Triple

T9986293
Position Surface form Disambiguated ID Type / Status
Subject Hotelling’s lemma E196774 entity
Predicate relatedTo P37 FINISHED
Object Shephard’s lemma
Shephard’s lemma is a result in microeconomics stating that the derivative of a cost (or expenditure) function with respect to input (or price) yields the corresponding conditional factor (or Hicksian demand) demand function.
E833554 NE FINISHED

How this triple was built (4 steps)

Every LLM step that produced this triple, in pipeline order — named-entity classification, the disambiguation choices (the exact options shown, with the pick highlighted), and the generated description. The batch + timestamp of each is in the Provenance table below.

NER Named-entity recognition gpt-5-mini
Instruction
Given a phrase, classify it is english named entity (e.g., persons, organizations, works of art) in Latin script, or not (e.g., literals, dates, URLs, verbose phrases). For disambiguation, the statement where the phrase occurs as object is also given. Please return a JSON object with `phrase` (string, the phrase being analyzed) and `is_ne` (boolean, indicating whether the phrase is a Named Entity).
Input
Phrase: Shephard’s lemma | Statement: [Hotelling’s lemma, relatedTo, Shephard’s lemma]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Shephard’s lemma
Context triple: [Hotelling’s lemma, relatedTo, Shephard’s lemma]
  • A. Hotelling’s lemma
    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.
  • B. Hicksian demand
    Hicksian demand is a concept in microeconomics that describes how a consumer’s demand for goods changes when prices vary while holding utility (satisfaction) constant, often used in welfare and consumer theory.
  • C. Gale–Nikaidō–Debreu theorem
    The Gale–Nikaidō–Debreu theorem is a fundamental result in mathematical economics that provides conditions ensuring the existence (and sometimes uniqueness) of equilibrium in certain nonlinear and general equilibrium models.
  • D. Marshallian demand
    Marshallian demand is the consumer demand function that expresses the quantity of a good chosen as a function of prices and income, derived from utility maximization under a budget constraint.
  • E. Hicks–Kaldor compensation criterion
    The Hicks–Kaldor compensation criterion is an economic efficiency test stating that a policy change is desirable if those who gain could in principle compensate those who lose and still be better off, regardless of whether compensation actually occurs.
  • F. None of above. chosen
  • G. Unsure - the case is ambiguous/there is not enough information to decide.
NEDg Description generation gpt-5.1
Instruction
Generate a one-sentence description of the target entity. 
You are given a context triple in the form (subject, predicate, object), where the object is the target entity. 
# Instructions
Use the triple to infer relevant information about the entity. Describe the entity based on what is most defining, well-known. 
Avoid repeating the information from the triple, unless really essential.
# Response Format
Return only the sentence: "Description: [one-sentence description of the target entity]"
Input
Entity: Shephard’s lemma
Triple: [Hotelling’s lemma, relatedTo, Shephard’s lemma]
Generated description
Shephard’s lemma is a result in microeconomics stating that the derivative of a cost (or expenditure) function with respect to input (or price) yields the corresponding conditional factor (or Hicksian demand) demand function.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Shephard’s lemma
Target entity description: Shephard’s lemma is a result in microeconomics stating that the derivative of a cost (or expenditure) function with respect to input (or price) yields the corresponding conditional factor (or Hicksian demand) demand function.
  • A. Hotelling’s lemma
    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.
  • B. Hicksian demand
    Hicksian demand is a concept in microeconomics that describes how a consumer’s demand for goods changes when prices vary while holding utility (satisfaction) constant, often used in welfare and consumer theory.
  • C. Gale–Nikaidō–Debreu theorem
    The Gale–Nikaidō–Debreu theorem is a fundamental result in mathematical economics that provides conditions ensuring the existence (and sometimes uniqueness) of equilibrium in certain nonlinear and general equilibrium models.
  • D. Marshallian demand
    Marshallian demand is the consumer demand function that expresses the quantity of a good chosen as a function of prices and income, derived from utility maximization under a budget constraint.
  • E. Hicks–Kaldor compensation criterion
    The Hicks–Kaldor compensation criterion is an economic efficiency test stating that a policy change is desirable if those who gain could in principle compensate those who lose and still be better off, regardless of whether compensation actually occurs.
  • F. None of above. chosen

Provenance (5 batches)

The batch behind each pipeline step, in order, with when it ran. Timestamps are batch-level — stages were processed in waves, so the object chain (NER → NED1 → NEDg → NED2) reads in order, but predicate / elicitation batches can sit in a different wave.

Step Stage Batch ID Status When
creating Elicitation batch_69ca82f1678c819093d06320a05f16a4 completed March 30, 2026, 2:04 p.m.
NER Named-entity recognition batch_69cdc79af13c81909349ae0b0d5da946 completed April 2, 2026, 1:34 a.m.
NED1 Entity disambiguation (via context triple) batch_69d258078488819086a58db79075e2b9 completed April 5, 2026, 12:39 p.m.
NEDg Description generation batch_69d258f0e91881909fdda5a5f3e50d29 completed April 5, 2026, 12:43 p.m.
NED2 Entity disambiguation (via description) batch_69d259bf38b08190b059dd7bd42d8862 completed April 5, 2026, 12:46 p.m.
Created at: March 30, 2026, 8:49 p.m.