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e theory of revealed preferences offers an elegant way to test the neoclassical model of utility maximization subject to a linear budget constraint. In many settings, however, the set of available consumption bundles does not take the form of a linear budget set. In this paper, we adjust the theory of revealed preferences to handle situations where the set of feasible bundles is finite. Such situations occur frequently in many real life and experimental settings. We derive the revealed preference conditions for consistency with utility maximization in this finite choice-set setting. Interestingly, we find that it is necessary to make a distinction between the cases where the underlying utility function is weakly monotone, strongly monotone and/or concave. Next, we provide conditions on the structure of the finite choice sets for which the usual revealed preference condition (i.e. GARP) is still valid. We illustrate the relevance of our results by means of an illustration based on two experimental data sets that contain choice behaviour from children and young adults.

We conducted an experiment to collect data on consumption decisions made by children of different age categories. In particular, our experiment involves unsophisticated discrete consumption choices, and we present a rationality test that is specially designed for the resulting choice data. Our first conclusion is that, in general, the observed children's consumption behavior is largely irrational. Next, we also investigate the relationship between the degree of rationality and the children's characteristics. Specifically, we use teacher based assessments on several personal characteristics to investigate whether and to what extent smart children tend to behave more rational. Here, our main conclusion is that it is important to recognize the multidimensional nature of intelligence to obtain a balanced insight into the effect of intelligence on rationality. JEL Classification: C14, C91, D12. Keywords: rationality, children, revealed preference, intelligence. IntroductionWe use experimental data to study the "rational" consumption behavior of children. Considering children of different ages, we assess the empirical validity of the rationality assumption. Next, we also explain the degree of rationality in terms of the children's personal characteristics. In this respect, a specific feature of our study is that we relate rational consumption to alternative dimensions of intelligence. In particular, we investigate how verbal skills (language) and non-verbal skills (mathematics) define the (ir)rational consumption behavior of children. Or putting it differently, are the "smart" kids more rational? And, if so, does the type of smartness matter? This introductory section motivates our research question, and indicates how this study relates to the existing literature.Motivation. The literature has devoted considerable attention to studying whether economic models are applicable to children.1 The aim is to understand the children's decision behavior, and to gain insight into the evolution of this behavior when children grow older. Clearly, a better understanding of children's economic behavior allows for a better modeling of this behavior. For instance, household consumption models that * We benefited from discussions with seminar participants in Leuven. We thank Pieter Markey for able research assistance. We are also grateful to the Fund for Scientific Research -Flanders (FWO-Vlaanderen) for financial support.

e theory of revealed preferences offers an elegant way to test the neoclassical model of utility maximization subject to a linear budget constraint. In many settings, however, the set of available consumption bundles does not take the form of a linear budget set. In this paper, we adjust the theory of revealed preferences to handle situations where the set of feasible bundles is finite. Such situations occur frequently in many real life and experimental settings. We derive the revealed preference conditions for consistency with utility maximization in this finite choice-set setting. Interestingly, we find that it is necessary to make a distinction between the cases where the underlying utility function is weakly monotone, strongly monotone and/or concave. Next, we provide conditions on the structure of the finite choice sets for which the usual revealed preference condition (i.e. GARP) is still valid. We illustrate the relevance of our results by means of an illustration based on two experimental data sets that contain choice behaviour from children and young adults.

In this paper, we combine elementary revealed preference principles and nonparametric estimation techniques in order to obtain nonparametric bounds on the distribution of the money metric utility over a population of heterogeneous households. e main benefit of our approach is that it is independent of any functional specification on the household utility functions, which means that our results are robust against parametric specification errors. We further demonstrate that our methodology can be used to establish bounds on the distribution of the demand function for counterfactual price regimes. In order to demonstrate the relevance of our approach, we illustrate our findings using a repeated cross-sectional household consumption data set. JEL-codes: D12, C14