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Reorg and cleanup of economics section of docs (#14868)

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* reorg validator economics

* overview cleanup

* terminology

* terminology formatting

* katex for docusaurus

* adjusted staking yield writeup

* more reorg

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* Update docs/src/inflation/terminology.md

Co-authored-by: Dan Albert <dan@solana.com>

* Update docs/src/inflation/terminology.md

Co-authored-by: Dan Albert <dan@solana.com>

* Update docs/src/inflation/terminology.md

Co-authored-by: Dan Albert <dan@solana.com>

* Update docs/src/inflation/terminology.md

Co-authored-by: Dan Albert <dan@solana.com>

* Update docs/src/inflation/terminology.md

Co-authored-by: Dan Albert <dan@solana.com>

* Update docs/src/transaction_fees.md

Co-authored-by: Dan Albert <dan@solana.com>

* addressing Dans comments in #14868

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Co-authored-by: Dan Albert <dan@solana.com>
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---
title: Solana Economics Overview
---
**Subject to change.**
Solana’s crypto-economic system is designed to promote a healthy, long term self-sustaining economy with participant incentives aligned to the security and decentralization of the network. The main participants in this economy are validation-clients. Their contributions to the network, state validation, and their requisite incentive mechanisms are discussed below.
The main channels of participant remittances are referred to as
protocol-based rewards and transaction fees. Protocol-based rewards
are generated from inflationary issuances from a protocol-defined inflation schedule. These rewards will constitute the total protocol-based reward delivered to validation clients, the remaining sourced from transaction fees. In the early days of the network, it is likely that protocol-based rewards, deployed based on predefined issuance schedule, will drive the majority of participant incentives to participate in the network.
These protocol-based rewards are calculated per epoch and distributed across the active
delegated stake and validator set (per validator commission). As discussed further below, the per annum inflation rate is based on a pre-determined disinflationary schedule. This provides the network with supply predictability which supports long term economic stability and security.
Transaction fees are participant-to-participant transfers, attached to network interactions as a motivation and compensation for the inclusion and execution of a proposed transaction. A mechanism for long-term economic stability and forking protection through partial burning of each transaction fee is also discussed below.
First an overview of the inflation design is presented. This section starts with defining and clarifying [Terminology](inflation/terminology.md) commonly used subsequently in the discussion of inflation and the related components. Following that, we outline Solana's proposed [Inflation Schedule](inflation/inflation_schedule.md), i.e. the specific parameters that uniquely parameterize the protocol-driven inflationary issuance over time. Next is a brief section on [Adjusted Staking Yield](inflation/adjusted_staking_yield.md), and how token dilution might influence staking behavior.
A overview of [Transaction Fees](transaction_fees.md) on Solana is followed by a discussion of [Storage Rent Economics](storage_rent_economics.md) in which we describe an implementation of storage rent to account for the externality costs of maintaining the active state of the ledger.

