A Note on Different Approaches to Index Number Theory
区分了指数理论的公理化方法和经济方法，指出两者差异在于是否假设优化行为来自同一效用函数，并探讨这对实际收入指标含义的影响。
In the literature, two approaches to index numbers are distinguished: the axiomatic approach and the economic approach. In this note we discuss the way in which these two approaches differ and how that affects what the numbers mean. The difference is regularly described as one between an approach that does and an approach that does not assume that quantities arise from optimizing behaviour. We argue that a more accurate description is that the difference lies in whether or not optimizing agents, or representative consumers, are assumed to optimize the same utility function. It is exactly this distinction that sets the (different) limitations of both approaches for constructing a meaningful indicator of real income.