# 🤖 From Labor to Capital

UQO Working Paper No. 24 — Artificial General Intelligence, General Equilibrium, and Asset Valuation

TL;DR — Restrepo (2025, NBER) shows that once compute can do every task, wages converge to the value of the compute a worker saves and the labor share goes to zero. This paper keeps his task block and makes compute a reproducible, priced, depreciating, energy-using capital good with physical complements (structures, land, energy), then adds households that own the claims. The labor-share result is robust to everything (it only needs within-task substitutability). The wage-level result is not: with gross complements and cheap compute, 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 is the user cost of the replacement compute. Income shares and asset values are different objects: compute is capitalized at the duration of chips (P/E ≈ 2), so capital's share can rise while wealth/income falls, and a growth boom raises the real rate and compresses valuation ratios when the EIS < 1. Calibrated to the US in 2026 and solved to 2300 under 25 conditional scenarios: labor share 0.56 → 0.28 (2050) → <0.001 (2075+); real return peaks at 40 % in 2060; wealth/GDP falls from 4.1 to 2.7 in 2042 before land captures 60 % of income and lifts it to 31 by 2100; the market value of compute never exceeds one fifth of GDP. A land tax redistributes without distortion, a compute tax raises wages one-for-one with the tax-inclusive user cost, a citizen fund bounds workers' consumption share below.

# 📌 Status

# 🎯 What this paper does

1. Audits and replicates Restrepo (2025) exactly in a finite-task CES economy (Propositions 1–6 hold to 1e-6; scripts/10_benchmark.py).
2. Proves eight propositions in a limit economy with one scarce complement and priced compute (Section 7, proofs in Appendix A): labor share → 0 always; wages → 0 vs positive depending on σ and the compute price; balanced AGI growth with w = (r+δ_Q) p̄ CEU; energy bottleneck ⇒ positive labor share; W/Y = Σ s_k/[(1+r)(1+π_k)−(1−δ_k)] + s_T/(r−g); discount-rate channel with sign(1−γ); wage = tax-inclusive user cost of the replacement.
3. Builds a quantitative model (4 tasks × 2 skills, 4 capital stocks with Tobin's q, energy from a fixed resource, housing = structures + land, two-class and heterogeneous households), calibrated to 2026 US shares, solved as 275-year perfect-foresight equilibria by a banded Newton method with numerical checks (Euler residuals < 1e-9, income identity < 1e-8, horizon check < 1e-7).
4. Runs 25 conditional scenarios (capability speed, Moore's law and its end, energy constraints, elasticities, scarce land, chip depreciation, monopoly, foreign ownership, land/compute/capital taxes, citizen fund, reinstatement, risk aversion) and decomposes valuations into cash-flow and discount-rate channels.
5. Writes an adversarial referee report (docs/referee_report.md) and a falsifiable short-run empirical design (Section 11).

# 🏆 Headline results (baseline, two-class economy)

The long run is pinned by two unidentified scenario inputs — the compute-price floor (×1/100 in the baseline) and the terminal compute per worker (α₁^∞ = 1) — and the paper reports the dependence (Table 4) rather than a number.

# 🗂 Repository layout

├── CLAUDE.md                      # research protocol (6 phases, deliverables, stop conditions)
├── Makefile · requirements.txt    # one-command reproduction (make all)
├── source_audit/                  # Restrepo (2025) PDF text extraction
├── docs/                          # source_audit, model_dictionary, assumptions_register, identification,
│                                  # research_log, replication, referee_report, literature_matrix, references_verification
├── data/                          # README (provenance), raw/ (downloads, git-ignored), processed/ (162 calibration targets, versioned)
├── src/agi_ge/                    # ces, tasks (static block + KKT polish), production, steady (BGP), calibration,
│                                  # transition (banded Newton), solve (driver), households (EGM, numba), ha_equilibrium,
│                                  # analysis (valuation ratios, Campbell–Shiller, welfare), scenarios
├── scripts/                       # 01/02 data, 10 benchmark, 11 regime map, 20/21 scenarios, 30/31 HA, 40 figures, 50 tables, 55 fallbacks
├── tests/                         # pytest: static (Restrepo P1–P6, KKT, accounting), transition (BGP, Jacobian, equilibria)
├── results/{data,scenarios,ha,figures,tables}/
├── paper/                         # main.tex → main.pdf (UQO template), sections/, appendix/, figures/, tables/, references.bib (118 verified)
└── slides/                        # main.tex → main.pdf (Beamer, metropolis)