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---
title: Adjusted Staking Yield
---
### Token Dilution
Similarly we can look at the expected *Staked Dilution* (i.e. *Adjusted Staking Yield*) and *Un-staked Dilution* as previously defined. Again, *dilution* in this context is defined as the change in fractional representation (i.e. ownership) of a set of tokens within a larger set. In this sense, dilution can be a positive value: an increase in fractional ownership (staked dilution / *Adjusted Staking Yield*), or a negative value: a decrease in fractional ownership (un-staked dilution).
We are interested in the relative change in ownership of staked vs un-staked tokens as the overall token pool increases with inflation issuance. As discussed, this issuance is distributed only to staked token holders, increasing the staked token fractional representation of the *Total Current Supply*.
Continuing with the same *Inflation Schedule* parameters as above, we see the fraction of staked supply grow as shown below.
![](/img/p_ex_staked_supply_w_range_initial_stake.png)
Due to this relative change in representation, the proportion of stake of any token holder will also change as a function of the *Inflation Schedule* and the proportion of all tokens that are staked.
Of initial interest, however, is the *dilution of **un-staked** tokens*, or $D_{us}$. In the case of un-staked tokens, token dilution is only a function of the *Inflation Schedule* because the amount of un-staked tokens doesn't change over time.
This can be seen by explicitly calculating un-staked dilution as $D_{us}$. The un-staked proportion of the token pool at time $t$ is $P_{us}(t_{N})$ and $I_{t}$ is the incremental inflation rate applied between any two consecutive time points. $SOL_{us}(t)$ and $SOL_{total}(t)$ is the amount of un-staked and total SOL on the network, respectively, at time $t$. Therefore $P_{us}(t) = SOL_{us}(t)/SOL_{total}(t)$.
$$
\begin{aligned}
D_{us} &= \left( \frac{P_{us}(t_{1}) - P_{us}(t_{0})}{P_{us}(t_{0})} \right)\\
&= \left( \frac{ \left( \frac{SOL_{us}(t_{2})}{SOL_{total}(t_{2})} \right) - \left( \frac{SOL_{us}(t_{1})}{SOL_{total}(t_{1})} \right)}{ \left( \frac{SOL_{us}(t_{1})}{SOL_{total}(t_{1})} \right) } \right)\\
\end{aligned}
$$
However, because inflation issuance only increases the total amount and the un-staked supply doesn't change:
$$
\begin{aligned}
SOL_{us}(t_2) &= SOL_{us}(t_1)\\
SOL_{total}(t_2) &= SOL_{total}(t_1)\times (1 + I_{t_1})\\
\end{aligned}
$$
So $D_{us}$ becomes:
$$
\begin{aligned}
D_{us} &= \left( \frac{ \left( \frac{SOL_{us}(t_{1})}{SOL_{total}(t_{1})\times (1 + I_{1})} \right) - \left( \frac{SOL_{us}(t_{1})}{SOL_{total}(t_{1})} \right)}{ \left( \frac{SOL_{us}(t_{1})}{SOL_{total}(t_{1})} \right) } \right)\\
D_{us} &= \frac{1}{(1 + I_{1})} - 1\\
\end{aligned}
$$
Or generally, dilution for un-staked tokens over any time frame undergoing inflation $I$:
$$
D_{us} = -\frac{I}{I + 1} \\
$$
So as guessed, this dilution is independent of the total proportion of staked tokens and only depends on inflation rate. This can be seen with our example *Inflation Schedule* here:
![p_ex_unstaked_dilution](/img/p_ex_unstaked_dilution.png)
### Estimated Adjusted Staked Yield
We can do a similar calculation to determine the *dilution* of staked token holders, or as we've defined here as the ***Adjusted Staked Yield***, keeping in mind that dilution in this context is an *increase* in proportional ownership over time. We'll use the terminology *Adjusted Staked Yield* to avoid confusion going forward.
