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.     

Is Kreps-Porteus utility distinguishable from intertemporal expected utility?

Summary In a Lucas (1978) model, with a Kreps-Porteus (1978) nonexpected utility, the following property of equilibrium holds generically in the space of finite-state, Markov output growth rate processes: equilibrium price of equity is distinct from that implied by any intertemporally additive expected utility satisfying specified regularity conditions. In that sense the more general utility functions are observationally distinguishable from the standard expected utility specification.I would like to thank Larry G. Epstein for posing to me the problem studied in this paper and for many suggestions and comments. I am also grateful to Darrell Duffie for helpful suggestions. I am responsible for errors. This papers is part of my Ph.D. thesis at University of Toronto.     

Competitive equilibrium when preferences change over time

Summary. We show the existence of a competitive equilibrium in an economy with many consumers whose preferences may change over time. The demand correspondence of an individual consumer is determined by the set of subgame-perfect equilibrium outcomes in his intrapersonal game. For additively separable preferences with concave period utility functions that are unbounded above, this demand correspondence will satisfy the usual boundary conditions. Whenever consumers can recall their own mixed actions, this correspondence is convex-valued. This ensures the existence of a symmetric competitive equilibrium.Received: 29 July 2004, Revised: 17 November 2004, JEL Classification Numbers: D51, D91, C73. Correspondence to: Thomas MariottiWe thank Michele Piccione for useful comments and suggestions. The views expressed herein are those of the authors and not necessarily those of the Federal Reserve Bank of Minneapolis or the Federal Reserve System.     

Market clearing, utility functions, and securities prices

Summary. We prove the existence of equilibrium in a continuous-time finance model; our results include the case of dynamically incomplete markets as well as dynamically complete markets. In addition, we derive explicitly the stochastic process describing securities prices. The price process depends on the risk-aversion characteristics of the utility function, as well as on the presence of additional sources of wealth (including endowments and other securities). With a single stock, zero endowment in the terminal period, and Constant Relative Risk Aversion (CRRA) utility, the price process is geometric Brownian motion; in essentially any other situation, the price process is not a geometric Brownian motion.JEL Classification Numbers: D52.This paper is part of my Dissertation (UC Berkeley). I am very grateful to my advisor Professor Robert M. Anderson. I also would like to thank Steve Evans, Roger Purves, Jacob Sagi, Chris Shannon and the participants of the 2002 NBER General Equilibrium Conference at the University of Minnesota (Minneapolis) for very helpful discussions and comments. This work was supported by Grant SES-9710424 from the National Science Foundation.     

An efficiency characterization of plurality social choice on simple preference domains

Summary. We consider a model of social choice dealing with the problem of choosing a subset from a set of objects (e.g. candidate selection, membership, and qualification problems). Agents have trichotomous preferences for which objects are partitioned into three indifference classes, goods, bads, and nulls, or dichotomous preferences for which each object is either a good or a bad. We characterize plurality-like social choice rules on the basis of the three main axioms, known as Pareto efficiency, anonymity, and independence.Received: 29 August 2003, Revised: 3 June 2004, JEL Classification Numbers: D70, D71, D72.Biung-Ghi Ju: I am grateful to William Thomson and Jianbo Zhang for their helpful comments and discussions. I also thank Brandon Dupont, the participants in seminars at Iowa State University, University of Kansas, and the Midwest Theory Meeting at University of Notre Dame. I thank an anonymous referee for detailed comments and suggestions that were very helpful in simplifying the proof of Theorem 1 and in revising the paper.     

An Agency Perspective on the Costs and Benefits of Privatization

This paper proposes a unified theoretical framework to discuss the costs and benefits of privatization using the recent advances of Incentive Theory. I begin by presenting a simple model in which the State (the principal) delegates a task (e.g., the production of a public good) to the private sector (the agent). I give and discuss conditions for the “Irrelevance Theorem” due to Sappington and Stiglitz [Sappington, D., & Stiglitz, J. (1987) Journal of Policy Analysis and Management, 6, 567–582] to hold under complete contracting. I then show how various contract incompletenesses can make either public or private ownership optimal. Finally, I provide critical assessments of these results. I thank Patrick Rey and Wilfried Zantman for useful comments on an earlier draft. The excellent comments of two referees have also improved substantially the presentation and organization of the paper. I am deeply indebted to Denis Gromb for his extremely detailed comments.     

