# Snark: Designing token price

We have previously discussed the equilibrium value of a token and its impact in a decentralized ecosystem. We settled on Pm < t < Cm, where Pm is the (P)roviders (m)inimum cost and Cm is the (C)onsumers (m)aximum expenditure.

The objective, solve for t within the proposed architecture. We have noticed a current design trend where token price does not take system equilibrium into consideration. We explain this statement shortly.

Solve for Pm

We start with an investigation on current Proof of Work based systems.

We define the following metrics

• Hashing Power (H/s)
• Power Consumption (W)
• Cost per KWh in \$(cpk)
• Cost / Day in \$(cd) (cpk x 24)
• Price in \$ (p)
• Mined / Day (md)
• Income / Day in \$ (id) (md x p)
• Profit / Day in \$ (pd) (id - cd)

Bitcoin

• 4730 GH/s
• 1293 W
• 0.12 cpk
• 3.72384 cd
• 6616.73 p
• 0.0002217 md
• 1.466929041 id
• -2.256910959 pd

Bitcoin currently has a profit per day of -\$2.26

For the sake of brevity we will simply list the averaged conclusions

• BTC -\$2.26 @ \$6616.73 / BTC
• ETH \$0.23 @ \$474.58 / ETH
• ETC \$0.11@ \$17.12 / ETC
• XMR \$-0.11 @ \$138.05 / XMR
• ZEC \$-0.24 @ \$181.85 / ZEC
• DASH -\$0.50 @ \$247.29 / DASH
• LTC -\$0.31 @ \$84.86 / LTC

There is a trend towards 0.

How does this have a direct impact on token price?

We will use Ethereum as our example. Ethereum has a block time of ~13 seconds. 6,646.153 blocks per day (24 hours x 60 minutes x 60 seconds / 13 second block time). 3 ETH ( ByzantiumBlockReward) per block. 19,938.46 ETH per day @ 282 978 GH/s

A GeForce 1070 can have 31.06 MH/s for 130 watts, or 0.0021 ETH per day for 130 watts. 0.0021 ETH @ \$474.58 gives and income of \$0.99 per day. 130 watts @ \$0.12 KWh costs \$0.37 per day. \$0,62 / day.

Let us reverse the Ethereum price and work it off of total hashing rate.

282 978 GH/s x 1000 (MH/s) / 31.06 (MH/s) gives us 9,110,688. This will require 1,184,389,568.57 watts. At \$0.12 KWh this would cost \$142,126.74 per hour (watts / 1000 x 0.12). \$3,411,041.95 per day (cost per hour x 24). This produces 19,938.46 ETH per day, production cost value of \$171.07 ETH (Total cost per day / total ETH per day produced)

The above is inaccurate as there are varying miners, each with a different hashing vs cost efficiency rate as well as price fluctuations from country to country. For a detailed model you would need average hash contribution per country and cost per country.

How do we derive a tokens value in a PoW based model?

Total daily hashing power (represented in kW) x KWd / total daily token production

If the total daily hashing power was 31.06 MH/s (represented as 130 w) then we could conclude that the cost of a single ETH would be \$0,0000018. (130 (w) / 1000 (kW) x 0.12 (KWh) x 24 (KWd) / 19,938.46 (ETH per day)

Unsurprisingly, the cost of an ETH is the cost of its production.

How do we transfer this to a Proof of Stake based model?

Cost of production is as simple as hosting a node and including stake.

Theory 1: Stake is tied to production cost.

Theory 2: Stake is equivalent to up front hardware expenditure and thus does not contribute.

Continuing on from theory 2.

Operational cost of running a node.

• AWS t2.nano \$0.0058 per hour
• AWS t2.medium \$0.0464 per hour
• AWS t2.2xlarge \$0.3712 per hour

Total network nodes x operational cost / total daily token production

Production leans towards higher tier nodes as production can occur faster, higher likelihood of being accepted in the network.

Ethereum currently has 16,970 nodes reported. Averaged to AWS t2.medium (\$0.0464 per hour, \$1,11 per day) we have a production cost of \$18,897.79 per day or an ETH price of \$0,94.

Let’s test with Qtum (Confirmed details are vague)

4 QTUM per block. 2 minute blocks. 2880 QTUM per day. May 21 reported ~7000 staked nodes. A cost of \$7,770 per day. \$2,69 QTUM, trading at ~\$16

We will be collecting more network participation test to confirm staked node participation relationship to production cost.

The theory proposes that network participation x cost of nodes / total daily rewards is the equilibrium of token value.

POA Network, 12 validators, 5 second blocktime, 1 POA per block. 17,280 POA per day. Assuming stronger hardware, \$0.3712 (t2.2xlarge x 12 validators x 24 hours) or \$106,90 production cost per day should gravitate the token equilibrium towards \$0.0061.

Calculating storage

Current gas used for SSTORE (Save 256 bit word to storage) is 20,000 gas. 1 KB (1024 bytes, 8,192 bits, 32 256 bit words) would cost 640,000 gas, at 50 gwei (0.00000005 ETH) it would cost 0.032 ETH, 32.768 ETH for an MB (1 KB x 1024).

AWS S3 costs \$0.023 per GB vs 33,553.432 ETH (1 MB x 1024), so for competitive storage 1 GB would need to cost 0.0000483 ETH

Can production cost and storage cost be consolidated? Production cost is a function of computational and network operational expenses. Storage cost is a function of production cost of 1 bit.

There are thus two economic incentives at play that are opposing forces. The primary use case for a system will prevail.

This suggest a secondary token requirement for storage cost. This will be explore in another article.

Solve for T

Consider a Proof of Stake based network with 1 node (n) and 1 Token (t) per day. t would be valued at \$1.11. For 100n = \$111t.

Reward rates must form part of evaluation. A token sold at \$1, with a block size of 1s and a reward of 1t would find a equilibrium towards \$0.00001284 (1n@\$1.11 / (24 (hours) x 60 (minutes) x 60 (seconds) x (token))). It would require a 100 000 node participation to reach over \$1.28

We must consider block size, block reward, and theoretical node participation for the value of t.

First design block rewards. Then design tokenomics. Be reasonable with regards to node participation.

T will gravitate towards Pm < t < Cm

100 nodes @ \$1.11 with a token price of \$0.24 should produce 462.5t per day or 0.005t per second.

Consider these metrics when you investigate the value of a token.