More Meters or More Prices? One- vs. Multi-dimensional Fee Mechanisms on Ethereum

1 Introduction

• The study provides an empirical, simulation-based comparison of Ethereum’s one- and multi-dimensional fee mechanisms under calibrated resource demand and capacity constraints.Prior analyses focused primarily on theoretical guarantees and did not establish performance under observed resource demand and capacity constraints.Source: §1 · pp. 1–2
• State is the most price-responsive resource and execution the least, based on demand calibrated from Ethereum’s 2025 gas-limit increases.Because those increases changed all resource prices together, the model treats each resource’s demand independently.Source: §1 · p. 2
• Under one-dimensional fees, state reaches its target first and sets the shared fee, leaving other resources below target; metering rescaling aligns targets only under constant demand.With varying demand, a single fee cannot track all resources, leaving them under target even with higher targets or an alternative update rule.Source: §1 · p. 2
• Separate fees remove price coupling, but execution still generates block-level access-list data and remains constrained by data pricing and capacity.Allocating more block time to data propagation can relieve that constraint until shorter execution time becomes binding.Source: Figure 1 · p. 1, §1 · p. 2
• At comparable congestion, selected multi-dimensional configurations deliver 4–34% more execution while keeping state growth near its target, unlike tested one-dimensional configurations.The comparison spans different allocations between execution and data propagation time.Source: §1 · p. 2

2 Background and Related Work

• A one-dimensional mechanism can meter resources in separate counters while charging them a shared price; multi-dimensional fees assign distinct prices to resources.The shared base fee responds to the larger regular or state branch, while the multi-dimensional proposal gives execution, data, and state separate base fees.Source: §2 · p. 2
• Execution and data must fit block-validation deadlines, and increasing propagation time raises data capacity while reducing execution capacity.The analysis restricts propagation time to at most five seconds, where data capacity approaches the consensus-layer limit.Source: §2 · p. 2
• Execution and state creation produce block-level access-list data that must propagate with the block, so separate prices do not eliminate resource dependencies.In the toy example, execution reaches at most 71% of its target when its generated BAL data faces a fixed data fee.Source: §2 · pp. 2–3
• The transaction floor charges the larger of execution gas and a per-byte floor, and raising its rate can permit a higher gas limit.The gain stops near 96 gas per byte, when a block of ETH transfers sets the constraint.Source: §2 · pp. 2–3
• Prior theoretical work studies welfare, resource prices, and capacity lost by combining constraints; this paper evaluates utilization trade-offs on Ethereum using calibrated demand and simulation.The cited work includes studies of EIP-1559, Ethereum resource use and metering, and demand elasticities from within-wallet fee variation on Arbitrum.Source: §2 · p. 3

3 Demand Model and Calibration

• The model represents execution, static-content data, and state activity in historical gas-equivalent units and assigns each an effective price based on its metering and base fee.A metering coefficient converts activity into counterfactual metered gas.Source: §3 · pp. 3–4
• The independent-demand assumption sets cross-price elasticities to zero because common-fee changes cannot separate own-price from cross-price effects.This assumption does not mean users demand resources separately; a transaction can consume all three.Source: §3 · p. 3
• Calibrated own-price elasticities are 0.121 for execution, 0.229 for static-content data, and 0.335 for state.The estimates use two retained capacity-increase events and 35-day pre- and post-event windows; the third event was excluded because its post-period overlapped a blob-capacity increase.Source: §3 · pp. 3–4, Table 3 · p. 4
• Across alternative window lengths, state remains the most price-responsive resource and execution the least.The ordering breaks only in the excluded November event, when data falls below execution, as expected if cheaper blob space drew rollup data away from calldata.Source: §3 · pp. 3–4

4.1 Metering and calibration

• The calibration reconstructs per-transaction execution, static content bytes, and runtime BAL bytes because the transaction floor cannot be applied to aggregate bytes.It samples 6,000 blocks and 1,899,748 transactions; the data-attributed regular-gas coefficient rises from 1.589 at F = 40 to 4.033 at F = 96.Source: §4.1 · p. 4

4.2 Equilibrium under a shared base fee

• State determines the shared fee across capacity allocations in the baseline and growth-matched benchmarks, leaving regular gas below target.At the regular-clearing fee, state demand is 5.4–8.4 times the target in the baseline and 13.4–19.1 times in the growth-matched benchmark.Source: §4.2 · p. 4
• A sustained 10% rise in state demand reduces equilibrium execution by about 3.4%, even when execution demand is unchanged.Changing the floor rate cannot relieve the bottleneck because the state-clearing fee does not depend on that rate.Source: §4.2 · p. 5

