Hotelling’s lemma
E196774
Hotelling’s lemma is a result in microeconomics that links a firm’s profit function to its supply and factor demand functions via partial derivatives.
All labels observed (2)
| Label | Occurrences |
|---|---|
| Hotelling’s lemma canonical | 2 |
| Hotelling's lemma | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T1762690 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Hotelling’s lemma Context triple: [Harold Hotelling, notableWork, Hotelling’s lemma]
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A.
Karush–Kuhn–Tucker conditions
The Karush–Kuhn–Tucker conditions are fundamental optimality criteria in nonlinear programming that generalize Lagrange multipliers to handle inequality constraints.
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B.
Pareto efficiency
Pareto efficiency is an economic concept describing an allocation of resources where no individual can be made better off without making someone else worse off.
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C.
Coase theorem
The Coase theorem is an economic theory stating that if property rights are well-defined and transaction costs are negligible, private bargaining will lead to an efficient allocation of resources regardless of the initial assignment of rights.
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D.
Hamiltonian economic program
The Hamiltonian economic program was Alexander Hamilton’s comprehensive plan to strengthen the early United States’ financial system through federal assumption of state debts, creation of a national bank, and support for manufacturing and commerce.
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E.
Frisch–Waugh–Lovell theorem
The Frisch–Waugh–Lovell theorem is a fundamental result in econometrics that shows how the coefficients of a multiple linear regression can be obtained by first partialling out (regressing out) other explanatory variables.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Hotelling’s lemma Target entity description: Hotelling’s lemma is a result in microeconomics that links a firm’s profit function to its supply and factor demand functions via partial derivatives.
-
A.
Karush–Kuhn–Tucker conditions
The Karush–Kuhn–Tucker conditions are fundamental optimality criteria in nonlinear programming that generalize Lagrange multipliers to handle inequality constraints.
-
B.
Pareto efficiency
Pareto efficiency is an economic concept describing an allocation of resources where no individual can be made better off without making someone else worse off.
-
C.
Coase theorem
The Coase theorem is an economic theory stating that if property rights are well-defined and transaction costs are negligible, private bargaining will lead to an efficient allocation of resources regardless of the initial assignment of rights.
-
D.
Hamiltonian economic program
The Hamiltonian economic program was Alexander Hamilton’s comprehensive plan to strengthen the early United States’ financial system through federal assumption of state debts, creation of a national bank, and support for manufacturing and commerce.
-
E.
Frisch–Waugh–Lovell theorem
The Frisch–Waugh–Lovell theorem is a fundamental result in econometrics that shows how the coefficients of a multiple linear regression can be obtained by first partialling out (regressing out) other explanatory variables.
- F. None of above. chosen
Statements (37)
| Predicate | Object |
|---|---|
| instanceOf |
economic theorem
ⓘ
result in microeconomics ⓘ |
| appliesTo |
competitive firm
ⓘ
multi-input firms ⓘ multi-output firms ⓘ |
| assumes |
differentiable profit function
ⓘ
price-taking behavior ⓘ profit maximization ⓘ well-behaved technology ⓘ |
| category | microeconomic lemma ⓘ |
| coreIdea |
factor demand equals negative partial derivative of profit with respect to input price
ⓘ
supply equals partial derivative of profit with respect to output price ⓘ |
| domain | dual approach to production ⓘ |
| field |
microeconomics
ⓘ
production theory ⓘ theory of the firm ⓘ |
| formalStatement |
partial derivative of profit with respect to an input price equals minus the firm’s optimal demand for that input
ⓘ
partial derivative of profit with respect to an output price equals the firm’s optimal supply of that output ⓘ |
| historicalContext | developed in early 20th century ⓘ |
| implies |
factor demand functions inherit properties from profit function
ⓘ
supply function inherits properties from profit function ⓘ |
| mathematicalForm | profit function is convex in prices under standard assumptions ⓘ |
| namedAfter | Harold Hotelling ⓘ |
| relatedTo |
Shephard’s lemma
ⓘ
duality theory in microeconomics ⓘ envelope theorem ⓘ |
| relates |
factor demand function
ⓘ
profit function ⓘ supply function ⓘ |
| requires | profit function defined as maximum over feasible production plans ⓘ |
| usedFor |
comparative statics in production theory
ⓘ
deriving factor demand from profit functions ⓘ deriving supply functions from profit functions ⓘ empirical estimation of supply behavior ⓘ |
| usedIn |
applied production economics
ⓘ
general equilibrium analysis ⓘ industrial organization ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: Hotelling’s lemma Description of subject: Hotelling’s lemma is a result in microeconomics that links a firm’s profit function to its supply and factor demand functions via partial derivatives.
Referenced by (3)
Full triples — surface form annotated when it differs from this entity's canonical label.
subject surface form:
Harold Hotelling
this entity surface form:
Hotelling's lemma