The Anomalies Of The Wold-Juréen (1953) Functional Form In Overview
Bibliographic record
Abstract
Both the Wold-Juréen (1953) utility function and the Wold-Juréen (1953) production function have played a central role in the modelling and the analysis of the Giffen behavior. Using an amalgam of these two functions, this paper defines the Wold-Juréen (1953) functional form, and then compares its properties to the properties of the arbitrary functional form, in an effort to provide a global perspective on the unique nature of the Wold-Juréen (1953) functional form. This paper then reports: (a) that the domain of the Wold-Juréen (1953) functional form (or the first functional form) is a subset of the domain of the arbitrary functional form (or the second functional form), (b) that the signs of the second derivatives of the Wold-Juréen (1953) functional form (or the first functional form) are the opposite of the signs of the second derivatives of the arbitrary functional form (or the second functional form), and (c) that (within the context of the unconstrained-maximization problem) the Wold-Juréen (1953) functional form (or the first functional form) is not concave, whereas the arbitrary functional form (or the second functional form) is concave.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.003 | 0.010 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.004 |
| Scholarly communication | 0.002 | 0.005 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.008 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".