PAYBACK: A Toy Economy of AI Capital Returns, and the Intelligence Elasticity of Demand

deslop.media editorial

v1 — September 13, 2026

Companion manuscript to PAYBACK · AI Economy Model v1

Abstract

Under what conditions does capital invested in an AI economy pay back? PAYBACK treats that question as a finite-grid experiment rather than a forecast. It runs 136,400 twelve-year policy-seasons in a seeded three-lab toy economy, varying demand, training credit, and strategy around data center buildout, training, serving, and market clearing. Within the eta 0.3 frontier-building policy sample, year-3 revenue coverage ranked eventual payback far better than the observable intelligence-elasticity diagnostic. In the structural grid, every tested price curve paid back through intelligence elasticity 0.89; outcomes diverged only in the two lowest rows. The analysis supplies an inspectable account of how capability, compute, and monetization interact, together with a bounded definition of intelligence elasticity of demand. Demand, task arrival, and price ceilings are model inputs, while posts, pay, and work allocation clear endogenously. The findings describe seeded model worlds, not calibrated forecasts of the real economy.

Keywords: artificial intelligence; capital returns; demand elasticity; model economy; simulation.

JEL codes: E22; O33.

1. Introduction

Whether the capital now flowing into AI infrastructure will pay back has become a general preoccupation, not a specialist one. The answer bears on three things at once: the pace of technical progress, the possibility of a capital bubble, and the future composition of work. Public argument about it, however, runs almost entirely on intuitions about demand — how much work smarter models will find to do, and at what pay — intuitions that are rarely stated precisely enough to be wrong.

The study turns that intuition into a testable object: AI Economy Model v1, a deliberately small economy whose fictional rules are abstracted from the real one. Capability makes new uses serviceable, but serving them requires compute that costs money to build and operate. Their interaction determines whether invested capital returns. Demand is exogenous: the catalog fixes which tasks arrive, their capability thresholds, and their price ceilings. Each task’s volume is a bounded seeded draw; posts, pay, and the division of work clear endogenously. The analysis sweeps those bounded inputs and reports distributions over seeded model worlds.

Three results organize the manuscript. First, in-sample year-3 monetization coverage strongly ranks eventual industry payback within the tested policy sample, while the observable intelligence-elasticity diagnostic is much weaker. Second, distance below the same-year on-course revenue curve remains associated with lower payback, although even the deepest tested shortfall bin retains substantial payback. Third, the finite structural-elasticity grid changes sharply at its sparse end but does not identify one universal boundary at the main eta. The contribution is an inspectable account of capital payback across a finite model grid, paired with a bounded definition of intelligence elasticity of demand. The findings are conditional on seeded model worlds and do not identify real-economy odds. Related work defines the nearest constructs; the model and study design expose the object; results and sensitivity separate the main setting from varied assumptions; Limitations and Reproducibility state the audit boundary.

2. Related work and nearest constructs

Exact-phrase searches of OpenAlex, Crossref, arXiv and Semantic Scholar were run on September 13, 2026. OpenAlex returned no records and Crossref returned 50; none of those 50 records used “intelligence elasticity of demand” in a title or abstract. arXiv and Semantic Scholar returned HTTP 429, so this search does not support a four-index no-prior-use claim (Appendix A). The shorter expression “intelligence elasticity” appears in a March 9, 2026 PitchBook report by Rudy Torrijos and Derek Hernandez, where it describes the relationship between AI fidelity and allocated compute (Torrijos and Hernandez 2026, 12, 34).

Price, income, and substitution. Marshall describes demand elasticity as the responsiveness of purchases to price and gives a proportional definition (Marshall 1920, book III, chapter IV, §1 and note 69). Hicks and Allen distinguish income elasticity from substitution between consumption goods along an indifference curve (Hicks and Allen 1934, 58–59, 63–67). Marshall also discusses new uses that become possible after a price decline (Marshall 1920, book V, chapter XII, §1).

