1\section{The baseline transition, 2026--2100}2\label{sec:results}34Every path in this section is a perfect-foresight equilibrium of the two-class economy under the baseline5scenario of Table~\ref{tab:calibration}: capability progress at 10\% per year, a compute price that falls by 15\%6per year until it reaches one hundredth of its 2026 level (around 2057), energy efficiency gains of 10\% per year7with a floor, and no policy. It is a conditional scenario, not a forecast; Section~\ref{sec:robustness} shows8how each statement changes with the inputs. Figure~\ref{fig:baseline} shows the real side,9Figure~\ref{fig:valuation} the balance sheet, Table~\ref{tab:baseline} selected years, and10Table~\ref{tab:diagnostics} in the appendix the residuals and the horizon check (maximum Euler residual11$\MaxResidualAll$; 50 extra years change the first 225 years of the paths by less than $10^{-7}$).1213\begin{figure}[htbp]14\centering15\includegraphics[width=\textwidth]{fig03_baseline.pdf}16\caption{Baseline transition. GDP relative to 2026; gross income shares; real wages per worker relative to 202617(the dotted line is trend growth); real return on wealth; compute capacity and the price of compute services;18energy; the compute share of each task's input; investment; consumption of the two classes detrended by19$(1+g_Z)^t$. Source: \texttt{results/scenarios/baseline\_paths.npz}.}20\label{fig:baseline}21\end{figure}2223\subsection{Sequence of automation and the two Restrepo transitions}2425Tasks are automated in the order of their compute requirements: the routine task uses compute for more than half26of its input from \AutoYearOne, the two cognitive tasks from \AutoYearTwo{} and \AutoYearThree, the expert task27from \AutoYearFour. Automation is an equilibrium decision --- it happens when $A_t\alpha_{i,t}$ falls below the28wage, not when $\alpha_{i,t}$ reaches its floor --- and the dates respond to both the price of compute (which29falls with the capital price and rises with energy) and the wage (which rises when the other task of the same30skill is automated and labor crowds in).3132The wage paths display both transitions of the source in sequence. For the lower skill the transition is33compute-binding (Restrepo's Proposition~7): the wage falls around each automation date and recovers between34them (\wLTwoZeroThreeZero{} of its 2026 level in 2030, \wLTwoZeroFourZero{} in 2040, \wLTwoZeroFiveZero{} in 2050),35with no jump. For the higher skill the transition is technology-binding (Proposition~8): while its expert task is36the last one that compute cannot do cheaply, the $H$ wage rises to $\wHTwoZeroFiveZero$ times its 2026 level in372050 --- the transitory premium of the skill that ``happened to be the last experiment to pan out'' (source,38p.~13) --- and then collapses once the expert task is automated (\wHTwoZeroSevenFive{} in 2075,39\wHTwoOneZeroZero{} in 2100). The labor share falls from 0.56 to \LSTwoZeroThreeZero{} in 2030,40\LSTwoZeroFiveZero{} in 2050 and \LSTwoZeroSevenFive{} in 2075 (Proposition~\ref{prop:laborshare}); after 2075 it is41below one in a thousand. Wages \emph{per efficiency unit} converge to the compute-equivalent user cost of42Proposition~\ref{prop:bgp}; wages \emph{per worker} then grow again at the trend rate $g_Z$ from a level that is a43small fraction of 2026 (Section~\ref{sec:robustness} shows how small depends on the floors).4445\subsection{Growth, the real rate and the news effect}4647Output grows by \GDPTwoZeroFourZero{} times by 2040, \GDPTwoZeroFiveZero{} times by 2050 and48\GDPTwoOneZeroZero{} times by 2100, against three times on the trend; the growth rate peaks at49\GDPgrowthPeak\% in \GDPgrowthPeakYear. The boom is a level effect: once compute is cheap, output is bounded by50the physical complements and growth returns to $g_Z$, with land, structures and energy capturing51\LandShareTwoOneZeroZero, 0.17 and 0.12 of income in 2100 and compute \CompShareTwoOneZeroZero{}52(Proposition~\ref{prop:regimes}c). The real return on wealth rises with the growth of capitalists' expenditure53--- \rrTwoZeroThreeZero\% in 2030, \rrTwoZeroFiveZero\% in 2050, a peak of \rPeak\% in \rPeakYear{} --- and returns54to $r^*=3.5\%$ by the end of the century. The jump already in 2026 (\rBase\% against 3.5\% on the frozen path) is55the perfect-foresight ``news'' effect: the entire path is anticipated, investment in compute surges56(Tobin's $q$ of compute is 1.5 in 2026), and the marginal investor demands a higher return to postpone57consumption. The direction --- anticipation of AI raises real rates and compute investment today --- is a58prediction of the structure; the size depends on $\gamma$ and on perfect foresight.5960\subsection{The balance sheet: income to capital, value to land}6162\begin{figure}[htbp]63\centering64\includegraphics[width=\textwidth]{fig04_valuation.pdf}65\caption{Baseline balance sheet. Market value of each claim relative to GDP; aggregate wealth; price--earnings66ratios of compute and structures; price--rent ratios of production land and of houses; Tobin's $q$ relative to67replacement cost; composition of house value and of wealth.