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.     

‘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.     

Testing for Utility Maximization with Error and the Loss of Power

A procedure is suggested to decide whether or not to treat a consumer who violates the Generalized Axiom of Revealed Preference as ‘close enough’ to utility maximization. It is based on the reduction of the power the test has against random behaviour. It can also be used to compare different efficiency indices.     

Revealed preference and differentiable demand

Summary. We prove that, for finitely many demand observations, the Strong Axiom of Revealed Preference tests not only the existence of a strictly concave, strictly monotone and continuous utility generator, but also one that generates an infinitely differentiable demand function. Our results extend those of previous related results (Matzkin and Richter, 1991; Chiappori and Rochet, 1987), yielding differentiable demand functions but without requiring differentiable utility functions.Received: 1 November 2001, Revised: 5 February 2004, JEL Classification Numbers: D11, D12. Correspondence to: Kam-Chau WongThis is a much revised version of Lee and Wong (2001). We are grateful to the Referee for valuable suggestions. We also thank Professor Marcel K. Richter for his comments.     

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.     

Two new proofs of Afriat’s theorem

Summary. We provide two new, simple proofs of Afriats celebrated theorem stating that a finite set of price-quantity observations is consistent with utility maximization if, and only if, the observations satisfy a variation of the Strong Axiom of Revealed Preference known as the Generalized Axiom of Revealed PreferenceReceived: 12 June 2003, Revised: 9 October 2003, JEL Classification Numbers: D11, C60.Correspondence to: A. Fostel     

Demand Aggregation and the Weak Axiom of Stochastic Revealed Preference

We address the problem of aggregating demand across a group of consumers, who are identical in terms of wealth and face identical price vectors, but vary in their chosen consumption bundles. We show that, when a stochastic demand function is constructed to aggregate a number of deterministic demand functions, satisfaction of the weak axiom of stochastic revealed preference by this stochastic demand function is weaker than the restriction that every underlying deterministic demand function satisfy Samuelson's weak axiom of revealed preference. Journal of Economic Literature Classification Number: D11.     

A simplified test for preference rationality of two-commodity choice

We provide a simplified test to determine if choice data from a two-commodity consumption set satisfies the Generalized Axiom of Revealed Preference (GARP), and thus the preference or utility maximization hypothesis. We construct an algorithm for this test and illustrate its application on experimental choice data. JEL Classification C91, D11, D12 An erratum to this article is available at .     

Learning buyers' valuation distribution in posted-price selling

Summary. For his proof of the existence of a general competitive equilibrium Abraham Wald assumed a strictly pseudomonotone inverse market demand function or, equivalently, that market demand satisfies the Weak Axiom of Revealed Preference. It is well known that more recent existence theorems do not need this assumption. In order to clarify its role in Wald's proof, the question of existence of an equilibrium for a modified version of the Walras-Cassel model is reduced to the solvability of a related variational inequality problem. In general, the existence of a solution to such a problem can only be proved by advanced mathematical methods. We provide an elementary induction proof which demonstrates the essence of Abraham Wald's famous contribution. Received: July 22, 1997; revised version: December 11, 1997     

Consistent firm choice and the theory of supply

Summary. This paper analyzes the problem of deriving predictions, regarding supply behavior of a competitive firm, from prior consistency postulates about input-output choices made by such a firm. It extends the literature by introducing a consistency postulate for firm choice, which is weaker than profit-maximization. This consistency postulate is nevertheless both necessary and sufficient for supply responses predicted by the standard theory of firm choice based on the postulate of profit-maximization. Furthermore, our rationality postulate, in conjunction with another condition, is shown to be equivalent to firm choice behavior that can be rationalized in terms of profit maximization.Received: 11 April 2003, Revised: 26 April 2004, JEL Classification Numbers: D21.Indraneel Dasgupta: I thank Bhaskar Dutta and two anonymous referees for helpful comments on earlier versions.     

The Law of Comparative Advantage Without Social Utility Functions

This paper derives sufficient conditions under which the Law of Comparative Advantage and the General Law of Comparative Advantage are true when the preferences of the trading countries may not be represented by "well-behaved" social utility functions. It shows that in the neoclassical framework with convex technologies, profit maximization and Walras' Law, the laws of comparative advantage under a natural trade are still valid if either the General Law of Demand or the Weak Axiom of Revealed Preference holds, or if losers are compensated using lump-sum transfers or consumption taxes.     

