About
The Optimal Income Tax Simulator implements the Saez (2001) optimal nonlinear income tax formula — the dominant analytical framework in modern public finance for deriving revenue-maximising and welfare-maximising top marginal tax rates. Despite being taught in every graduate public finance course and cited in virtually every serious policy debate about top marginal rates, no clean interactive browser-based implementation existed before this tool.
The tool allows researchers, students, and policy analysts to explore how the optimal top rate responds to different assumptions about the elasticity of taxable income, the shape of the income distribution, and the government's social welfare preferences. All computation is performed in the browser — no data is sent to any server.
This tool is part of the sciencetools.org portfolio of serious scientific calculators. The design language — dark theme, instrument-grade typography, explicit epistemic labels — is shared with the Unknotting Number Calculator.
Every result carries an explicit epistemic label distinguishing revenue-maximising results (empirical, derived from the Laffer peak) from welfare-maximising results (normative, dependent on the social welfare weight g). Amber warnings appear when parameter values fall outside the empirically supported range.
Results from this tool should be cited as follows:
When g > 0, the citation must disclose the welfare weight as a normative choice. The "Cite this result" button on the calculator page generates the full citation text automatically, including any applicable warnings.
This tool is one of a growing portfolio of serious scientific calculators built for researchers, students, and practitioners who need reliable, citable, browser-based implementations of important scientific results.
Given a knot in any standard notation, determine its unknotting number u(K) — the minimum number of crossing changes required to produce the unknot.
Compute the revenue-maximising and welfare-maximising top marginal tax rate using the Saez (2001) formula.
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