PROPOSITIONS OF FIVE EQUILIBRIA EXAMPLES FOR 3×2 CES/LES PURE EXCHANGE ECONOMIES
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Bibliographic record
Abstract
This paper reports numerical examples for a 3 individual 2 good CES/LES pure exchange economy in which 5 equilibria exist. We explore the size of the regions of the parameter space for which 5 equilibria persist, and show these ranges to be very small in each parameter. Other features of the equilibrium manifolds are examined. The number of equilibria can jump from 5 to 3 to 1, or even from 5 to 1. We also find changes of (Kehoe) equilibrium indices from -1 to +1 or from +1 to -1. Then, we provide parameter changes simultaneously in a large range that preserve given 5 equilibria.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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 it