# 🚀 Quick start

make setup                 # pinned requirements
make test                  # ≈ 1 min
make benchmark             # fig01/fig02, tab01
make scenarios N=12        # 25 scenarios × 275 years, 12 in parallel (≈ 7–15 min each; one core each)
make ha                    # heterogeneous-agent GE (baseline, frozen, citizen fund)
make figures tables paper  # results/figures, results/tables + numbers.tex → paper/main.pdf
make slides

# 📊 Data

Public, key-less endpoints only, retrieved 2026-10-27 with URLs, vintages and SHA-256 hashes in data/raw/manifest.json: 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/D/P and home prices, LBNL data-center electricity (4.4 % in 2023), EIA generation, Epoch AI GPU price–performance (doubling 2.02 years), BEA 2023 use table, Statistics Canada (comparison). See data/README.md and Appendix D.

# 🧮 Methodology (one paragraph)

Static block: concave program over labor/compute allocations (SLSQP + Newton polish on the active set), prices by the envelope theorem, energy residual, utilization margin. Dynamics: unknowns per year = four log stocks, log capitalists' expenditure, r; residuals = four Tobin's-q Euler equations, goods market, household Euler; banded Jacobian by colored finite differences; direct solve on 275 years from a partial-equilibrium guess, homotopy fallback; base point re-calibrated per scenario. Households: EGM with housing price index, 2 skills × 3 discount types × 5 productivity states, non-stochastic simulation, GE by damped quasi-Newton on the return path.

# 🖼 Figures & tables

fig01 benchmark replication · fig02 regime map · fig03 baseline transition · fig04 valuation · fig05 technology scenarios · fig06 substitutability/scarcity · fig07 Campbell–Shiller decomposition · fig08 policy · fig09 preferences/reinstatement/Moore · fig10 distribution (HA) · tab01 benchmark · tab02 calibration · tab03 baseline · tab04 scenarios · tab05 decomposition · tab06 policy & welfare · tab07 distribution · tab08 diagnostics.

# ⚠️ Limitations

Perfect foresight (no risk premia; the 2026 jump of r is the news effect); the wage level after 2060 ∝ compute-price floor × terminal compute per worker (scenario inputs); no endogenous innovation, new tasks (except one reinstatement scenario), nonhomothetic demand, labor supply or return heterogeneity (top-1 % share under-predicted); energy = electricity; conditional scenarios, not forecasts.

# 📖 Citation

@techreport{Boucher2026WP24,
  author      = {Boucher, Simon-Pierre},
  title       = {From Labor to Capital: Artificial General Intelligence, General Equilibrium, and Asset Valuation},
  institution = {Universit\'e du Qu\'ebec en Outaouais, D\'epartement des sciences administratives},
  type        = {UQO Working Paper},
  number      = {24},
  year        = {2026},
  month       = {October}
}

# 👤 Author & contact

Simon-Pierre Boucher — Département des sciences administratives, Université du Québec en Outaouais — simon-pierre.boucher@uqo.ca

# 📝 Notes

Built 2026-10-27 from the research protocol in CLAUDE.md. Three specification changes were made for numerical reasons and are documented in docs/research_log.md: accessory tasks are kept in the replication only; capitalists' expenditure is an unknown of the dynamic system; the base point is re-calibrated for each scenario's anticipated price path. paper/tables/fallbacks.tex must be empty of ?? in the final version (scripts/55_fallbacks.py).