A quantitative framework to analyse cooperation between rural households

Different types of cooperative agreements between smallholders continue to play an important role in rural areas in developing countries. While some empirical studies examine the conditions catalysing the successful formation of cooperatives, quantifications of the net benefits, i.e., difference between revenues and costs, of cooperation and how farmers divide these net benefits are scarce. Therefore, we develop a quantitative framework to analyse and allocate net benefits in a cooperative production agreement. The framework allows for cooperative exchange of several types of resources and the production of multiple products. Linear programming provides insight into optimal production levels, both for individual and cooperating farmers, and gives optimal revenue levels. A transaction cost function is used to account for costs of cooperation, such as meeting costs, moral hazard and free ridership of labour use and the risks of farmers defaulting from the agreement. Transaction costs are likely to increase with the number of households participating, the total cropping area and the heterogeneity of resources of the cooperating farmers. Therefore, we introduce a measure of heterogeneity in the resources for each cooperative. Finally, cooperative game theory is used to generate fair divisions of the net benefits in a cooperative. This framework may be used to give additional explanations to the findings in empirical studies on cooperatives. We illustrate this with an empirical example from northern Nigeria. It is found that cooperation between farmers sharing complementary resources gives the highest revenues. Next, we illustrate the effects of two different transaction cost functions. For reasonable assumptions on these functions, cooperation remains economically attractive. Nevertheless, larger and more diverse coalitions are not always the most beneficial, while the returns in some small coalitions are negative, possibly impeding the formation of cooperatives in some locations.