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And the miners profit is the distance of the revenue curve above the cost curve.
And the miners profit is the distance of the revenue curve above the cost curve.
Yes, nice work. In my paper I was looking at the Miner's Surplus, which is not in general equal to the Miner's Profit as your graphs illustrate (but they both are maximized at the same value of Q*). Your graphs show the miner's profit explicitly.
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The nice thing about plotting it this way is that we can also consider what would happen if transaction fees become a significant source of revenue and the block reward is not sufficient to profitably mine empty blocks:
We can see that in this case, it would only make sense for the miners to include enough transactions to be in the region of the graph where revenue exceeds cost.
We can see that in this case, it would only make sense for the miners to include enough transactions to be in the region of the graph where revenue exceeds cost.
This chart brings up a very good point. Like you point out, in such a scenario, the miner can only earn a profit if he can include a sufficient number of fee-paying TXs in his block. But what happens if the miner before him cleaned out the mempool? It seems the rational miner will stop hashing1 entirely until enough new transactions have built up to push his block into the "profitable" zone in your graph (the zone where the supply curve is below the demand curve).
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This would also work in the extreme case where R=0.
I'm not sure. I think the model suggests that the supply curve turns into a horizontal line at M=0 in such a case. We still need to get around the problem that Eq. (11) suggests the cost to write to the Blockchain falls to zero:
Smooth has brought this up a few times now (and I've been ignoring him because I think this can of worms is best left closed). Anyways, to really understand what happens when R->0 I think we need to make a new model that takes into account what we just learned from your chart above (that miners won't necessarily be hashing all the time).
1Assuming the cost to turn the hardware on and off is small.