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Who Prices Cognitive Labor in the Age of Agents? Compute-Anchored Wages

Siqi Zhu

arXiv:2605.05558v2cs.AIcs.CY

TL;DR

The paper asks whether AI agents should be treated as an elastically supplied labor input when they substitute for human cognitive work. It instead models agents as a technology converting compute capital into cognitive labor, derives a compute-anchored wage bound, and generalizes it with CES substitution across task types. The central conclusion is that, for substitutable cognitive tasks, compute-market conditions—not the labor market—set the wage ceiling.

  • Problem

    The paper challenges the view that near-zero-marginal-cost AI agents are an infinitely supplied labor input that directly determines cognitive-labor wages.

  • Method

    The paper models agents as a compute-capital-to-labor conversion technology, derives the CAW bound, and extends it through CES aggregation and task heterogeneity.

  • Results

    On substitutable tasks, the competitive human wage satisfies WH ≤ λkrc, with equality when human and agent labor are both used positively.

  • Takeaways & Limitations

    The relevant elasticity is substitution across task categories, while the relevant wage-setting margin and policy levers are in compute markets.

  • Takeaways & Limitations

    The bound applies only where human and agent labor are approximately perfect substitutes, while algorithmic improvement can reduce k over time and make CAW a moving target.

Abstract

from arXiv · show

A natural intuition about the economics of AI agents is that, because agents can be replicated at very low marginal cost, agent labor may be supplied highly elastically, placing downward pressure on cognitive-labor wages when it closely substitutes for human labor. We argue this framing is wrong in mechanism but partially correct in conclusion, and that the correction matters for both theory and policy. \textbf{Agents are not labor; they are a production technology that converts compute capital $K_c$ into effective units of cognitive labor $L_A$.} Once this is recognized, the elastic-supply margin that anchors the equilibrium wage migrates from the labor market to the compute capital market. Building on the classic factor-pricing framework \citep{mankiw2020}, we derive a \emph{Compute-Anchored Wage} (CAW) bound stating that, on tasks where human and agent-produced cognitive labor are substitutes, the competitive human wage is bounded above by $λ\cdot k \cdot r_c$, where $r_c$ is the rental rate of compute capital, $k$ is the compute intensity of one effective agent-produced cognitive labor unit, and $λ$ is the relative human-to-agent productivity. We generalize the result through constant elasticity of substitution (CES) aggregation, separate substitutable from complementary tasks, and discuss factor-share consequences. The conclusion is concise: \emph{the price-setter for cognitive labor is no longer the labor market.}

1 Introduction

The paper argues that AI agents should be modeled as a technology converting compute capital into cognitive labor, relocating the elastic supply margin from labor markets to compute markets. This reframing yields a task-specific account of wage pressure and extends existing automation, skill, and macroeconomic frameworks.

  • Core reframing: Agents are a technology converting compute capital into effective cognitive labor, not a new labor input supplied at near-zero marginal cost.Their supply elasticity is inherited from compute capital, whose short-run supply is constrained by fabs, electricity, water, land, and geopolitics.
  • Motivation: A contract-review paralegal illustrates the mechanism: frontier models can perform clause extraction, template redlining, and summary memos at near-paralegal quality.The passage places the wage-setting margin for these substitutable hours in compute rental costs rather than paralegal supply.
  • Contribution: The paper derives a Compute-Anchored Wage ceiling and argues that cognitive-labor pricing must be analyzed through the market supplying compute capital.The contribution combines a closed-form wage bound, CES substitution, task heterogeneity, compute-price calibration, and policy analysis.
  • Related work: Relative to task-based automation, the framework identifies compute capital as the measurable elastic margin and uses task-level substitution elasticity σ instead of binary automation coding.It also connects wage pricing to compute-market concentration and rental rate rc.
  • Related work: The framework predicts that AI exposure within cognitive labor depends on occupations’ substitutable–complementary task mix rather than a one-dimensional skill ranking.This connects the paper to research on skill-biased technical change, occupational exposure, and cognitive-task complementarity.
  • Related work: CAW refines declining-labor-share accounts by identifying compute’s share of capital income as a channel for capital-income concentration and cognitive-wage compression.The paper situates this mechanism within macroeconomic, general-purpose-technology, and compute-supply research.