Characterization of generalized weak orders and revealed preference

Summary This short paper provides an alternative framework to axiomatize various binary preference relations such as semiorder, weak semiorder etc. A set of simple axioms is presented in terms of revealed-preferred and revealed-inferior alternatives which makes the connection between various binary preference relations transparent; and every single axiom is necessary and sufficient for the existence of a binary preference relation of a specified type.We thank Bhasker Dutta, Peter Fishburn, Prasanta Pattanaik, Robert Russell and Thomas Schwartz for helpful suggestions     

A note on Bossert,Pattanaik and Xu's “Choice under complete uncertainty: axiomatic characterization of some decision rules”

Summary. Recent work by Bossert, Pattanaik and Xu provides axiomatic characterizations of some decision rules for individual decision making under complete uncertainty. This note shows that, in the case of two of these rules, they do not satisfy one of the axioms used for their characterization. A counterexample illustrating this fact is provided, as well as an alternative way to characterize the two rules under consideration, mantaining as far as possible the original axioms proposed by Bossert, Pattanaik and Xu. Received: November 3, 2000; revised version: March 1, 2002 RID="*" ID="*" I am grateful for the encouragement and support of Professor Prasanta Pattanaik. I thank also the suggestions of two anonymous referees. This work was made during an academic visit to the Department of Economics of the University of California in Riverside (UCR). The visit was possible thanks to an invitation by the UCR and the financial support of the Public University of Navarra, the Government of Navarra, and the CICYT (SEC96-0858).     

A class of fair distribution rules à la Rawls and Sen

Summary. This paper discusses and develops “non-welfaristic” arguments on distributive justice à la J. Rawls and A. K. Sen, and formalizes, in cooperative production economies, “non-welfaristic” distribution rules as game form types of resource allocation schemes. First, it conceptualizes Needs Principle which the distribution rule should satisfy if this takes individuals' needs into account. Second, one class of distribution rules which satisfy Needs Principle, a class of J-based Capability Maximum Rules, is proposed. Third, axiomatic characterizations of the class of J-based Capability Maximum Rules are provided. Received: July 30, 1999; revised version: March 11, 2002 RID="*" ID="*" We are grateful to an anonymous referee of this journal, Professors Marc Fleurbaey, Nicolas Gravel, Ryo-ichi Nagahisa, Prasanta Pattanaik, Kotaro Suzumura, Koich Tadenuma, and Yongsheng Xu for their fruitful comments. An earlier version of this paper was published with the title name, “A Game Form Approach to Theories of Distributive Justice: Formalizing Needs Principle” as the Discussion Paper No. 407 of the Institute of Social and Economic Research, Osaka University, and in the proceedings of the International Conference on Logic, Game, and Social Choice held at Oisterwijk in May 1999. That version was also presented at the 3rd Decentralization Conference in Japan held at Hitotsubashi University in September 1997, at the annual meeting of the Japan Association of Economics and Econometrics held at Waseda University in September 1997, and the 4th International Conference of Social Choice and Welfare held at University of British Colombia in July 1998. This research was partially supported by the Japanese Ministry of Education and the Ministry of Health and Welfare. Correspondence to: N. Yoshihara     

Weak axiomatic demand theory

This paper identifies a class of complete but not necessarily transitive preferences which generate demand functions that obey the weak axiom of revealed preference and within which any function obeying the weak axiom can be rationalized.     

Environmental Risk and Averting Behavior: Predictive Validity of Jointly Estimated Revealed and Stated Behavior Data

We conduct predictive validity tests using revealed and stated behavior data from a panel survey of North Carolina coastal households. The application is to hurricane evacuation behavior. Data was initially collected after Hurricane Bonnie led to hurricane evacuations in North Carolina in 1998. Respondents were asked for their behavioral intentions if a hurricane threatened the North Carolina coast during the 1999 hurricane season. Following Hurricanes Dennis and Floyd in 1999, a follow-up survey was conducted to see if respondents behaved as they intended. A jointly estimated revealed and stated behavior model indicates that the hypothetical and real evacuation behavior is based on the same choice process. Using predictions from this model with a hypothetical bias correction, we find that it predicts actual evacuation behavior with a small forecast error. These results suggest that stated behavior data has some degree of predictive validity.     