To see the functional form, we calculate, $Y_{adj}$, or the *Adjusted Staked Yield* (to be compared to *D_{us}* the dilution of un-staked tokens above), where $P_{s}(t)$ is the staked proportion of token pool at time $t$ and $I_{t}$ is the incremental inflation rate applied between any two consecutive time points. The definition of $Y_{adj}$ is therefore:
$$
Y_{adj} = \frac{P_s(t_2) - P_s(t_1)}{P_s(t_1)}\\
$$
As seen in the plot above, the proportion of staked tokens increases with inflation issuance. Letting $SOL_s(t)$ and $SOL_{\text{total}}(t)$ represent the amount of staked and total SOL at time $t$ respectively:
$$
P_s(t_2) = \frac{SOL_s(t_1) + SOL_{\text{total}}(t_1)\times I(t_1)}{SOL_{\text{total}}(t_1)\times (1 + I(t_1))}\\
$$
Where $SOL_{\text{total}}(t_1)\times I(t_1)$ is the additional inflation issuance added to the staked token pool. Now we can write $Y_{adj}$ in common terms $t_1 = t$:
$$
\begin{aligned}
Y_{adj} &= \frac{\frac{SOL_s(t) + SOL_{\text{total}}(t)\times I(t)}{SOL_{\text{total}}(t)\times (1 + I(t))} - \frac{SOL_s(t)}{SOL_{\text{total}}(t)} }{ \frac{SOL_s(t)}{SOL_{\text{total}}(t)} } \\
&= \frac{ SOL_{\text{total}}(t)\times (SOL_s(t) + SOL_{\text{total}}(t)\times I(t)) }{ SOL_s(t)\times SOL_{\text{total}}\times (1 + I(t)) } -1 \\
\end{aligned}
$$
which simplifies to:
$$
Y_{adj} = \frac{ 1 + I(t)/P_s(t) }{ 1 + I(t) } - 1\\
$$
So we see that the *Adjusted Staked Yield* a function of the inflation rate and the percent of staked tokens on the network. We can see this plotted for various staking fractions here:
![p_ex_adjusted_staked_yields](/img/p_ex_adjusted_staked_yields.png)
It is also clear that in all cases, dilution of un-staked tokens $>$ adjusted staked yield (i.e. dilution of staked tokens). Explicitly we can look at the *relative dilution of un-staked tokens to staked tokens:* $D_{us}/Y_{adj}$. Here the relationship to inflation drops out and the relative dilution, i.e. the impact of staking tokens vs not staking tokens, is purely a function of the % of the total token supply staked. From above
$$
\begin{aligned}
Y_{adj} &= \frac{ 1 + I/P_s }{ 1 + I } - 1,~\text{and}\\
D_{us} &= -\frac{I}{I + 1},~\text{so} \\
\frac{D_{us}}{Y_{adj}} &= \frac{ \frac{I}{I + 1} }{ \frac{ 1 + I/P_s }{ 1 + I } - 1 } \\
\end{aligned}
$$
which simplifies as,
$$
\begin{aligned}
\frac{D_{us}}{Y_{adj}} &= \frac{ I }{ 1 + \frac{I}{P_s} - (1 + I)}\\
&= \frac{ I }{ \frac{I}{P_s} - I}\\
\frac{D_{us}}{Y_{adj}}&= \frac{ P_s }{ 1 - P_s}\\
\end{aligned}
$$
Where we can see a primary dependence of the relative dilution of un-staked tokens to staked tokens is on the function of the proportion of total tokens staked. As shown above, the proportion of total tokens staked changes over time (i.e. $P_s = P_s(t)$ due to the re-staking of inflation issuance thus we see relative dilution grow over time as:
![p_ex_relative_dilution](/img/p_ex_relative_dilution.png)
As might be intuitive, as the total fraction of staked tokens increases the relative dilution of un-staked tokens grows dramatically. E.g. with $80\%$ of the network tokens staked, an un-staked token holder will experience ~$400\%$ more dilution than a staked holder.
Again, this represents the change in fractional change in ownership of staked tokens and illustrates the built-in incentive for token holder to stake their tokens to earn *Staked Yield* and avoid *Un-staked Dilution*.

