1. Agent Objective
(max)┬(a_(i,t) ) W_(i,t)
Agents choose strategies a_(i,t)to maximize attainable household wealth W_(i,t), subject to the constraint and system dynamics below. The constraint defines the feasible set.
2. Core Constraint
W_(i,t)≤k⋅W_(“median” ,t)
W_(i,t): household net worth at time t
W_(“median” ,t): national median household net worth
k: proportional scaling parameter
3. Enforcement: Recapture Function
T_(i,t)=max(0,” ” W_(i,t)-max(kW_(“median” ,t),G_i))
T_(i,t): excess accumulation above the boundary
G_i: conditionally protected nominal, non-increasing baseline for legacy accumulation
Enforces the constraint at terminal wealth; not flow-based or revenue-maximizing. Applied at the household level independent of asset composition.
4. Aggregate Recapture and Allocation
R_t=∑_i▒T_(i,t) (1/3)R_t→”sovereign wealth fund”,(2/3)R_t→”states”
5. Sovereign Wealth Fund Dynamics
F_T=∑_(t=1)^T▒R_(swf,t) (1+r)^(T-t)
V_t=(ωF_t)/N_(“adult” ,t)
F_T: fund value
r: real rate of return
V_t: per-capita distribution (ω: yield; N_(“adult” ,t): population)
6. Median as Endogenous State Variable
W ̃_(“median” ,t+1)=g(a_(1,t),…,a_(N,t),X_t)
W_(“median” ,t+1)=W ̃_(“median” ,t+1)+V_t
W ̃_(“median” ,t+1): median from market outcomes
X_t: exogenous macroeconomic conditions
7. Temporal Smoothing
W_(“median” ,t)=1/5 ∑_(s=t-4)^t▒W_(“median” ,s)^”obs”
8. Parameter Constraints
k∈[1,000,” ” 10,000]
Downward adjustment ≤20% in the first 20 years after implementation
9. Jurisdictional Constraint
For households satisfying:
W_(i,t)≥0.8⋅k⋅W_(“median” ,t)
Foreign-held assets ≤20% of total net worth in the boundary zone
10. Notes
- Sector-invariant, household-level mechanism operating on terminal balance sheets; no activity classification or sectoral measurement required.
- No estimation of counterfactual income, productivity, or returns required.
- Alters the feasible set without imposing behavioral mandates.
- Dual equilibrium internalization pathways: Cooperative – agents raise g(a) to expand the boundary; Mechanical – excess accumulation triggers T_(i,t), funding V_t.
- In-kind settlement preserves market neutrality, avoids forced liquidation, and utilizes existing custody structures (e.g., state endowments).
- 5-year smoothing mitigates short-term volatility.
- If g(a)→0, V_t provides a positive contribution to the median, maintaining a well-defined non-zero state variable; the boundary constraint alters incentives in such states.
- Initially, binding incidence is limited to ≤10^3 apex households; all households below the boundary – including all centimillionaires – are exempt from federal wealth taxation.
- Implementation requires definitions for aggregation, valuation, audit, and settlement.
- Dormancy condition: S_t∈{0,1}, with T_(i,t)=S_t⋅(⋅), and S_t=0 when middle three quintiles ≥50% of wealth, while fund distributions continue.
- Ratification feasibility: ∑_(s=1)^50▒V_s ≥38, leveraging concentrated geographic incidence (e.g., ≈60% of billionaire households in four states) against broadly distributed fiscal benefits.
- Forward-looking constraint on expansion, not retrospective adjustment; grandfathering conditioned on repatriation, reporting, and compliance.
