29 research outputs found

    Essential Data, Budget Sets and Rationalization

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    According to a minimalist version of Afriat’s theorem, a consumer behaves as a utility maximizer if and only if a feasibility matrix associated with his choices is cyclically consistent. An ”essential experiment” consists of observed consumption bundles (x1,xn) and a feasibility matrix α. Starting with a standard experiment, in which the economist has specific budget sets in mind, we show that the necessary and sufficient condition for the existence of a utility function rationalizing the experiment, namely, the cyclical consistency of the associated feasibility matrix, is equivalent to the existence, for any budget sets compatible with the deduced essential experiment, of a utility function rationalizing them (and typically depending on them). In other words, the conclusion of the standard rationalizability test, in which the economist takes budget sets for granted, does not depend on the full specification of the underlying budget sets but only on the essential data that these budget sets generate. Starting with an essential experiment (x1,...,xn;α), we show that the cyclical consistency of α, together with a further consistency condition involving both (x1,...,xn) and α, guarantees that the essential experiment is rationalizable almost robustly, in the sense that there exists a single utility function which rationalizes at once almost all budget sets which are compatible with (x1,...,xn;α). The conditions are also trivially necessary.Afriat’s theorem, budget sets, cyclical consistency, rational choice, revealed preference

    Revealed Preference in a Discrete Consumption Space

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    We show that an agent maximizing some utility function on a discrete (as opposed to continuous) consumption space will obey the generalized axiom of revealed preference (GARP) so long as the agent obeys cost efficiency. Cost efficiency will hold if there is some good, outside the set of goods being studied by the modeler, that can be consumed by the agent in continuous quantities. An application of Afriat's Theorem then guarantees that there is a strictly increasing utility function on the discrete consumption space that rationalizes price and demand observations in that space.Generalized axiom of revealed preference; Afriat's Theorem; discrete demand; utility maximization

    On Revealed Preference and Indivisibilities

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    We consider a market model in which all commodities are inherently indivisible and thus are traded in integer quantities. We ask whether a finite set of price-quantity observations satisfying the Generalized Axiom of Revealed Preference (GARP) is consistent with utility maximization. Although familiar conditions such as non-satiation become meaningless in the current discrete model, by refining the standard notion of demand set we show that Afriat's celebrated theorem still holds true. Exploring network structure and a new and easy-to-use variant of GARP, we propose an elementary, simple, intuitive, combinatorial, and constructive proof for the result.Afriat's theorem, GARP, indivisibilities, revealed preference.

    A measure of rationality and welfare

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    There is evidence showing that individual behavior often deviates from the classical principle of maximization. This evidence raises at least two important questions: (i) how severe the deviations are and (ii) which method is the best for extracting relevant information from choice behavior for the purposes of welfare analysis. In this paper we address these two questions by identifying from a foundational analysis a new measure of the rationality of individuals that enables the analysis of individual welfare in potentially inconsistent subjects, all based on standard revealed preference data. We call such measure minimal index.Rationality; Individual Welfare; Revealed Preference.

    The Strong Law of Demand

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    We show that a demand function is derived from maximizing a quasilinear utility function subject to a budget constraint if and only if the demand function is cyclically monotone. On finite data sets consisting of pairs of market prices and consumption vectors, this result is equivalent to a solution of the Afriat inequalities where all the marginal utilities of income are equal. We explore the implications of these results for maximization of a random quasilinear utility function subject to a budget constraint and for representative agent general equilibrium models. The duality theory for cyclically monotone demand is developed using the Legendre-Fenchel transform. In this setting, a consumer's surplus is measured by the conjugate of her utility function.Permanent income hypothesis, Afriat's theorem, Law of demand, Consumer's surplus, Testable restrictions

    Is Utility Transferable? A Revealed Preference Analysis

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    We provide a revealed preference analysis of the transferable utility hypothesis, which is widely used in economic models. First, we establish revealed preference conditions that must be satisfied for observed group behavior to be consistent with Pareto efficiency under transferable utility. Next, we show that these conditions are easily testable by means of integer programming methods. The tests are entirely nonparametric, which makes them robust with respect to specification errors. Finally, we demonstrate the practical usefulness of our conditions by means of an application to Spanish consumption data. To the best of our knowledge, this is the first empirical test of the transferable utility hypothesis.transferable utility hypothesis;generalized quasi-linearity;nonparamet- ric tests;revealed preferences

    Revealed Preference Test and Shortest Path Problem; Graph Theoretic Structure of the Rationalizability Test

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    * Revised: [15-17, 2015]* Revised: [15-17-Rev, 2015

    Is utility transferable? A revealed preference analysis.

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    We provide a revealed preference analysis of the transferable utility hypothesis, which is widely used in economic models. First, we establish revealed preference conditions that must be satisfied for observed group behavior to be consistent with Pareto efficiency under transferable utility. Next, we show that these conditions are easily testable by means of integer programming methods. The tests are entirely nonparametric, which makes them robust with respect to specification errors. Finally, we demonstrate the practical usefulness of our conditions by means of an application to Spanish consumption data. To the best of our knowledge, this is the first empirical test of the transferable utility hypothesis.

    Three Papers on Revealed Preference

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    The titles of the three papers are: Revealed Preference with a Subset of Goods; Estimating Risk Aversion from Arrow-Debreu Portfolio Choice; and, On the Goodness-of-Fit of Revealed Preference ConditionsCenter for Research on Economic and Social Theory, Department of Economics, University of Michiganhttp://deepblue.lib.umich.edu/bitstream/2027.42/101037/1/ECON474.pd

    Goods Versus Characteristics: Dimension Reduction and Revealed Preference

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    This paper compares the goods and characteristics models of the consumer within a non-parametric revealed preference framework. Of primary interest is to make a comparison on the basis of predictive success that takes into account dimension reduction. This allows us to nonparametrically identify the model which best fits the data. We implement these procedures on household panel data from the UK milk market. The primary result is that the better fit of the characteristics model is entirely attributable to dimension reduction.Characteristics; demand; dimension reduction; nested models; revealed preference
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