The demand functions that satisfy the weak axiom of revealed preference and generalized monotonicity

We prove that the individual demand function satisfying the Weak Axiom of Revealed Preference and the excess demand function satisfying the Wald’s Axiom are pseudomonotone_*⁺, a new class of generalized monotonicity. With this new concept, we refine the characterization of Zhou for the individual demand function. In particular, a full characterization for the excess demand functions satisfying the Wald’s Axiom is derived.     

What kind of preference maximization does the weak axiom of revealed preference characterize?

A (multivalued) choice is justified if no two chosen alternatives are preferred to each other, and if all chosen alternatives are preferred to all rejected alternatives. This concept permits a connection between the behavioral property expressed by WARP and a weak form of preference maximization. I am grateful to Michele Lombardi, Michael Mandler, Paola Manzini and an anonymous referee for useful discussions and comments.     

‘Regular’ choice and the weak axiom of stochastic revealed preference

We explore the relation between two ‘rationality conditions’ for stochastic choice behavior: regularity and the weak axiom of stochastic revealed preference (WASRP). We show that WASRP implies regularity, but the converse is not true. We identify a restriction on the domain of the stochastic choice function, which suffices for regularity to imply WASRP. When the universal set of alternatives is finite, this restriction is also necessary for regularity to imply WASRP. Furthermore, we identify necessary and sufficient domain restrictions for regularity to imply WASRP, when the universal set of alternatives is finite and stochastic choice functions are all degenerate. Results in the traditional, deterministic, framework regarding the relation between Chernoff’s condition and the weak axiom of revealed preference follow as special cases. Thus, general conditions are established, under which regularity can substitute for WASRP as the axiomatic foundation for a theory of choice behavior.     

Chernoff's dual axiom,revealed preference and weak rational choice functions

A new and a weaker concept of rationalizability is introduced and its implications on the properties of individual choice are investigated. Especially, (i) it is shown that a property of choice functions, called Chernoff's dual axiom in this paper, plays a crucial role for the rationality of choice, and (ii) weakening the concept of rationalizability facilitates characterization of revealed preference relations.     

强偏好、弱偏好与制度演化

通过区分强偏好与弱偏好,来分析制度的演化轨迹。强、弱偏好对制度的演化有不同的影响。由于与生存竞争关系密切,基于强偏好的制度更容易服从于进化选择,好的制度最终将被普遍接受,从而在一个同一的环境内,基于强偏好的制度将趋同。相反,弱偏好则更容易多样化。在制度形成的过程中,不同的人的影响是不对称的,而且环境是开放性的还是封闭性的,对制度形成也关系重大。在开放的环境中,好制度更容易被选择;而在封闭的环境中,个人有可能将自己不好的偏好强加于社会,形成不好的制度。     

Fuzzy revealed preference theory

Rationality has traditionally been defined as choice behaviour which can be explained in terms of some implicit binary preference. The point of departure of this paper lies in permitting the binary preference relation to be “fuzzy.” Concepts from fuzzy set theory are used to formalise different notions of rationality, including degrees of rationality. The relation between these and traditional concepts is formally explored. In welfare economics, quasi-orderings have often been used to capture the inherent imprecisions of human value judgements. It is argued here that, in many situations, a more appropriate tool for this may be fuzzy orderings.     

A revealed preference test of rationing

This paper derives a revealed preference test for utility maximization under rationing and can detect, for which goods rationing is binding without specifying a functional form or imposing rationing constraints prior to estimation. For UK data from 1920–55, we find evidence of utility maximization under rationing with rationing binding for food and other services. Estimated virtual prices exceed observed food prices by 16.5% in 1947 and observed prices of other services by 10.9% in 1952.     

Self-control,revealed preference and consumption choice

We provide a time-consistent model that addresses the preference reversals that motivate the time-inconsistency literature. The model subsumes the behavior generated by the time-inconsistency approach in finite settings but, unlike the time-inconsistent models, allows for self-control. This paper provides a brief summary of theoretical results shown elsewhere [Gul and Pesendorfer, Econometrica 69 (2001) 1403; Econometrica, (2002), in press; Rev. Econ. Stud. (2002), in press] and contrasts the predictions and welfare implications of our model and the time-inconsistent β−δ model.     

The dynamics and revealed preference of status-quo optimality

Summary In a preceding companion paper, a static model of individual decision making was proposed that, due to imprecise perceptions, induces simple and inertial behavior at equilibrium (status-quo optimal) points. This paper addresses two complementary issues. Firstly, it studies the learning dynamics induced by the model and shows that its well-defined limit behavior ranges from status-quo optimal to fully optimal, depending on the underlying features of the problem. Secondly, the paper characterizes the behavioral implications of the model and compares them with those derived from standard decision-theoretic frameworks. Specifically, it is shown that, from a Revealed-Preference perspective, status-quo optimal behavior may be identified with that rationalizable by an acyclic preference relation, possibly intransitive.     

