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.