3 Setup: Factor Markets in the Mankiw Framework

The setup begins with textbook competitive factor pricing, where wages are determined by labor demand and household labor supply. It then replaces the presumed AI labor input with a compute-based conversion technology whose supply follows compute-capital constraints.

  • Textbook factor markets: In the textbook model, competitive firms equate factor prices with the value of marginal products, while labor-market equilibrium is determined by labor demand and household labor supply.Household time allocation and demographics determine Ls, and the wage is set where the curves intersect.
  • AI agents: Treating AI as a labor type with infinitely elastic zero-price supply would mechanically force the human wage toward zero, but the paper rejects this primitive.The alternative is to model agents as a technology rather than as labor.
  • Capital-to-labor conversion: An agent-produced cognitive labor unit is generated by operating a fixed compute bundle k for one unit of time, with LA = ϕ(Kc) ≈ Kc/k.The function ϕ represents the model architecture, training run, and inference stack.
  • Technology: Algorithmic efficiency raises ϕ for a given Kc and therefore reduces k, without entering a household labor-supply problem.Examples include distillation, speculative decoding, mixture-of-experts routing, and KV-cache reuse.
  • Compute-capital heterogeneity: Compute capital combines rival physical compute, non-rival model-weight intellectual property, and amortized sunk training capital.The CAW bound is governed primarily by variable inference costs, while IP rents reflect training sunk costs and licensing.
  • Supply: Because agent-produced labor has no household supply curve, its supply is inherited from compute capital, constrained by infrastructure and policy.The paper describes these constraints as finite and relatively inelastic in the short run, becoming only moderately elastic in the long run.

5 The Compute-Anchored Wage Bound

Under perfect substitution between human and agent-produced cognitive labor, the paper derives a wage ceiling determined by compute costs and relative productivity. The bound applies only on substitutable tasks and can coexist with complementary work and positive human employment.

  • Assumption: Under perfect substitutability, one human unit equals λ agent-produced units in effective cognitive output, with λ capturing relative human-to-agent productivity.Effective labor aggregates as Leff = LH + λ^-1LA on the relevant task set.
  • Proposition: WH ≤ λkrc is the Compute-Anchored Wage bound for human cognitive labor on substitutable tasks.With positive employment of both human and agent labor, the inequality holds with equality: WH = λkrc.
  • Mechanism: The effective-labor unit cost is min{WH, λkrc}, so firms use whichever input supplies effective cognitive labor more cheaply.If human labor is cheaper, agents are unused; if agents are cheaper, positive human supply cannot be sustained on the substitutable task.
  • Price setter: The equilibrium wage on substitutable cognitive tasks is determined by compute-market parameters k and rc together with λ, rather than by the labor supply curve.This is the paper’s formal migration of the price-setting margin.
  • Scope: The bound does not imply zero wages or universal unemployment: λkrc may be high or low, and workers may relocate to complementary tasks.Its scope is limited to tasks where the perfect-substitution assumption approximately holds.

6 CES Generalization: Imperfect Substitution

The CES extension allows human and agent-produced cognitive labor to be imperfect substitutes, making task-level substitution elasticity the key empirical object. It shows how the perfect-substitute CAW bound and alternative supply constraints emerge as limiting cases.

  • CES framework: The CES formulation replaces perfect substitution with elasticity σ between human and agent-produced cognitive labor.This generalization captures intermediate substitution patterns across tasks.
  • Cost structure: The effective unit cost of agent-produced labor is W_eff,A = krc because LA = Kc/k and compute rents at rc.Cost minimization then yields conditional factor demands and a relative-wage condition.
  • Perfect-substitute limit: As σ →∞, the CES wage relation recovers the perfect-substitute CAW bound WH = λW_eff,A = λkrc.The normalization α/β = λ connects the CES weights to the perfect-substitute productivity ratio.
  • Comparative statics: Holding human-labor supply and effective-labor demand fixed, greater compute supply or lower k reduces effective agent wages and lowers human wages in the CES model.The result is stated as a compute-driven wage-compression proposition at fixed rc.
  • Leontief limit: As σ →0, human and agent labor are used in fixed proportion, and the factor in shorter supply becomes binding.In this Leontief limit, the comparative-static channel from agent effective wages to human wages vanishes.
  • Empirical implication: The paper’s empirical claim is that CAW pressure is governed by task-level σ, replacing binary “AI replaces / does not replace” classifications.Observed factor demands can provide inputs for estimating this elasticity.