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---
title: Solana's Proposed Inflation Schedule
---
As mentioned above, the network's *Inflation Schedule* is uniquely described by three parameters: *Initial Inflation Rate*, *Dis-inflation Rate* and *Long-term Inflation Rate*. When considering these numbers, there are many factors to take into account:
- A large portion of the SOL issued via inflation will be distributed to stake-holders in proportion to the SOL they have staked. We want to ensure that the *Inflation Schedule* design results in reasonable *Staking Yields* for token holders who delegate SOL and for validation service providers (via commissions taken from *Staking Yields*).
- The primary driver of *Staked Yield* is the amount of SOL staked divided by the total amount of SOL (% of total SOL staked). Therefore the distribution and delegation of tokens across validators are important factors to understand when determining initial inflation parameters.
- [Yield throttling](https://forums.solana.com/t/validator-yield-throttling-proposal-discussion/855/5) is a mechanism currently under consideration that would impact *staking-yields*. **This is not taken into consideration in the discussion here or the modeling below.**
- Overall token issuance - i.e. what do we expect the Current Total Supply to be in 10 years, or 20 years?
- Long-term, steady-state inflation is an important consideration not only for sustainable support for the validator ecosystem and the Solana Foundation grant programs, but also should be tuned in consideration with expected token losses and burning over time.
- The rate at which we expect network usage to grow, as a consideration to the dis-inflationary rate. Over time, we plan for inflation to drop and expect that usage will grow.
Based on these considerations and the community discussions following the initial [design](https://forums.solana.com/t/solana-inflation-design-overview/920), the Solana Foundation proposes the following Inflation Schedule parameters:
> Initial Inflation Rate: $8\%$
> Dis-inflation Rate: $-15\%$
> Long-term Inflation Rate: $1.5\%$
These parameters define the proposed *Inflation Schedule*. Below we show implications of these parameters. These plots only show the impact of inflation issuances given the Inflation Schedule as parameterized above. They *do not account* for other factors that may impact the Total Supply such as fee/rent burning, slashing or other unforeseen future token destruction events. Therefore, what is presented here is an **upper limit** on the amount of SOL issued via inflation.
![](/img/p_inflation_schedule.png)
In the above graph we see the annual inflation rate [$\%$] over time, given the inflation parameters proposed above.
![](/img/p_total_supply.png)
Similarly, here we see the *Total Current Supply* of SOL [MM] over time, assuming an initial *Total Current Supply* of `488,587,349 SOL` (i.e. for this example, taking the *Total Current Supply* as of `2020-01-25` and simulating inflation starting from that day).
The expected Staking Yield and Adjusted Staking Yield metrics are then primarily a function of the % of total SOL staked on the network. Therefore we can we can estimate the *Staking Yield*, if we introduce an additional parameter *% of Staked SOL*:
$$
\%~\text{SOL Staked} = \frac{\text{Total SOL Staked}}{\text{Total Current Supply}}
$$
This parameter must be estimated because it is a dynamic property of the token holders and staking incentives. The values of *% of Staked SOL* presented here range from $60\% - 90\%$, which we feel covers the likely range we expect to observe, based on feedback from the investor and validator communities as well as what is observed on comparable Proof-of-Stake protocols.
![](/img/p_ex_staked_yields.png)
Again, the above shows an example *Staked Yield* that a staker might expect over time on the Solana network with the *Inflation Schedule* as specified. This is an idealized *Staked Yield* as it neglects validator uptime impact on rewards, validator commissions, potential yield throttling and potential slashing incidents. It additionally ignores that *% of Staked SOL* is dynamic by design - the economic incentives set up by this *Inflation Schedule* are more clearly seen when *Token Dilution* is taken into account (see the **Adjusted Staking Yield** section below).

