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

deslop.media AI Futures desk

Working draft — August 7, 2026. Companion manuscript to the PAYBACK read/play piece. Pre-submission draft: every reference is verification-pending (§2, References); every exhibit regenerates from the deterministic sweep harness (Appendix A).

Abstract

(August 7, 2026)

We present PAYBACK, a toy economy of AI capital returns: three frontier labs allocate fixed Gold troves across data-center compute, training, and serving, while task arrivals, price ceilings, and market volumes are exogenous draws from bounded, uniformly weighted priors. From 68,200 seeded 12-year seasons across four sweeps, we report three results. First, a cash diagnostic, monetization coverage (cumulative revenue over invested capital), separates payback from stranded worlds by year 3 (discrimination 0.89), while an observable intelligence-elasticity estimator built from the same public series scores below a coin flip (0.43). Second, payback is backloaded: the median on-course world earns 95% of lifetime revenue after year 3, and eventual-payback probability decays from 98.1% to 19.0% as year-3 shortfall deepens. Third, payback is nearly a step function in the intelligence elasticity of demand, a structural quantity we define: above 1, every seeded world pays back; near 0.9 and below, almost none do unless the price ladder is flat. All percentages are shares of seeded model worlds, not calibrated forecasts.

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.

This paper states one such intuition precisely enough to be wrong. We build a deliberately small model economy — the AI Economy Model v1, a fictional world whose rules are abstracted from the real one — and run it as an instrument. A toy economy lets us watch capability, compute, and monetization interact without the noise of the real one: capability unlocks new uses, but every use must be served with compute that costs money to build and operate, and the interplay of the three decides whether invested capital returns. We make demand explicitly exogenous — which tasks arrive, at what capability threshold, at what price ceiling, and in what volume are draws from bounded priors — while pay determination and the division of work remain endogenous clearing. We then sweep the priors and report distributions over seeded model worlds.

Three findings organize the paper. First (§6.1), the earliest honest evidence about payback is not a capability signal but a cash signal: monetization coverage — cumulative revenue as a share of invested capital — read at year 3. Second (§6.2), payback is backloaded; worlds that eventually pay back earn most of their revenue late, and early shortfall closes the door gradually but decisively. Third (§6.3), the deep structural driver is a quantity we call the intelligence elasticity of demand (IED): the rate at which each capability step unlocks new demand. Payback is close to a step function in this elasticity. §2 positions the term against neighboring constructs and states its novelty status honestly. §3 specifies the model economy. §4 develops both elasticities formally and distinguishes the structural IED from its observable estimator. §5 describes the simulation design; §6 the results; §7 the discussion and limitations.

2. Related work and the status of the term

The term "intelligence elasticity of demand" is, to our knowledge, coined in this paper. That claim is provisional by design: the survey below names the neighboring formulations we intend to verify against the literature before any submission, and none of the works named here has yet been re-read and confirmed for this draft. Each is therefore cited as a related formulation, never as a confirmed prior. If verification finds a prior construct that matches, we will cite it and withdraw the coinage; if it finds only neighbors, we will state the delta from the nearest one.

The classical elasticity toolkit. Price and income elasticity of demand (Marshall's Principles of Economics is the classical anchor) measure how much more of an existing good buyers take as its price falls or their income rises — intensive-margin responses. The elasticity of substitution (Hicks; Allen) measures response in the input mix. All hold the set of goods fixed. IED does not: it is an extensive-margin elasticity, the rate at which new tasks — demand that did not previously exist in serviceable form — unlock as capability rises.

Task-based models of automation and new-task creation. The task-based literature (Acemoglu and Restrepo) models growth and labor demand through the arrival of new tasks and the reallocation of old ones. Our task fan is a task-arrival structure of exactly this family, and IED can be read as a one-parameter summary of arrival density along the capability axis. The AI-and-growth literature (Aghion, Jones, and Jones; Nordhaus's demand-side tests; Korinek) asks the aggregate version of our question — whether and when AI-driven supply meets demand willing to pay for it.

Quality ladders and demand response to quality. The closest formal neighbor is the quality-ladder tradition (Grossman and Helpman) and the industrial-organization literature on demand response to quality. IED is a quality elasticity in which the quality dimension is capability measured in doublings and the response margin is task unlocking rather than increased purchases of an existing good. That two-part delta — capability-as-quality, extensive-margin-as-response — is, pending verification, what distinguishes the construct.