Tasks and quality improvements. Acemoglu and Restrepo model automation of tasks previously performed by labor and creation of new tasks in which labor has a comparative advantage; their full model makes capital accumulation and the direction of innovation endogenous (Acemoglu and Restrepo 2016, revised 2017, abstract and §§2–4). Grossman and Helpman model repeated quality improvements across a continuum of product sectors, with research incentives determining the pace of innovation (Grossman and Helpman 1989, abstract and §§I–II). In these baseline specifications, new tasks replace lower-index tasks and product improvements occur within a fixed set of goods (Acemoglu and Restrepo 2016, revised 2017, §2.1; Grossman and Helpman 1989, §II). Gaynor, Ho, and Town distinguish demand responses to quality from responses to price in their analysis of health care providers (Gaynor, Ho, and Town 2014, §4.2, equation (5)).

AI and aggregate growth. Aghion, Jones, and Jones examine automation in production and innovation, including growth constraints from activities that remain hard to improve (Aghion, Jones, and Jones 2017, abstract and §§2–3). Nordhaus tests whether sectors with falling relative prices gain expenditure shares, as part of an analysis of conditions for accelerating economic growth (Nordhaus 2015, §§V–VI). Trammell and Korinek review growth, wages, and labor shares under scenarios that automate production and research (Trammell and Korinek 2023, revised 2025, abstract).

Goods ordered by comparative advantage. Dornbusch, Fischer, and Samuelson arrange a continuum of goods by relative labor requirements and derive international specialization and relative wages; their baseline demand specification assigns fixed expenditure shares to goods (Dornbusch, Fischer, and Samuelson 1977, §I).

The nearest constructs considered here are price and income elasticities, substitution between goods, new-task creation, quality ladders, and quality elasticity of demand (Marshall 1920; Hicks and Allen 1934; Acemoglu and Restrepo 2016, revised 2017; Grossman and Helpman 1989; Gaynor, Ho, and Town 2014). The model’s intelligence elasticity measures how recurring work made serviceable changes with capability, as defined in section 4.2.

3. Model

This section describes the model economy as implemented; the fixed engine rules govern any inconsistency with this description. The model has two vocabularies: a player-facing vocabulary used by the game and article, and a formal vocabulary used here.

The model avoids the bare word “price” throughout: a task’s exogenous price ceiling (maximum Gold per work unit), each lab’s endogenous post, and the public going rate statistic are distinct objects. The going rate is a posted-price summary, not a single payment applied to every task and lab.

3.1 Agents and capital

Three labs populate the economy. Each begins with a trove of 1,000 Gold — 3,000 Gold across the industry, treated as the invested capital of the season. There is no funding market: no raises, no debt, no investor dynamics. Each year, a solvent lab chooses its investment level, serving/train split, and post; the engine resolves serving revenue, operating cost, build bill, training, and any allowed terminal recovery. Solvency constrains the decision. Each season runs 12 years, so a year’s build and training choices are evaluated against the remaining horizon rather than an immediate payback date.

3.2 Data centers

Data centers are bought through a demand-responsive build market: requests price against a supply curve, and delivery is rationed when the industry over-orders, so a lab can receive less than it requested. Construction arrives with a one-year lag — a data center bought this year can neither serve nor train until next year. Data centers incur a recurring operating cost and depreciate each year. A lab must remain solvent: it must be able to cover next year’s operating cost plus its worst-case build bill, a requirement surfaced in the game as MUST COVER.

3.3 The Intelligence ladder and the "<" task fan

Capability X rises through training and is measured in notches n = log₂ X, so one notch is one doubling. The player-facing name, the Intelligence ladder, is retained as its proper name in formal prose. Demand arrives as a catalog of 12 tasks, each carrying three exogenous properties: a capability threshold (the model level required to serve it), a price ceiling (maximum Gold per work unit), and a volume (true recurring jobs). A task’s work, the quantity the clearing walk consumes and the quantity pay is quoted against, is its jobs multiplied by a per-task compute-per-job constant; a work unit is one unit of serving compute applied for one year. Thresholds sit on the log₂ rungs of the ladder.

