This paper develops a spatial-dynamic framework to analyze the theoretical and quantitative effects of a Land Value Tax (LVT) on urban land markets, capital accumulation, and spatial redistribution. Building upon the Georgist distinction between produced value and unearned rent, the model departs from the static equilibrium tradition by introducing an explicit diffusion process for land values and a local investment dynamic governed by profitability thresholds. Land value $V (x, y, t)$ and built capital $K(x, y, t)$evolve over a two-dimensional urban domain according to coupled nonlinear partial differential equations, incorporating local productivity $A(x, y)$, centrality effects $μ(x, y)$, depreciation $δ$, and fiscal pressure $τ$ . Analytical characterization of the steady states reveals a transcritical bifurcation in the parameter $τ$ , separating inactive (low-investment) and active (self-sustaining) spatial regimes. The equilibrium pair $(V ^*, K^*)$ is shown to exist only when the effective decay rate $α= r + τ- μ(x, y)$ exceeds a profitability threshold $θ= κ+ δ/ I_0$, and becomes locally unstable beyond this boundary. The introduction of diffusion, $D_V ΔV$, stabilizes spatial dynamics and generates continuous gradients of land value and capital intensity, mitigating speculative clustering while preserving productive incentives. Numerical simulations confirm these analytical properties and display the emergence of spatially heterogeneous steady states driven by urban centrality and local productivity. The model also quantifies key aggregate outcomes, including dynamic tax revenues, adjusted capital-to-land ratios, and net present values under spatial heterogeneity and temporal discounting. Sensitivity analyses demonstrate that the main qualitative mechanisms-critical activation, spatial recomposition, and bifurcation structure-remain robust under alternative spatial profiles $(A, μ)$, discretization schemes, and moderate differentiation of the tax rate $τ(x, y)$. From an economic perspective, the results clarify the dual nature of the LVT: while it erodes unproductive rents and speculative land holding, its dynamic incidence on built capital depends on local profitability and financing constraints. The taxation parameter $τ$ thus acts as a control variable in a nonlinear spatial system, shaping transitions between rent-driven and production-driven equilibria. Within a critical range around $τ_c$, the LVT functions as an efficient spatial reallocation operator-reducing inequality in land values and investment density without impairing aggregate productivity. Beyond this range, excessive taxation induces systemic contraction and investment stagnation. Overall, this research bridges static urban tax theory with dynamic spatial economics by formalizing how a land-based fiscal instrument can reshape the geography of value creation through endogenous diffusion and nonlinear feedback. The framework provides a foundation for future extensions involving stochastic shocks, adaptive policy feedbacks, or endogenous public investment, offering a unified quantitative perspective on the dynamic efficiency and spatial equity of land value taxation.

翻译：本文构建了一个空间动态框架，用于分析土地价值税（LVT）对城市土地市场、资本积累与空间再分配的理论与量化效应。基于乔治主义对生产价值与非劳动租金的区分，该模型突破了静态均衡传统，引入了土地价值的显式扩散过程以及由盈利阈值调控的本地投资动态。土地价值 $V (x, y, t)$ 与建成资本 $K(x, y, t)$ 在二维城市域上根据耦合非线性偏微分方程演化，其中纳入本地生产率 $A(x, y)$、中心性效应 $μ(x, y)$、折旧率 $δ$ 与财政压力 $τ$。稳态的解析特征揭示了参数 $τ$ 中的跨临界分岔，分隔了非活跃（低投资）与活跃（自维持）的空间机制。均衡对 $(V ^*, K^*)$ 仅当有效衰减率 $α= r + τ- μ(x, y)$ 超过盈利阈值 $θ= κ+ δ/ I_0$ 时存在，并在此边界之外呈现局部不稳定性。扩散项 $D_V ΔV$ 的引入稳定了空间动态，并产生土地价值与资本密度的连续梯度，在抑制投机聚集的同时保留了生产激励。数值模拟验证了这些解析性质，并展示了由城市中心性与本地生产率驱动的空间异质稳态的出现。该模型还量化了关键宏观结果，包括动态税收收入、调整后的资本-土地比率，以及空间异质性与时间贴现下的净现值。敏感性分析表明，主要定性机制——临界激活、空间重组与分岔结构——在替代空间分布 $(A, μ)$、离散化方案及税率 $τ(x, y)$ 适度差异化条件下保持稳健。从经济学视角看，结果阐明了LVT的双重性质：在侵蚀非生产性租金与投机性土地持有的同时，其对建成资本的动态影响取决于本地盈利性与融资约束。因此，税收参数 $τ$ 在非线性空间系统中作为控制变量，塑造了租金驱动与生产驱动均衡之间的转变。在 $τ_c$ 附近的临界范围内，LVT作为高效的空间再分配算子发挥作用——在不损害总体生产率的前提下减少土地价值与投资密度的不平等。超出此范围，过度征税将引发系统性收缩与投资停滞。总体而言，本研究通过形式化土地财政工具如何通过内生扩散与非线性反馈重塑价值创造的地理格局，将静态城市税收理论与动态空间经济学相连接。该框架为未来拓展研究（如随机冲击、适应性政策反馈或内生公共投资）奠定了基础，为土地价值税的动态效率与空间公平性提供了统一的量化视角。