7 A Numerical Calibration of CAW

The calibration illustrates how the CAW ceiling varies with compute prices, compute intensity, and relative productivity. Under the paper’s illustrative assumptions, the ceiling is already low for some substitutable tasks and declines as compute becomes more efficient.

  • The calibration is illustrative rather than an estimation, showing that λkrc varies by orders of magnitude across tasks.The exercise plugs in plausible 2024–2025 compute prices to give the CAW bound empirical traction.
  • $2/GPU-hour is used as the midpoint rental rate for on-demand H100 compute.Observed on-demand prices were $2–$5/GPU-hour in 2024, with multi-year contracts closer to $1.50/GPU-hour.
  • Compute intensity is set at 1 H100-hour per agent-labor-hour for frontier models and 0.05 for small distilled models.The plausible frontier range is 0.5–2 H100-hours, depending on whether workloads are interactive or batched.
  • λ spans 0.5, 1.0, and 2.0, representing agent advantage, parity, and human productivity advantage respectively.The calibration draws on reported 14–40% time savings with quality at or above the human baseline.
  • The CAW ceiling is the binding human wage implied by each λ, k, and rc configuration in Table 1.The bound is WH ≤ λkrc, and the table reports the resulting ceilings in US$/hour for substitutable cognitive tasks.
  • For frontier-model reasoning, CAW is currently roughly $1–$10/hour, while small-model tasks are pinned below plausible human reservation wages.The small-model cases include high-volume classification, summarization, and first-pass document review; all cells fall as k declines or ϕ improves.

8 Visualizing the Migration of the Price-Setter

The figure relocates the price-setting margin from the human labor market to the compute capital market. Compute supply and demand determine r∗c, which conditionally sets the CAW ceiling for human cognitive labor on substitutable tasks.

  • Short-run compute supply is steep because of fab capacity, energy, and data-center lead times, so compute demand pins r∗c.Agent labor has no household supply curve; its supply is derived from compute capital Kc.
  • Figure 1 contrasts textbook wage determination by Ld ∩ Ls with compute-market determination of the rental rate r∗c.The figure’s panels move from the classic labor market to compute capital and then to CAW-anchored cognitive labor.
  • The wage ceiling is WH ≤ λkr∗c, with the equilibrium rental rate inherited from the compute capital market.The figure draws the human labor supply curve and employment relationships on TS conditional on r∗c.
  • On substitutable tasks TS, the horizontal CAW line is a conditional ceiling on human cognitive wages, not an infinitely elastic agent-labor supply curve.The human labor supply curve is drawn but does not determine the equilibrium wage on TS.
  • Shifts in compute demand reprice r∗c, and the CAW line shifts in lockstep in general equilibrium.The wage ceiling therefore moves with the compute-market rental rate rather than being fixed by human labor supply.

9 Task Heterogeneity: A Directional Inversion of Skill-Biased Technical Change (SBTC)

AI agents create a directional inversion within cognitive labor: substitutable tasks face wage pressure linked to compute, while complementary tasks can support higher wages. Consequently, cognitive workers’ wage differences depend more on their TS/TC exposure mix than on traditional skill categories.

  • Task partition: Substitutable cognitive tasks include drafting, code generation against specifications, summarization, first-pass analysis, scheduling, retrieval, and classification.
  • Task partition: Complementary cognitive tasks include judgment under deep uncertainty, accountability, relational work, cross-domain integration, taste, and principal-agent monitoring.
  • Wage effects: On substitutable tasks, wages are anchored by λkrc, while complementary tasks can experience rising wages as agent labor increases.
  • Occupational exposure: A junior contract-review paralegal performs roughly 80% substitutable and 20% complementary work, whereas a senior litigation associate performs roughly 30% substitutable and 70% complementary work.
  • Occupational exposure: Occupations with similar traditional skill requirements can diverge sharply in compensation because their TS/TC exposure mixes differ.
  • Factor shares: As compute substitutes for human cognitive labor, the labor share falls on affected tasks while compute’s capital share rises, benefiting compute infrastructure owners, energy producers, and model-IP holders.
  • Policy implications: Compute taxation, public compute provision, accelerator-market antitrust, and lower data-center electricity costs operate through compute prices and affect cognitive-labor wage distribution.

