Assessing Cost Efficiency Thresholds in Fragmented Agriculture: A Gamma-Based Model of the Trade-Off Between Unit and Total Parcel Costs

Elena Sánchez Arnau, Antonia Ferrer Sapena, Maria Carmen Cárcel-Mas, Claudia Sánchez Arnau (Universitat Politècnica de València), Enrique A. Sánchez Pérez. Assessing Cost Efficiency Thresholds in Fragmented Agriculture: A Gamma-Based Model of the Trade-Off Between Unit and Total Parcel Costs. AppliedMath (2026), 6(1), 17; https://doi.org/10.3390/appliedmath6010017

2673-9909/6/1/17

Abstract:

Parcel size strongly influences agricultural production costs, and combining spatial and economic information within a mathematical setting helps to clarify this relationship. In this study, we introduce a Gamma-based stochastic framework to integrate actual parcel size distributions into cost estimates, an approach that, to our knowledge, has not been applied in this context. Using a representative traditional orchard system as a case study, parcel sizes (characterized by strong right skewness) are modelled with a Gamma distribution; for highly fragmented landscapes, a truncated Gamma on (0.01,1] ha yields a mean parcel area of about 0.255 ha. Results show that parcel-size heterogeneity substantially affects expected per-parcel costs; for example, calibrating ploughing at 800 EUR/ha leads to an average of ∼160 EUR/parcel, whereas intensive vegetable harvesting at 5000 EUR/ha reaches ∼2100 EUR/parcel. In our simulation, in which the main parameters have been roughly fixed with the aim of showing the methodology, results are given on an expected costs scale relative to parcel area and operation intensity. Overall, the framework shows how parcel-size distributions condition cost estimates and provides a transferable basis for comparative analyses, while acknowledging limitations related to the area-only specification.

Aplicación:

La aplicación de este enfoque a la Huerta Valenciana resulta especialmente pertinente debido a su marcada fragmentación parcelaria, su origen histórico y la coexistencia de sistemas productivos tradicionales con cultivos de alta intensidad. En este contexto, el uso de un marco basado en distribuciones Gamma permite representar de forma realista la fuerte asimetría en el tamaño de las parcelas y evaluar cómo dicha heterogeneidad condiciona los costes de producción agrícolas. Al integrar información espacial real con parámetros económicos de distintas labores (desde operaciones mecanizadas básicas hasta tareas intensivas en mano de obra), el modelo pone de relieve las desventajas económicas asociadas a la atomización del suelo agrícola característica de la Huerta.

We would like to acknowledge funding from the Generalitat Valenciana (Spain) through the PROMETEO 2024 CIPROM/2023/32 grant.