\section{The benchmark: Restrepo's economy, reproduced and audited}
\label{sec:benchmark}

\subsection{Primitives}

\citet{Restrepo2025} describes an economy that produces output $Y_t=F(\{X_t(\omega)\}_{\omega\in\Omega})$ by
completing a finite set $\Omega$ of types of work, each of which can be done by people or by computers:
\begin{equation}
X_t(\omega)=L_t(\omega)+\frac{Q_t(\omega)}{\alpha_t(\omega)},
\label{eq:work}
\end{equation}
where $\alpha_t(\omega)$ is the compute needed to replicate one worker and may be infinite. $F$ is increasing,
differentiable, concave and constant returns to scale. Skills $s\in\mathcal{S}$, in supply $H(s)$, can do the work
in $\Omega(s)$, and the $\Omega(s)$ partition $\Omega$. Total compute is $Q_t$. Two premises drive the results:
AGI (Premise~1: every $\alpha_t(\omega)$ becomes finite and converges to $\alpha(\omega)\in(0,\infty)$) and abundant
compute (Premise~2: $Q_t$ grows without bound). Work $\omega$ is a \emph{bottleneck} if output cannot grow without
bound unless $X_t(\omega)$ or its marginal product does; it is \emph{accessory} otherwise.

The chapter's results, with the page of the July 2025 draft, are: all bottlenecks are eventually automated
while some accessory work may be left to humans (Proposition~1, p.~7); output converges to
$A[Q_t+\sum_{s\in\mathcal{A}}\CEU(s)H(s)+\sum_{s\in\mathcal{N}}\CEUt(s)H(s)]$ with $\CEU(s)=\max_{\omega\in\Omega(s)}\alpha(\omega)$
and $\CEUt(s)<\CEU(s)$ for the skills whose most compute-intensive work is not automated (Proposition~2, p.~8);
output grows at the rate of compute (Proposition~3, p.~9); the real price of compute converges to $A$ and wages
to $A\,\CEU(s)$ or $A\,\CEUt(s)$ (Proposition~4, p.~10); the compute share of GDP converges to one and the labor
share to zero (Proposition~5, p.~10); and the sum of wages is higher with AGI than without (Proposition~6,
p.~11). Section 1.2 of the source, labelled preliminary, describes two transitions: when compute binds, the price
of compute falls monotonically and wages fall gradually around each automation date and otherwise grow
(Proposition~7, p.~12); when technology binds, wages can jump down and the last-automated skills earn a
transitory premium (Proposition~8, p.~13). No proofs are given; every proposition is followed by a heuristic
argument.

\subsection{Replication}

We implement the economy with six types of work: four bottleneck classes aggregated by a CES with elasticity
$\sigma_B=0.5$ and two accessory classes entering output linearly, $Y=X_B+\sum_a\gamma_aX_a$. Skill $L$ does
work in $\{1,2,a_L\}$ with $\alpha=(1,2,3)$, skill $H$ in $\{3,4,a_H\}$ with $\alpha=(4,8,6)$, supplies
$(H_L,H_H)=(0.6,0.4)$, $\gamma_a=0.05$. The competitive allocation is the solution of the concave program
$\max Y$ subject to the labor and compute constraints, and factor prices are its multipliers
(Appendix~\ref{app:algorithms}). Figure~\ref{fig:benchmark} traces the equilibrium as the endowment $Q$ grows
from $10^{-2}$ to $10^{5}$; Table~\ref{tab:benchmark} reports selected points.

\begin{figure}[htbp]
\centering
\includegraphics[width=\textwidth]{fig01_benchmark.pdf}
\caption{Replication of \citet{Restrepo2025} in the finite-task CES economy. Output becomes linear in compute
(dashed line, upper left) once every bottleneck task is automated ($Q\ge5$); the price of compute falls in steps
and converges (upper right); wages are pinned at $A$ times the compute-equivalent of each skill (lower left);
the labor share converges to zero (lower right). Source: \texttt{scripts/10\_benchmark.py}.}
\label{fig:benchmark}
\end{figure}

\begin{table}[htbp]
\centering\small
\caption{Selected points of the benchmark economy.}
\label{tab:benchmark}
\resizebox{\textwidth}{!}{\input{tables/tab01_benchmark}}
\end{table}

Every statement of Propositions~1--6 holds exactly in the replication, and the shape of the transition is the
compute-binding one of Proposition~7: $A$ is non-increasing, wages fall around the two automation dates of each
skill and then grow until the last date, after which they are pinned at $A$ times the compute-equivalent. Two
details that the source states only in a footnote (fn.~6, p.~9) are visible. First, skill $H$ earns
$A\cdot\CEU(H)=8A$: its most compute-intensive task (task~4) is automated and labor concentrates there. Second,
skill $L$ earns $2A$, below $A\cdot\CEU(L)=3A$: the accessory task with $\alpha=3$ is never automated --- its
marginal value $\gamma_a=0.05$ is below $A\alpha=0.24$ --- and, in our parametrization, it is not performed at all,
because the same marginal value is below what $L$-workers earn in task~2. The ``discount'' of Proposition~4
arises whenever the max-$\alpha$ work of a skill is left unautomated, whether or not anyone does it; the source's
description of group $\mathcal{N}$ as ``skills that perform accessory work not automated'' is one of the two
cases.

\subsection{What the benchmark cannot say}

Three features of the source make it silent on the questions of this paper. Compute is an endowment: there is no
price of compute capital, no investment, no saving, no interest rate, no depreciation, and therefore no answer to
what compute owners' \emph{wealth} is worth. There are no complementary inputs: energy appears only as a
reinterpretation of $Q_t$ (p.~4), and the source itself notes (p.~11) that Proposition~6 breaks when the AGI
economy ``uses some finite resource that is also needed by human labor''. And there are no households: nothing is
said about who owns what, how ownership evolves, or what the welfare of workers is beyond their wage bill.
Sections~\ref{sec:model}--\ref{sec:assetpricing} supply these elements; Section~\ref{sec:theory} shows which of
Propositions~2--6 survive and which do not.