TL;DR burning gas in EIP-1559 will have no effect on the price of ETH. Getting rid of proof of work will have a huge, upward impact on the price of ETH.
Preamble: people buy and sell ETH for many reasons. Below we look at only at reasons directly related to the functioning of the Ethereum network. If a whale validator reaches their moon and buys a lambo, that transaction is downward pressure on the price of ETH, but isn’t part of our scope here.
Consider the buying pressure vs sell pressure for Eth1’s network operations:
Buy pressure in Eth1
— users buy ETH to pay for transaction fees
Sell pressure in Eth1
— miners sell ETH from transaction fees
— miners sell ETH from block rewards
Miners must pay for hardware, electricity, and other things. Mining is a very competitive industry. Profit margins are slim. Miners must sell all the ETH they get from mining blocks or else they would eventually go out of business. Sure, some miners have better access to new hardware or cheaper electricity. We’re talking global averages here. On average miners must sell all the ETH they get from mining blocks. The root cause here is that proof of work gets more expensive as Ethereum gets more successful.
Eth1’s network has more sell pressure than buy pressure. Buy pressure for transaction fees is canceled out by sell pressure for those same fees. But, sell pressure from block rewards is not canceled out and is a net drain on the price of ETH.
This picture changes dramatically when we transition to Eth2 and proof of work is stopped:
Buy pressure in Eth2
— users buy ETH to pay for transaction fees
Sell pressure in Eth2
— validators sell ETH from block rewards to pay for the flat cost of validating
Note the critical difference between miner costs vs validator costs. Miner costs must grow as they buy bigger computers in an arms race with other miners. Validator costs are flat and never grow. The point of this essay is to identify the necessary exchange of ETH for fiat currency during the operation of the network. Validators don’t necessarily have to sell as much ETH as miners because they have (low) flat costs.
Eth2’s buy pressure grows as total transaction fees grow. Eth2’s sell pressure is the (low) flat cost of validating, it never grows.
Transitioning to proof of stake and stopping proof of work will immediately remove the sell pressure from miners necessarily having to sell block rewards to pay for their hardware and electricity costs. From an ETH price accounting perspective, this is the real and dominant value of moving to proof of stake.
By the numbers:
In 2019 total transaction fees were about $40M, but block rewards were $900M. That’s a total of $940M in miner compensation. Miners, in an arms race with other miners, are willing and able to spend up to ~$940M to capture that $940M in revenue. That is to say, miners buy more and bigger computers until their profit margin shrinks to ~0 because mining is very competitive. Again, we’re looking at this behavior in the aggregate, on average, from a sixty-thousand foot view. I’m not saying that no miners make money. Some miners probably do quite well. In the aggregate, this means that in 2019 miners contributed $940M of sell pressure to Ethereum. Validators are estimated to have a flat cost of $20M to $300M for the entire Eth2 network. (This estimate is based off some number crunching from an ethhub value and is probably out of date.) Let’s say the total flat cost of validating is $200M for the entire network. That means that validators would have contributed $200M in sell pressure if proof of stake was used in 2019. That’s $940M of sell pressure for Eth1 vs $200M for Eth2. So proof of stake would have saved like seven hundred million bucks of sell pressure in 2019, or 2,350 lambos. That’s why proof of stake is going have a huge, positive impact on the price of ETH.
Also, the $700M of savings is directly tied to the price of ETH. If the price of ETH was 10x higher in 2019 then the savings would have been $9.4B - $200M = $9.2B.
What about burning gas from EIP-1599? What about the inflation rate from validator block rewards? These are actually related to wealth transfers from non-validators to validators. They are not buy pressure or sell pressure. Buy pressure and sell pressure represent somebody giving up fiat currency for ETH, affecting the market cap of ETH. In contrast, burning gas and inflationary block rewards do not affect the market cap of ETH. They are more like a stock split or shareholder dilution. When a validator gets (or doesn’t get) a block reward or transaction fee, this represents a wealth transfer from non-validator ETH holders to that validator. The total ETH market cap stays the same. To explain a bit more with an example, imagine if the validator block reward inflation rate was 100% per year. Every validator starts the year with 100 ETH and ends with 200 ETH. What’s going to happen? First, printing 100% more ETH out of thin air doesn’t change the total market cap of ETH. Second, the price of ETH (each Ether token) will be cut in ~half because total token supply ~doubled. But, only staked ETH is doubled. Non-validators lose out. So they have a strong incentive to become validators. The point is that burning gas and inflationary block rewards do not affect the total market cap of ETH, they only affect who wants to become a validator. I expand on this argument here.
— proof of work is extremely expensive for ETH holders, costing $700M+ per year in sell pressure
— Eth1.5 is being actively researched and will get rid of proof of work asap, hopefully in mid-2021
— Burning gas (or not) and inflationary block rewards are a wealth transfer from non-validator ETH holders to validators and don’t affect the total market cap of ETH