3. The model economy

We describe the candidate economy exactly as implemented; on any conflict between this description and the engine's invariants document and constants, the engine is ground truth. The model has two registers of vocabulary — a player-facing register used by the game and article, and a formal register used here. The mapping:

We avoid the bare word "price" throughout: a task's exogenous price ceiling (Maximum Gold Coins per work-unit) and the endogenous going rate (a computed clearing output) are distinct objects, and conflating them is the most common way to misread the model.

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, which we treat as the invested capital of the season. There is no funding market: no raises, no debt, no investor dynamics. Cash comes only from serving work; solvency is the only financial constraint. Each season runs 12 years. Each year, a lab's decision loop is: spend Gold on data-center construction, then split its operational fleet between serving (which earns revenue now) and training (which raises capability later). The payback horizon is deliberately long — returns on a year's spending arrive over the remaining season, not within the year.

3.2 Compute

Fleet is 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. Fleet incurs a recurring operating cost and depreciates 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; we measure it in notches n = log₂ X, so one notch is one doubling. 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 Coins per work-unit), and a volume (True recurring Jobs). Thresholds sit on the log₂ rungs of the ladder.

The catalog is arranged as a "<"-shaped fan that widens toward the frontier: each threshold unlocks both a dearer and a cheaper task, with the extremes of the integer ceiling ladder — 40/16/8/4/2/1 Gold per work-unit — both sitting at the frontier. This decouples a task's ceiling from the capability it requires, because the two are independent in reality: drug discovery and mass email automation both demand frontier capability and command wildly different pay. Eligibility is per task (deployed X ≥ threshold), not a nested prefix. Smarter models open new markets, and only sufficiently capable models can serve them — but a new frontier rung adds dear and cheap work at once, so the going rate can move either way on an unlock. Monotonic "smarter means cheaper" deflation is gone by design; supply-driven deflation (more serving compute pushes the going rate down) is preserved.

3.4 Once-revealed volumes

A task's volume is a bounded seeded draw, rolled once when the task first unlocks and persistent for the rest of the run. The draw is keyed by (rulesVersion, worldSeed, "volume", taskId) — no year term — so volumes are a pure function of world and task, cannot be path-manipulated by when a lab unlocks, and replay is byte-stable; volumes are derived, never stored. The volume of newly unlocked work is unknown ex ante: a newly unlocked task's size reveals only after that year's commitments are sealed, so reaching a new rung is a genuine bet. Already-sized tasks never revert.

3.5 Clearing

Each year, the aggregate serving capacity of all solvent labs walks the task stack in ceiling order to set one common going rate: the deeper aggregate serving reaches, the lower the rate. A task clears only when the going rate is at or below its ceiling (ceiling closure) — the willingness-to-pay threshold in mechanism form. Dispatch is dear-first, in strictly descending ceiling order (tie-break: threshold descending, then taskId); this ordering is load-bearing, because it is the only mechanism routing scarce compute to the frontier before the cheap end. Within a task, work splits equally among labs that are both capability-eligible and still have serving compute (water-filling with deterministic shortfall redistribution): identical work at one clearing pay is a commodity, and scale's edge is having compute left when rivals have spent theirs at the top. A lab that is the sole capable server of a task earns the sole-capable premium, pay = rate + 0.5 × (ceiling − rate). Idle compute earns zero. Too little industry compute and only the dearest work gets served; too much and the excess sits idle. Capability unlocks use, 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

We state the fences of the exercise here, 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 (§3.1). Demand priors are bounded ranges with every draw weighted equally — a modeling assumption, not an estimate (§5). The industry pays back when the labs together finish the 12-year season holding at least the 3,000 Gold they collectively started with. And the epistemic frame that governs every number in this paper: each reported percentage is the share of seeded model worlds in which something happened, never a forecast about the real economy (§7).

4. Elasticities

4.1 Price elasticity of demand in the model

Price elasticity of demand (PED) is the standard construct (Marshall — related formulation, verification pending): the proportional change in quantity demanded of an existing good per proportional change in its price. Elasticity near 1 means demand stretches almost in proportion as the good gets cheaper; near zero, buyers barely respond.

In this economy PED has a model-specific carrier: the shape of the ceiling ladder. The discrete per-task ceilings (Maximum Gold Coins per work-unit) form a ladder, and the sweep harness summarizes each ladder shape it tests as a single elasticity label — 0.88 for the flattest, most spread ladder down through 0.50, 0.35, 0.25 to 0.18 for the steepest, most frontier-concentrated. These labels are derived from the harness, not by hand. A high label spreads the money across cheap markets; a low label concentrates it at the frontier. The going rate remains a computed clearing output (§3.5) and is never the object PED describes.