The catalog is arranged as a "<"-shaped fan that widens toward the frontier: each threshold makes both a dearer and a cheaper task serviceable, with the extremes of the integer ceiling ladder — 40/16/8/4/2/1 Gold per work unit — both sitting at the frontier. The model configures task ceilings separately from capability thresholds: its frontier includes both high-paying and low-paying tasks. This is a modeling choice, not an established relationship in the real economy. Eligibility is per task (deployed X ≥ threshold), not a nested prefix. Smarter models open new markets, and only sufficiently capable models can serve them; the public going-rate statistic can move either way when capability reaches a new frontier rung. Monotonic “smarter means cheaper” deflation is gone by design.

3.4 Once-revealed volumes

A task’s volume is a bounded seeded draw, rolled when the task first enters the revealed set and persistent for the rest of the run. The draw is keyed by [DEMAND_ROLL_KEY, worldSeed, "volume", taskId] — no year term — so volumes are a pure function of world and task; derived volumes are included in exported records. At the start of a decision year, prepareYearInputs promotes tasks reachable from the pending deployed capability, rolls their volumes, and supplies those inputs before the current build/train/post actions are sealed. Earlier training and build commitments therefore affect which tasks are revealed for the current decision, but the current year’s choices do not wait for a post-commitment volume reveal. The public view exposes task thresholds, ceilings, volume outcomes, expected work, revealed IDs, and current rolls; a classifier may still restrict itself to its prespecified public time series.

3.5 Clearing

Each year, a solvent lab submits an admissible post for its current capability; an insolvent lab submits no post. A task can be served only by labs that are capability-qualified, still have serving capacity, and post at or below that task’s ceiling. The engine processes the fixed task order — descending ceiling, then descending capability threshold, then task ID — and shares each task’s remaining work among willing labs with deterministic shortfall redistribution.

Payment is task- and lab-specific. For served work, pay per work unit is post + scarcity sigma × (task ceiling − post). Scarcity sigma is clamp((2 × realized work − installed qualified data centers) / realized work, 0, 1); it uses all installed data centers of qualified labs, not their serving split. The public going rate is computed afterward as the work-weighted mean posted price of served work (with the top served post also retained), so it is a reported statistic rather than a universal market-clearing payment.

Demand dispersion sigma in the sweep design is a separate quantity from this market scarcity sigma. Refusal-induced idle capacity earns the eta-weighted training credit in the training-accrual rule; ordinary unused serving capacity does not. These distinctions keep the model’s fixed task volumes, posts, dispatch, payments, and training accounts separate.

Idle compute earns no Gold. Refusal-induced idle can still contribute to training through the eta-weighted credit described above. Too little industry compute and only the dearest work gets served; too much and the excess sits idle. Capability makes use possible, but use needs compute — neither alone produces revenue.

3.6 Catch-up and the Blueprint

The Blueprint is the frontier model of the year — the maximum opening deployed capability across labs — entering with a one-year lag. Training below the Blueprint earns 4× catch-up efficiency until the gap closes; beyond it, gains revert to the ordinary log-linear resources-to-capability relationship. Laggards are therefore pulled toward the frontier, and a faster frontier makes laggard catch-up faster and cheaper.

3.7 Scope fences

This section states the fences of the exercise once, as limitations rather than fine print. The field is three labs, two of them deterministic bots playing fixed strategies. There is no funding market; each lab lives on its starting trove (section 3.1). Demand inputs are bounded ranges with every draw weighted equally, a modeling assumption rather than an estimate (section 4). The industry pays back when the labs together finish the 12-year season holding at least the 3,000 Gold they collectively started with; a world that finishes below that terminal cutoff is stranded. Each reported percentage is the share of seeded model worlds in which something happened, never a forecast about the real economy (section 7).

4. Study design

4.1 Price elasticity of demand in the model

Price elasticity of demand (PED) is the standard construct (Marshall 1920, book III, chapter IV): the proportional change in quantity demanded of an existing good per proportional change in its price. Elasticity at unity means demand stretches almost in proportion as the good gets cheaper; near zero, buyers barely respond.

