# Phase 0 — Source audit of Restrepo (2025), "We Won't Be Missed: Work and Growth in the Era of AGI"

**Source.** Pascual Restrepo (Yale), *We Won't be Missed: Work and Growth in the Era of AGI*, NBER conference
paper f227505, dated July 4, 2025, 20 pages (18 pages of text + references). Downloaded 2026-10-27 from
`https://conference.nber.org/conf_papers/f227505.pdf` to `source_audit/pdf/restrepo_2025_we_wont_be_missed.pdf`
(261 497 bytes); text extracted with `pdftotext -layout` to `source_audit/restrepo_nber_f227505.txt`.
Page numbers below are the printed page numbers of the chapter. The chapter is explicitly a *preliminary*
draft: Section 1.2 is labelled "[Preliminary]" (p. 12), footnote 1 reads "Infinitesimal similar results
but technical complications" (p. 3), and no formal proofs are given anywhere — every proposition is followed
by a heuristic argument. The audit therefore reconstructs the exact statements and the heuristic arguments,
and flags where our formalization has to add assumptions.

## 1. Primitives (Section 1, pp. 2–6)

| Object | Definition in the source | Page |
|---|---|---|
| Work set | Ω finite "(but large)" set of types of work ω; infinitesimal version deferred (fn. 1) | 2–3 |
| Work equation | X_t(ω) = L_t(ω) + Q_t(ω)/α_t(ω) (eq. 1): human output per unit time normalized to 1; α_t(ω) units of compute replicate one human; α_t(ω) = ∞ allowed | 3 |
| Output | Y_t = F({X_t(ω)}), F increasing, differentiable, concave, constant returns to scale; marginal products converge in [0,∞] along any converging input sequence | 3 |
| Skills | s ∈ 𝒮 with supply H(s); skill s can do work in Ω(s) ⊆ Ω, the Ω(s) partition Ω (no overlap, "simplifies exposition") ; Σ_{ω∈Ω(s)} L_t(ω) ≤ H(s) | 3 |
| Compute | Q_t total computations per unit of time; Σ_ω Q_t(ω) ≤ Q_t | 3 |
| Premise 1 (AGI) | for every ω, α_t(ω) becomes finite at a date T(ω) and converges to α(ω) ∈ (0,∞) | 3–4 |
| Premise 2 (abundant compute) | Q_t finite at each date, grows without bound | 5 |
| Equilibrium concept | competitive equilibrium = output-maximizing allocation of compute and labor with factors paid marginal products | 6–7 |

Interpretive remarks in the source worth preserving: (i) AGI is "the recipe", distinct from compute "the input"
(p. 4); feasibility ≠ realization: automating ω may be feasible but not worth scarce compute (p. 4);
(ii) physical work: Q_t may be re-read as "a bundle of energy and computational resources" (p. 4) — the chapter
does not model energy separately; (iii) "social" work is captured by high α(ω) (pp. 4–5); (iv) compute growth is
exogenous and "subsumed in the path for Q_t" (p. 5); the only requirement is that Q_t becomes large (p. 5).
Compute is an *endowment*: there is no price of compute capital, no depreciation, no investment, no saving and
no ownership structure anywhere in the chapter. This is the gap our paper fills.

## 2. Bottleneck vs accessory work (pp. 6)

* **Definition 1 (bottleneck).** ω is bottleneck if, for any path {X_t(ω)} along which F is unbounded, either
  X_t(ω) is unbounded or F_ω is unbounded.
* **Definition 2 (accessory).** ω is accessory if there is a path with F unbounded while both X_t(ω) and F_ω
  are bounded.

Examples offered (p. 6): bottlenecks — food, shelter, energy, infrastructure maintenance, science, decision
making, logistics, security; accessory — arts, performance, literature, hospitality, design, customer support,
judicial and civic work, "even the work performed by academic economists". The partition is explicitly said to
depend on "future preferences, the structure of production" (p. 6).

Formal observation (ours, needed for the replication): with F a CES aggregator, every task is a bottleneck
unless the elasticity is infinite. For σ < 1 any unbounded-F path has all X(ω) unbounded; for 1 < σ < ∞,
F_ω = ν_ω (F/X(ω))^{1/σ} is unbounded whenever X(ω) stays bounded while F grows. Accessory work in the sense
of Definition 2 requires asymptotically *linear* entry of the task into F (e.g. F = F_B({X_B}) + Σ_a γ_a X(a)),
which is the specification we adopt for the accessory block.

