A variational inequality trade network model in prices and quantities under commodity losses
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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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 | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.002 | 0.001 |
| Insufficient payload (model declined to judge) | 0.004 | 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 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".