A Model of Agricultural Supply Chains, Market Structure and Farm Constraints

In this chapter, we introduce the model used to study the interplay between market structure and domestic complementary factors in the production and consumption decisions of agricultural families (farms) in Africa. We are interested in modeling the production allocation of factors of production to various cash and food crops and in how this allocation depends on competition along the supply chain and on the constraints faced by different types of farmers. The model describes the behavior of farms, exporters and importers in a simple partial equilibrium setting. In particular, we build three different versions of the model to deal with the three basic scenarios that we face in our empirical work. That is, we build a model to explore the case of cash crop production (mostly for exports) in Sect. 2.1. This version can be used to study crops such as cotton, coffee, tea, tobacco, cacao, vanilla, etc. We adapt this model to deal with the case of a country that is a net exporter of a food crop in Sect. 2.2. Food crop exports can include any relevant crop in a particular country, namely maize, rice, fish, livestock, etc. Finally, we develop a different version of the model for the case of a country that is a net importer of a food crop in Sect. 2.3. The three versions of the model share common elements, such as the structure of the utility function, the constraints in production, and the market structure, but differ in the way the models are solved to account for export and import prices.