This chapter sets out a more formal theoretical framework for discussing the issues underlying capitation funding or case payments. The fundamental building block is the personal production function (PPF) for a public service, which describes the link between spending on an individual and the associated outcome. The intention is to model the optimal payment for each individual, given a payer’s efficiency and equity objectives. In order to simplify the presentation, the chapter focuses throughout on capitation methods. However, with a trivial change of terminology, the discussion is equally applicable to case payments, for example in the form of per pupil school payment mechanisms.