The shape of ray average cost and its role in multioutput scale economies: some generalizations
Bibliographic record
Abstract
Establishing a link between the so-called ‘neoclassical’ and ‘axiomatic’ approaches to production theory, we deal with some central and unresolved issues concerning scale economies in multi-output technologies. First, we extend Panzar and Willig’s (1977) results on the duality between primal and dual scale elasticity measures, which helps pointing out the unknown role played in this regard by the monotonicity of the local degree of homogeneity of the technology. Second, under a general representation of a convex technology – allowing for non-differentiability of the cost function and multiple optima – we determine the shape of the ray average cost function. Third, in the same setting, we determine an unambiguous relationship between cost scale elasticity and cost scale efficiency, and therefore between local and global scale economies. Fourth, we develop a complete map of values taken by primal and dual scale elasticities and point out that the equality between returns to scale and scale economies local measures breaks down in a convex technology at points where the cost function is not differentiable. This highlights the importance of considering non-differentiability when analysing scale economies in production technologies.
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How this classification was reachedexpand
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 | 0.002 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".