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

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.