^ i know, i know. another alliteration, an arguably arduous articulation at that – as if anyone actually asked… admonish away; any advice appreciated.
^ p.s. we can only aspire to be both precise and pleasant while measuring pie slices. 🥧📐
by mike – friday, june 21, 2024.
^turns out 2024 is the only year in the entire range of 2021-2027 where the summer solstice is on june 20
many thanks to Nate for discussions around the framing of this article.
tl;dr;
Hello & welcome to the third installment of the Issuance Issues®. The first issue highlighted the broad-stroke arguments for why we may end up in a high-stake rate paradigm and the associated negative externalities. The second issue focused on real & nominal yield, supply curves, and how a lower issuance may result in higher real yield in equilibrium.
This article deep dives 🔥the burn🔥 and its role in the issuance discourse. One of the most common themes in The Great Issuance Debate© is confusion around the burn. "How is issuance too high if the net supply of ETH
is barely inflationary (or even deflationary)?" This confused me for a long time, so in this article, we start slowly and use a lot of plots and numerical examples to build intuition. We make our way to the key insight that higher burn increases the gap between staking and not staking. Hopefully, this article demonstrates that regardless of the burn, the issuance remains a redistribution mechanism that shifts network ownership from non-stakers to stakers. Once we convince ourselves of that, it follows that the burn is mostly orthogonal to the issuance discussion (and marginally increases the ownership gap). Let's get it – "and here … we … go."
Contents
(1) Nominal yield & inflation refresher
(2) A new dimension – network ownership
(2.1) Unstaked ETH
, no burn
(2.2) Staked ETH
, no burn
(2.3) Ownership gap, no burn
(3) Bring on the burn
(3.1) Unstaked ETH
, burn
(3.2) Staked ETH
, burn
(3.3) Ownership gap, burn
(4) Wrapping up
The plotting code is available here.[1]
Related work
Article | Description |
---|---|
Minimum Viable Issuance | Anders' first post |
Properties of issuance level (part 1) | Anders' second post |
Endgame Staking Economics: A Case for Targeting | Caspar & Ansgar's post |
Electra: Issuance Curve Adjustment Proposal | Caspar & Ansgar's Electra proposal |
UCC2: Ethereum's Staking Endgame | Jon, Hasu, Caspar, & Ansgar's discussion |
Initial Analysis of Stake Distribution | Julian's post |
Minimum Viable Issuance | Anders' third post |
Reward curve with tempered issuance | Anders' fourth post |
Foundations of MVI | Anders' fifth post |
FAQ: Ethereum issuance reduction | Anders' sixth post |
As a quick refresher, recall that the current Ethereum issuance rate is what we referred to as the "inverse-root curve" in the previous post,
Here, ETH
, and the ETH
, then
We use the supply of ETH
, so we can rewrite the inflation as,
For example, let ETH
, then ETH
values. The dotted line shows the example values we calculated on both plots.
The main characteristic of the yield curve (left) is that it grows extremely quickly as ETH
(because the yields are relatively similar). The inflation curve (right) is monotone increasing, so each marginal new staker increases the overall inflation rate of the system.
The figure below includes example values for ETH
(dashed lines) for reference.
OK, great. Hopefully, this was mainly a review and pretty easy to follow. Now, to the new stuff.
Before building up to the burn, we first need to examine changes in "network ownership," which we define here as "the portion of the ETH
supply you own." We start with the non-burn case as it is simpler to understand and helps set the table for incorporating the burn in Section 3. To begin, ETH
is either staked or unstaked. Using this partition, we can examine the annual change in network ownership for each case.
ETH
, no burnLet's start with unstaked ETH
. We want to answer, "If I don't stake my ETH
, what is the annual change in the percentage of the total supply that I own?" You could also think of this as "dilution," but the "change in network ownership" framing may be more intuitive (albeit more verbose). Let
Again, we use the relative change equation to see how much the network ownership decreases after a year. Note that, by definition, ETH
pays for security through a reduction in network ownership. Examining the
The
Putting this into algebra, let ETH
. Also, let
The figure below shows
ETH
ETH
These are interpreted as, e.g., "with ETH
, the percent of the total supply a non-staker owns decreases by
Notice that these values are negative because the non-stakers always decrease the portion of the supply they own (because the stakers are creating new ETH
while the non-stakers retain the same number of tokens). Also, the values are monotone decreasing in the amount of stake because the inflation is always increasing, meaning the the total supply is growing faster with more ETH
staked.
ETH
, no burnMoving to staked ETH
, the situation is much different. Here, the change in my network ownership is, by definition increasing. The rate at which it increases depends on both the yield and the overall inflation rate. Let
Again focusing in on
Putting this into algebra, let
Notice that this value is positive if and only if
The figure below shows
ETH
ETH
These are interpreted as, e.g., "with ETH
, the percent of the total supply a staker owns increases by
We see that
Nifty! The natural next question is, "What is the difference in the change of supply ownership for staked versus unstaked ETH
?" We define this quantity as the "ownership gap"; we just take the difference
The figure below helps visualize this. The left plot shows ETH
to help with the scaling.
We can interpret this as, e.g., "at ETH
, the change in the stakers' ownership is about
Numerical example (no burn) – Let the total supply be
tokens. Consider a non-staker and a staker, each starting with tokens. The staker earns token in yield over a year, while the total inflation is tokens. No burn, non-staker
Ownership share before
Ownership share after
Ownership change decrease. No burn, staker
Ownership share before
Ownership share after
Ownership change increase. No burn, ownership gap
Gap difference.
Right – hope you are hanging in there. We can now incorporate the burn to see how this all fits together!
The burn decreases the total supply of ETH
, which affects the network ownership calculations because it changes the value of
ETH
, burnThe quantity of interest remains the same but incorporates the burn into the derivation of
Now the
The
In algebraic terms, let
Notice that this is very similar to our
The figure below shows the values of
This seems counterintuitive; how can the network ownership of a non-staker go up? The key insight here is that because the burn adjusts the supply for both non-stakers and stakers, the change in network ownership of the stakers must be going up faster. There is still a redistribution going on! We must factor the burn into our staker network ownership change calculation to compare apples-to-apples.
ETH
, burnLet
Just as in Section 3.1, the burn shows up when we calculate the
Putting this into algebraic terms, we have
This equation should look familiar by now, as the burn is included in the denominator. The figure below shows these values for various amounts of burn. The dashed and solid lines are the
Again, we turn to the ownership gap, or the difference between the change in network ownership for staked versus unstaked ETH
. In terms of the figure above, that means taking the differences between the solid and dashed lines that have the same color (same burn level).
(Sixth and final algebraic thing, soz.) Using the expressions derived in the previous sections, we have the ownership gap with the burn as
In Section 2.3, we calculated the value when the burn was ETH
range.
Key takeaway: the ownership gap is greater when you increase the burn because the staking issuance is a relatively larger portion of the total supply. This is shown on the right with the tan line (
Let's include the burn in our calculations by extending our numerical example from Section 2.3.
Numerical example (with burn) – Let the total supply be
tokens. Consider a non-staker and a staker, each starting with tokens. The staker earns token in yield over a year. Let the total inflation be tokens, and the total burn be tokens (net decrease of tokens in the supply). Burn, non-staker
Ownership share before
Ownership share after
Ownership change increase. Burn, staker
Ownership share before
Ownership share after
Ownership change increase. Burn, ownership gap
Gap difference.
Recall that the previous ownership gap (with no burn) was
That was a lot of [n]umbers & [a]lgebra & [p]lots (need a [nap]?), so we'll keep the summary short and sweet.
Thanks for reading!
— made with ♥ by mike.