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Gross substitutes

Gross substitutes 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 Gross substitutes rather than just read about it. In short: The term gross substitutes is used in two slightly different meanings: In microeconomics, two commodities X {\displaystyle X} and Y {\displaystyle Y} are called gross substitutes, if Δ demand ( X ) Δ price ( Y ) > 0 {\displaystyle {\frac {\Delta {\text{demand}}(X)}{\Delta {\text{price}}(Y)}}>0} . I.e., an increase in the price of one commodity causes people to want strictly more of the other commodity, since the com…

Key takeaways

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

Reference excerpt

The term gross substitutes is used in two slightly different meanings:

In microeconomics, two commodities X {\displaystyle X} and Y {\displaystyle Y} are called gross substitutes, if Δ demand ( X ) Δ price ( Y ) > 0 {\displaystyle {\frac {\Delta {\text{demand}}(X)}{\Delta {\text{price}}(Y)}}>0} . I.e., an increase in the price of one commodity causes people to want strictly more of the other commodity, since the commodities can substitute each other (bus and taxi are a common example). In auction theory and competitive equilibrium theory, a valuation function is said to have the gross substitutes (GS) property if for all pairs of commodities: Δ demand ( X ) Δ price ( Y ) ≥ 0 {\displaystyle {\frac {\Delta {\text{demand}}(X)}{\Delta {\text{price}}(Y)}}\geq 0} . I.e., the definition includes both substitute goods and independent goods, and only rules out complementary goods. See Gross substitutes (indivisible items).

References

Worked examples

Example 1 — a first encounter with Gross substitutes

Start with the simplest possible case. Write down what Gross substitutes 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 Gross substitutes 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 Gross substitutes 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 Gross substitutes

In research
Gross substitutes 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 Gross substitutes 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
Gross substitutes is common in secondary-school and first-year university syllabi. It links to neighbouring topics Economic terminology stubs, Utility function types, so understanding it makes those chapters shorter.
In everyday life
Look for Gross substitutes 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 Gross substitutes in 20 minutes

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

Frequently asked questions

What is Gross substitutes in simple terms?

The term gross substitutes is used in two slightly different meanings: In microeconomics, two commodities X {\displaystyle X} and Y {\displaystyle Y} are called gross substitutes, if Δ demand ( X ) Δ price ( Y ) > 0 {\displaystyle {\frac {\Delta {\text{demand}}(X)}{\Delta {\text{price}}(Y)}}>0} . I…

Why does Gross substitutes 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 Gross substitutes?

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 Gross substitutes.

Tags

  • Economic terminology stubs
  • Utility function types

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