首页|The Tiebout-Oates Trilemma: Factor Mobility, Superlinear Tax Bases, and the Impossibility of Spatial Convergence
The Tiebout-Oates Trilemma: Factor Mobility, Superlinear Tax Bases, and the Impossibility of Spatial Convergence
Xingpan Jiang
The Tiebout-Oates Trilemma: Factor Mobility, Superlinear Tax Bases, and the Impossibility of Spatial Convergence
The Tiebout-Oates Trilemma: Factor Mobility, Superlinear Tax Bases, and the Impossibility of Spatial Convergence
摘要
This paper establishes a fiscal impossibility theorem—the Tiebout-Oates Trilemma—for decentralized public finance. Consider an economy where mobile factors migrate across a geographic manifold according to utility gradients (Wasserstein gradient flow), local governments finance public goods from a territorial tax base with superlinear elasticity α > 1 in population density, and a benevolent planner seeks even minimal spatial non-divergence of welfare. We prove that these three conditions—factor mobility, territorial fiscal autonomy with α > 1, and bounded spatial inequality—are mutually incompatible. The proof proceeds by showing that the continuity equation governing population dynamics reduces to a backward nonlinear diffusion equation (negative effective diffusivity), which is ill-posed in the sense of Hadamard: no continuous solution path connects an arbitrary initial distribution to a spatially stable state. We provide full general equilibrium microfoundations via a Cobb-Douglas spatial economy with agglomeration externalities, proving that property-based taxation endogenously generates α > 1 and that the effective diffusivity is an exactly computable negative constant. Three constructive corollaries follow: a sharp phase transition at α = 1, the exponential unsustainability of equalization transfers, and the structural instability of the knife-edge case α = 1. An empirical illustration using Detroit's fiscal trajectory corroborates the theorem's predictions.
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