1\section{Households, saving and the ownership of compute}2\label{sec:households}34Income can flow from labor to capital without anything happening to the distribution of wealth if everybody5owns capital in proportion to their consumption, and it can concentrate wealth without any change in factor6shares if only some households save. The model therefore tracks ownership explicitly, in two layers.78\subsection{The two-class economy}910The analytical layer has two types of households. Capitalists, of unit mass, own all the claims of11Section~\ref{sec:model}, have no labor income, and choose expenditure $x^K_t$ on goods and housing to maximize12$\sum_t\beta^tu(c_t,h_t)$ with $u=(c^{1-\theta_H}h^{\theta_H})^{1-\gamma}/(1-\gamma)$. With the Cobb--Douglas13inner aggregator the problem reduces to one over total expenditure with the ideal price index14$P_t\propto(R^H_t)^{\theta_H}$, and the Euler equation is15\begin{equation}16\Big(\frac{x^K_{t+1}}{x^K_t}\Big)^{\gamma}\Big(\frac{P_{t+1}}{P_t}\Big)^{1-\gamma}=\beta(1+r_{t+1}).17\label{eq:euler}18\end{equation}19Workers of skill $s$, of mass $H_s$, consume their wage income plus transfers each period. The two-class economy20is the one in which Propositions~\ref{prop:bgp}--\ref{prop:tax} are proved and in which all scenarios of21Section~\ref{sec:results} are solved; it is also the limit of the heterogeneous economy in which a group of22patient households holds almost all wealth. It has two purposes: the capitalists' Euler equation23\eqref{eq:euler} is the stochastic discount factor that prices every claim, and the hand-to-mouth workers make24the ``demand compression'' channel of Section~\ref{sec:results} visible, because any fall in the wage bill is a25one-for-one fall in workers' expenditure.2627\subsection{The heterogeneous-agent economy}2829The quantitative distributional layer replaces the two types by a continuum. A household is characterized by a30permanent skill $s\in\{L,H\}$, a permanent discount factor $\beta_j\in\{\beta_1,\beta_2,\beta_3\}$ with masses31$(0.5,0.3,0.2)$ within each skill \citep{KrusellSmith1998,Carroll2017}, an idiosyncratic productivity32$e_t$ following a five-state Rouwenhorst approximation to an AR(1) in logs with persistence $0.95$ and33innovation standard deviation $0.20$, and assets $a_t\ge0$ invested in the fund. Income is34$w_{s,t}e_t+\tau_t$ with $\tau_t$ the lump-sum transfer of the policy scenarios; expenditure $x_t$ and savings35$a_{t+1}$ satisfy $x_t+a_{t+1}=a_t(1+r_t)+w_{s,t}e_t+\tau_t$, and the Euler equation holds with equality36whenever the borrowing constraint is slack. The problem is solved by the endogenous grid method37\citep{Carroll2006} on a 300-point grid and the distribution by non-stochastic simulation38(Appendix~\ref{app:algorithms}). The discount factors are set so that stationary savings at the 2026 prices equal39the two-class wealth $W_0$, so that both layers start from the same balance sheet; the resulting wealth Gini and40top-10\% share are reported against the Distributional Financial Accounts in Section~\ref{sec:calibration}41\citep{FedDFA2026}. The model has no return heterogeneity and cannot reproduce the top-1\% share42\citep{Gabaix2016,HubmerKrusellSmith2021}; we report it as an untargeted moment.4344General equilibrium in the heterogeneous economy is the requirement that the fund's shares are willingly held:45$\int a_{t+1}\,\dd\mu_t=W_t$ at every date, where $W_t$ is the ex-dividend value of all claims. We solve for the46path of returns by relaxation: given a path $\{r_{t+1}\}$, the production side (four capital Euler equations and47the goods market) is solved with the banded Newton method of Appendix~\ref{app:algorithms}, the household block48is solved backward and simulated forward, and the return is lowered where households demand more claims than49exist. The two-class solution is the starting point.5051\subsection{Wealth accounting}5253For both layers we decompose the change in aggregate wealth between any two dates into net saving, net payouts54received and reinvested, and revaluation:55\begin{equation}56W_{t+1}-W_t=\underbrace{\big[(1+r_{t+1})W_t-W_t\big]}_{\text{return}}57-\underbrace{\big[\textstyle\sum_kD^k_{t+1}+R^T_{t+1}T+R^{TH}_{t+1}T^H\big]}_{\text{payouts}}+\ldots,58\end{equation}59where the return splits further into the payout yield and the capital gain $\sum_k(q^k_{t+1}K^k_{t+2}-q^k_tK^k_{t+1})$60and the land-price change. In the heterogeneous economy the same decomposition is applied household by61household in simulation, which is what allows the paper to say whether wealth concentrates because the rich save62more or because what they already own is revalued (Section~\ref{sec:results}).63