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---
title: Terminology
---
Many terms are thrown around when discussing inflation and the related components (e.g. rewards/yield/interest), we try to define and clarify some commonly used concept here:
### Total Current Supply [SOL]
The total amount of tokens (locked or unlocked) that have been generated (via genesis block or protocol inflation) minus any tokens that have been burnt (via transaction fees or other mechanism) or slashed. At network launch, 500,000,000 SOL were instantiated in the genesis block. Since then the Total Current Supply has been reduced by the burning of transaction fees and a planned token reduction event. Solana’s *Total Current Supply* can be found at https://explorer.solana.com/supply
### Inflation Rate [%]
The Solana protocol will automatically create new tokens on a predetermined inflation schedule (discussed below). The *Inflation Rate [%]* is the annualized growth rate of the *Total Current Supply* at any point in time.
### Inflation Schedule
A deterministic description of token issuance over time. The Solana Foundation is proposing a dis-inflationary *Inflation Schedule*. I.e. Inflation starts at its highest value, the rate reduces over time until stabilizing at a predetermined long-term inflation rate (see discussion below). This schedule is completely and uniquely parameterized by three numbers:
- **Initial Inflation Rate [%]**: The starting *Inflation Rate* for when inflation is first enabled. Token issuance rate can only decrease from this point.
- **Dis-inflation Rate [%]**: The rate at which the *Inflation Rate* is reduced.
- **Long-term Inflation Rate [%]**: The stable, long-term *Inflation Rate* to be expected.
### Effective Inflation Rate [%]
The inflation rate actually observed on the Solana network after accounting for other factors that might decrease the *Total Current Supply*. Note that it is not possible for tokens to be created outside of what is described by the *Inflation Schedule*.
- While the *Inflation Schedule* determines how the protocol issues SOL, this neglects the concurrent elimination of tokens in the ecosystem due to various factors. The primary token burning mechanism is the burning of a portion of each transaction fee. While $100\%$ of each transaction fee is currently being destroyed, it is planned on reducing this burn rate to $50\%$ of each transaction fee, with the remaining fee to be retained by the validator that processes the transaction.
- Additional factors such as loss of private keys and slashing events should also be considered in a holistic analysis of the *Effective Inflation Rate*. For example, it’s estimated that $10-20\%$ of all BTC have been lost and are unrecoverable and that networks may experience similar yearly losses at the rate of $1-2\%$.
### Staking Yield [%]
The rate of return (aka *interest*) earned on SOL staked on the network. It is often quoted as an annualized rate (e.g. "the network *staking yield* is currently $10\%$ per year").
- *Staking yield* is of great interest to validators and token-holders holders who wish to delegate their tokens to avoid token dilution due to inflation (the extent of which is discussed below).
- $100\%$ of inflationary issuances are to be distributed to staked token-holders in proportion to the SOL they have staked with validators.
- There may be future consideration for an additional split of inflation issuance with the introduction of *Archivers* into the economy. *Archivers* are network participants who provide a decentralized storage service and should also be incentivized with token distribution from inflation issuances for this service.
- Similarly, early designs specified a fixed percentage of inflationary issuance to be delivered to the Foundation treasury for operational expenses and future grants. However, inflation will be launching without any portion allocated to the Foundation.
- *Staking yield* can be calculated from the *Inflation Schedule* along with the fraction of the *Total Current Supply* that is staked at any given time. Since inflation interest is split between staked-token holders, the Foundation pool and, potentially, *Archivers* - only the portion delivered to validators should be considered in the calculation of *Staking Yield*. Currently, the only split discussed is the $5\%$ to the Foundation, which is likely to be directly staked upon receipt, so not impacting the yield calculation. Below, this is specified by setting the 'Fraction to Validators' to $100\%$. The explicit relationship is given by:
$$
\begin{aligned}
\text{Staking Yield} &= \text{Inflation Rate}\times \text{Fraction to Validators}\times \left( \frac{1}{\%~\text{SOL Staked}} \right) \\
\text{where:}\\
\%~\text{SOL Staked} &= \frac{\text{Total SOL Staked}}{\text{Total Current Supply}}
\end{aligned}
$$
### Token Dilution [%]
Dilution is defined here as the change in proportional representation of a set of tokens within a larger set due to the introduction of new tokens. In practical terms, we discuss the dilution of staked or un-staked tokens due to the introduction and distribution of inflation issuance across the network. As will be shown below, while dilution impacts every token holder, the *relative* dilution between staked and un-staked tokens should be the primary concern to un-staked token holders. Staking tokens, which will receive their proportional distribution of inflation issuance, should assuage any dilution concerns for staked token holders. I.e. dilution from 'inflation' is offset by the distribution of new tokens to staked token holders, nullifying the 'dilutive' effects of the inflation for that group.
### Adjusted Staking Yield [%]
A complete appraisal of earning potential from staking tokens should take into account staked *Token Dilution* and its impact on the *Staking Yield*. For this, we define the *Adjusted Staking Yield* as the change in fractional token supply ownership of staked tokens due to the distribution of inflation issuance. I.e. the positive dilutive effects of inflation.

