The AI Production Function

Code Capital, Context Capital, and Computational Labor

A generalized production function for AI-native economies. Industrial economics models production as physical capital combined with human labor; this paper re-grounds the factors as Code Capital (C), Context Capital (X), and computational labor — the factor in the labor slot, measured by computational work $W$ — and derives $Y = A,C^{\alpha}X^{\beta}W^{\gamma}$, which nests the classical Cobb-Douglas function. It specifies how each factor is measured, confronts the simultaneity problem in identifying the elasticities, and states falsifiable hypotheses.

Preprint: SSRN abstract 7242925 (posted 12 August 2026).

Contents

paper.pdf · paper.md          the paper (submission copy + source); proofs are in Appendix B,
                              Section 9 estimation diagnostics in Appendix C
code/                         executable model, tests, and the identification demo
code/repro/                   Section 9 regenerator: frozen anonymized panel + estimators
references/bibliography.bib
figures/                      figure1 (factor remapping) plus the Section 9 figures 2-5,
                              regenerated by code/repro/make_figures.py

The formal proofs (Theorems A.1–A.4, B.1–B.3) are part of the paper itself, in Appendix B, and the Section 9 estimation diagnostics — the data-hygiene correction, the estimating-sample construction, and the item-by-item reading of Table 1 including the seed-convention sensitivity — in Appendix C. The bundle is self-contained.

Reproduce the verification

cd code
pip install -r requirements.txt      # numpy, pytest
python3 -m pytest -q                  # 41 tests: 27 (production, accumulation, estimation) + 14 (Section 9 repro, seed sweep, synthetic recovery)
python3 experiments.py                # scenario tables
python3 estimation.py                 # OLS bias under selection-on-the-shock; oracle isolates the confounding

Each theorem in Appendix B is cross-referenced to a test; the identification argument (Section 7.2) is demonstrated on synthetic ground-truth data (recovery under exogeneity, upward bias under simultaneity, and an infeasible oracle that isolates the confounding) — method validation, not empirical evidence.

Reproduce Section 9

The Section 9 empirical illustration regenerates from a frozen, repository-anonymized panel (18 repositories → repo01…repo18) shipped in code/repro/:

cd code/repro
pip install numpy pytest
python3 reproduce_section9.py --check   # regenerates the corrected + as-shipped readings; matches the frozen result
python3 sweep_seed_delta.py --check     # Appendix C(vi): seed/depreciation sweep matches results_sweep.json
python3 -m pytest -q                     # 14 tests: Table 1 pins (both correction rounds), sweep pins, synthetic-panel estimator recovery

Only weekly aggregates travel with the bundle. The extraction layer that builds the panel from the organization's private session logs and version-control history is not shipped (the data are the authors' own and not independently auditable, as Section 9 discloses); what is reproducible is every Section 9 number, from the frozen panel forward.

Classification

• JEL: D24, O33, O47, E22, L86
• Keywords: production function; artificial intelligence; agentic economy; intangible capital; endogenous growth; computational labor; productivity measurement

Citation & license

Cite via the repository CITATION.cff, or cite the preprint:

Lee, Sangseng, The AI Production Function: Code Capital, Context Capital, and Computational Labor (August 06, 2026). Available at SSRN: https://ssrn.com/abstract=7242925

Each tagged release is archived to Zenodo through the GitHub–Zenodo integration; v1.0.0 is archived at 10.5281/zenodo.21824554. Text CC BY 4.0, code MIT — see LICENSE.