This is Chapter 3 of my PhD thesis Understanding the World Wool Market: Trade, Productivity and Grower Incomes, UWA, 2006. The full thesis is available as Discussion Papers 06.19 to 06.24. The purpose of this chapter is twofold: first, to present the theoretical structure of the model to be applied in Chapters 5 and 6; second, to derive alternative model closures. This and the next section provide a brief overview of the methodology underlying the theoretical structure of the model.