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(n) be cumulative addressable demand unlocked at or below notch n, measured in recurring work (equivalently, in ceiling-value: work weighted by price ceiling). The intelligence elasticity of demand is

the proportional growth of unlocked demand per one-notch (one-doubling) capability step.

Units matter: ε_I is measured per notch, i.e., per doubling of X. At ε_I = 1, each step up the Intelligence ladder opens roughly as much new demand as the step before. Below 1, the market demands ever-bigger capability leaps before it hands over new work, 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 (§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.

Operationally, IED enters the sweeps as a structural parameter: the spacing of task-arrival thresholds on the Intelligence ladder. The ladder-stretch device behind the 24,000-season sweep (§5, §6.3) widens the spacing between arrivals — "one notch sparser" corresponds to roughly 30% bigger capability leaps between arrivals — and the grid's row values (3.24, 1.81, 1.23, 0.89, 0.70, 0.57) are derived from the sweep harness, never by hand.

On novelty: §2 states the term's status. We believe the construct as defined — capability-as-quality, task-unlocking as the response margin, units of per-doubling — is not a renaming of an existing elasticity, but the claim remains conditional on the verification survey, and the References mark every neighbor as a related formulation only.

4.3 Structural versus observable elasticity

The structural IED of Definition 1 is set by the world and hidden from its inhabitants. What an observer inside the economy can compute is an observable IED: an estimate from the public series alone — cumulative revenue, served work, and the going rate. Formally, the observable estimator is the realized proportional growth of served demand per notch of frontier capability progress, computed over the observation window from the public series; its exact windowing and functional form are pinned in the sweep harness (Appendix A) rather than restated here.

The load-bearing finding is that the two diverge where it matters. As a classifier of eventual payback (§6.1's discrimination metric, where 0.5 is a coin flip), the observable estimator scores 0.43 at year 3 and 0.37 at year 6 — below chance. Ranking worlds by apparent early demand response actively misleads, and §7.1 explains the mechanism: stranded worlds often look more demand-responsive early, because a thin frontier makes each capability step look productive while the aggregate stays small. The structural quantity drives outcomes (§6.3); its naive estimator inverts the signal.

5. Simulation design

The evidence base is 68,200 seeded 12-year seasons across four sweeps of demand regimes. Three components are named in the companion article: a 10,800-season hidden-regime sweep, in which the structural regime is hidden and classification uses only the public series (§6.1); a 24,000-season ladder-stretch sweep over the structural IED × ladder-shape grid (§6.3); and a 4,000-season baseline sweep of the standard economy (§6.5). The playable game runs at one fixed threshold ladder; the analysis stretches that ladder. The remaining sweep — the scale-and-lumpiness family of §6.4 — has its composition recorded in the sweep logs; per the reproducibility protocol we transcribe that composition from the logs at exhibit regeneration, never derive it by subtraction from the total. (Composition to be transcribed from WP1-SWEEP.log / WP2-SWEEP.log; see Appendix A.)

Demand regimes are drawn from bounded ranges with uniform weights: we do not claim to know what demand looks like, and we do not tilt the priors toward any view. Every world is seeded and deterministic — the same (rulesVersion, worldSeed) reproduces the same season byte-for-byte, bot decisions included — so every exhibit in §6 is a regenerable distribution over seeded model worlds, not a curated selection of runs. Throughout the paper, every percentage reported from the sweeps is the share of seeded model worlds satisfying the stated condition. None is a calibrated forecast, and no weighting toward real-world likelihood is implied or intended.

6. Results

6.1 The coverage diagnostic

In the hidden-regime sweep (10,800 seasons), an observer sees only what a real observer sees: revenue, served work, and the going rate. Define monetization coverage as cumulative revenue divided by invested capital. The question is which early observable best predicts eventual payback.

Against a base rate of 59.9%, year-3 coverage discriminates payback from stranding at 0.89. The operational rule is simple: worlds whose cumulative revenue has reached 4.2% of invested capital — 126 Gold on the 3,000 invested — by year 3 go on to pay back in 92% of seeded model worlds; worlds below the line pay back in 31%. Robustness: the same cash diagnostic wins at every checkpoint tested — at each later checkpoint, coverage remains the best of the candidate early signals, so the result is not an artifact of the year-3 reading. The instructive contrast is with the observable intelligence-elasticity estimator, which scores 0.43 at year 3 and 0.37 at year 6 — below the coin flip. The cheapest possible signal, cash against capital, beats the sophisticated one (§7.1).