Identifying optimal contingent fiscal policies in a business cycle model

Optimal fiscal policy is indeterminate in a dynamic and stochastic environment. The complete characterization of the fiscal policy requires the use of identification constraints. In the literature either capital taxes or debt have been restricted to be not contingent on the state of nature. We propose a different type of identification constraints to have both policy variables state-contingent. Three alternative identification conditions are considered: (i) restrictions on the dynamic and stochastic behavior of the debt path; (ii) an exogenous debt path, and (iii) an exogenous belief function. The main result indicates that the optimal capital tax is zero and constant over the business cycle for any of the identification conditions used, suggesting that is optimal for the government to use debt return as a shock absorber, keeping capital taxes constant. The result is quite different from the previous literature, which obtains very volatile capital taxes. JEL Classification: E62, H21. We are grateful to Alfonso Novales, Víctor Ríos-Rull, Javier Vallés and two anonymous referees for helpful comments and suggestions. We acknowledge financial support from Spanish Ministerio de Ciencia y Tecnología (Ruiz and Pérez: BEC 2003-039; Manzano: BEC 2002-01995). Baltasar Manzano also acknowledges support from Xunta de Galicia (PGIDIT03PXIC30001PN, PGIDIT03CSO30001PR).     

Revealed stochastic preference: a synthesis

Summary. The problem of revealed stochastic preference is whether probability distributions of observed choices in a population for various choice situations are consistent with a hypothesis of maximization of preference preorders by members of the population. This is a population analog of the classical revealed preference problem in economic consumer theory. This paper synthesizes the solutions to this problem that have been obtained by Marcel K. Richter and the author, and by J. C. Falmagne, in the case of finite sets of alternatives, and utilizes unpublished research of Richter and the author to give results for the non-finite choice sets encountered in economic consumer theory.Received: 13 March 2003, Revised: 11 February 2004, JEL Classification Numbers: D1, C6.The preparation of this paper was supported by the E. Morris Cox endowment at the University of California, Berkeley. I am indebted to Robert Anderson, Salvador Barbara, Werner Hildenbrand, Rosa L. Matzkin, and Aviv Nevo for useful suggestions and comments. I am especially indebted to Marcel K. Richter, who was the source of many of the ideas and arguments contained in this paper.     

Options can induce risk taking for arbitrary preferences

Summary. It is widely believed that call options induce risk-taking behavior. However, Ross (2004) challenges this intuition by demonstrating the impossibility of inducing managers with arbitrary preferences to always act as if they were less risk averse. If preferences and price distributions are unknown, risk-taking behavior cannot be always induced by an option contract. Here, we prove a new result showing that, with no information about preferences and some knowledge about prices, one can write a call option that makes all managers prefer riskier projects to safer ones. This points out that in order to design options that induce risk taking it is sufficient to have information about price distributions.Received: 5 November 2003, Revised: 1 November 2004, JEL Classification Numbers: D81, G00, J33, M21. Correspondence to: Luis H.B. BraidoWe thank Renée Adams, Heitor Almeida, Carlos E. da Costa, Andrew Horowitz, Paulo K. Monteiro, Walter Novaes, Sergio O. Parreiras, Rodrigo R. Soares, and especially Marcos Tsuchida for many helpful comments.     

Stochastic growth with a likelihood-increasing estimation process

Summary. We formulate an optimal estimation process in a stochastic growth model with an unknown true probability model. We consider a general reduced model of capital accumulation with an infinite horizon and introduce a learning process in the stochastic dynamic programming. When the only available information is a sample realization generated by a stationary and ergodic stochastic process, we prove that the optimal estimation process based on likelihood-increasing behavior converges to the true probability measure and the likelihood-increasing estimator defines a transition function on the sample space.Received: 24 January 2004, Revised: 18 February 2005, JEL Classification Numbers: C13, C44, C61, O41.An earlier version of this paper was presented at the annual Meeting of the Japanese Economic Association at the University of Tokyo, at the annual Conference of the Japan Society for Industrial and Applied Mathematics at Keio University, and at the 7th Czech-Japan Seminar on Data Analysis and Decision Making under Uncertainty in Awaji Island. I have benefited from useful comments from Hidetoshi Komiya, Andrew McLennan, Toru Maruyama, Nancy Stokey, Shinichi Suda, Shin-Ichi Takekuma, Akira Yamazaki, and an anonymous referee. I would also like to thank Fumihiro Kaneko for invaluable technical discussions. This research was partly supported by Grant-in-Aid for Scientific Research (No. 14730021) from the Japan Society for the Promotion of Science.