price x demand curve will be depressed, so that the actual demand Dauc will be maybe 80-90% of Dmax, and the actual fees Fauc paid by users will be much lower than one would get by solving D(F) = Dauc for F.  Whichis what we have been seeing for the last 6 months or more.

That is, the profit that miners can "extract" from the users is maximized when the network is NOT congested and the miners set the minimum fee appropriately.  

Miners will then compete for that total profit P(Fopt) by increasing their hashpower. That increases their fixed costs, so they will stop expanding (as now) when their profit is barely sufficient to keep them mining.  Thus the hashpower of the network too will be maximized when the network is NOT congested.  Imposing an arbitrary capacity limit below D(Fopt) will mean LESS hashpower, because the miners can collect LESS money and hence can afford LESS work.

If 51% of the miners can agree on a single fee Fopt, then they can impose that fee on the other miners, by orphaning any block that contains transactions that pay less than that. 

If the miners cannot agree on a single Fopt, then each miner will set his minimum fee according to his costs and what the other miners will charge.  They will compete by lowering the fees, besides expanding their hashrates.  

That competition will be somewhat like the fRee market competition; but not quite the same, because the consumers (users) are assigned to suppliers (miners) randomly, proportionally to the miners' hashpower, instead of lower-price-takes-all.  

Therefore, instead of converging to a single common min fee, the equilibrium situation will see miners with somewhat different min fees.  Users who pay the higest of those fees will have "next-block" confirmation.  Users who pay lower fees will have to wait for a thriftier miner.  So the result would be what the "fee market" was supposed to induce (but doesn't), without all its bad consequences.

Needless to say, the miners will then make less total profit in this "semi-free market" situation than they could make with a cartel-fixed price.  But they (of course) would still be profitable (as in a free market).  

Suppose that all miners have fixed their fees, and consider a miner with 20% of the hashpower that wants to adjust his own fee.  Even if he charges less than all his competitors, he would NOT get all the demand, because those who pay that fee will have to wait 5 blocks for confirmation.  Conversely, if he charges more than the lowest competitor, he will still get a significant demand.  

So he will be faced with a modified price x demand curve D'(F), and for that too there will be an optimum fee Fopt' that maximizes his profit.  As his competitors lower their prices, his optimum Fopt' cannot keep decreasing forever, because of his fixed costs and the minimum acceptable profit. So there will be an equilibrium when all miners charge positive fees that are optimal for them: while each miner could capture more demand by charging less, that would lower his profit.