A Note on Commodity Taxation: The Choice of Variable and the Slutsky, Hessian and Antonelli Matrices (SHAM)
为政策问题中政府选择变量（价格或数量）和偏好表示（直接效用或距离函数）的切换提供统一框架，整理相关矩阵结果并揭示不同分析间的联系与解释差异。
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).