1<!-- Author: Simon-Pierre Boucher — simon-pierre.boucher@uqo.ca -->2# 🤖 From Labor to Capital34**UQO Working Paper No. 24** — *Artificial General Intelligence, General Equilibrium, and Asset Valuation*56[](paper/main.pdf)7[](slides/main.pdf)8[](requirements.txt)9[](data/README.md)10[](Makefile)11[](https://uqo.ca)12[](mailto:simon-pierre.boucher@uqo.ca)1314> **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.1516---1718## 📌 Status1920| Item | Value |21|---|---|22| Version | 1.0 (October 2026) |23| SSRN | not yet submitted |24| Journal | — (candidates: a macro-finance or growth field journal) |25| Code & data | fully reproducible from `make all`; public data only (FRED/BEA/Fed/Shiller/LBNL/EIA/Epoch), nothing typed from memory |26| Source audited | Restrepo (2025), NBER conference paper f227505, July 4 2025 draft (`docs/source_audit.md`) |2728## 🎯 What this paper does29301. **Audits and replicates** Restrepo (2025) exactly in a finite-task CES economy (Propositions 1–6 hold to 1e-6; `scripts/10_benchmark.py`).312. **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.323. **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).334. **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.345. **Writes an adversarial referee report** (`docs/referee_report.md`) and a falsifiable short-run empirical design (Section 11).3536## 🏆 Headline results (baseline, two-class economy)3738| Object | 2026 | 2050 | 2100 |39|---|---|---|---|40| Labor share | 0.56 | 0.28 | 3e-5 |41| Wage of skill L per worker (2026 = 1) | 1 | 0.06 | 0.005 |42| Wage of skill H per worker (2026 = 1) | 1 | 3.5 (transitory premium of the last-automated skill) | 0.02 |43| GDP (2026 = 1; trend would give 1.4 / 3.0) | 1 | 3.7 | 233 |44| Real return on wealth | 6.3 % | 22 % (peak 40 % in 2060) | 5.5 % |45| Wealth / GDP | 4.1 | 3.0 (min 2.7 in 2042) | 31 |46| Land share of income / of wealth | 0.09 / 0.29 | 0.11 / — | 0.60 / 0.90 |47| Value of compute capital / GDP (P/E) | 0.14 (5.0) | 0.16 (1.8) | 0.13 (3.3) |48| Energy used by compute | 4.4 % | 47 % (peak 62 % in 2060) | 26 % |49| Tasks automated (of 4) | 1 | 3 | 4 |5051The 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.5253## 🗂 Repository layout5455```56├── CLAUDE.md # research protocol (6 phases, deliverables, stop conditions)57├── Makefile · requirements.txt # one-command reproduction (make all)58├── source_audit/ # Restrepo (2025) PDF text extraction59├── docs/ # source_audit, model_dictionary, assumptions_register, identification,60│ # research_log, replication, referee_report, literature_matrix, references_verification61├── data/ # README (provenance), raw/ (downloads, git-ignored), processed/ (162 calibration targets, versioned)62├── src/agi_ge/ # ces, tasks (static block + KKT polish), production, steady (BGP), calibration,63│ # transition (banded Newton), solve (driver), households (EGM, numba), ha_equilibrium,64│ # analysis (valuation ratios, Campbell–Shiller, welfare), scenarios65├── scripts/ # 01/02 data, 10 benchmark, 11 regime map, 20/21 scenarios, 30/31 HA, 40 figures, 50 tables, 55 fallbacks66├── tests/ # pytest: static (Restrepo P1–P6, KKT, accounting), transition (BGP, Jacobian, equilibria)67├── results/{data,scenarios,ha,figures,tables}/68├── paper/ # main.tex → main.pdf (UQO template), sections/, appendix/, figures/, tables/, references.bib (118 verified)69└── slides/ # main.tex → main.pdf (Beamer, metropolis)70```7172## 🚀 Quick start7374```bash75make setup # pinned requirements76make test # ≈ 1 min77make benchmark # fig01/fig02, tab0178make scenarios N=12 # 25 scenarios × 275 years, 12 in parallel (≈ 7–15 min each; one core each)79make ha # heterogeneous-agent GE (baseline, frozen, citizen fund)80make figures tables paper # results/figures, results/tables + numbers.tex → paper/main.pdf81make slides82```8384## 📊 Data8586Public, 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.8788## 🧮 Methodology (one paragraph)8990Static 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.9192## 🖼 Figures & tables9394fig01 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.9596## ⚠️ Limitations9798Perfect 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.99100## 📖 Citation101102```bibtex103@techreport{Boucher2026WP24,104 author = {Boucher, Simon-Pierre},105 title = {From Labor to Capital: Artificial General Intelligence, General Equilibrium, and Asset Valuation},106 institution = {Universit\'e du Qu\'ebec en Outaouais, D\'epartement des sciences administratives},107 type = {UQO Working Paper},108 number = {24},109 year = {2026},110 month = {October}111}112```113114## 👤 Author & contact115116Simon-Pierre Boucher — Département des sciences administratives, Université du Québec en Outaouais — simon-pierre.boucher@uqo.ca117118## 📝 Notes119120Built 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`).121