1\section{Results I: delegation, model noise and the efficiency benchmark}2\label{sec:results_a}34All numbers in this section are produced by \texttt{scripts/10\_model\_a.py} from the baseline of5Table~\ref{tab:a_baseline}; the information parameters are illustrative and are swept in6Section~\ref{sec:robustness}.78\input{tables/model_a_baseline}910\subsection{Which decision carries a stake}1112The savings mapping gives $\kappa_0=\numkappaSav$: a one-log-point news about next year's productivity moves13desired savings by less than a hundredth of a percent, because the wealth effect of higher future wages and the14substitution effect of a higher return nearly cancel at $\gamma=2$; the general-equilibrium response is the15familiar comovement puzzle (Figure~\ref{fig:A_savings}, $\kappa_{full}=\numkappaFullSav$). Delegating the16consumption--savings decision to a better forecaster is therefore nearly worthless in this economy, and the17remaining results use the portfolio mapping, $\kappa_0=\numkappaPort$ and $\alpha=\numalphaPort$: allocation18decisions respond strongly to expected-return news and are strongly strategic substitutes through diminishing19returns.2021\subsection{Private value, adoption and the breakdown of the law of large numbers}2223\begin{figure}[htbp]24\centering25\includegraphics[width=\textwidth]{figA_private_value_noise.pdf}26\caption{(a) Private value of delegation (per cent of consumption per year) as a function of the delegation share, for27four qualities of the foundation model (human noise s.d.\ 0.10; one model). (b) Variance of the log wage created by28model noise, $\alpha_K^2\Var(\text{model noise})$, for different effective numbers of independent models; it scales29with $D^2/M$. Source: \texttt{scripts/10\_model\_a.py}.}30\label{fig:A_pv_noise}31\end{figure}3233Figure~\ref{fig:A_pv_noise}(a) shows Proposition~\ref{prop:threshold} at work. With a model whose forecast noise is340.04 against a human's 0.10, the first adopter gains \numpvZero\% of consumption per year; the last adopter, when35everyone else has delegated, gains only \numpvOne\%. The decline is the ``knowing what others know'' effect under36strategic substitutability: the common signal is already in the aggregate, so acting on it adds less. A model only37marginally better than the median human (noise 0.08) is worth \emph{less than nothing} to a marginal user once a38third of the economy relies on it. Adoption is interior and self-limiting: at a compute rental of 0.6 the equilibrium39delegation share is $D^*=\numDstar$ in the baseline (Figure~\ref{fig:A_threshold}), increasing in model quality and40decreasing in the compute price and in supervision time, as in H1.4142\begin{figure}[htbp]43\centering44\includegraphics[width=0.62\textwidth]{figA_threshold.pdf}45\caption{Equilibrium delegation share as a function of the foundation model's forecast noise (lower is better), for46three compute rentals (inference intensity $\bar q=0.05$). Source: \texttt{scripts/10\_model\_a.py}.}47\label{fig:A_threshold}48\end{figure}4950Panel (b) is the aggregate face. Non-delegators' errors average out; delegators' errors do not. With one model and51full delegation the model-noise component of the log wage has a standard deviation of \numwageSdOneOne\% per year;52with eight independent models it is \numwageSdOneEight\%. These are large numbers relative to the wage volatility53generated by productivity itself at the calibrated TFP innovation (about 1.3\%), and they come from an information54structure, not from a technology shock.5556\subsection{The efficiency benchmark and the wedges}5758\begin{figure}[htbp]59\centering60\includegraphics[width=\textwidth]{figA_wedge.pdf}61\caption{(a) Wedge between the private and the social marginal value of delegation (per cent of consumption) for62different curvature ratios $\upsilon$ ($U_{XX}=-\upsilon U_{xX}$); $\upsilon=1$ is the constant-returns benchmark.63(b) Pigouvian delegation tax implied by uninsurable wage risk of hand-to-mouth workers (mass 0.5), relative to the64delegation fee, for different numbers of independent models. Source: \texttt{scripts/10\_model\_a.py}.}65\label{fig:A_wedge}66\end{figure}6768Figure~\ref{fig:A_wedge}(a) confirms Proposition~\ref{prop:benchmark} numerically: at $\upsilon=1$ the wedge is zero69for every $D$ (the largest absolute value on the grid is $\nummaxWedge$, numerical noise). Model noise is real, yet in70the benchmark economy the market's delegation share is the planner's. The wedge opens when the aggregate action has71effects that are not pure transfers: with $\upsilon=0$ (the aggregate action affects individuals only through72first-order price effects that are not internalised, as when investors and workers are different people) the private73value exceeds the social value by up to 1.8\% of consumption---over-delegation---and with $\upsilon=1.5$ the sign74flips. Panel (b) quantifies Proposition~\ref{prop:wedges}(b): if half of the population lives hand-to-mouth on wages75that load on the aggregate action, the Pigouvian delegation tax at full adoption is \numtaxFeeMone\ times the fee with76one model and \numtaxFeeMeight\ times the fee with eight. Model diversity is a substitute for the tax, at the rate77$1/M$ predicted by the theory---but only because of the friction; in the benchmark it is irrelevant.7879\subsection{Compute market, automation and the labour share}8081\begin{figure}[htbp]82\centering83\includegraphics[width=\textwidth]{figA_compute_market.pdf}84\caption{Short-run (fixed compute stock, solid) and long-run (elastic compute at user cost, dashed) responses of the85compute rental, the automated task share and the labour share to the inference intensity of delegated decisions86$\bar q$, for three compute stocks. Source: \texttt{scripts/10\_model\_a.py}.}87\label{fig:A_compute}88\end{figure}8990Proposition~\ref{prop:compute} says that with a fixed compute stock, inference demand crowds out production91automation. Figure~\ref{fig:A_compute} shows that the effect exists and that it is small and non-monotone: as92inference intensity rises from zero, delegation first draws compute away from tasks---at $\bar q=\numqbarmax$ and93$K_Q=0.02$ inference absorbs \numinfshare\% of the compute stock, the rental rises from \numpQqzero\ to \numpQqmax,94automation falls from \numiotaqzero\ to \numiotaqmax, and the labour share rises by \numshareLgainpp\ percentage95points---and then, as the fee overtakes the private value, delegation collapses and compute flows back to96production. The crowding-out channel of H6 is therefore confirmed in sign but, at any compute stock large enough to97matter for automation, it is quantitatively minor: the value of a better financial decision is a few per cent of98consumption, which cannot buy much compute at production prices. In the long run (dashed) both margins expand99together. We regard this as a useful negative result: the dramatic scenarios in which agentic inference starves100production of compute require either far more valuable delegated decisions or a compute stock an order of magnitude101smaller than what automation itself uses.102103\subsection{Ownership}104105Figure~\ref{fig:A_ownership} plots Proposition~\ref{prop:ownership}. As the automated task share rises, the labour106share falls one for one with $(1-\alpha_K)\iota$; whether income concentrates depends entirely on who owns the107compute. If the top 1\% own it, their income share rises from a third of capital income to that plus the entire108compute share; under broad ownership nothing happens to the distribution at given factor prices. The109general-equilibrium version, with endogenous wealth accumulation and scarcity rents, is Model B.110111\begin{figure}[htbp]112\centering113\includegraphics[width=0.62\textwidth]{figA_ownership.pdf}114\caption{Income share of compute owners as a function of the automated task share, for three ownership115structures, together with the labour share. Source: \texttt{scripts/10\_model\_a.py}.}116\label{fig:A_ownership}117\end{figure}118