6.2 Backloading

Payback, when it comes, comes late. Among worlds that eventually pay back, the median world earns 95% of its lifetime revenue after year 3 and 77% after year 6: the season pays in its back half or not at all. Early shortfall therefore mortgages the out-years. Grouping worlds by how far behind the revenue curve they have fallen at year 3 — from on course to more than 80% behind (band edges pinned in the harness) — the share of seeded model worlds that eventually pay back decays from 98.1% through 79.8% and 50.7% to 19.0%.

The door then narrows across checkpoints. For the deepest band, more than 80% behind, the eventual-payback share of seeded model worlds falls from 19.0% at year 3 to 10.7% at year 6 to 4.6% at year 10. At year 6 that is roughly 1-in-9 — and decomposing those recoveries shows they occur only on a top-decile out-year revenue surge; absent such a surge, the band does not pay. By year 10 the door is effectively shut. As an extreme-case exhibit of how late "late" can be: the most back-loaded payer in the sweep earned 97.3% of its lifetime revenue in its final two years.

Backloading also inverts the intuitive reading of early activity. The failing worlds are the front-loaded ones: by year 6, a world headed for stranding has typically served 27% of its lifetime work, against 18% for an eventual payer. The revenue gap is starker still — 29% versus 38% of lifetime revenue by year 6, payer versus failure — and the work payers serve later in the season clears at higher pay. The companion article compresses this into its signature line: "If the work you can find today is most of the work there is, the capital is already stranded."

6.3 The step function

The ladder-stretch sweep (24,000 seasons) varies the structural IED (§4.2) across grid rows 3.24, 1.81, 1.23, 0.89, 0.70, 0.57 and the ceiling-ladder shape across elasticity labels 0.88 to 0.18 (§4.1). The full payback-share grid is a harness-generated exhibit (Appendix A); its structure is a step:

• At or above ε_I = 1: the industry paid back in every seeded model world, under every ladder shape tested.
• Around 0.9 and below: the payback share of seeded model worlds collapses toward zero — unless the ceiling ladder is flat, in which case money spread across cheap, low-capability markets carries the industry.

The transition is sharp. One notch sparser than the game's calibrated ladder — task arrivals spaced roughly 30% farther apart — and the payback share drops to 45% of seeded model worlds; two notches sparser and it is near zero. The hedge is real, however: at the flattest ladder shape tested, payback holds at or near 100% of seeded model worlds even at the sparsest arrival tested. Demand thinning toward the frontier is survivable if the cheap end of the market is broad enough to fund the industry.

6.4 Scale and lumpiness

The model keeps books for the whole economy, so we can vary the demand side's aggregate scale and its lumpiness — how total volume is concentrated across individual task markets (sweep parameterization pinned in the harness). Market size sets the stakes of the structural gamble: the payback contrast across elasticity regimes spans 75 points of payback share at half market size and 40 points at double. Lumpiness cuts both ways, and which way depends on the size of the pie. At quarter scale, lumpiness raises the payback share of seeded model worlds from 0% to ~24%: when the pie is small, a chance of drawing one outsized market is the only route to payback. At standard scale it lowers the share from 100% to 58%: when the pie is large, concentration risk destroys otherwise-safe worlds. The compression we offer: market lumpiness is insurance for a small pie and a tax on a big one.

6.5 The industry ledger

Because the model keeps books for everyone, the industry is visibly bigger than its labs, and the payback question decomposes by balance sheet.

Builders. The data-center builders are paid on delivery: across the sweeps they collect 330–964 Gold per season, up front, in payback worlds and stranded worlds alike. The supplier never carries payback risk; the labs do.

Customers. Served work generates value above what customers pay for it. Across seeded model worlds, 50–78% of demand goes unserved — the industry never comes close to exhausting the market — and the consumer surplus on the work that is served runs 2–4× lab revenue. Most of the value the industry creates is kept by its customers.

Labs. Industry payback and lab payback are different events. The standard economy paid back at the industry level in all 4,000 baseline seasons, while a serve-only lab in the same worlds recovered its own 1,000-Gold trove in just 11% of seeded model worlds. Aggregate payback with individual stranding is the usual story, not a corner case: the industry's books can close while a particular strategy's do not.

7. Discussion and limitations

7.1 Why observable elasticity misleads

The divergence between the structural IED and its observable estimator (§4.3, §6.1) has a mechanism we call the thin-frontier illusion. In a world whose arrivals thin toward the frontier — a low structural IED, headed for stranding — early capability steps land in a small market. Each step looks productive: served work and revenue grow by large proportions, because the base is small, so the estimator reads a steep apparent demand response. In a world with dense arrivals, the level of served demand accumulates quickly, and proportional growth per notch reads lower even as cash piles up. The estimator is scale-free where the phenomenon is scale-dependent: payback is decided by levels of cash against capital, not by proportional responsiveness. Stranded worlds therefore often look more demand-responsive early — the estimator does not merely add noise; in the sweeps it inverts the ranking, which is why it scores below a coin flip while the crude cash ratio scores 0.89. The practical reading: early "the market is responding to every capability gain" narratives are, in this economy, weak evidence against payback when the cash line has not moved.

