\section{The baseline transition, 2026--2100}
\label{sec:results}

Every path in this section is a perfect-foresight equilibrium of the two-class economy under the baseline
scenario of Table~\ref{tab:calibration}: capability progress at 10\% per year, a compute price that falls by 15\%
per year until it reaches one hundredth of its 2026 level (around 2057), energy efficiency gains of 10\% per year
with a floor, and no policy. It is a conditional scenario, not a forecast; Section~\ref{sec:robustness} shows
how each statement changes with the inputs. Figure~\ref{fig:baseline} shows the real side,
Figure~\ref{fig:valuation} the balance sheet, Table~\ref{tab:baseline} selected years, and
Table~\ref{tab:diagnostics} in the appendix the residuals and the horizon check (maximum Euler residual
$\MaxResidualAll$; 50 extra years change the first 225 years of the paths by less than $10^{-7}$).

\begin{figure}[htbp]
\centering
\includegraphics[width=\textwidth]{fig03_baseline.pdf}
\caption{Baseline transition. GDP relative to 2026; gross income shares; real wages per worker relative to 2026
(the dotted line is trend growth); real return on wealth; compute capacity and the price of compute services;
energy; the compute share of each task's input; investment; consumption of the two classes detrended by
$(1+g_Z)^t$. Source: \texttt{results/scenarios/baseline\_paths.npz}.}
\label{fig:baseline}
\end{figure}

\subsection{Sequence of automation and the two Restrepo transitions}

Tasks are automated in the order of their compute requirements: the routine task uses compute for more than half
of its input from \AutoYearOne, the two cognitive tasks from \AutoYearTwo{} and \AutoYearThree, the expert task
from \AutoYearFour. Automation is an equilibrium decision --- it happens when $A_t\alpha_{i,t}$ falls below the
wage, not when $\alpha_{i,t}$ reaches its floor --- and the dates respond to both the price of compute (which
falls with the capital price and rises with energy) and the wage (which rises when the other task of the same
skill is automated and labor crowds in).

The wage paths display both transitions of the source in sequence. For the lower skill the transition is
compute-binding (Restrepo's Proposition~7): the wage falls around each automation date and recovers between
them (\wLTwoZeroThreeZero{} of its 2026 level in 2030, \wLTwoZeroFourZero{} in 2040, \wLTwoZeroFiveZero{} in 2050),
with no jump. For the higher skill the transition is technology-binding (Proposition~8): while its expert task is
the last one that compute cannot do cheaply, the $H$ wage rises to $\wHTwoZeroFiveZero$ times its 2026 level in
2050 --- the transitory premium of the skill that ``happened to be the last experiment to pan out'' (source,
p.~13) --- and then collapses once the expert task is automated (\wHTwoZeroSevenFive{} in 2075,
\wHTwoOneZeroZero{} in 2100). The labor share falls from 0.56 to \LSTwoZeroThreeZero{} in 2030,
\LSTwoZeroFiveZero{} in 2050 and \LSTwoZeroSevenFive{} in 2075 (Proposition~\ref{prop:laborshare}); after 2075 it is
below one in a thousand. Wages \emph{per efficiency unit} converge to the compute-equivalent user cost of
Proposition~\ref{prop:bgp}; wages \emph{per worker} then grow again at the trend rate $g_Z$ from a level that is a
small fraction of 2026 (Section~\ref{sec:robustness} shows how small depends on the floors).

\subsection{Growth, the real rate and the news effect}

Output grows by \GDPTwoZeroFourZero{} times by 2040, \GDPTwoZeroFiveZero{} times by 2050 and
\GDPTwoOneZeroZero{} times by 2100, against three times on the trend; the growth rate peaks at
\GDPgrowthPeak\% in \GDPgrowthPeakYear. The boom is a level effect: once compute is cheap, output is bounded by
the physical complements and growth returns to $g_Z$, with land, structures and energy capturing
\LandShareTwoOneZeroZero, 0.17 and 0.12 of income in 2100 and compute \CompShareTwoOneZeroZero{}
(Proposition~\ref{prop:regimes}c). The real return on wealth rises with the growth of capitalists' expenditure
--- \rrTwoZeroThreeZero\% in 2030, \rrTwoZeroFiveZero\% in 2050, a peak of \rPeak\% in \rPeakYear{} --- and returns
to $r^*=3.5\%$ by the end of the century. The jump already in 2026 (\rBase\% against 3.5\% on the frozen path) is
the perfect-foresight ``news'' effect: the entire path is anticipated, investment in compute surges
(Tobin's $q$ of compute is 1.5 in 2026), and the marginal investor demands a higher return to postpone
consumption. The direction --- anticipation of AI raises real rates and compute investment today --- is a
prediction of the structure; the size depends on $\gamma$ and on perfect foresight.

