\section{Results II: who delegates, who owns, and the wealth distribution}
\label{sec:results_b}

Table~\ref{tab:b_scenarios} reports the stationary equilibria of Model B across the pre-registered scenarios and
Table~\ref{tab:b_decomp} (Appendix~\ref{app:extra}) the channel decomposition relative to the no-AI economy. The
no-AI economy is a standard Aiyagari calibration: $r=\numrnoai\%$, Gini \numgininoai, top-10\% share
\numtoptennoai. All numbers come from \texttt{scripts/20\_model\_b.py}.

\input{tables/model_b_scenarios}

\subsection{The decision-quality channel concentrates wealth even without any production effect}

The ``delegation only'' scenario switches on the information channel alone: no compute in production, no change
in factor prices other than through saving. The rich delegate first (Figure~\ref{fig:B_lorenz}(b)): with a fixed
component in the fee and a stake proportional to wealth, delegation is zero in the bottom deciles and universal at
the top, the cross-sectional counterpart of Proposition~\ref{prop:threshold}. Because delegated savings earn a
higher and less noisy return, the delegators accumulate faster: the Gini rises from \numgininoai\ to
\numginidelegationonly\ and the top-10\% share from \numtoptennoai\ to \numtoptendelegationonly, while output rises by
only \numdYdelegationonly\% (the resource cost of human mistakes is saved). This is H3 in a form that does not depend
on who owns the AI infrastructure: better decisions are a scale-dependent return, and scale-dependent returns
concentrate wealth.

\begin{figure}[htbp]
\centering
\includegraphics[width=\textwidth]{figB_lorenz_delegation.pdf}
\caption{Model B. (a) Lorenz curves of wealth across scenarios. (b) Share of households delegating within each wealth
decile (households only; the owner class of the concentrated scenarios is excluded). Source:
\texttt{scripts/20\_model\_b.py}.}
\label{fig:B_lorenz}
\end{figure}

\subsection{AI as a production input works in the opposite direction}

Adding compute to production (``production only'' and the ``both'' scenarios) raises output by
\numdYfullbroad\% in the broad-ownership case, lowers the labour share from 0.67 to about 0.44, and lowers the
interest rate. With broad ownership this \emph{reduces} wealth inequality (Gini \numginifullbroad, top 10\%
\numtoptenfullbroad): wages rise, the return to wealth falls, and the compute income flows to everyone in proportion
to savings. The net effect of the two channels under broad ownership is therefore an equalisation---a result that
depends entirely on the ownership assumption.

\subsection{Ownership}

Under concentrated ownership (a measure-0.10 owner class holding the scarcity rents, Proposition~\ref{prop:ownership})
the same technology yields a Gini of \numginifullconcentrated\ and a top-10\% share of \numtoptenfullconcentrated,
against \numginifullbroad\ and \numtoptenfullbroad\ under broad ownership; the scarce-compute variants (fixed
stock, larger rents) show the same ordering. Figure~\ref{fig:B_shares} summarises: automation moves the factor
shares identically in both cases, and the distributional outcome is decided by the ownership structure of
algorithmic capital, which is H3 as stated. The interest rate is also higher under concentration because the rents are
not available to finance capital accumulation through the household fund.

\begin{figure}[htbp]
\centering
\includegraphics[width=\textwidth]{figB_shares_concentration.pdf}
\caption{Model B. (a) Factor income shares (labour, capital, compute) by scenario. (b) Top-10\%, top-1\% wealth
shares and Gini. Source: \texttt{scripts/20\_model\_b.py}.}
\label{fig:B_shares}
\end{figure}

\subsection{Welfare by wealth percentile and the controls}

Figure~\ref{fig:B_welfare} converts the value functions at given wealth percentiles into consumption-equivalent
gains relative to the no-AI economy. Delegation alone benefits the top of the distribution and leaves the bottom
unchanged; AI in production benefits every percentile through wages, more so at the bottom where labour income
dominates; concentration shifts the gains upward. Two controls behave as pre-registered: when human mistakes are
switched off (``no mistakes''), nobody delegates ($D=0$, the $\tau_A=\tau_H$ falsification test of H1 in the
cross-section), and a cheaper fee raises adoption (\numDfullbroad\ to 0.87) and lowers inequality slightly because
delegation reaches further down the distribution. Removing borrowing (``no borrowing'') changes little, because the
borrowing limit binds for households who do not delegate in any case.

\begin{figure}[htbp]
\centering
\includegraphics[width=0.7\textwidth]{figB_welfare_percentile.pdf}
\caption{Model B: consumption-equivalent welfare gain relative to the no-AI economy at selected wealth percentiles.
Source: \texttt{scripts/20\_model\_b.py}.}
\label{fig:B_welfare}
\end{figure}