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92 lines
3.2 KiB
TeX
92 lines
3.2 KiB
TeX
\section{Appchain Cost Model}
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\label{sec:costs}
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%%==========================================================================
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\subsection{Cost Components}
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The total cost of operating a Lux appchain has three components:
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\begin{enumerate}[leftmargin=1.5em]
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\item \textbf{Infrastructure costs} $C_{\text{infra}}$: Hardware and bandwidth for
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validator nodes.
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\item \textbf{Validation incentives} $C_{\text{val}}$: Rewards paid to validators
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above Primary Network opportunity cost.
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\item \textbf{Protocol fees} $C_{\text{protocol}}$: LUX fees paid to the Primary Network
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(via fee sharing, Section~\ref{sec:feesharing}).
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\end{enumerate}
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\[
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C_{\text{total}} = C_{\text{infra}} + C_{\text{val}} + C_{\text{protocol}}.
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\]
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\subsection{Infrastructure Cost Model}
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Validator hardware costs are a function of throughput tier. We define five tiers:
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\begin{table}[H]
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\centering
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\caption{Appchain Throughput Tiers and Infrastructure Costs}
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\label{tab:tiers}
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\begin{tabular}{llrrrrr}
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\toprule
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\textbf{Tier} & \textbf{Name} & \textbf{TPS} & \textbf{Block Gas} & \textbf{State DB} & \textbf{Node Cost/mo} & \textbf{Min Validators} \\
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\midrule
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T1 & Micro & $<$100 & 8M & 50 GB & \$120 & 5 \\
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T2 & Standard & 100--1K & 30M & 200 GB & \$280 & 7 \\
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T3 & High & 1K--10K & 100M & 1 TB & \$650 & 10 \\
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T4 & Ultra & 10K--100K & 500M & 5 TB & \$1,800 & 15 \\
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T5 & Hyper & $>$100K & 2B & 20 TB & \$4,500 & 20 \\
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\bottomrule
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\end{tabular}
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\end{table}
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Annual infrastructure cost for a Tier $k$ appchain with $n_k$ validators:
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\[
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C_{\text{infra}}(k) = 12 \cdot n_k \cdot \text{NodeCost}_k.
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\]
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\subsection{Validation Incentive Cost}
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Let $r_{\text{primary}}$ be the annualized Primary Network staking yield and $\delta_k$
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be the premium required to attract validators to a Tier $k$ appchain. The annual
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validation incentive cost is:
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\[
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C_{\text{val}}(k) = n_k \cdot \bar{w} \cdot P_{\text{LUX}} \cdot (r_{\text{primary}} + \delta_k),
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\]
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where $\bar{w}$ is the mean validator stake weight. We estimate $\delta_k$ empirically
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in Section~\ref{sec:validators}.
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\subsection{Break-Even Analysis}
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For an appchain to be economically sustainable, its fee revenue must exceed total costs:
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\[
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R_{\text{fee}} \geq C_{\text{total}}.
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\]
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Define the \emph{break-even transaction count} as the number of transactions $N^*$
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such that average fee per transaction $f$ satisfies $N^* \cdot f = C_{\text{total}}$.
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Table~\ref{tab:breakeven} shows break-even estimates by tier:
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\begin{table}[H]
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\centering
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\caption{Appchain Break-Even Transaction Counts (Annual, Assuming \$0.01 Avg Fee)}
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\label{tab:breakeven}
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\begin{tabular}{lrrrr}
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\toprule
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\textbf{Tier} & \textbf{$C_\text{infra}$/yr} & \textbf{$C_\text{val}$/yr} & \textbf{$C_\text{total}$/yr} & \textbf{Break-Even Tx} \\
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\midrule
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T1 & \$7,200 & \$112,000 & \$119,200 & 11.9M \\
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T2 & \$23,520 & \$313,600 & \$337,120 & 33.7M \\
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T3 & \$78,000 & \$896,000 & \$974,000 & 97.4M \\
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T4 & \$324,000 & \$2,688,000 & \$3,012,000 & 301.2M \\
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T5 & \$1,080,000 & \$8,960,000 & \$10,040,000 & 1.0B \\
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\bottomrule
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\end{tabular}
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\end{table}
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These figures assume LUX at \$8.00, 7\% primary staking yield, and 5\% validator premium
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($\delta = 0.05$). They serve as minimum viability benchmarks.
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%%==========================================================================
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