mathematics

Suits index

Suits index is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Suits index rather than just read about it. In short: The Suits index of a public policy is a measure of tax progressiveness, named for economist Daniel B. Suits.

Key takeaways

Suits index belongs to mathematics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Suits index to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Suits index from memory before moving on to harder problems.

Reference excerpt

The Suits index of a public policy is a measure of tax progressiveness, named for economist Daniel B. Suits. Similar to the Gini coefficient, the Suits index is calculated by comparing the area under the Lorenz curve to the area under a proportional line. For a progressive tax (for example, where higher income tax units pay a greater fraction of their income as tax), the Suits index is positive. A proportional tax (for example, where each unit pays an equal fraction of income) has a Suits index of zero, and a regressive tax (for example, where lower income tax units pay a greater fraction of income in tax) has a negative Suits index. A theoretical tax where the richest person pays all the tax has a Suits index of 1, and a tax where the poorest person pays everything has a Suits index of −1. Tax preferences (credits and deductions) also have a Suits index.

Types of tax

Income tax By definition, a flat income tax has a Suits index of zero. However, almost all income tax systems allow for some amount of income to be earned without tax (an exemption amount) to avoid collecting tax from very low income units. Also, most income tax systems provide for higher marginal tax rates at higher income. These effects combine to make income taxes generally progressive, and therefore have a positive Suits index.

Sales tax Sales taxes are generally charged on each purchase, with no low income exemption. Additionally, lower income tax units generally spend a greater proportion of income on taxable purchases, while higher income units will save or invest a larger part of income. Therefore, sales taxes are generally regressive, and have a negative Suits index.

Excise taxes Excise taxes are typically charged on items like gasoline, alcohol or tobacco products. Since the tax rate is typically high, and there is a practical limit to the amount of product that can be consumed, this tax is generally more regressive and has a very negative Suits index.

Properties The Suits index has the useful property that the total Suits index of a group of taxes or policies is the revenue-weighted sum of the individual indexes. The Suits index is also related closely to the Gini coefficient. While a Gini coefficient of zero means that everyone receives the same income or benefit as a per capita value, a Suits index of zero means that each person pays the same tax as a percentage of income. Additionally, a poll tax has a Suits index equal to the negative of the Gini coefficient for the same group.

Examples

Worked examples

Example 1 — a first encounter with Suits index

Start with the simplest possible case. Write down what Suits index claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Suits index before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Suits index ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Suits index

In research: Suits index appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Suits index in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Suits index is common in secondary-school and first-year university syllabi. It links to neighbouring topics Economic indicators, Fiscal policy, Index numbers, so understanding it makes those chapters shorter.
In everyday life: Look for Suits index outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Suits index in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Suits index means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Suits index out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Suits index in simple terms?

The Suits index of a public policy is a measure of tax progressiveness, named for economist Daniel B. Suits.

Why does Suits index matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Suits index?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Suits index.