```
ZIP: 234
Title: Smooth Out The Block Subsidy Issuance
Owners: Jason McGee <jason@shieldedlabs.com>
Mark Henderson <mark@equilibrium.co>
Tomek Piotrowski <tomek@eiger.co>
Mariusz Pilarek <mariusz@eiger.co>
Original-Authors: Nathan Wilcox
Credits:
Status: Draft
Category: Consensus
Created: 2023-08-23
License: BSD-2-Clause
```

The key words “MUST”, “SHOULD”, “SHOULD NOT”, “MAY”, “RECOMMENDED”, “OPTIONAL”, and “REQUIRED” in this document are to be interpreted as described in RFC 2119. [1]

“Network upgrade” - to be interpreted as described in ZIP 200. [2]

“Block Subsidy” - to be interpreted as described in the Zcash Protocol Specification (TODO ZIP Editors: link from comment).

“Issuance” - the sum of Block Subsidies over time. (TODO ZIP Editors: work out if this definition is correct or can be removed).

“`ZsfBalanceAfter(h)`

” is the total ZEC available in the
Zcash Sustainability Fund (ZSF) after the transactions in block
`h`

, described in ZIP draft-zsf.md. In this ZIP, the
Sustainability Fund is used to pay out Block Subsidies from unmined ZEC,
and other fund deposits.

Let `PostBlossomHalvingInterval`

be as defined in
[#protocol-diffadjustment]_.

This ZIP proposes a change to how nodes calculate the block subsidy.

Instead of following a step function around the 4-year halving intervals inherited from Bitcoin, we propose a slow exponential “smoothing” of the curve. The new issuance scheme would approximate the current issuance over 4-year intervals.

This ZIP depends on the ZIP introducing the Zcash Sustainability Fund (ZIP-XXX).

The current Zcash economic model, inherited from Bitcoin, includes a halving mechanism which dictates the issuance of new coins. While this has been foundational, halvings can lead to abrupt changes in the rate of new coins being introduced to the market. Such sudden shifts can potentially disrupt the network’s economic model, potentially impacting its security and stability. Furthermore, the halvings schedule is fixed and does not provide any way to “recycle” funds into future issuance.

To address this, we propose issuing a fixed portion of the pending funds-to-be-issued in each block. This has the effect of smoothing out the issuance curve of ZEC, ensuring a more consistent and predictable rate of coin issuance, while still preserving the overall supply cap of 21,000,000 coins. This mechanism by itself (without other anticipated changes) seeks to preserve the core aspects of Zcash’s issuance policy and aims to enhance predictability and avoid sudden changes. By making this shift, the average block subsidy over time will remain predictable with very gradual changes.

However, we anticipate schemes proposed in [#draft-zsf]_ where the amount of funds-to-be-issued may increase. In that scenario, this issuance mechanism would distribute that increase starting in the immediately following block and subsequent blocks. Because this distribution mechanism has an exponential decay, such increases will be spread out in miniscule amounts to future blocks over a long time period. This issuance mechanism thus provides a way for potential increases or decreases of issuance while constraining those changes to be small on a short time scale to avoid unexpected disruptions.

Additionally, the current Bitcoin-style issuance does not take into
account the current balance of `ZsfBalanceAfter(h)`

. If
[#draft-zsf]_ were to activate without a change to the issuance
mechanism, then some funds would never be disbursed after they are
deposited back into the ZSF.

Smoothing the issuance curve is possible using an exponential decay formula that satisfies the following requirements:

- The issuance can be summarised into a reasonably simple explanation
- Block subsidies approximate a continuous function
- If there are funds in the ZSF, then the block subsidy must be non-zero, preventing any final “unmined” zatoshis
- For any 4 year period, all paid out block subsidies are approximately equal to half of the ZSF at the beginning of that 4 year period, if there are no deposits into the ZSF during those 4 years

TODO daira: add a requirement that makes the initial total issuance match the previous total issuance

We want to decrease the short-term impact of the deployment of this ZIP on block reward recipients, and minimise the potential reputational risk to Zcash of changing the block reward amount.

