Farming contract design with random yield and private farmer information

We study an agricultural supply chain in which a distributor purchases products from a farmer who holds private information regarding their own random yield and costs. We develop an efficiency index to streamline the farmer's three pieces of private information and categorise the farmer as either efficient or inefficient. Following the principal-agent model, we design the optimal forward contract menu for the distributor. Our findings indicate that when the probability of an efficient farmer is low, the distributor will engage both types of farmers. Conversely, when this probability is high, a contract is exclusively offered to the efficient farmer. Interestingly, while improvements in the farmer's efficiency consistently benefit the distributor, they may either increase or decrease the farmer's expected profit. Additionally, the farmer's production cost has a more substantial impact on both parties' profits and values of information than the backup cost. Finally, we analyse the contract design problem with risk-averse farmers to highlight the impact of the farmers' risk aversion on the agriculture supply chain.