7.2 What the model offers

The through-line of §6 is that payback is decided by whether demand arrives within reach of affordable Intelligence — and that the earliest honest evidence about it is monetization coverage by year 3. The model's offer is a discipline, not a verdict: which line to watch, and when. It values no stock and ranks no lab. The decisions, from here, are the reader's.

7.3 Limitations

We state plainly what this exercise is and is not.

1. A toy economy. The clearing mechanism, integer ceiling ladder, and 12-task catalog are stylizations. Results are statements about the model, offered as intuition pumps for the real question, not measurements of it.
2. Three labs. The industry is a three-seat field. Entry, exit, and many-firm competitive dynamics are absent.
3. Deterministic bots. Two of the three seats play fixed strategies. The strategy space is not searched adversarially, and equilibrium claims are out of scope.
4. No funding market. Labs live on their starting troves. Capital formation, raises, debt, and investor behavior — central to the real payback question — are deliberately fenced out.
5. Bounded priors. Demand regimes are drawn from bounded ranges; every result is conditional on that support. Worlds outside the ranges are not represented.
6. Uniform weighting. Draws are weighted equally within bounds. No prior mass is calibrated to real-world likelihood, so distribution shares carry no forecast content.

The epistemic frame follows: every percentage in this paper is the share of seeded model worlds in which something happened under assumed demand ranges. None is a probability of any real 2030s outcome, and we publish no predictive numbers here. Where these results inform judgment about the real economy, they do so as structural intuition — which variables matter, which signals mislead — not as forecasts.

Appendix A. Reproducibility

Every exhibit in this paper regenerates deterministically:

• Determinism. A season is a pure function of (rulesVersion, worldSeed): the same pair reproduces the run byte-for-byte, including bot decision traces. Volume draws are keyed (rulesVersion, worldSeed, "volume", taskId) and derived, never stored.
• Harness. The sweep harness lives at site/tests/payback-play/ — the 128-seed, multi-policy, two-gate protocol used for every economics change (before/after gates on the balance targets). Distribution-grade exhibits come from full sweeps, never from selected runs.
• Sweep logs. Component compositions are recorded in _docs/reviews/round-5/WP1-SWEEP.log and _docs/reviews/round-5/WP2-SWEEP.log. The fourth sweep's composition is transcribed from these logs (§5), not derived by subtraction.
• Estimators. The observable-IED estimator's exact functional form and windowing (§4.3), the shortfall band edges (§6.2), the ladder-shape elasticity labels (§4.1), the IED row values (§4.2), and the lumpiness parameterization (§6.4) are all pinned in the harness and its fixtures.
• Regeneration. (Exact regeneration commands to be transcribed from the harness at camera-ready; they are not restated here to avoid drift against the pinned versions.)

Appendix B. Parameter tables

Parameters restated here are those already stated in the body; all remaining constants (volume prior bounds, build-market supply curve, operating cost, depreciation, training-efficiency constants) are pinned in the engine's constants file at the pinned rulesVersion and are transcribed from it at camera-ready rather than restated by hand.

References

Every entry below is a related formulation named for the novelty-diligence survey of §2. None has been verified for this draft; none is cited as a confirmed prior. Entries deliberately carry no invented bibliographic detail — full citations are completed only upon verification.

1. Marshall, A. Principles of Economics — classical anchor for price and income elasticity of demand. (related formulation; verification pending)
2. Hicks, J. R.; Allen, R. G. D. — the elasticity of substitution. (related formulation; verification pending)
3. Acemoglu, D.; Restrepo, P. — task-based models of automation and new-task creation. (related formulation; verification pending)
4. Aghion, P.; Jones, B.; Jones, C. — AI and economic growth. (related formulation; verification pending)
5. Nordhaus, W. — demand-side tests of transformative growth. (related formulation; verification pending)
6. Korinek, A. — economics of transformative AI. (related formulation; verification pending)
7. Grossman, G.; Helpman, E. — quality-ladder models of growth. (related formulation; verification pending)
8. Industrial-organization literature on demand response to quality — nearest formal neighbor family for IED as a quality elasticity. (related formulation category; verification pending)