1\section{Scenarios, heterogeneous households, policy and welfare}2\label{sec:robustness}34Table~\ref{tab:scenarios} summarizes the scenario catalogue in 2050 and 2100; Figures~\ref{fig:tech}--\ref{fig:policy}5show the paths. Every scenario re-calibrates the 2026 base point to the same shares, so that differences are6differences in the anticipated future, not in the starting balance sheet.78\begin{table}[htbp]9\centering\scriptsize10\caption{Scenario catalogue: selected outcomes in 2050 and 2100 (two-class economy). $w_L$ per worker relative to112026; GDP relative to 2026; $W$/GDP aggregate wealth to GDP; land P/R price--rent ratio of production land;12$V^Q$/GDP market value of compute capital; $C_W$/GDP workers' consumption share.}13\label{tab:scenarios}14\resizebox{\textwidth}{!}{\input{tables/tab04_scenarios}}15\end{table}1617\subsection{Technology: how fast, how cheap, how constrained}1819\begin{figure}[htbp]20\centering21\includegraphics[width=\textwidth]{fig05_technology_scenarios.pdf}22\caption{Technology scenarios. GDP relative to trend; labor share; wage of the lower skill; real return;23wealth-to-GDP; land price--rent ratio.}24\label{fig:tech}25\end{figure}2627The \emph{timing} of the transition is governed by the rate of capability progress and by the compute price28path; the \emph{destination} by the floors. With capability progress at 20\% a year (fast) the labor share is29below 0.07 by 2050 and the real return peaks above 50\%; at 5\% a year (slow) the labor share is still 0.27 in302050 and the wage of the lower skill is three times higher than in the baseline at that date, but by 2100 the31two paths are within a factor of two of each other. The rapid-AGI scenario, in which every task reaches its32terminal compute requirement in 2032, is the source's technology-binding transition in its purest form: output33rises forty-fold by 2050, the real return exceeds 100\% during the 2030s, the labor share is one in a thousand by342050, and the expert skill's premium never materializes because nothing is the last task to be automated.35The frozen-capability scenario (``no capability'') --- 2026 algorithms with hardware that keeps getting cheaper36--- is instructive: Moore's law alone, at 2026 capability, automates three of the four task classes by 2060 and37halves the labor share, because the compute requirements of 2026 are finite and a hundredfold cheaper compute38eventually meets them. Only the fully frozen economy (``AI frozen'') stays on its balanced path.3940The compute price floor is the parameter the long run depends on. With Moore's law ending in 2040 (compute41only eight times cheaper than today) the wage of the lower skill in 2100 is \wLMooreEndsTwoOneZeroZero{} of its422026 level against \wLTwoOneZeroZero{} in the baseline; with a floor of one thousandth it is lower still, and when43the terminal compute requirements are five times higher (``$\alpha^\infty\times5$'') wages are five times higher44than in the baseline at every date after 2070, exactly as Proposition~\ref{prop:bgp} says. The level of wages in45the AGI limit is the product of two unidentified numbers; the paper can only report the dependence.4647Energy is where the physical world pushes back, and it is also where the solver reaches its limits. In the48baseline the share of electricity used by compute peaks near 60\% and the energy price rises eighteen-fold, but49capacity is never idle. The scenario that combines the fast compute-price decline with \emph{no} efficiency50gains (``energy-constrained'') could not be solved to tolerance: the Newton iterations stall on the kinks created51by the utilization margin (capacity switches between idle and fully used across periods), and the same happens52for the scenario in which Moore's law never ends. For these two cells the paper reports only what53Proposition~\ref{prop:energy} establishes --- a bounded energy supply with a floor on energy per unit of compute54bounds compute, keeps its price positive and keeps the labor share positive --- and the fact that in every solved55scenario the energy price rises by an order of magnitude during the boom. Energy efficiency, not energy56capacity, is the margin that matters, because capacity is reproducible and the resource share in energy is57modest.5859\subsection{Substitutability and scarcity}6061\begin{figure}[htbp]62\centering63\includegraphics[width=\textwidth]{fig06_structure_scenarios.pdf}64\caption{Substitutability between tasks and physical complements, scarce land, and chip depreciation.}65\label{fig:structure}66\end{figure}6768The regime map of Section~\ref{sec:theory} is visible in Figure~\ref{fig:structure}. With strong complementarity69($\sigma_N=\sigma_T=0.4$) output rises only twenty-fold by 2100 (against \GDPTwoOneZeroZero{} in the baseline), the70land price--rent ratio stays high throughout because the real rate never rises much, and the wealth-to-income71ratio does not fall during the boom: there is not enough of a boom to raise the discount rate. The Cobb--Douglas72and substitutes cells ($\sigma=1$ and $\sigma=1.5$) could not be solved to tolerance on the 275-year horizon73--- with substitutes the task composite is not bounded by the physical inputs, the economy approaches the74source's additive limit, and the compute stock grows by factors that the solver cannot handle together with the75terminal conditions --- so for those cells the paper relies on Proposition~\ref{prop:regimes} and