Concepts Tokenomics Chain Buys

Chain Buys

ALPHA bought by the protocol itself, paid for with TAO emissions that could not be injected into a subnet's pool. When a block's TAO emission cannot all be injected at the current ALPHA price, the chain spends the leftover buying ALPHA and supporting the price.

Every block , a subnet's TAO emission is injected into the subnet's pool together with a matching amount of ALPHA. There is a budget though, on how much ALPHA the protocol can inject in a single block, so it does not inject too much.

When that matching amount of ALPHA would exceed the budget, the protocol injects only as much ALPHA as the budget allows, together with the TAO that matches it. The protocol then spends the leftover TAO buying ALPHA through the subnet's pool. Those purchases are called "Chain Buys", and because the protocol is a buyer in that situation, they push the ALPHA price up.

A subnet receives chain buys whenever the ALPHA that matches its TAO emission at the current price would exceed its injection budget. A low ALPHA price pushes toward this, since more ALPHA is then needed to match the TAO emission. So does age, a subnet's ALPHA injection budget shrinks as it matures (and the root proportion decreases), so an older subnet exceeds it more easily. Chain Buys are therefore strongest for relatively low-priced, mature subnets and rare for high-priced or young ones.

The protocol first works out how much ALPHA would match the TAO emission at the current price:

$$ \text{ALPHA}_{\text{to inject}} = \frac{\text{TAO}_{\text{emission}}}{\text{ALPHA}_{\text{price}}} $$

If that amount is over the injection budget, it is held to that budget. The TAO injected with it is then recalculated from the ALPHA to inject:

$$\text{TAO}_{\text{to inject}} = \text{ALPHA}_{\text{to inject}} \times \text{ALPHA}_{\text{price}}$$

Whatever TAO was allocated to the subnet but not injected becomes the "Chain Buy". Here an example:

  1. A subnet is allocated 0.1 TAO for the block, and its ALPHA price is 0.1 TAO
  2. Keeping the price the same would need 0.1 / 0.1 = 1 ALPHA
  3. The subnet's ALPHA injection budget is 0.5 ALPHA (its root proportion of "0.5" times its ALPHA emission of "1")
  4. The TAO to inject with it is 0.5 x 0.1 = 0.05 TAO
  5. The remaining 0.05 TAO is spent as a "Chain Buy"

Injecting liquidity into a subnet pool does not push its price up, only buying does, which is why the leftover TAO is spent buying ALPHA rather than injected. Holding the ALPHA to the budget and using the leftover TAO as "Chain Buys" puts the whole emission to use while supporting the price.

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