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---
title: Storage Rent Economics
---
Each transaction that is submitted to the Solana ledger imposes costs. Transaction fees paid by the submitter, and collected by a validator, in theory, account for the acute, transactional, costs of validating and adding that data to the ledger. Unaccounted in this process is the mid-term storage of active ledger state, necessarily maintained by the rotating validator set. This type of storage imposes costs not only to validators but also to the broader network as active state grows so does data transmission and validation overhead. To account for these costs, we describe here our preliminary design and implementation of storage rent.
Storage rent can be paid via one of two methods:
Method 1: Set it and forget it
With this approach, accounts with two-years worth of rent deposits secured are exempt from network rent charges. By maintaining this minimum-balance, the broader network benefits from reduced liquidity and the account holder can trust that their `Account::data` will be retained for continual access/usage.
Method 2: Pay per byte
If an account has less than two-years worth of deposited rent the network charges rent on a per-epoch basis, in credit for the next epoch. This rent is deducted at a rate specified in genesis, in lamports per kilobyte-year.
For information on the technical implementation details of this design, see the [Rent](implemented-proposals/rent.md) section.

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---
title: Transaction Fees
---
**Subject to change.**
Each transaction sent through the network, to be processed by the current leader validation-client and confirmed as a global state transaction, contains a transaction fee. Transaction fees offer many benefits in the Solana economic design, for example they:
- provide unit compensation to the validator network for the CPU/GPU resources necessary to process the state transaction,
- reduce network spam by introducing real cost to transactions,
- and provide potential long-term economic stability of the network through a protocol-captured minimum fee amount per transaction, as described below.
Network consensus votes are sent as normal system transfers, which means that validators pay transaction fees to participate in consensus.
Many current blockchain economies \(e.g. Bitcoin, Ethereum\), rely on protocol-based rewards to support the economy in the short term, with the assumption that the revenue generated through transaction fees will support the economy in the long term, when the protocol derived rewards expire. In an attempt to create a sustainable economy through protocol-based rewards and transaction fees, a fixed portion (initially 50%) of each transaction fee is destroyed, with the remaining fee going to the current leader processing the transaction. A scheduled global inflation rate provides a source for rewards distributed to validation-clients, through the process described above.
Transaction fees are set by the network cluster based on recent historical throughput, see [Congestion Driven Fees](implemented-proposals/transaction-fees.md#congestion-driven-fees). This minimum portion of each transaction fee can be dynamically adjusted depending on historical *signatures-per-slot*. In this way, the protocol can use the minimum fee to target a desired hardware utilization. By monitoring a protocol specified *signatures-per-slot* with respect to a desired, target usage amount, the minimum fee can be raised/lowered which should, in turn, lower/raise the actual *signature-per-slot* per block until it reaches the target amount. This adjustment process can be thought of as similar to the difficulty adjustment algorithm in the Bitcoin protocol, however in this case it is adjusting the minimum transaction fee to guide the transaction processing hardware usage to a desired level.
As mentioned, a fixed-proportion of each transaction fee is to be destroyed. The intent of this design is to retain leader incentive to include as many transactions as possible within the leader-slot time, while providing an inflation limiting mechanism that protects against "tax evasion" attacks \(i.e. side-channel fee payments\).
Additionally, the burnt fees can be a consideration in fork selection. In the case of a PoH fork with a malicious, censoring leader, we would expect the total fees destroyed to be less than a comparable honest fork, due to the fees lost from censoring. If the censoring leader is to compensate for these lost protocol fees, they would have to replace the burnt fees on their fork themselves, thus potentially reducing the incentive to censor in the first place.