Temporal and thermodynamic irreversibility in production theory

Summary. The two notions of temporal and thermodynamic irreversibility are distinguished. It is shown that the irreversibility concept of Arrow-Debreu, while establishing temporal irreversibility, does not encompass thermodynamic irreversibility. This means, the standard irreversibility concept of production theory is too weak to be in full accordance with the laws of nature.Received: 8 October 2001, Revised: 5 April 2004, JEL Classification Numbers: D20,D51,D92.For helpful comments and discussion I am grateful to Malte Faber, Andreas Lange, Martin Quaas, Armin Schmutzler and seminar participants at Berkeley, Il Ciocco, Delft, Strasbourg and Rethymno.     

The structure of the set of sunspot equilibria in economies with incomplete financial markets

Summary This paper considers the set of equilibria of two-period, sunspot economies withS purely extrinsic states of nature in the second period andI assets with linearly independent nominal payoffs. The span of the payoff matrix contains the vector [1, ... , 1] (i.e., inside money). The set of economies is described in terms of (sunspot-invariant) utility functions. IfS>I> 0, there is an open, dense set of economies such that, given a vector of no arbitrage asset prices, the set of equilibrium allocations contains a smooth manifold of dimensionS—I. Such a manifold contains at least one nonsunspot equilibrium (and at most a finite number of such equilibria).The paper was written while I was a visitor at C.O.R.E., Universitè Catholique de Louvain, with the financial support of a S.P.E.S. fellowship. I would like to thank D. Cass, H. Polemarchakis and P. Siconolfi for their helpful comments.     

Nash and Walras equilibrium via Brouwer

Summary. The existence of Nash and Walras equilibrium is proved via Brouwer's Fixed Point Theorem, without recourse to Kakutani's Fixed Point Theorem for correspondences. The domain of the Walras fixed point map is confined to the price simplex, even when there is production and weakly quasi-convex preferences. The key idea is to replace optimization with “satisficing improvement,” i.e., to replace the Maximum Principle with the “Satisficing Principle.” Received: July 9, 2001; revised version: February 25, 2002 RID="*" ID="*" I wish to thank Ken Arrow, Don Brown, and Andreu Mas-Colell for helpful comments. I first thought about using Brouwer's theorem without Kakutani's extension when I heard Herb Scarf's lectures on mathematical economics as an undergraduate in 1974, and then again when I read Tim Kehoe's 1980 Ph.D dissertation under Herb Scarf, but I did not resolve my confusion until I had to discuss Kehoe's presentation at the celebration for Herb Scarf's 65th birthday in September, 1995. RID="*" ID="*"Correspondence to: C. D. Aliprantis     

The cone condition,properness, and extremely desirable commodities

Summary This note links two conditions which have generated some interest in the literature and have an important role in proving the existence of an equilibrium, the second welfare theorem and the core equivalence theorem in infinite dimensional commodity spaces: These are thecone condition introduced in Chichilnisky and Kaiman (1980), and theproperness condition in Mas-Colell (1986a), which were studied also in Yannelis and Zame (1986), Aliprantis et al. (1987a, b) and (1989), Aliprantis and Burkinshaw (1988), Mas-Colell (1986b), Chichilnisky and Heal (1984, 1992), and Rustichini and Yannelis (1991) among others. I establish that these two conditions are the same. Indeed, the cone condition coincides also with the assumption of anextremely desirable commodity used in Yannelis and Zame (1986) and Rustichini and Yannelis (1991). The motivation for studying these conditions comes from the same economic application, showing the need to bring within the scope of equilibrium theory commodity spaces whose positive orthants have empty interior, a typical situation in infinite dimensional linear spaces.I thank the participants of several seminars and workshops, two anonymous referees, CD. Aliprantis, D. Brown, D. Cass, D. Foley, G. Heal, H-M. Wu, A. Khan, R. Radner, A. Rustichini and N. Yannelis, for their comments and suggestions. Hospitality and financial support from the Stanford Institute for Theoretical Economics during the summer of 1991 is gratefully acknowledged.     

