# Research Note for SubSpace: Dynamic Issuance
*This research note is a short digest of extensions and topics you might find relevant to your work. Feel free to ignore, criticize, extend, or reach out to discuss further.*

Dynamic Issuance of block rewards is a promising strategy to ensure stability in the network. The idea is that when demand is low, and storage rewards are few, block producers get increased issuance to compensate them for continuing to produce blocks.

Define $S_t$ as a farmer's shortfall at epoch $t$, representing the amount by which their costs exceeded their revenue. Define a full block as having size $B^*$ and so let $B^* - B_{t}$ be the output gap at time $t$, or the amount of unused space in the block during epoch $t$. Lastly, propose some subsidy parameter $\alpha$ that rewards farmers as a function of the realized block size.

We can write a farmer's profitability $\pi$ as the sum
$$
\pi_{t=0} = ∑_{t=1}^∞ δ^{t-1} \cdot E[α (B^* - B_{t}) - S_{t}]
$$

Which is the discounted sum of future subsidies and shortfalls (negative shortfalls are profit, but we aren't focused on such cases here). Want to choose $\alpha^*$ such that expectation is non-negative across some epoch $t$, which gives

$$
\alpha^*= \frac{S_{t}}{(B^* - B_{t}) }
$$

This suggests naturally that alpha should increase in proportion to the farmer shortfall and decrease in the magnitude of the output gap measurement. In practice some precision around the output gap will be required, as it will be better to consider $B_{t}$ as the number of acceptable transactions in the mempool so farmers aren't indifferent between the subsidy and inclusion.

*n.b.: a full model might consider shortfall as a function the output gap itself, as well as being more explicit about expectations and fixed vs variable costs. If neccessary this could be added.*

## Should Issuance Increase Over Time?
Nominally this is plausible. if e.g. periods of positive output gap create some inflation cost $I_t = -\sum_{k=1}^{t} \gamma^{t-k} (B^* - B_k)$ then the nominal value of $\alpha (B^* - B_{t})$ might need to increase.

However a real-valued increase in $\alpha (B^* - B_{t})$ over time would have a cost that grows geometrically, since the token value is declining as more is being given out.

## Is this dynamic issuance an effective stimulus?

Arguably this is a supply side stimulus but it's dubious that normal "stimulus" type of effects would apply on the supply side here.