# CC vs Deal Sealing

We explore the viability of sealing sector types considering the difference in cost profiles. This in part, extends from an earlier [analysis](https://hackmd.io/tQFbJ25tQsiwOKWXKEyM4w?both) investigating bounds on the QAP multiplier for Filecoin Plus.

**Defining Terms**

- $Q(t)$ : Network QAP
- $M(t)$ : Newly Minted Block Rewards
- $C(t)$ : and cost of sealing and maintaining a CC sector (in FIL) (note that this depends Filecoin's Exchange Rate)
- $C_D(t)$ : capital and operational expenditures incurred over the lifetime of a sector with client data.
- $D(t)$: The amount clients/users are wiling to pay and SP for a sector's worth of data storage. Note, for sealing and proving CC Sectors, $D(t) = 0$, unless an SP decides to snap deal
- $m$ - Sector Quality Multiplier

The profit $P$ Storage Provider (SP) receives over the lifetime of a sector is:

$$ P = TR - TC $$

where $TR$ is Total Revenues and $TC$ is total costs incurred.

Assuming SPs look to maximize profit, When choosing between sealing sector types, they will choose sealing and maintaing the sector type for which they expect to receive the greatest profit. Let $P_C$, and $P_V$ denote the profit for received for sealing and maintaining a committed capacity, and filecoin plus sector with data from verified clients respectively. Then:

$$ P_C(t) = \frac{M(t)}{Q(t)} - C(t) $$

$$ P_V(t) = D(t) + \frac{mM(t)}{Q(t)} - C_D(t) $$

- We assume that the cost of sealing and maintaing a CC sector places a **lower bound on the costs incurred for all sector types**, such that $C(t) < C_D(t)$.
- We then can rewrite $C_D(t)$ in terms of $C(t)$ such that:
$$ C_D(t) = kC(t) $$

where $k>1$. Note, SPs are heterogenous with respect to comparative advantages for committing capacity, engaging with clients to store deals etc, so $D(t)$, $C(t)$ and $k$ will be different across SP profiles. If, for an SP, $P_V > P_C$ then they would prefer to onboard Fil+ sectors, and vice versa.

In order for $P_V > P_C$:

$$ \frac{mM(t)}{Q(t)} + D(t) - kC(t) > \frac{M(t)}{Q(t)} - C(t) $$

Therefore, mining with Filecoin plus will only be viable for an SP if:

$$ m > 1 + \frac{Q(t)}{M(t)} \cdot [(k-1)C(t) - D(t)] $$

if SPs cannot charge clients for data storage, this reduces to:

$$ m > 1 + \frac{Q(t)}{M(t)} \cdot [(k-1)C(t)] $$

If there were **no** data storage incentives on the network (i.e. $m=1$), then the profit $P_D$ for storing data on the network is:

$$ P_D(t) = D(t) + \frac{M(t)}{Q(t)} - C_D(t) $$

Therefore, in order for SP's to prefer to engage with clients to store data $P_D > P_C$ :

$$ D(t) + \frac{M(t)}{Q(t)} - C_D(t) > \frac{M(t)}{Q(t)} - C(t)$$

and so,

$$ D(t) > (k-1)C(t)$$

Note that this result does not depend on network reward or on QAP. It states that in order for there to be any incentive to store data on the network, an SP's clients to be willing to pay **atleast** the difference in cost incurred for storing and maintaining client data versus simply committing an equivalent amount of capacity.