Policy problems require the specification of government choice variables, which may be prices or quantities, and the representation of preferences e.g. direct utility or distance functions. The purpose of this note is to provide an appropriate framework for switches between different descriptions of the optimization problem. We first assemble the relevant results on the matrices (Slutsky, Hessian and Antonelli) which arise in the different formulations. We then use the results to show the relationships between various analyses in the literature and finally point out how the results, whilst formally equivalent can lead to different emphases and interpretations (or misinterpretations).