In this economy PED summarizes the shape of the ceiling ladder. At each distinct ceiling, the study totals the expected work whose buyers can afford that price, then fits log cumulative work against log price. The reported elasticity is the magnitude of that slope across six price levels. The tested shapes yield labels of approximately 0.88, 0.50, 0.35, 0.25, and 0.18. A larger label means a stronger proportional increase in affordable work as price falls in the fitted relationship. Both high- and low-paying tasks occur at the capability frontier, so payment concentration and capability concentration are different. The public going rate is a posted-price statistic (section 3.5).

4.2 The intelligence elasticity of demand

Definition 1 (intelligence elasticity of demand). Let X be model capability and n = log₂ X the capability notch, so that one notch is one doubling of X. Let W(X) be cumulative addressable demand made serviceable at or below capability X, measured in recurring work — the work weighting is fixed for the study (Appendix A), not derived. The intelligence elasticity of demand is

the proportional growth of serviceable demand per proportional growth of capability.

The work and ceiling-value weightings are not equivalent. In the canonical catalog, weighting work by its price ceiling changes the fitted intelligence elasticity from approximately 1.23 to 1.55. This alternative weighting would also make the intelligence-elasticity measure depend on the price-ladder setting, so the two grid controls would no longer be independent.

Units matter: ε_I is dimensionless, a ratio of proportional changes. At ε_I = 1, serviceable demand grows in proportion to capability: each doubling of X roughly doubles W. Below 1, the market demands ever-larger proportional capability gains per unit of new demand, and arrivals thin toward the frontier; above 1, they thicken.

The contrast with PED is a contrast of margins and arguments. PED is an intensive-margin elasticity along a price dimension: more purchases of goods that already exist. IED is an extensive-margin elasticity along a capability dimension: tasks that come into serviceable existence. In the fan (section 3.3) the two are orthogonal controls — the ladder shape sets PED, the threshold spacing sets IED — which is precisely what makes the sandbox useful. In field data, capability, deployment, price, and volume co-move and the counterfactual arrival ladder is unobservable; identification of IED from observational series is confounded essentially by construction. In the sandbox, threshold spacing is an exogenous, sweepable parameter, so the causal effect of IED on payback is measurable by direct experiment.

IED enters the study as a structural parameter: the spacing of task-arrival thresholds on the Intelligence ladder. The 24,000-season elasticity test (Study design and Results) varies the spacing between task thresholds, and the grid’s row values (3.24, 1.81, 1.23, 0.89, 0.69, 0.57) come from the tested settings.

On novelty, section 2 records the exact-phrase search and its limits, then sets out the nearest constructs considered.

4.3 Structural versus observable elasticity

The structural IED of Definition 1 is a property of the configured world and task ladder. The study’s observable IED uses the recorded history: (log current cumulative served work − log year-1 cumulative served work) / (log current max deployed capability − log year-1 max deployed capability). It is defined only when year-1 served work is positive and the denominator, log capability growth since year 1, is at least 1e-9. The public game exposes the task catalog and revealed volumes as well; the prespecified predictor uses a deliberately narrower set of inputs. Its observable diagnostic and the structural catalog slope are distinct quantities.

The two diverge empirically in the prespecified frontier-building sample. At eta 0.3, the observable intelligence-elasticity diagnostic has AUC 0.5213 at year 3 and 0.5557 at year 6 (every eligible value at each checkpoint), compared with coverage AUCs of 0.9119 and 0.9895. The observable metric is therefore much less discriminating in this sample; the result does not show below-chance inversion. Structural elasticity remains a configured grid axis in Results, not a line inferred from the observed history.

The complete evidence base contains 136,400 policy-seasons across 364 sources. It is two parallel grids: eta 0.3 is the main analysis and eta 0.8 is a separately reported sensitivity. The two settings are not pooled. Within each eta, the on-course family contributes 10,800 seasons, the structural-elasticity grid 24,000, the interaction cube 5,400, the volume/lumpiness grid 24,000, and the canonical baseline 4,000. These are policy-season observations over a finite set of configured cells and seeds, not 136,400 independent economy designs.

