A revealed preference test for normal demand.

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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.