\section{Results I: delegation, model noise and the efficiency benchmark}
\label{sec:results_a}

All numbers in this section are produced by \texttt{scripts/10\_model\_a.py} from the baseline of
Table~\ref{tab:a_baseline}; the information parameters are illustrative and are swept in
Section~\ref{sec:robustness}.

\input{tables/model_a_baseline}

\subsection{Which decision carries a stake}

The savings mapping gives $\kappa_0=\numkappaSav$: a one-log-point news about next year's productivity moves
desired savings by less than a hundredth of a percent, because the wealth effect of higher future wages and the
substitution effect of a higher return nearly cancel at $\gamma=2$; the general-equilibrium response is the
familiar comovement puzzle (Figure~\ref{fig:A_savings}, $\kappa_{full}=\numkappaFullSav$). Delegating the
consumption--savings decision to a better forecaster is therefore nearly worthless in this economy, and the
remaining results use the portfolio mapping, $\kappa_0=\numkappaPort$ and $\alpha=\numalphaPort$: allocation
decisions respond strongly to expected-return news and are strongly strategic substitutes through diminishing
returns.

\subsection{Private value, adoption and the breakdown of the law of large numbers}

\begin{figure}[htbp]
\centering
\includegraphics[width=\textwidth]{figA_private_value_noise.pdf}
\caption{(a) Private value of delegation (per cent of consumption per year) as a function of the delegation share, for
four qualities of the foundation model (human noise s.d.\ 0.10; one model). (b) Variance of the log wage created by
model noise, $\alpha_K^2\Var(\text{model noise})$, for different effective numbers of independent models; it scales
with $D^2/M$. Source: \texttt{scripts/10\_model\_a.py}.}
\label{fig:A_pv_noise}
\end{figure}

Figure~\ref{fig:A_pv_noise}(a) shows Proposition~\ref{prop:threshold} at work. With a model whose forecast noise is
0.04 against a human's 0.10, the first adopter gains \numpvZero\% of consumption per year; the last adopter, when
everyone else has delegated, gains only \numpvOne\%. The decline is the ``knowing what others know'' effect under
strategic substitutability: the common signal is already in the aggregate, so acting on it adds less. A model only
marginally better than the median human (noise 0.08) is worth \emph{less than nothing} to a marginal user once a
third of the economy relies on it. Adoption is interior and self-limiting: at a compute rental of 0.6 the equilibrium
delegation share is $D^*=\numDstar$ in the baseline (Figure~\ref{fig:A_threshold}), increasing in model quality and
decreasing in the compute price and in supervision time, as in H1.

\begin{figure}[htbp]
\centering
\includegraphics[width=0.62\textwidth]{figA_threshold.pdf}
\caption{Equilibrium delegation share as a function of the foundation model's forecast noise (lower is better), for
three compute rentals (inference intensity $\bar q=0.05$). Source: \texttt{scripts/10\_model\_a.py}.}
\label{fig:A_threshold}
\end{figure}

Panel (b) is the aggregate face. Non-delegators' errors average out; delegators' errors do not. With one model and
full delegation the model-noise component of the log wage has a standard deviation of \numwageSdOneOne\% per year;
with eight independent models it is \numwageSdOneEight\%. These are large numbers relative to the wage volatility
generated by productivity itself at the calibrated TFP innovation (about 1.3\%), and they come from an information
structure, not from a technology shock.

\subsection{The efficiency benchmark and the wedges}

\begin{figure}[htbp]
\centering
\includegraphics[width=\textwidth]{figA_wedge.pdf}
\caption{(a) Wedge between the private and the social marginal value of delegation (per cent of consumption) for
different curvature ratios $\upsilon$ ($U_{XX}=-\upsilon U_{xX}$); $\upsilon=1$ is the constant-returns benchmark.
(b) Pigouvian delegation tax implied by uninsurable wage risk of hand-to-mouth workers (mass 0.5), relative to the
delegation fee, for different numbers of independent models. Source: \texttt{scripts/10\_model\_a.py}.}
\label{fig:A_wedge}
\end{figure}

Figure~\ref{fig:A_wedge}(a) confirms Proposition~\ref{prop:benchmark} numerically: at $\upsilon=1$ the wedge is zero
for every $D$ (the largest absolute value on the grid is $\nummaxWedge$, numerical noise). Model noise is real, yet in
the benchmark economy the market's delegation share is the planner's. The wedge opens when the aggregate action has
effects that are not pure transfers: with $\upsilon=0$ (the aggregate action affects individuals only through
first-order price effects that are not internalised, as when investors and workers are different people) the private
value exceeds the social value by up to 1.8\% of consumption---over-delegation---and with $\upsilon=1.5$ the sign
flips. Panel (b) quantifies Proposition~\ref{prop:wedges}(b): if half of the population lives hand-to-mouth on wages
that load on the aggregate action, the Pigouvian delegation tax at full adoption is \numtaxFeeMone\ times the fee with
one model and \numtaxFeeMeight\ times the fee with eight. Model diversity is a substitute for the tax, at the rate
$1/M$ predicted by the theory---but only because of the friction; in the benchmark it is irrelevant.

\subsection{Compute market, automation and the labour share}

\begin{figure}[htbp]
\centering
\includegraphics[width=\textwidth]{figA_compute_market.pdf}
\caption{Short-run (fixed compute stock, solid) and long-run (elastic compute at user cost, dashed) responses of the
compute rental, the automated task share and the labour share to the inference intensity of delegated decisions
$\bar q$, for three compute stocks. Source: \texttt{scripts/10\_model\_a.py}.}
\label{fig:A_compute}
\end{figure}

Proposition~\ref{prop:compute} says that with a fixed compute stock, inference demand crowds out production
automation. Figure~\ref{fig:A_compute} shows that the effect exists and that it is small and non-monotone: as
inference intensity rises from zero, delegation first draws compute away from tasks---at $\bar q=\numqbarmax$ and
$K_Q=0.02$ inference absorbs \numinfshare\% of the compute stock, the rental rises from \numpQqzero\ to \numpQqmax,
automation falls from \numiotaqzero\ to \numiotaqmax, and the labour share rises by \numshareLgainpp\ percentage
points---and then, as the fee overtakes the private value, delegation collapses and compute flows back to
production. The crowding-out channel of H6 is therefore confirmed in sign but, at any compute stock large enough to
matter for automation, it is quantitatively minor: the value of a better financial decision is a few per cent of
consumption, which cannot buy much compute at production prices. In the long run (dashed) both margins expand
together. We regard this as a useful negative result: the dramatic scenarios in which agentic inference starves
production of compute require either far more valuable delegated decisions or a compute stock an order of magnitude
smaller than what automation itself uses.

\subsection{Ownership}

Figure~\ref{fig:A_ownership} plots Proposition~\ref{prop:ownership}. As the automated task share rises, the labour
share falls one for one with $(1-\alpha_K)\iota$; whether income concentrates depends entirely on who owns the
compute. If the top 1\% own it, their income share rises from a third of capital income to that plus the entire
compute share; under broad ownership nothing happens to the distribution at given factor prices. The
general-equilibrium version, with endogenous wealth accumulation and scarcity rents, is Model B.

\begin{figure}[htbp]
\centering
\includegraphics[width=0.62\textwidth]{figA_ownership.pdf}
\caption{Income share of compute owners as a function of the automated task share, for three ownership
structures, together with the labour share. Source: \texttt{scripts/10\_model\_a.py}.}
\label{fig:A_ownership}
\end{figure}