Define constants:

“`BLOCK_SUBSIDY_FRACTION`

” = 4126 / 10,000,000,000 or
`0.0000004126`

“`DEPLOYMENT_BLOCK_HEIGHT`

” = 2726400

At the `DEPLOYMENT_BLOCK_HEIGHT`

, nodes should switch from
the current issuance calculation, to the following:

Given the block height `h`

define a function
**BlockSubsidy(h)**, such that:

**BlockSubsidy(h)** = Block subsidy for a given
`h`

, that satisfies above requirements.

Using an exponential decay function for **BlockSubsidy**
satisfies requirements **R1** and **R2**
above:

`BlockSubsidy(h) = BLOCK_SUBSIDY_FRACTION * ZsfBalanceAfter(h - 1)`

Finally, to satisfy **R3** above we always round up to
the next zatoshi.

`BlockSubsidy(h) = ceiling(BLOCK_SUBSIDY_FRACTION * ZsfBalanceAfter(h - 1))`

`BLOCK_SUBSIDY_FRACTION`

Let `IntendedZSFFractionRemainingAfterFourYears`

=
0.5.

The value `4126 / 10_000_000_000`

satisfies the
approximation within +0.002%:

`(1 - BLOCK_SUBSIDY_FRACTION)^PostBlossomHalvingInterval ≈ IntendedZSFFractionRemainingAfterFourYears`

Meaning after a period of 4 years around half of
`ZSF_BALANCE`

will be paid out as block subsidies, thus
satisfying **R4**.

The largest possible amount in the ZSF is MAX_MONEY, in the theoretically possible case that all issued funds are deposited back into the ZSF. If this happened, the largest interim sum in the block subsidy calculation would be MAX_MONEY * 4126 + 10000000000.

This uses 62.91 bits, which is just under the 63 bit limit for 64-bit signed two’s-complement integer amount types.

The numerator could be brought closer to the limit by using a larger denominator, but the difference in the amount issued would be very small. So we chose a power-of-10 denominator for simplicity.

TODO for ZIP owners: How many ZEC per day?

`DEPLOYMENT_BLOCK_HEIGHT`

The deployment should happen at the next halving, which is block
`2726400`

.

Since there is a planned halving at this point, there will already be
a significant “shock” caused by the drop in issuance caused by the
halving. This reduces surprise and thus increases security. Also, due to
the nature of the smoothed curve having a portion of the curve above the
respective step function line at times, this will maximally
*reduce* the issuance shock at the
`DEPLOYMENT_BLOCK_HEIGHT`

.

The following graph illustrates compares issuance for the current halving-based step function vs the smoothed curve.

The graph below shows the balance of the ZSF assuming smooth issuance is implemented.

The implementation of this ZIP MUST be deployed at the same time or after the Zcash Sustainability Fund is established (ZIP-XXX).

The ZSF simulator allows us to simulate the effects of this ZIP on the ZSF balance and the block subsidy, as well as generate plots like the ones above. Its output:

`Last block is 47917869 in ~113.88 years`

indicates that, assuming no ZEC is ever deposited to the ZSF, its balance will be depleted after 113.88 years, and the block subsidy will be 0 ZEC after that point.

This fragment of the output

```
Halving 1 at block 1680000:
ZSF subsidies: 262523884819889 (~ 2625238.848 ZEC, 1.563 ZEC per block)
legacy subsidies: 262500000000000 (~ 2625000.000 ZEC, 1.562 ZEC per block)
difference: 23884819889 (~ 238 ZEC), ZSF/legacy: 1.0001
```

shows that the difference between the smoothed out and the current issuance schemes is 238 ZEC after 1680000 blocks (aroound 4 years).

[1] RFC-2119: https://datatracker.ietf.org/doc/html/rfc2119

[2] ZIP-200: https://zips.z.cash/zip-0200

[3] ZIP-XXX: Placeholder for the ZSF ZIP