A seasonal model of contracts between a monopsonistic processor and smallholder pepper producers in Costa Rica

We model the contractual arrangements between smallholder pepper (Piper nigrum L.) producers and a single processor in Costa Rica. Producers in the El Roble settlement sell their pepper to only one processing firm, which exerts its monopsonistic bargaining power by setting the purchase price of fresh pepper. It also sets quality norms that result in the rejection of considerable amounts of the pepper produced by individual farmers. Because the firm is not able to produce its own raw pepper and requires a sufficiently stable flow of the fresh product to be processed into high quality white pepper, it usually relies on contracts with individual smallholders. Nevertheless, the latter considered collective marketing and took the initiative to propose a group contract with the firm. Such a contract increases the producers' bargaining power vis-à-vis the processing firm and reduces rejection rates as more care is taken when transporting the pepper to be processed. Although a group contract causes the firm to lose part of its monopsonistic rents, it also reduces transaction costs as only one contract must be negotiated instead of many. Both the firm and the producers benefit, yet from the very beginning of the association, the producers breached the group contract. We have used a mixed integer linear model which, given a set of constraints, maximises the weighted sum of the expected incomes of the firm and producers. We modelled the contract chosen by the firm and the producers according to the conditions included, such as minimum income requirements and risk considerations of both processor and farmers. We calibrated the model with data from pepper producers and the firm in El Roble. The results show that at different fresh pepper prices, the contract preferred changes with the bargaining power attributed to the firm and smallholders. However, in general, it can be concluded that fresh pepper prices high enough to cover the costs, for the farmers, of a group contract lead to lower rejection rates, and thus to more pepper of an acceptable quality, increasing the incomes of both the processor and the farmers. This is also of interest in agricultural policy-making.