}68\label{fig:valuation}69\end{figure}7071Figure~\ref{fig:valuation} contains the paper's main quantitative message. Between 2026 and the early 2040s the72share of income accruing to capital rises and the wealth-to-income ratio \emph{falls}, from73\WoverGDPbase{} to \WYmin{} in \WYminYear: the real rate is high, long-duration claims are discounted heavily74(the land price--rent ratio falls from 17 to \LandPRmin, the house price--rent ratio from 12 to 5), and the75claim that captures the new income --- compute --- is capitalized at a price--earnings ratio of about76\PEcomputebase{} in 2026 and 2 in the 2040s, as Proposition~\ref{prop:wealth} predicts for an asset that77depreciates at 25\% and cheapens at 15\% a year. The market value of compute capital never exceeds one fifth of78GDP and its share of wealth peaks near 10\% around 2045. After 2050 the picture reverses: as the physical79complements bind, income flows to land, the real rate normalizes, and the wealth-to-income ratio rises to80\WYTwoZeroSevenFive{} in 2075 and \WYTwoOneZeroZero{} in 2100, with land making up 90\% of wealth and three81quarters of house values. The economy ends up with a Piketty-like balance sheet, but by a route that has nothing82to do with $r>g$ for reproducible capital: it is the scarcity of what compute cannot make.8384Table~\ref{tab:decomposition} decomposes the 2026 value of each claim --- baseline versus the frozen economy ---85into the cash-flow and discount-rate channels (exact under perfect foresight,86Section~\ref{sec:assetpricing}). The cash-flow channel is large and positive for every claim, since the boom raises87every rent and rental; the discount-rate channel is large and negative for every claim; and the net effect on882026 \emph{values} is \DeclandTot\% for production land, \DecNTot\% for structures and \DecQTot\% for compute.89The two channels are of the same order of magnitude, which is why the sign of the valuation response to AI90is a quantitative question, not a theorem.9192\begin{table}[htbp]93\centering\small94\caption{Decomposition of the 2026 value of each claim, baseline relative to the frozen economy (log points95$\times100$; exact Campbell--Shiller decomposition along deterministic paths).}96\label{tab:decomposition}97\resizebox{\textwidth}{!}{\input{tables/tab05_decomposition}}98\end{table}99100\subsection{Energy, utilization and the physical constraint}101102The share of electricity used by compute rises from 4.4\% to a peak of about 60\% around 2060 and settles near10325\%; the energy price rises eighteen-fold by the late 2060s relative to 2026 and declines afterwards as energy104capital catches up. Utilization of compute capacity stays at one throughout the baseline: firms anticipate the105energy price and do not build capacity they cannot power. The energy-constrained scenarios of106Section~\ref{sec:robustness} are the ones in which the constraint binds on the margin.107108\subsection{The two classes}109110Workers' consumption --- their wage bill --- rises in level until the early 2050s (the higher skill's premium111outweighs the lower skill's losses), then falls to a few percent of its 2026 level by 2100112(Figure~\ref{fig:baseline}, bottom right), while capitalists' consumption rises more than a hundredfold. Workers'113share of GDP goes from 0.47 to \CWshareTwoZeroFiveZero{} in 2050 and essentially zero in 2100. In the two-class114economy this is Proposition~\ref{prop:distribution}: with no claim on the fund, workers end up with the115compute-equivalent of their labor, which is what cheap compute is worth. Section~\ref{sec:robustness} reports the116heterogeneous-agent economy, in which workers do own claims, and the policies that change this allocation.117118\begin{table}[htbp]119\centering\small120\caption{Baseline transition, selected years (two-class economy).}121\label{tab:baseline}122\resizebox{\textwidth}{!}{\input{tables/tab03_baseline}}123\end{table}124