Demand settings use bounded, equally weighted seeded draws. With rules, economic settings, eta, seed, and policy fixed, the model reproduces the same outcome and rival decisions. Task volume is drawn once per world and task and remains fixed through the 12-year season. The two rival seats follow deterministic state-responsive policies; the study contains no language-model moves or learning across seasons.

The design is finite. The on-course family pairs two policies across 90 demand cells and 60 seeds per cell. The frontier-building policy (operator-frontier) requests the highest affordable build up to level 2 every year and assigns half of compute to training until deployed IQ reaches 16, then none; the balanced policy (balanced) holds level 1, falling back to level 0 when level 1 is unaffordable, and assigns one-quarter of compute to training every year. Each uses the model forecast’s matching recommended post when available. The elasticity family crosses six structural intelligence-elasticity rows with five price-ladder shapes and four policies. The interaction cube crosses threshold spacing, ladder shape, and volume scale under two policies. The volume/lumpiness family crosses six scales, five dispersion settings, and four policies. The baseline runs eight policies with 500 seeds each. No result is extrapolated beyond these grids. The policy grid contains no strategy that switches at a fixed year from maximum build and training to no build and no training, so the results do not speak to that strategy.

5. Results

All percentages in this section are shares of seeded model worlds. They are not calibrated probabilities for the real economy.

The coverage diagnostic

In-sample at eta 0.3, industry payback occurred in 4,591/5,400 (85.02%) frontier-building policy-seasons and 4,632/5,400 (85.78%) balanced policy-seasons. Monetization coverage is cumulative industry revenue divided by the initial 3,000 Gold. In the frontier-building scope its Mann-Whitney AUC rose from 0.7594 at year 1 to 0.8312 at year 2, 0.9119 at year 3, 0.9597 at year 4, 0.9895 at year 6, and 0.9938 at year 8.

The frontier-building policy’s year-3 Youden cutoff, selected within the same policy sample, was 2.44%, equivalent to 73 Gold of cumulative industry revenue. At or above it, 3,706/3,791 paid back (97.7578%); below it, 885/1,609 paid back (55.0031%). The threshold was selected and evaluated on the same seasons; no held-out evaluation was run for this release. The balanced scope independently selected 1.70%; 3,879/3,918 (99.0046%) paid back above and 753/1,482 (50.8097%) below. These in-sample cutoffs are descriptive and are not out-of-sample guarantees.

The observable intelligence-elasticity AUC was 0.5213 at year 3 and 0.5557 at year 6, with all 5,400 values defined. The mean public going-rate history through year 6 had AUC 0.9241. The year-6 going-rate diagnostic (H12) therefore measures going-rate history, not price elasticity.

Revenue shortfall by checkpoint

In-sample, the on-course curve is the same-year median cumulative revenue among eventual payback worlds. The shortfall comparison assigns each frontier-building policy-season to one of six bands at years 3, 6, and 10; membership is recalculated at each checkpoint. At eta 0.3, all 2,296 observations at or above the reference paid back at each checkpoint. In the deepest band, more than 80% below the reference, payback was 584/1,190 (49.0756%) at year 3, 417/1,212 (34.4059%) at year 6, and 382/1,189 (32.1278%) at year 10. The result is a graded association, not an absorbing failure boundary.

The finite structural-elasticity grid

At eta 0.3, all 800 policy-seasons in every price-ladder cell paid back at structural intelligence elasticities 3.24, 1.81, 1.23, and 0.89. At 0.69, cell rates across the five price ladders were 100%, 97.25%, 67.75%, 46.375%, and 19.25%; at 0.57 they were 100%, 69.375%, 35.375%, 12.75%, and 0%. On the canonical price ladder, the adjacent declines were 32.25 and 32.375 percentage points, so the registered 40-point test (S01) is null: the prespecified decline was not observed at the main eta.

