If AGI simply transfers value rather than creating it, widespread substitution of human labor can erode surplus value and push the social rate of profit toward zero; without the emergence of new labor‑demanding fields, near‑complete AGI adoption collapses living labor, surplus value and profits.

Main Finding

Under a strict political-economy value assumption (living labor creates new value; AGI only transfers or redistributes it), progressive AGI adoption that substitutes living labor raises the organic composition of capital and, if adoption outpaces the creation of new labor fields, compresses surplus value and drives the social profit rate down. In the limit of near-complete actual adoption with no compensating expansion of new labor domains, living labor, surplus value, and the profit rate all tend toward zero — making near-complete AGI substitution a structural boundary for value production, not merely an efficiency endpoint.

Key Points

• Two distinct concepts: technical substitutability q(A) (what AGI can in principle do as capability A grows) versus actual adoption α(t) (what capital actually replaces, constrained by cost/profitability/frictions). Adoption evolves continuously toward the technical ceiling rather than jumping instantly.
• AGI capability A(t) increases over time (A′>0). Technical substitutability is modeled as q(A)=1−e^{−βA} (increasing, concave; limit 1). Unit replacement cost falls with capability: m(A)=m0 e^{−γA}.
• Strict value-theoretic assumption: only living labor creates new value. AGI-based systems only reorganize/transfer/cheapening production; they do not themselves generate new value.
• Living labor remaining: H(α) = (1−α)L where L is total task mass. Per-unit value created φ and wage w ⇒ surplus value s = (φ−w)(1−α)L, so total surplus is proportional to remaining living labor.
• Constant capital includes pre-existing c0 plus AGI-related capital cA = m(A)αL. Total capital K = c0 + m(A)αL + w(1−α)L.
• Organic composition Ω = c / v = [c0 + m(A)αL] / [w(1−α)L] increases monotonically with α (proved analytically).
• Social profit rate r = s / (c + v) falls as α rises (given the assumption that only living labor generates surplus); in the limit α→1 (and no new labor fields) s→0, r→0.
• The model highlights two thresholds/epochs: (i) first economic feasibility of substitution, (ii) near-complete technical/actual substitution — with different timing because of frictions and cost dynamics.

Data & Methods

• Method: formal dynamic political-economy model using closed-form functional specifications; analytic derivations (no empirical data).
• Key state variables:
  • Time t ≥ 0.
  • AGI capability A(t) with A′(t) > 0.
  • Actual adoption α(t) ∈ [0,1].
  • Total task mass L (fixed in baseline).
• Technical substitutability q(A) with q′>0, q′′<0; example: q(A)=1−e^{−βA}.
• Unit AGI replacement cost m(A) with m′<0; example: m(A)=m0 e^{−γA}.
• Value structure:
  • Living labor employed H(α) = (1−α)L.
  • Per-unit value created φ, wage w. Surplus s(α) = (φ−w)(1−α)L. Surplus-rate e = (φ−w)/w independent of α.
  • Variable capital v = w(1−α)L.
• Capital composition:
  • AGI-related constant capital cA = m(A)αL.
  • Total constant capital c = c0 + m(A)αL.
  • Organic composition Ω(α,A) = c / v. Analytical differentiation shows ∂Ω/∂α > 0 under c0>0, m(A)>0, w>0, L>0, α∈[0,1).
• Profit rate: r(α,A) = s(α) / [c(α,A) + v(α)]. Using s∝(1−α)L and c, v above, the model shows r declines as α increases and tends to zero if α→1 and new labor fields do not grow.
• Important model assumptions documented explicitly: L fixed (in baseline), AGI does not create new value, φ>w (to assure positive surplus), functional forms exponential for tractability.
• The paper is analytic/theoretical — no empirical estimation; identifies comparative statics and limit behavior rather than calibrated forecasts.

Implications for AI Economics

• Conceptual: Distinguishing technical substitutability from actual adoption is essential for realistic forecasting of AGI effects. Capability ceilings (what AGI could do) do not equal immediate economic replacement (what capital will adopt).
• Structural macro implications:
  • Deep AGI adoption mechanically raises capital intensity (organic composition) and lowers the wage-bill share of production in this framework.
  • If displaced labor is not reabsorbed into new labor-demanding sectors, aggregate surplus and the aggregate profit rate shrink — potentially undermining an economy organized around surplus-driven accumulation.
• Empirical predictions to test:
  • Rising ratio of constant capital to wages in sectors with high AGI adoption.
  • Falling total wage bill and employment in task-composed sectors absent compensating sectoral growth.
  • Downward pressure on aggregate profit rates where AGI adoption is deep and task-creation is insufficient.
• Policy and institutional implications:
  • Technical progress alone may not be welfare-positive under this value assumption without mechanisms to (re)create labor demand or redistribute income (universal basic income, public employment, taxes on capital, social ownership, or profit-sharing).
  • Regulatory or industrial policy that fosters new labor-intensive tasks or steers AGI deployment could mitigate contractionary outcomes.
  • Redistribution and consumption-support policies may be necessary to sustain demand if wage-based income contracts.
• Modeling recommendations for AI-economics research:
  • Relax the strict-value assumption in extensions (allow AGI to create value or augment labor productivity in ways that generate additional effective demand).
  • Endogenize task creation: model the rate at which new labor fields arise as a function of technology, institutions, and demand.
  • Explicitly model adoption frictions, organizational constraints, and demand-side feedbacks that can slow or accelerate α(t).
  • Introduce heterogeneity across sectors, complementarities between human labor and AGI, and distributional/finance channels that affect investment and profit dynamics.
• Limitations to bear in mind:
  • The main result depends critically on the assumption that only living labor creates new value. If AGI can create (or enable) net new value or demand, conclusions weaken or change.
  • No demand-side dynamics, finance, or political responses (taxes, wage bargaining, labor market institutions) are modeled; these could significantly alter outcomes.
  • L is fixed in the baseline; allowing endogenous L (task expansion) is central to determining whether the contractionary limit is realized.

Overall, the paper provides a clear, parsimonious formalization of how AGI-driven substitution could structurally alter capital-labor composition and profit-generation under a classical value-theoretic lens, and it highlights critical modeling and policy levers that determine whether AGI becomes destabilizing for value production.