4.3 Simulation under fluctuating demand

• The baseline grows state by 288.1–403.4 GiB/year, while growth matching holds growth near 120 GiB/year but cuts execution to 67.5–70.2M.The baseline retains the original CPSB; growth matching raises CPSB to restore the state-growth objective, which further suppresses regular gas.Source: §4.2 · p. 4, §4.3 · p. 5
• Under fluctuating demand, normalized state gas raises execution to 177.9M at a 3.5-second allocation, but both branches remain below target on average.Regular utilization is 88.5%–90.6%, normalized state utilization is 71.6%–73.4%, and state growth is 86.0–88.1 GiB/year.Source: §4.3 · p. 5
• Raising the normalized benchmark’s target ratio from 1/2 to 4/5 increases execution at a 3.5-second allocation from 177.9M to 215.0M, while state growth falls from 86.0 to 56.8 GiB/year.With ratios of 2/3 and above, more than 10% of blocks reach a hard limit, versus about 4% at 1/2.Source: §4.3 · p. 5, Figure 2 · p. 5

5 Multi-dimensional Fee Mechanism

• EIP-7999 assigns execution, data, and state separate base fees, with execution and data limits and a state target of 75M gas per block.The design retains state metering and its target, while execution and data targets are design choices tied to their propagation-dependent limits.Source: §5 · p. 6

5.1 Demand with BAL charge

• Execution and state generate BAL data, so a higher data fee raises their effective prices and a binding data limit can exclude their activity with its generated BAL.The model includes BAL charges in parent-activity prices; when the data limit binds, bundle inclusion removes execution or state activity together with the BAL it generates.Source: §5.1 · p. 6, §5 · p. 6

5.2 Execution–data target frontier

• The execution–data frontier marks the largest execution target that clears at each data target; under the central calibration, the maximum execution target is about 309M.The required data target rises from 57.4M at a 250M execution target to about 144M at the ceiling.Source: §5.2 · p. 6

5.3 Utilization under fluctuating demand

• At E275, execution utilization rises from 53.7% at D22.5 to 90.9% at D67.5, then falls to 82.1% at D80 as the binding constraint shifts from data price to data capacity.At D22.5, the execution fee is at its 1-wei minimum in 95.2% of blocks while the data limit binds in only 0.1%; at D80, the data limit binds in 59.2%.Source: §5.3 · p. 7
• At E275/D80, the data limit binds in 59.2% of blocks and execution averages 225.7M, or 82.1% of target, despite clearing all targets in equilibrium.Bundle inclusion excludes execution that generates excess BAL data, so equilibrium feasibility does not ensure sufficient data capacity under block-by-block demand variation.Source: §5.3 · p. 7
• At 4 seconds of propagation, execution usage reaches 95.5% of its target; beyond 4 seconds, execution limits cap gains and usage plateaus around 263M as remaining data-limit relief is offset.The execution limit falls to 450M and 400M, while its binding frequency rises to 5.5% and 12.0%, overtaking the data limit after 4.5 seconds.Source: §5.3 · p. 8

6 Comparison

• 6.8–56.0M more mean execution at every allocation is delivered by conservative multi-dimensional configurations than by the normalized benchmark at a 1/2 target ratio, with near-limit shares of 1.9%–4.4% versus 4.0%–4.5%.Allowing 25% more near-limit blocks raises the execution gain to 31.2–57.7M.Source: §6 · p. 8
• 46.5–72.0M more execution at every allocation is delivered by maximum-throughput configurations than by the normalized benchmark at a 4/5 target ratio, with near-limit shares of 16.6%–32.1% versus 13.2%–20.6%.The execution fee is at its minimum in 54.3%–68.7% of blocks; at 3- and 3.5-second allocations, the benchmark exceeds conservative configurations only with far more congestion.Source: §6 · p. 8
• Multi-dimensional configurations keep state growth near its 120 GiB/year target, while none of the tested one-dimensional benchmarks combines near-target state growth with high execution.The growth-matched benchmark reaches 121.4–121.6 GiB/year only as execution falls to 67.5–70.2M; the tested fake-exponential update reaches 244.2M execution and 94.0–96.0 GiB/year of state growth, while both branches still underfill targets.Source: §6 · p. 8

Limitations

• Results are conditional on calibrated demand: tested execution targets are 7–9 times the metered anchor, and historical data cannot establish whether demand at that scale will materialize.The central calibration uses five-week windows; throughput levels depend on calibration, although results hold qualitatively across alternatives.Source: §7 · p. 8
• BAL demand response cannot be estimated historically, so the one-dimensional model folds its floor uplift into static-content demand, an approximation weaker at high floor rates.For the multi-dimensional mechanism, the model applies the parent activity’s elasticity to its BAL-inclusive price.Source: §7 · p. 8
• The analysis omits the blob fee market and EIP-7999’s blob-linked reserve price, and does not quantify transition costs such as EVM accounting and user fee estimation changes.The paper identifies the interaction between data and blob prices and whether protocol-generated BALs should face a reserve as topics for further study.Source: §7 · p. 8

