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A Comprehensive Visual 'Wheel of Duality' in Consumer Theory

机译：消费者理论中的综合视觉“二元性轮盘”

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摘要

Duality is the heart of advanced microeconomics. It exists everywhere throughout advanced microeconomics, from the beginning of consumer theory to the end of production theory. The complex, circular relationships among various theoretical microeconomic concepts involved in the setting of duality theory have led it to be called the "wheel of pain" by many graduate economics students. Put simply, the aim of the present paper is to turn this "wheel of pain" into a "wheel of joy." This paper graphically decodes the logical, complex relationships among a quartet of dual functions which present preferences as well as a quartet of demand-related functions in a visual manner. The quartet of dual functions comprises the Direct Utility Function (DUF), Indirect Utility Function (IUF), Expenditure Function (EF), and Distance Function (DF). The quartet of demand-related functions consists of the Marshallian Demand Function (MDF), Hotelling-style Inverse Demand Function (HIDF), Hicksian Demand Function (HDF), and Antonelli-style Inverse Demand Function (AIDF).
机译：对偶性是高级微观经济学的核心。从消费者理论的开始到生产理论的结束，它存在于整个先进的微观经济学中。涉及二元性理论的各种理论微观经济学概念之间复杂而又循环的关系，导致许多研究生经济学学生将其称为“痛苦之轮”。简而言之，本文的目的是将“痛苦之轮”转变为“欢乐之轮”。本文以图形方式解码了四重对偶函数之间的逻辑，复杂关系，这些对偶函数以视觉方式呈现了偏好以及四重需求相关函数。双重功能四重奏包括直接效用函数（DUF），间接效用函数（IUF），支出函数（EF）和距离函数（DF）。与需求相关的函数四方包括Marshallian需求函数（MDF），Hotelling式逆需求函数（HIDF），Hicksian需求函数（HDF）和Antonelli式逆需求函数（AIDF）。

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