\subsection{The balance sheet: income to capital, value to land}

\begin{figure}[htbp]
\centering
\includegraphics[width=\textwidth]{fig04_valuation.pdf}
\caption{Baseline balance sheet. Market value of each claim relative to GDP; aggregate wealth; price--earnings
ratios of compute and structures; price--rent ratios of production land and of houses; Tobin's $q$ relative to
replacement cost; composition of house value and of wealth.}
\label{fig:valuation}
\end{figure}

Figure~\ref{fig:valuation} contains the paper's main quantitative message. Between 2026 and the early 2040s the
share of income accruing to capital rises and the wealth-to-income ratio \emph{falls}, from
\WoverGDPbase{} to \WYmin{} in \WYminYear: the real rate is high, long-duration claims are discounted heavily
(the land price--rent ratio falls from 17 to \LandPRmin, the house price--rent ratio from 12 to 5), and the
claim that captures the new income --- compute --- is capitalized at a price--earnings ratio of about
\PEcomputebase{} in 2026 and 2 in the 2040s, as Proposition~\ref{prop:wealth} predicts for an asset that
depreciates at 25\% and cheapens at 15\% a year. The market value of compute capital never exceeds one fifth of
GDP and its share of wealth peaks near 10\% around 2045. After 2050 the picture reverses: as the physical
complements bind, income flows to land, the real rate normalizes, and the wealth-to-income ratio rises to
\WYTwoZeroSevenFive{} in 2075 and \WYTwoOneZeroZero{} in 2100, with land making up 90\% of wealth and three
quarters of house values. The economy ends up with a Piketty-like balance sheet, but by a route that has nothing
to do with $r>g$ for reproducible capital: it is the scarcity of what compute cannot make.

Table~\ref{tab:decomposition} decomposes the 2026 value of each claim --- baseline versus the frozen economy ---
into the cash-flow and discount-rate channels (exact under perfect foresight,
Section~\ref{sec:assetpricing}). The cash-flow channel is large and positive for every claim, since the boom raises
every rent and rental; the discount-rate channel is large and negative for every claim; and the net effect on
2026 \emph{values} is \DeclandTot\% for production land, \DecNTot\% for structures and \DecQTot\% for compute.
The two channels are of the same order of magnitude, which is why the sign of the valuation response to AI
is a quantitative question, not a theorem.

\begin{table}[htbp]
\centering\small
\caption{Decomposition of the 2026 value of each claim, baseline relative to the frozen economy (log points
$\times100$; exact Campbell--Shiller decomposition along deterministic paths).}
\label{tab:decomposition}
\resizebox{\textwidth}{!}{\input{tables/tab05_decomposition}}
\end{table}

\subsection{Energy, utilization and the physical constraint}

The share of electricity used by compute rises from 4.4\% to a peak of about 60\% around 2060 and settles near
25\%; the energy price rises eighteen-fold by the late 2060s relative to 2026 and declines afterwards as energy
capital catches up. Utilization of compute capacity stays at one throughout the baseline: firms anticipate the
energy price and do not build capacity they cannot power. The energy-constrained scenarios of
Section~\ref{sec:robustness} are the ones in which the constraint binds on the margin.

\subsection{The two classes}

Workers' consumption --- their wage bill --- rises in level until the early 2050s (the higher skill's premium
outweighs the lower skill's losses), then falls to a few percent of its 2026 level by 2100
(Figure~\ref{fig:baseline}, bottom right), while capitalists' consumption rises more than a hundredfold. Workers'
share of GDP goes from 0.47 to \CWshareTwoZeroFiveZero{} in 2050 and essentially zero in 2100. In the two-class
economy this is Proposition~\ref{prop:distribution}: with no claim on the fund, workers end up with the
compute-equivalent of their labor, which is what cheap compute is worth. Section~\ref{sec:robustness} reports the
heterogeneous-agent economy, in which workers do own claims, and the policies that change this allocation.

\begin{table}[htbp]
\centering\small
\caption{Baseline transition, selected years (two-class economy).}
\label{tab:baseline}
\resizebox{\textwidth}{!}{\input{tables/tab03_baseline}}
\end{table}