## 3. Propositions as stated (Section 1.1, pp. 7–11) and the arguments given

| # | Statement (verbatim content) | Argument given | Page |
|---|---|---|---|
| P1 | All bottlenecks are eventually automated while some accessory work may be left to labor. | Ricardo-type heuristic: specialization of compute on a subset would leave non-automated bottleneck work fixed, unbalanced growth cannot be optimal; only accessory work can stay fixed (fn. 5 on the "large country" case). | 7 |
| CEU | CEU(s) ≡ max_{ω∈Ω(s)} α(ω), finite under Premise 1. | definition | 7–8 |
| P2 | Output converges to Y_t = A[ Q_t + Σ_{s∈𝒜} CEU(s)H(s) + Σ_{s∈𝒩} \widetilde{CEU}(s) H(s) ] with \widetilde{CEU}(s) < CEU(s) (eq. 2); 𝒜 = skills performing only automated work, 𝒩 = skills performing non-automated accessory work (fn. 6). | Pooling of effective compute Q̃_t(ω) = Q_t(ω) + α_t(ω)L_t(ω); CRS ⇒ Y = A[Q + Σ α L]; labor of skill s goes to argmax α; for accessory work not automated, A α(ω) > MPL(s) and convergence to an additive constant is "a nontrivial implication of constant returns" (no proof). | 8–9 |
| P3 | Output grows at the same rate as Q_t. | direct from P2 | 9 |
| P4 | Real price of compute → A; real wages W(s) = A·CEU(s) for s ∈ 𝒜 and A·\widetilde{CEU}(s) for s ∈ 𝒩. | marginal products read off eq. (2) | 10 |
| P5 | Compute share of GDP → 1, labor share → 0. | labor share ≤ "share of human compute" Σ CEU(s)H(s)/(Q_t + Σ CEU(s)H(s)) → 0; orders of magnitude 10^15–10^18 flops per brain vs 10^21 today and up to 10^54 | 10–11 |
| P6 | The sum of all wages is higher in the AGI limit than pre-AGI (Q_t = 0, α = ∞). | "no-AGI zone" revealed-efficiency argument with CRS; **the author notes the argument breaks if "the AGI economy uses some finite resource that is also needed by human labor or there are diminishing returns to scale"** | 11 |

The two sets of workers are defined in fn. 6 (p. 9): group 𝒜 = skills for which one element of their
best-α set is automated; the rest form 𝒩.

## 4. Transition (Section 1.2 "[Preliminary]", pp. 12–13)

Assumptions for the section: all work is bottleneck; α_t(ω) jumps from ∞ to α(ω) at T(ω).

* **P7 (compute binds).** A_t decreases monotonically to A > 0; within Ω(s) work is automated sequentially from
  lowest to highest α; W_t(s) falls gradually (at the rate of A_t) around each automation date and then grows
  until the next; when the max-α work of the skill is automated, W_t(s) = A_t CEU(s) and decreases at the rate of
  A_t thereafter; total wages weakly increase. (p. 12)
* **P8 (technology binds).** A_t may be non-monotonic and jump up; work ω is automated exactly at T(ω); wages may
  jump down at T(ω) "if displacement effects dominate", necessarily jump down when the last work in Ω(s) is
  automated, and may exceed A_t CEU(s) at points of the transition; total wages may jump down. (p. 13)

No proofs; the prose (p. 13) interprets P8 as a "jagged, uncertain, and haphazard" transition in which the
last-automated skills earn a transitory premium "by a sheer act of luck".

## 5. Science (Section 2, pp. 13–16)

Y_t = Z_t F(·); Ż/Z = Z^{-β} G({X_t(σ)}), G CRS; scientific skills 𝒮_R disjoint from production skills 𝒮_P;
compute shared between science and production. Premise 1′ (AGI for science), Premise (exponential compute at
g_Q). With a constant science share λ: P9 (p. 15) Y_t = Z_t A[(1−λ)Q_t + Σ_{𝒮_R}CEU H], Z_t ∝ [BλQ_t + Σ_{𝒮_P}CEU H]^{1/β}
(note: the typesetting of eq. (3)–(4) swaps 𝒮_R/𝒮_P relative to the text; we keep the text's logic);
P10 (p. 15) g_Y = g_Q(1 + 1/β), g_Z = g_Q/β; P11 (p. 16) λ* = 1/(1+β+ρ) with science prioritized early.
We do not extend the science block (our contribution is on the production/ownership/valuation side); we only
use P10 as the source of the "endogenous AI productivity growth" robustness scenario.

## 6. Discussion and policy (Section 3, pp. 17–18)

Wages stagnate and the labor share collapses but labor is not worthless; accessory care/hospitality work may
persist at capped wages; when technology binds, "inequality may rise sharply during the transition"; policy
questions raised but not modelled: risk sharing, gradual deployment (Lehr–Restrepo 2022), "universal
dividends", compute "as a public or semi-public resource, akin to land or natural capital" (p. 18).

## 7. What the source does *not* contain (gaps we address)

1. No capital: compute is an endowment, not an accumulated, depreciating, priced capital good; no investment,
   saving or Euler equation; no interest rate.
2. No complementary physical inputs (structures, machines, land, energy) distinct from "work"; energy is only
   mentioned as reinterpretation of Q (p. 4). P6's own caveat (p. 11) acknowledges this is where the wage
   result can fail.
3. No households, no ownership distribution, no wealth, no asset prices, no welfare beyond total wages.
4. No proofs; finite-Ω statements with "technical complications" for the continuum.
5. No quantitative or empirical content; magnitudes only for flops (pp. 5, 10–11).

## 8. Separation of claims

Throughout the paper, "Restrepo (2025) shows/states" refers only to P1–P11 as reproduced above. Everything
involving prices of capital, saving, ownership, asset values, scarce complements, energy, housing, taxation,
heterogeneous households, and the regime classification is *our* extension and is labelled as such.