11 Limitations and Boundary Conditions

The paper identifies boundary conditions for the Compute-Anchored Wage claim, including demand expansion, comparative advantage, omitted wage premiums, compute-market structure, technological change, shifting task boundaries, and heterogeneous compute capital.

  • CAW bounds the wage, not the wage bill; total compensation depends on demand elasticity for cognitive output.
  • Comparative advantage can preserve human employment even when agents are absolutely more productive, but allocation does not determine substitutable-margin wages.
  • Liability, accountability, signaling, trust, and physical co-presence can add a human-labor premium beyond the marginal-product component bounded by CAW.
  • The derivation assumes competitive compute markets; monopolization, vertical integration, or rationing replaces the bound with a markup-adjusted version.
  • Algorithmic improvement lowers k over time, making CAW depend on the joint trajectory of compute intensity and compute rental rates.
  • The substitutable and complementary task partition shifts with capability, so empirical tests require a measurable, time-indexed task taxonomy.
  • Compute capital combines rival physical compute, often-monopolistic model-weight IP, and sunk training capital, motivating separate factor-pricing equations.
  • The paper’s conclusion is that substitutable cognitive-labor wage ceilings are set in compute capital markets rather than labor markets.

Appendix

The appendix defines the paper’s notation for output, capital, labor, agent-produced labor, productivity, task sets, substitution, and compute-anchored prices.

  • Y is aggregate firm output, K is generic physical capital, L is generic labor, and Ko is non-compute physical capital.
  • Kc is compute capital, including GPUs, accelerators, data-center capacity, energy, and model-weight IP rents.
  • rc is the competitive compute-capital rental rate, LH is human cognitive labor, and LA satisfies LA = ϕ(Kc) ≈ Kc/k.
  • ϕ denotes the capital-to-labor conversion technology embedding model architecture and the inference stack.
  • λ is relative human-to-agent productivity on substitutable tasks, with λ > 1 favoring humans and λ < 1 favoring agents.
  • WH is the human cognitive wage, while W eff A ≡ krc is the effective agent unit wage.
  • σ measures the elasticity of substitution between human and agent cognitive labor in the CES aggregator.
  • TS and TC denote substitutable and complementary cognitive task sets, respectively.

B Detailed Derivation of the CAW Bound

The derivation models effective substitutable cognitive labor as a combination of human and agent units and obtains the CAW ceiling through competitive cost minimization.

  • Effective cognitive labor on substitutable tasks is Leff = LH + λ−1LA.
  • The firm minimizes WHLH + rc k LA subject to producing at least one unit of effective labor.
  • When WH < λkrc, cost minimization selects human labor exclusively on substitutable tasks.
  • When WH > λkrc, the firm selects agent labor exclusively, leaving positive human supply unemployed on substitutable tasks.
  • Across equilibria with positive human employment, WH ≤ λkrc, with equality when human and agent labor are simultaneously employed.
  • If agents are absent because compute is unavailable or prohibitively expensive, the standard labor-market wage prevails and the bound is slack.

C CES Algebra

The CES extension describes how human wages respond to effective agent wages across substitution regimes, from perfect substitutes to Leontief complements.

  • CES cost minimization yields conditional factor demands and a relative-wage relationship involving human and effective agent wages.
  • As σ →∞, the relative-wage condition gives WH → (α/β)W eff A, recovering the perfect-substitute CAW bound when α/β = λ.
  • As σ →0, human and agent labor are used in a fixed ratio, and the binding factor is whichever is shorter in supply.
  • When human labor binds, the compute-wage channel to WH vanishes; when compute binds, WH tracks W eff A scaled by the technology proportion.
  • With perfectly elastic human-labor supply, WH tracks W eff A; with inelastic supply, a cross-derivative term partially offsets the direct effect.
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