A variational inequality trade network model in prices and quantities under commodity losses
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Bibliographic record
Abstract
Multicommodity trade enables the production, consumption, and flow of commodities across the globe from agricultural ones to precious metals.Mathematical formalisms to model, analyze, and solve such problems have advanced and are also relevant to policy and decision-making.In this paper, we construct a variational inequality trade network model in price and quantity variables, which captures possible losses on transportation routes, which can occur because of perishability of commodities, as in the case of agricultural ones, or outright thefts.The equilibrium conditions are stated and the variational inequality formulation derived.Qualitative properties of existence and uniqueness of the equilibrium supply price, commodity shipment, and demand price pattern are provided under reasonable conditions.Illustrative examples help to demonstrate the model.An algorithm that is proposed yields closed form expressions at each iteration and can also be interpreted as a discrete time adjustment process for the evolution of the economic variables.A spectrum of algorithmically solved numerical examples, with full input and output data provided, yields insights into the impacts of commodity losses, increased congestion, as well as enhanced marketing on producers as well as consumers.This new model expands the scope of spatial price equilibrium modeling under commodity losses.
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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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 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