Stable schedule matching under revealed preference

Baiou and Balinski (Math. Oper. Res., 27 (2002) 485) studied schedule matching where one determines the partnerships that form and how much time they spend together, under the assumption that each agent has a ranking on all potential partners. Here we study schedule matching under more general preferences that extend the substitutable preferences in Roth (Econometrica 52 (1984) 47) by an extension of the revealed preference approach in Alkan (Econom. Theory 19 (2002) 737). We give a generalization of the Gale-Shapley algorithm and show that some familiar properties of ordinary stable matchings continue to hold. Our main result is that, when preferences satisfy an additional property called size monotonicity, stable matchings are a lattice under the joint preferences of all agents on each side and have other interesting structural properties.     

Equivalence of the weak and strong axioms of revealed preference without demand continuity assumptions: A “regularity condition” approach

The main result of this paper is that, provided the range of the demand function is convex and the whole budget is spent, the strong axiom of revealed preference holds if and only if the weak axiom of revealed preference and a certain “regularity” condition both hold. The regularity condition is a relationship between two definitions of expenditure compensation function that must hold if the strong axiom holds. The paper distinguishes itself from previous work in that no continuity assumptions are made on the demand function. It also discusses the relationship of the regularity condition used in this paper to the one used by Uzawa and van Moeseke.     

The subjective expected utility hypothesis and revealed preference

Summary A choice behavior of a decision maker is said to satisfy the subjective expected utility hypothesis if there exist a utility and a subjective probability such that a decision maker chooses acts with the highest expected utility. We present a revealed preference characterization of choice behavior that is consistent with the subjective expected utility hypothesis. Our result applies to any state space and compact sets of prizes and observations (either finite or infinite).     

Continuous choice functions and the strong axiom of revealed preference

Summary In this note, it is shown that a result due to Uzawa showing that the weak axiom of revealed preference together with a regularity condition implies the strong axiom of revealed preference can be derived from the regularity conditionalone, if the choice function is continuous in prices and in income. The observation that the weak axiom of revealed preference is not needed suggests that this regularity condition is remarkably strong. The main result of the paper is quite general in the sense that the only additional assumption on the choice function is that the whole budget be spent.I thank Charles Blackorby for his comments on an earlier version.     

A general revealed preference theorem for stochastic demand behavior

Summary. We present a general revealed preference theorem concerning stochastic choice behavior by consumers. We show that, when the consumer spends her entire wealth, the Weak Axiom of Stochastic Revealed Preference due to Bandyopadhyay, Dasgupta, and Pattanaik (1999) is equivalent to a restriction on stochastic demand behavior that we call stochastic substitutability. We also show that the relationship between the Weak Axiom of Revealed Preference and Samuelson's inequality in the deterministic theory, and the main result of Bandyopadhyay, Dasgupta, and Pattanaik (1999) are both special cases of our result.Received: 10 September 2001, Revised: 4 April 2003, JEL Classification Numbers: D11. Correspondence to: Prasanta K. PattanaikOur greatest debt is to the referee of this paper, who made numerous helpful suggestions. We thank Robin Cubitt, Kunal Sengupta and seminar audiences at Jawaharlal Nehru University, Indian Statistical Institute, University of East Anglia, Universidad Carlos III, University of Essex and University of Montreal for their helpful comments. Prasanta K. Pattanaik acknowledges his intellectual debt to Salvador Barbera, Tapas Majumdar and Amartya Sen.     

A nonparametric revealed preference test of optimal intra-firm resource allocation

The collective rationality hypothesis initiated by Chiappori (1988a Chiappori, PA. 1988a. Rational household labor supply. Econometrica, 56: 63–89. [Crossref], [Web of Science ®] , [Google Scholar]) and applied by Seaton (1997 Seaton, JS. 1997. Neoclassical and collective rationality in household labour supply. Applied Economics Letters, 4: 529–33. [Taylor & Francis Online], [Web of Science ®] , [Google Scholar], 2001) for a two-person household is used to distinguish the organizational behaviour of firms. Firms produce satisfaction to groups as traditional managerial and early behavioural theories of the firm of Williamson, Baumol and Marris suggest, as well as more modern principle agent models. Under certain conditions, intra-firm bargaining leads to a Pareto optimal outcome. What makes this work an important contribution is that it identifies a set of nonvacuous testable restrictions to empirically detect if firm-level data satisfy Pareto optimal behaviour for the main decision makers in the organization.     

The housing problem and revealed preference theory: duality and an application

This paper exhibits a duality between the theory of revealed preference of Afriat and the housing allocation problem of Shapley and Scarf. In particular, it is shown that Afriat’s theorem can be interpreted as a second welfare theorem in the housing problem. Using this duality, the revealed preference problem is connected to an optimal assignment problem, and a geometrical characterization of the rationalizability of experiment data is given. This allows in turn to give new indices of rationalizability of the data and to define weaker notions of rationalizability, in the spirit of Afriat’s efficiency index.