UQO Working Papers · WP24 · v1.0
From Labor to Capital: Artificial General Intelligence, General Equilibrium, and Asset Valuation
- Year
- 2026
- First release
- October 2026
- Latest revision
- October 2026
- Publication status
- Working paper
Labor's share vanishes under AGI; its wage level depends on compute scarcity
In the calibrated baseline the labor share falls from 0.56 to 0.283 by 2050, the real return on wealth peaks at 40.5% in 2060, and the wealth-to-income ratio falls to 2.7 before land lifts it to 31.0 by 2100.
Abstract
Restrepo (2025) shows that once artificial general intelligence lets compute perform every task, output becomes linear in compute, wages converge to the value of the compute a worker saves, and the labor share goes to zero. This paper extends his task economy by treating compute as a reproducible, priced, depreciating capital good that needs energy and works alongside structures and land, and by adding households that own the claims to income.
The labor-share result survives any constant-returns production structure: it needs only within-task substitutability. The wage-level result does not: when physical complements are gross complements and compute becomes cheap, the price of compute and wages go to zero in level and the income that labor loses goes to the owners of the scarcest complement; with a floor on the compute price, the wage equals the user cost of the replacement compute. Income shares and asset values are different objects: compute is capitalized at the duration of chips, so capital's share can rise while the wealth-to-income ratio falls, and a growth boom raises the real rate and compresses valuation ratios when the elasticity of intertemporal substitution is below one.
In a calibrated model solved along perfect-foresight paths to 2300 under conditional scenarios, the labor share falls to 0.283 by 2050, the real return peaks at 40.5%, the wealth-to-income ratio falls to 2.7 before land captures 0.605 of income and raises it to 31.0 by 2100, and the market value of compute never exceeds one fifth of GDP. A compute tax raises wages one-for-one with the tax-inclusive user cost; a land tax redistributes without distortion; a citizen fund keeps workers' consumption share bounded away from zero.
Key findings
0.283
labor share in 2050, down from 0.56 in 2026
40.5%
peak real return on wealth, in 2060
2.7 → 31.0
wealth-to-income ratio, 2042 trough to 2100
0.605
share of income captured by land by 2100
≤ 1/5 of GDP
market value of compute capital along every path
25
conditional scenarios solved over 275 years
Scientific contributions
- The labor-share result is more robust than claimed
- The labor share goes to zero under any constant-returns production structure, with or without complements and whether compute is an endowment or a priced capital good, because it needs only perfect substitutability of labor and compute within tasks (Proposition 1).
- The wage-level result is less robust
- With gross complements (σ < 1) and cheap compute, the price of compute and wages go to zero in level and lost labor income accrues to the owners of the scarcest complement; with a price floor the wage equals the user cost of the replacement compute, (r + δ_Q) p̄ CEU (Propositions 2–4); an energy bottleneck keeps the labor share positive (Proposition 5).
- Income shares and asset values diverge
- On a balanced path the wealth-to-income ratio is Σ s_k/[(1+r)(1+π_k) − (1−δ_k)] + s_T/(r−g): compute, depreciating at 25% and cheapening at 15% a year, is capitalized at a price–earnings ratio of about two against eight for structures and fifty for land, so capital's share can rise while wealth-to-income falls (Propositions 6–7).
- A calibrated transition to 2300
- In the baseline the routine task is automated by 2029 and the expert task by 2057; output rises 3.7-fold by 2050 and 233-fold by 2100; the high-skill wage reaches 3.51 times its 2026 level while its task is the last unautomated, then collapses.
- Policy in general equilibrium
- A compute tax raises wages one-for-one with the tax-inclusive user cost at a cost in output, a land tax redistributes without changing allocations, a citizen fund holding one fifth of all claims bounds workers' consumption share away from zero, and an AI monopoly protects wages like a compute tax while rents go to the monopolist.
- An audited replication of the source
- Restrepo (2025) is reproduced exactly in a finite-task CES economy (Propositions 1–6 hold to 1e-6), and the quantitative equilibria satisfy Euler residuals below 1e-9 and income identities below 1e-8.
Methodology
Methodology (5)
Task block with priced compute
The static allocation of labor and compute across tasks is a concave program solved by SLSQP with a Newton polish on the active set; prices follow from the envelope theorem, with an energy residual and a utilization margin.
Propositions in a limit economy
Eight propositions on labor share, wage levels, balanced AGI growth, energy bottlenecks, valuation ratios, the discount-rate channel and tax incidence are proved in a one-complement limit economy (Appendix A).
Perfect-foresight transition by banded Newton
Unknowns per year are four log stocks, capitalists' expenditure and the real rate; residuals are four Tobin's-q Euler equations, goods-market clearing and the household Euler equation, solved directly over 275 years with a colored finite-difference banded Jacobian and a homotopy fallback.
Heterogeneous households in general equilibrium
Endogenous grid method with a housing price index and non-stochastic simulation; general equilibrium by damped quasi-Newton on the return path, with welfare and distribution statistics by skill and wealth.
Valuation decomposition
Campbell–Shiller decomposition of 2026 valuations into cash-flow and discount-rate news, which are of the same order and opposite sign, plus a falsifiable short-run empirical design on the compute-equivalent wage (Section 11).
Research data
- Model environment
- A task economy with four tasks and two skills, four capital stocks with Tobin's q (compute, equipment, structures, housing structures), land, energy drawn from a fixed resource, a two-class economy whose capitalists price every claim, and a heterogeneous-agent economy (2 skills × 3 discount types × 5 productivity states) holding claims through a fund; perfect-foresight paths over 275 years to 2300.
- Calibration to the United States in 2026
- 162 public targets retrieved 2026-10-27 with URLs, vintages and SHA-256 hashes: PWT labor share, BEA fixed assets and NIPA via FRED, Fed Z.1 and Distributional Financial Accounts, TIPS and Cleveland Fed real rates, Shiller CAPE and home prices, LBNL data-centre electricity (4.4% in 2023), EIA generation, Epoch AI GPU price–performance (doubling every 2.02 years) and the BEA 2023 use table.
- Conditional scenarios
- 25 scenarios on capability speed, Moore's law and its end, energy constraints, elasticities, scarce land, chip depreciation, monopoly, foreign ownership, land, compute and capital taxes, a citizen fund, task reinstatement and risk aversion; the baseline has capability improving 10% a year and compute prices falling 15% a year to one hundredth of today's level.
Reproducibility
- One-command reproduction (make all: setup, test, benchmark, scenarios, ha, figures, tables, paper, slides) with pinned requirements; pytest covers the Restrepo replication, KKT conditions, accounting identities, balanced growth and equilibria
- 25 scenarios × 275 years solved with numerical diagnostics reported (Euler residuals < 1e-9, income identity < 1e-8, horizon check < 1e-7); 10 figures, 8 tables and numbers.tex regenerated by scripts
- Public data only, with a manifest of URLs, vintages and SHA-256 hashes; source audit of the Restrepo (2025) NBER draft, assumptions register, identification note and an adversarial referee report in docs/
- Full LaTeX source of the 55-page paper (118 verified references) and Beamer slides
Research artifacts
Version history
| Version | Date | Description | File |
|---|---|---|---|
| v1.0current | October 2026 | Current manuscript as published on www.spboucher.ai (revised edition after the 2026-10-17 scientific review for papers 1–17). | PDF · 55 p. |