Robustly Optimal Contracts for Agricultural Supply Chains

Because of various factors (such as a lack of adequate statistical knowledge or data, unforeseen weather events), the yields of agricultural products often exhibit a high level of ambiguity. When facing distributional ambiguity in yields, farmers and landowners may base their contracting decisions on descriptive statistics, such as the mean and variance. To investigate how limited information could reshape optimal contract forms, we consider an agricultural supply chain in which a landowner contributes farmland and a skilled farmer exerts costly private effort to cultivate a crop. Both parties face distributional ambiguity in crop yield and employ a robust max-min decision rule. When the landowner possesses the bargaining power to draft the contract (the L model), we find that a hybrid contract of debt and equity is robustly optimal. In contrast, when the farmer possesses the bargaining power (the F model), the optimal contract could be a linear (equity) contract or a nonlinear quadratic debt contract, depending on the coefficient of variation (CV) and the landowner’s reservation profit. We use U.S. Department of Agriculture data to calibrate the model and find that, as the CV increases, the party that possesses the bargaining power tends to share more risk. We also find that when both the CV and the landowner’s reservation profit are sufficiently large, the L model induces a higher effort level; otherwise, the F model achieves better effort. Finally, we extend the model to consider various features, such as random crop price, farmer’s risk aversion and bounded crop yield. This paper was accepted by Chung Piaw Teo, optimization. Funding: G. Liang was supported by the National Natural Science Foundation of China [Grant 72101097] and the Basic and Applied Basic Research Foundation of Guangdong Province [Grant 2024B1515020056]. Supplemental Material: The online appendix and data files are available at https://doi.org/10.1287/mnsc.2022.01673 .