on the static76regime map of Figure~\ref{fig:regimes}: constant shares and a wage that falls at the rate of the compute price in77the Cobb--Douglas case, a compute share going to one and a positive wage in the substitutes case.78Scarce land (a rent79share of 8\% and $\sigma_T=0.4$) is the Piketty-like cell: land's share of income exceeds two thirds by 2100 and80the wealth-to-income ratio is the highest in the catalogue. Severe chip depreciation ($\delta_Q=0.45$) raises the81user cost of compute by nearly half, raises the wage of the lower skill in 2050 by a fifth relative to the82baseline, as Proposition~\ref{prop:bgp} implies, and lowers the price--earnings ratio of compute further (1.483against 1.8 in 2050); it does not change the destination of income.84The reinstatement scenario, in which the expert task is never automated, keeps the higher skill's premium85permanently: its wage rises with output, the labor share converges to the expert task's share of income rather86than to zero, and the lower skill's wage path is unchanged. This is the one scenario in which labor as a whole is87missed, and it requires that some bottleneck task stay beyond compute forever.8889\subsection{Preferences and the discount-rate channel}9091With log utility ($\gamma=1$) the real return peaks at 26\% instead of \rPeak\%, the land price--rent ratio92does not dip during the boom (it starts far higher, because a lower $\gamma$ makes the anticipated growth path93raise the 2026 price of land, and declines slowly as rent growth slows), and the wealth-to-income ratio rises94monotonically from 9.5 in 2026; with $\gamma=4$ the return peaks at 67\%, the price--rent ratio of land falls95below three in the mid-2050s and the wealth-to-income ratio falls from 3.5 to 1.4 before recovering96(Figure~\ref{fig:pref}). The sign of the valuation response to the boom is a preference parameter, as the97proposition says; its size in the data would depend on how much of the boom the marginal investor anticipates.9899\begin{figure}[htbp]100\centering101\includegraphics[width=\textwidth]{fig09_preference_scenarios.pdf}102\caption{Risk aversion, reinstatement of a human task, and the end of Moore's law.}103\label{fig:pref}104\end{figure}105106\subsection{Heterogeneous households}107108Figure~\ref{fig:distribution} and Table~\ref{tab:distribution} report the heterogeneous-agent economy of109Section~\ref{sec:households} for the baseline, the frozen economy and the citizen fund, solved in general110equilibrium up to a maximum log excess demand for claims of \HAmaxGap{} (the quasi-Newton on the return path111stops improving at that precision; the frozen economy converges to $10^{-4}$). Three results stand out.112113First, the equilibrium return path of the heterogeneous economy tracks the two-class one closely through the114boom (\rHATwoZeroFiveZero\% against \rTCTwoZeroFiveZero\% in 2050, a lower peak) and lies above it afterwards115(\rHATwoOneZeroZero\% against \rTCTwoOneZeroZero\% in 2100), because the marginal savers who must absorb the116growing supply of claims are less patient than the two-class capitalist ($\beta_3=\betaHigh$ against 0.995);117the one-year spike in 2026 is the adjustment of the initial distribution to the announced path. The pricing logic118of Section~\ref{sec:results} carries over --- every claim earns the same return, land is where value ends up ---119with a somewhat higher discount rate. The frozen economy's distribution is calibrated separately (its 2026120wealth is larger) and is flat by construction.121122Second, wealth inequality is \emph{non-monotonic}. The Gini coefficient falls from \GiniBase{} in 2026 to123\GiniTwoZeroFiveZero{} in 2050 and then rises to \GiniTwoOneZeroZero{} in 2100 and above its 2026 level124afterwards; the top-10\% share goes from \TopTenBase{} to \TopTenTwoZeroFiveZero{} and back to125\TopTenTwoOneZeroZero; the bottom half's share triples by 2050 and then falls below its 2026 value. The simulation126separates the two phases. During the boom, the transitory premium of the higher skill and the high return on127savings let households in the middle of the distribution accumulate; this is Restrepo's technology-binding128transition seen from the wealth side, and it is equalizing. After the last task is automated, labor income129disappears for everybody and the distribution of wealth converges to the distribution of patience: households130with the highest discount factor hold a growing share, the bottom half holds nothing, and the Gini rises toward131the value of a pure rentier economy. The historical analogy is not the twentieth century's $r>g$; it is the132disappearance of the one asset that most households own, their labor.133134Third, the citizen fund changes what households own, not only what they receive. With the fund holding one135fifth of all claims, private wealth is the remaining four fifths, every household receives the same payout, and136households at the bottom save less because the transfer substitutes for precautionary wealth: the measured137Gini of \emph{private} wealth is slightly higher than in the baseline (0.63 against 0.60 in 2050, 0.76 against1380.73 in 2100) while the share of the fund's payout in the consumption of the bottom half is, by construction, the139same as for everybody else. The right comparison is therefore in consumption, which the two-class140Table~\ref{tab:policy} reports: workers' consumption share in 2100 is three orders of magnitude higher with the141fund. The top-1\% share stays near 0.12 throughout every run: without return heterogeneity the model has no142mechanism for a Pareto tail, and the number is reported as a known miss rather than a prediction.143144\begin{figure}[htbp]145\centering146\includegraphics[width=\textwidth]{fig10_distribution.pdf}147\caption{Heterogeneous-agent economy: wealth Gini, top-10\%, top-1\% and bottom-50\% shares, the equilibrium148return path against the two-class one, and household expenditure relative to GDP.