6. Sensitivity

Sensitivity checks vary training credit, demand scale, dispersion, interaction settings, and the capability-credit test. Baseline payback survives those checks, while low-grid outcomes and the registered boundary test change.

6.1 Training credit

At eta 0.8, the canonical cells were 84.25% at 0.69 and 38.75% at 0.57, a 45.5-point decline. The registered 40-point test therefore brackets a sensitivity result between those sampled structural-elasticity rows and does not identify a boundary across training-credit settings. In the deepest shortfall band, the eta 0.8 rates were 687/1,200 (57.25%), 397/1,044 (38.0268%), and 425/1,083 (39.2428%).

6.2 Scale and lumpiness

At eta 0.3, the 30 volume/lumpiness cells aggregate four policies and 800 policy-seasons per cell. Payback ranged from 70.625% at scale 0.25 and dispersion 2.3 to 100% in 23 cells; the corresponding minimum at eta 0.8 was 72.875%. In the separate interaction cube, which aggregates two policies and 200 policy-seasons per cell, eta 0.3 payback ranged from 2% at g=3, beta=1.6, S=0.5 to 100% in 23 of 27 cells. The same minimum cell reached 35.5% at eta 0.8. These finite cells show strong interactions among spacing, price shape, and scale; they do not support the previous general claim that lumpiness is always insurance for a small market and a tax on a large one.

6.3 The industry ledger and mechanism quantities

All 4,000 baseline policy-seasons paid back at both eta anchors. At eta 0.3 the pooled mean terminal industry payback ratio was 4.1278 (p10 2.9461; median 3.8056; p90 5.8784). The all-serving player’s terminal Gold exceeded its 1,000-Gold starting trove in 500/500 baseline runs. Industry and company cutoffs remain separate even though both happen to be universal in this baseline sample.

Baseline build bills averaged 605.3189 Gold per policy-season, with observed run values from 191.6089 to 995.4691. They are payments recorded when incurred. The model contains no supplier balance sheet, receivable, default, or loss state, so it cannot support supplier-risk, supplier-profit, or winner-loss claims. Mean buyer headroom was 254.6724 Gold, a separate surplus proxy rather than lab return.

The three unmet-work categories (Q01–Q03) partition recorded unmet work into no-capable, post-restricted, and capacity-exhausted units. The no-capable category (Q01) was zero across the tasks in all five families at both eta anchors; that scope does not establish the absence of capability constraints outside the studied tasks. Using total unmet work, the sum of the three categories, as denominator, eta 0.3 restricted/exhausted shares were 6.18%/93.82% in volume/lumpiness, 39.08%/60.92% in baseline, 27.52%/72.48% in the cube, 28.28%/71.72% in elasticity, and 14.81%/85.19% in on-course. The refusal-idle share (Q04) is a different ratio: refusal-induced idle divided by serving capacity. Its eta 0.3 values were 18.17%, 24.77%, 25.96%, 22.27%, and 23.29% in those same families. Refusal-idle capacity is not unserved work.

6.4 Credit-band dominance

The credited-capability test (Stage E) asks whether the submitted post weakly maximizes capability gain across six prespecified forecast cases when refusal credit is active. All 144,000 baseline states were eligible at each eta. Dominance occurred in 11,904 states (8.2667%) at eta 0.3 and 21,823 (15.1549%) at eta 0.8. Both fail the prespecified 95% threshold. The test did not reach a boundary through eta 0.8; eta 1 is not an observed boundary. This is neither hindsight advisor accuracy nor a recommendation-error rate.

7. Limitations

The result supports a limited comparison: within the eta 0.3 frontier-building population, the level of cumulative cash relative to initial industry capital ranks eventual payback far better than the observable intelligence-elasticity diagnostic. It does not establish that observed demand response is negatively related to payback, and it does not identify a real-world causal mechanism. The public going-rate history also ranks outcomes strongly at year 6, but that descriptive AUC does not convert the statistic into price elasticity.