Conclusion

• Under calibrated demand, separate pricing delivers 4–34% more execution at comparable congestion across propagation allocations, with higher target utilization and state growth near its target.The conclusion specifies that data targets and limits must account for execution-generated data and execution targets within the execution–data frontier.Source: §7 · pp. 8–9

• ChatGPT and Claude assisted with model discussion, checking derivations, simulation code, and shortening selected passages; the authors made final decisions and take responsibility.Source: Use of Generative AI · p. 9

Elasticity calibration

• The central elasticity calibration matches average observed total-gas response at the 45M-gas regime’s mean daily resource shares, with a common shift of 0.004.Matching finite-change aggregate responses to local elasticities is approximate; using 2026 activity shares raises each elasticity by about 0.007.Source: A Metering and calibration · p. 10
• State activity rose 97.6% after the February capacity event, versus 2.3% for execution; in July, execution rose 21.8%, but the events lack an untreated control.The observed patterns cannot separate capacity effects from contemporaneous demand changes.Source: A Metering and calibration · p. 10, Figure 7 · p. 11

Execution metering

• Execution metering reconstruction raises the historical anchor from 23.942M to 34.667M gas per block, yielding m_E ≈ 1.448.The estimate covers 860,505 mainnet blocks and incorporates repricing, intrinsic-gas changes, and refunds.Source: A Metering and calibration · p. 10

Data metering

• At floor rates of 82 and 96, BALs change regular gas for 4.46% and 6.79% of sampled transactions, respectively.Because historical data do not identify responses to these charges, the aggregate BAL uplift is assigned to static-data activity as an assumption.Source: A Metering and calibration · p. 10

BAL attribution

• At 16 gas per byte, mean runtime BAL gas was 1.919M per block, attributed to state creation and execution using reconstructed runtime BAL bytes.The resulting weights were w_S = 0.0417 and w_E = 0.0710.Source: A Metering and calibration · p. 10, Table 6 · p. 10

Demand path construction

• Demand paths remove estimated historical fee responses and adjust for BAL relative to the amount predicted by parent activities, preserving the BAL anchor.Observed activity reflects both demand variation and responses to historical fees.Source: B Demand path construction · p. 11
• Joint resampling of contiguous 3,200-block segments, eight-day conditions, and hourly profiles preserves persistence and co-movement across resources and timescales.The 32 shared paths each use a one-day burn-in followed by seven measured days.Source: B Demand path construction · p. 11

Block inclusion

• When execution exceeds its limit, it is capped first; if remaining data demand exceeds its limit, all remaining activity is scaled, including execution.This data-limit scaling applies even when the execution limit is slack; one-dimensional simulations instead use a common factor when either branch exceeds its limit.Source: B Demand path construction · p. 11

Fake-exponential update

• At 3.5 seconds, the fake-exponential update raises execution from 215.0M to 244.2M as mean fees fall from 18.26 to 3.56 wei.State growth rises from 56.8 to 94.0 GiB/year, while regular and normalized state utilization remain 85.8% and 78.4%.Source: C Comparison details · p. 12, Table 9 · p. 12

Paired-path comparison

• 19.5–56.2M more execution per block was achieved by maximum-throughput configurations than by the fake-exponential normalized benchmark across allocations.The paired-path gains were positive on every path at every allocation, though configurations were selected on those same paths.Source: C Comparison details · p. 12, Table 9 · p. 12
• The selection delivers more execution on 30 of 32 paths at 3 seconds and every path at other allocations, despite a minimum path-level difference of -3.6M; this is in-sample.Source: C Comparison details · p. 12

One-dimensional mechanisms

• In baseline and growth-matched benchmarks, state is the equilibrium bottleneck under every calibration, setting the shared fee in at least 92.5% and 97.7% of blocks, respectively.At the regular-clearing fee, state demand exceeds target by at least 5.4-fold and 13.4-fold, respectively.Source: D Robustness to elasticity calibration · p. 12, Table 8 · p. 13

Comparison

• Across elasticity calibrations and propagation allocations, reselected multi-dimensional configurations deliver more execution than the normalized benchmark, including its fake-exponential update, while holding state growth near target.Gains are smaller under the 60- and 75-day calibrations, where lower execution elasticities limit the execution any mechanism can attract.Source: D Robustness to elasticity calibration · p. 12, Table 8 · p. 13

One-dimensional mechanisms

• With central k held fixed, normalized state demand reaches 2.1–2.8 times target under other calibrations, while regular gas falls to 64–81% of target even in equilibrium.Realignment would require scaling k by a factor of 5–44, so a one-time calibration may not suffice if demand changes.Source: D Robustness to elasticity calibration · p. 12

Multi-dimensional mechanism

• Under 60- and 75-day calibrations, lower execution elasticity reduces the execution ceiling to 151.6M and 143.2M, so nearly all tested grid configurations cannot clear.The tested grid is extended to execution targets of 100–140M.Source: D Robustness to elasticity calibration · p. 12, Table 8 · p. 13