}149\label{fig:distribution}150\end{figure}151152\begin{table}[htbp]153\centering\small154\caption{Wealth distribution along the transition (heterogeneous-agent economy, general equilibrium).}155\label{tab:distribution}156\resizebox{\textwidth}{!}{\input{tables/tab07_distribution}}157\end{table}158159\subsection{Ownership, competition and policy}160161\begin{figure}[htbp]162\centering163\includegraphics[width=\textwidth]{fig08_policy_scenarios.pdf}164\caption{Ownership, competition and policy scenarios.}165\label{fig:policy}166\end{figure}167168\begin{table}[htbp]169\centering\small170\caption{Policy and ownership scenarios: output, wages, workers' consumption and welfare (consumption-equivalent171variations over 2026--2065 relative to the baseline, two-class economy).}172\label{tab:policy}173\resizebox{\textwidth}{!}{\input{tables/tab06_policy}}174\end{table}175176Table~\ref{tab:policy} compares five instruments with the baseline. A \emph{land tax} of 50\% of rents, rebated177lump-sum to workers, changes no first-order condition of production (Proposition~\ref{prop:tax}): output in 2050178differs from the baseline by less than half a percent (the difference comes from the change in who saves), and179because land captures \LandShareTwoOneZeroZero{} of income in 2100 the180rebate gives workers a quarter of GDP in the long run; capitalists lose \CEVKlandtaxFiveZero\% of consumption over1812026--2065, and the wealth-to-income ratio in 2100 is halved because land is worth half as much. A182\emph{compute tax} of 30\% raises the wage of the lower skill by about thirty percent in 2050 --- the tax-inclusive183user cost of the replacement compute is higher --- and lowers output by eight percent at that date; it is the184instrument that changes what workers \emph{earn} rather than what they are \emph{given}. A \emph{capital-income185tax} of 20\% has the largest output cost in the catalogue (output in 2050 sixteen percent below the baseline)186because it taxes the accumulation of every complement as well as of compute. An \emph{AI monopoly} with a187markup of 1.5 on compute services behaves like a compute tax whose proceeds go to the monopolist: the wage of the188lower skill is fifty-five percent higher in 2050 than in the baseline and output thirteen percent lower, and workers189gain while capitalists, who own the monopolist, are nearly indifferent. \emph{Foreign ownership} of half of190compute equity leaves every real path unchanged and sends half of compute payouts abroad; since compute payouts191are small relative to the rents that stay at home, the effect on national income is modest, and the result192reverses only in the substitutes scenario where compute captures most of income. The \emph{citizen fund} holding193one fifth of all claims does what Proposition~\ref{prop:distribution} says: workers' consumption share is bounded194below by a fifth of the net payout share, it is three orders of magnitude higher than in the baseline by 2100,195and capitalists give up \CEVKcitizenfundTwoZero\% of consumption over 2026--2065 for it.196197The welfare numbers for workers in Table~\ref{tab:policy} are large because their baseline consumption falls198toward zero: any instrument that gives them a claim on the scarce complements is worth a great deal to them. The199comparison that the table allows is across instruments at a given cost to capitalists: per point of capitalists'200consumption-equivalent loss, the land tax and the citizen fund deliver far more to workers than the compute or201capital-income taxes, because they do not reduce output. This is the general-equilibrium content of the source's202suggestion to treat compute ``akin to land'': in our economy it is land itself, not compute, that should be203treated as land.204205\subsection{AGI-arrival risk: a one-period illustration}206207The paths above are deterministic. To see the direction in which uncertainty about the arrival of AGI would move208asset prices, we take the 2026 stocks as given and let the economy learn in 2027, with probability $\pi$, that209the baseline path is realized and otherwise the frozen path, pricing each claim with the capitalists' marginal210utility in each branch (Section~\ref{sec:assetpricing}). The exercise is not an equilibrium under uncertainty ---2112026 decisions ignore the lottery --- and the magnitudes are not meaningful, because capitalists' consumption212jumps in the baseline branch. The signs are: compute capital carries a large positive premium (it pays in the213state in which the marginal investor is rich), land and housing land carry negative premia (they pay relatively214more in the state in which the marginal investor is poor, and are therefore hedges), and structures are in215between. A full stochastic solution, in which the premium of the last-automated skill is itself a lottery, is216the first item on the agenda of Section~\ref{sec:conclusion}.217