The model offers finite conditional statements. Coverage has a strong in-sample ranking relationship; shortfall bands retain a graded relationship with eventual payback; structural elasticity, ladder shape, and market scale interact across tested cells; and baseline industry and all-serving company payback are universal in the canonical sample. The old expected bands failed often, which is itself a result rather than a reason to tune the economy.

Toy economy

Three labs, deterministic rivals, a 12-task catalog, and a 12-year horizon are stylizations. Percentages are shares of seeded policy-seasons, not calibrated probabilities for the real economy.

Finite grids

The study covers only the tested parameter cells and excludes any strategy that switches at a fixed year from maximum build and training to no build and no training. The year-3 cutoff is selected and evaluated within one policy sample, and structural thresholds are brackets between tested rows rather than continuous estimates.

No funding market

Labs live on fixed starting troves. The model omits equity, debt, refinancing, and investor behavior.

Supplier accounts absent

Build payments exist, but supplier costs, profits, receivables, balance sheets, defaults, and losses do not.

Customer value proxy

Buyer headroom is ceiling minus realized pay on served work. It is not total welfare and excludes unserved value.

Recorded task scope

The zero no-capable-work count applies only to tasks included in the study. It is not an economy-wide theorem about capability constraints.

Distinct ledgers

Restricted and exhausted work are components of unmet work; refusal idle is unused serving capacity and uses a different denominator.

Descriptive diagnostics

Coverage, observable intelligence-elasticity history, and mean going-rate history are AUC predictors within a sampled population. The year-6 going-rate diagnostic is not price elasticity, and the credited-capability test measures dominance rather than hindsight advisor accuracy.

Mechanism

Labs post prices, work is split equally among qualified willing labs with deterministic reallocation as capacity exhausts, and task/lab payments can differ. The public going rate is a served-work-weighted post statistic.

Other omissions

The study does not vary season length, funding structure, adoption lag, depreciation, training-cost geometry, residual free progress, or strategic learning.

7.5 The Model Boundary

Every mechanism in this economy earns its place by how it serves one question: does the capital invested pay back, and when does the evidence show it. Three decisions are the player's to make each year: how much to build, how much to train, what to charge. Nothing else is. A second set of mechanisms is fixed on purpose: starting capital, the task catalog, the clearing rule, depreciation, solvency, and the twelve-year horizon hold still across every season, so a changed outcome reflects a changed strategy or demand regime, not a changed ruler. A third set is left out entirely — more competitors, a funding market, supplier accounts, energy and labor markets, regulation, marketing spend, and political friction such as data-center pushback — because modeling them would test a different, larger question than payback under this fence.

Two omissions matter most for reading the results. The model discounts nothing: terminal Gold is compared with starting Gold with no cost-of-capital hurdle, which flatters payback relative to a real investor's return requirement. And the model has no funding market, which removes both rescue funding and debt costs: a lab cannot raise fresh capital after a bad year, but it also carries no debt and faces no investor bailout — stricter than a real lab that can sometimes keep operating on continued investor patience alone. The full three-bucket inventory, with every omission's likely direction, is published in full at the Model Boundary.

8. Reproducibility

This revision covers the complete 136,400-policy-season study: 68,200 policy-seasons at eta 0.3 and 68,200 at eta 0.8, drawn from 364 sources with matched identities. Figure selections retain their populations, denominators, and exclusions. No additional model experiment or post-result tuning enters these findings.

Before publication, all 136,400 policy-seasons were checked against the study’s fixed rules and matched source identities. The checks reproduced every 12-year path, reconciled annual totals with task and lab records, confirmed the stated unmet-work categories, and kept eta 0.3 and eta 0.8 separate. Figure values use the stated populations, denominators, and exclusions; incomplete inputs are rejected rather than plotted.

Determinism

Fixed rules, eta, economic setting, seed, and policy reproduce the same season.

Population

Counts are policy-seasons. Multiple policies can evaluate one configured economy cell and seed.

