A new approach to the theory of optimal income tax

Paper: arXiv 2408.14476

Abstract

The Nobel-price winning Mirrlees’ theory of optimal taxation inspired a long sequence of research on its refinement and enhancement. However, an issue of concern has been always the fact that, as was shown in many publications, the optimal schedule in Mirrlees’ paradigm of maximising the total utility (constructed from individually optimised individual ones) usually did not lead to progressive taxation (contradicting the ethically supported practice in developed economies), and often even assigned minimal tax rates to the higher paid strata of society. The first objective of this paper is to support this conclusion by proving a theorem on optimal tax schedule in (practically most exploited) piecewise-linear environment under a simplest natural utility function. The second objective is to suggest a new paradigm for optimal taxation, where instead of just total average utility maximization one introduces a standard deviation of utility as a second parameter (in some analogy with Marcowitz portfolio optimization). We show that this approach leads to transparent and easy interpreted optimality criteria for income tax.

Complexity vs Empirical Score

• Math Complexity: 8.0/10
• Empirical Rigor: 1.0/10
• Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper presents rigorous mathematical derivations using calculus, optimization, and proofs for theorems, but offers no empirical data, backtests, or implementation details, focusing purely on theoretical economic modeling.

Research Flowchart

  flowchart TD
  A["Research Goal:<br>Optimal Income Taxation"] --> B{"Methodology"}
  B --> C["Objective 1:<br>Verify Mirrlees' Counter-intuitive Results"]
  B --> D["Objective 2:<br>Propose Utility Variance<br>Optimization Paradigm"]
  
  C --> E["Compute Optimal Tax<br>via Piecewise-Linear Model"]
  D --> F["Apply Markowitz-like<br>Portfolio Optimization"]
  
  E & F --> G["Key Findings & Outcomes"]
  
  G --> H["Theorem 1:<br>Optimal Schedule is Non-Progressive<br>and favors low rates for high income"]
  G --> I["Novel Criteria:<br>Transparent & Interpretable<br>using Average Utility + Std Dev"]
  
  H --> J["Conclusion:<br>New Paradigm Resolves<br>Mirrlees' Ethical Paradox"]
  I --> J

Cited References (14)

1. Optimal Piecewise Linear Income Taxation (2014) — link
2. The Optimal Income Tax When Poverty Is a Public Bad (2001) — link
3. The Optimal Two-Bracket Linear Income Tax (1991) — link
4. Note on the shape of the optimum income tax schedule (1989) — link
5. On the shape of optimal tax schedules (1977) — link
6. On Income Distribution, Incentive Effects and Optimal Income Taxation (1976) — link
7. The Optimal Linear Income-tax (1972) — link
8. An Exploration in the Theory of Optimum Income Taxation (1971) — link

0 of 14 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.