This study reports the results of farmers’ production via irrigation resources utilization and efficiency parameters of technical efficiency and allocative efficiency by way of sustainable environmental economics. The hypothesis is that factors of farmers’ production affect technical efficiency and allocative efficiency in the irrigation scheme as sustainable environmental economics. Data from cross section and panel data were used and then the productivity parameters measurement of the production function are outlined in two scenarios: first, the data report that the parameters such as output elasticity determine factors of inefficiency and technical efficiency. Second, it presents the scores for the allocative efficiency to explain whether production factors (resources) are optimally, under- or over-allocated by farmers in the irrigation systems under environmental sustainability. This paper presents the productivity and efficiency parameters estimated using stochastic frontier analysis for the translog production function, which was estimated by the MLE method, and the allocative efficiency for the factor inputs allocation in the irrigation systems estimated by ordinary least square for the Cobb-Douglas production function. This study concludes that collective farmers lead into technical inefficiency and over use of factors of production.

Rwanda’s sustainable green economy agenda has placed irrigation and input-support schemes at the centre of efforts to raise tropical fruit productivity in the Mugesera region, yet the econometric analysis presented, in a Cobb–Douglas production function estimated by panel OLS and a Nerlove partial-adjustment model of agricultural supply response required the analyst to pre-specify a log-linear, constant-elasticity functional form. This paper asks whether machine learning methods that learn input–output relationships directly from data can cross-check those findings, and presents a documented Python version 3.10.12 pipeline for doing so. Using a synthetic panel dataset (six regions, 2009–2018, N = 346 farm-year observations) calibrated to match the elasticity magnitudes reported in the original Cobb–Douglas estimation, three models—multiple linear regression, random forest, and gradient boosting—are trained on land, fertilizer, seed, lagged price, and lagged output features, and are evaluated on held-out data. All three models explain a substantial share of variation in output (R² between 0.72 and 0.75 under a random split; for results under panel-aware validation), with tuned gradient boosting achieving the best accuracy under the random split (R² = 0.751, RMSE = 0.268). Permutation feature importance recovers the same relative ranking of input variables as the original regression—fertilizer, then seeds, then land area—without the model being given the Cobb–Douglas functional form in advance. Because the synthetic data were explicitly generated to reproduce these elasticities, this recovery demonstrates that the modelling pipeline behaves as intended; it is a calibrated methodological demonstration and not an independent empirical validation of the original findings. The results are consistent with lagged price and output operating mainly through farmers’ input decisions rather than as direct predictors of output once input quantities are known, although we present this as a hypothesis for future testing rather than a demonstrated finding. Re-running the identical pipeline on real Mugesera farm-level survey microdata is the necessary next step before these results can be treated as genuine empirical findings; this caveat applies to every quantitative result reported below, not only to the conclusion.