Payback

Industry terminal payback is final Gold across three labs divided by the initial 3,000 Gold. Company comparisons use that company’s 1,000-Gold starting trove.

Coverage

Annual cumulative revenue coverage uses cumulative industry revenue divided by 3,000 Gold; it is not terminal payback.

Figures

Coverage and shortfall use the frontier-building policy only. The elasticity heatmap weights four policies by their actual denominators. Missing values are never plotted as zero.

Artifact record and replay boundary

The published artifact set is PAYBACK · AI Economy Model v1: the article, interactive model, and this manuscript. The rules record identifies payback-play/0.3.0 and the rival policies frontier-racer/v3 and volume-server/v3. Fixed rules, eta, economic setting, seed, and policy reproduce a season. Appendix A supplies the exact-search protocol; Appendix B supplies the parameter inventory.

The publication record does not supply a runnable command, runtime or operating-system manifest, seed list, standalone dataset, or public code archive. Those materials cannot be independently replayed from this page alone. The playable view exposes the model, while the article and manuscript expose the interpretation and audit trail.

Data provenance

The result grid is generated by the PAYBACK model rather than observed from the real economy. deslop.media editorial publishes the grid under the front-matter dateline. The engine emits annual task and lab records plus derived task volumes. The analysis matches source identities, rejects incomplete inputs, keeps the eta settings separate, aggregates policy-seasons, and computes the reported payback shares, AUCs, medians, cutoffs, and weighted cells. No external join, separate license, or permission statement is documented in the available publication record.

Exclusions are part of the data boundary. The model has no funding-market or supplier-account fields, and it omits the real-economy variables named in Limitations. No proprietary or private input is claimed. No additional field-level data, withheld contamination-sensitive material, or unavailable private records are identified by the article, playable view, manuscript, or guide.

How this manuscript was made

OpenAI GPT-5.6 Sol and GPT-6 Astra, run through the OpenAI Codex CLI, assisted manuscript restructuring, drafting, copy editing, code editing, and verification at build time between September 12 and September 15, 2026; Anthropic Claude Fable 5.1 orchestrated those lanes and verified their output against the files and the hosted preview. The Editor in Chief and Head of Research are responsible for checking cited sources, calculations, final claims, voice, accessibility, and publication approval. Model output was not accepted as evidence. Models ran during production only; the published views make no model call at read or play time.

Contributor roles. The Editor in Chief owns question framing, prose, copy editing, accessibility, and publication approval. The Head of Research owns source verification, model design, analysis, code review, claim precision, methods, and reproducibility. deslop.media editorial holds both roles for this manuscript, and the operator’s review of the staged manuscript is its publication approval.

Conflicts and funding. None.

Acknowledgments. None.

9. References

All cited entries are resolved against the direct source identified by the stable link. Appendix A records the exact-search candidates as not-found or unresolved-live.

1. Acemoglu, Daron, and Pascual Restrepo. 2016, revised 2017. “The Race Between Machine and Man: Implications of Technology for Growth, Factor Shares and Employment.” NBER Working Paper 22252. resolved.
2. Aghion, Philippe, Benjamin F. Jones, and Charles I. Jones. 2017. “Artificial Intelligence and Economic Growth.” NBER Working Paper 23928. resolved.
3. deslop.media editorial. 2026. “PAYBACK · AI Economy Model v1.” Article and interactive model, v1. resolved.
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Appendix A. Exact-term search

A returned record counted as a prior use only if the exact phrase appeared in its title or abstract. Quoted queries can return fuzzy matches; HTTP 429 responses were not screened as zero-result searches.

OpenAlex and Crossref are not-found for the exact phrase. arXiv and Semantic Scholar are unresolved-live because the recorded access failures prevented screening. The latter pair do not support a no-prior-use claim.

Appendix B. Parameter table

Each row identifies where the parameter acts. “Body” marks rules stated in sections 3–6; “engine only” marks values verified from code but not printed numerically in the body. Every value was checked against the rules version named in Reproducibility; study-result counts are omitted because they are output rather than engine parameters.