Duality and Modern Economics.
本书用几何方法直观解释对偶理论的基本结构，介绍偏好、技术、间接效用、支出、成本、利润等函数的表示与关系，适合想理解对偶分析的经济学学生和研究者。
Dual arguments have become a standard tool for analysis of problems involving optimization by consumers and producers. The principal aim of this book is to provide a fairly systematic yet simple exposition of the basic structure of such arguments. The emphasis is not on providing mathematically general proofs; instead, a geometric approach is used to provide, in an informal way, an intuitive understanding of duality theory. This book introduces the most common alternative ways of representing preferences and technologies, such as indirect utility and distance functions, expenditure and cost functions, and profit and revenue functions. and it discusses the assumptions under which alternative formulations contain precisely the same information. Results such as Roy's identity. the Hotelling-Wold identity, and Shephard's lemma are fully explained. as are their roles in facilitating analysis of behaviour.