A revealed preference test for normal demand.

在本研究中，我们通过揭示偏好理论，考察了正常需求的可测性含义。需求正态定义为消费者需求相对于收入水平的单调性，这在微观经济学中经常被强加(主要是应用)。本研究的主要目的是对价格-消费对等可观测数据集的正常需求假设进行检验，从而得到了在两种商品模型中，有限的价格-消费数据集与收入水平上单调的需求函数一致的充要条件。我们的构造性证明还表明，效用函数的凹性和超模联合假设在有限数据下是不可反驳的。效用函数的这一性质是单调比较统计文献中众所周知的正常需求的充分条件。此外，通过应用我们的正态检验，我们得到了可以从给定的有限数据集和正态需求的假设中计算出的最紧需求界限(需求预测集)。对于一般的n-商品模型，通过推广两种商品情形的充要条件，得到了与正常需求一致的充要条件，该条件在给定的数据集上也很容易执行。

In this study, through the revealed preference theory, we investigate testable implications of normal demand. The normality of demand is defined as the monotonicity of consumer's demand with respect to income level, which is often imposed in (mainly applied) microeconomics. Our primal goal in this study is to construct a test for the hypothesis of normal demand that can be executed from observable data set like price-consumption pairs.As a result, in two-commodity model, we derived a set of necessary and sufficient condition under which a finite set of price-consumption data is consistent with some demand function that is monotonic in income level. Our constructive proof also shows that the joint assumption of concavity and supermodularity on utility functions is non-refutable from finite data. This property of a utility function is a well-known sufficient condition for normal demand in the literature of monotone comparative statics.In addition, by applying our test for normality, we derive the tightest demand bound (demand prediction set) that can be calculated from a given finite data set and the hypothesis of normal demand. Note that, given a finite set of observation, both the test for our necessary and sufficient condition and the calculation of demand bounds are easily executed.For general n-commodity models, by extending the necessary and sufficient condition for two-commodity case, we get a necessary condition for the consistency with normal demand, which is also easily executed from a given data set.