Candidate stability and probabilistic voting procedures

Summary. We extend the analysis of Dutta, Jackson and Le Breton (Econometrica, 2001) on strategic candidacy to probabilistic environments. For each agenda and each profile of voters preferences over running candidates, a probabilistic voting procedure selects a lottery on the set of running candidates. Assuming that candidates cannot vote, we show that random dictatorships are the only unanimous probabilistic voting procedures that never provide unilateral incentives for the candidates to withdraw their candidacy at any set of potential candidates. More flexible probabilistic voting procedures can be devised if we restrict our attention to the stability of specific sets of potential candidates.Received: 4 February 2003, Revised: 14 September 2004, JEL Classification Numbers: D71, D72.This is a revised version of a chapter of my Ph.D. Dissertation submitted to the Universitat Autónoma de Barcelona. I am indebted to my supervisor Salvador Barberá for his advice and constant support. I am grateful to Dolors Berga and an anonymous referee for their detailed comments and suggestions. I thank José Alcalde, Walter Bossert, Bhaskar Dutta, Lars Ehlers, Jordi Massó, Diego Moreno, Clara Ponsatí, Yves Sprumont, and William Thomson for many helpful comments and discussions. I thank the hospitality of the C.R.D.E. at the Université de Montréal and the Department of Economics of the University of Warwick where parts of this research were conducted. Financial support through Research Grant 1998FI00022 from Comissionat per Universitats i Recerca, Generalitat de Catalunya, Research Project PB98-870 from the Ministerio de Ciencia y Tecnología, and Fundación Barrié de la Maza is gratefully acknowledged.     

Eliciting the core of a supermodular capacity

Summary. The paper utilizes duality theory to derive an exact representation of the core of a supermodular capacity for finite-state-space Choquet expected utility preferences. Using the dual representation we develop an algorithm that uses information on willingness to pay and willingness to sell to elicit a supermodular capacity in a finite number of iterations.Received: 21 February 2003, Revised: 26 May 2004, JEL Classification Numbers: D81. Correspondence to: Robert G. ChambersThe authors thank J. Quiggin and an anonymous referee for comments that improved the paper.     

A short proof of the Bulow-Klemperer auctions vs. negotiations result

Summary. Bulow and Klemperer [1] have provided an upper bound on the value of bargaining power for a seller of an indivisible object. Specifically, negotiating optimally with N buyers yields lower revenue than an English auction with N + 1 buyers. In this paper, a short and intuitive proof of this result is presented.Received: 2 August 2004, Revised: 6 December 2004, JEL Classification Numbers: C78, D44, D82.I would like to thank Per B. Overgaard and an anonymous referee for many valuable comments.     

Intertemporal substitution, risk aversion and ambiguity aversion

Summary. This paper axiomatizes a form of recursive utility on consumption processes that permits a role for ambiguity as well as risk. The model has two prominent special cases: (i) the recursive model of risk preference due to Kreps and Porteus [18]; and (ii) an intertemporal version of multiple-priors utility due to Epstein and Schneider [8]. The generalization presented here permits a three-way separation of intertemporal substitution, risk aversion and ambiguity aversion.Received: 5 August 2003, Revised: 12 March 2004, JEL Classification Numbers: D80, D81, D90.I am grateful to Larry Epstein for his guidance and invaluable advice, and to a referee for helpful comments and suggestions.     

Linear Inequality Methods to Enforce Partnerships under Uncertainty: An Overview

We review different (generic) conditions on stochastic outcome functions to enforce either efficient or nearly efficient partnerships. Their logical relationship is explored. Two kinds of conditions are considered. However, the property for an action profile to be “compatible” plays a crucial role in both kinds. Also, two kinds of enforcement mechanisms are considered: enforcement through utility transfers and enforcement through repetition.Journal of Economic LiteratureClassification Numbers: D2, D7.     

Expected utility inequalities: theory and applications

Suppose we know the utility function of a risk averse decision maker who values a risky prospect X at a price CE. Based on this information alone I develop upper bounds for the tails of the probabilistic belief about X of the decision maker. In the paper I also illustrate how to use these expected utility bounds in a variety of applications, which include the estimation of risk measures from observed data, option valuation, and the study of credit risk. I would like to thank John Cochrane, Tom Cosimano, Amanda Friedenberg, George Korniotis, Markus Brunermeier and Paul Schultz for helpful discussions and to participants at two Notre Dame seminars, at the 2006 Spring Midwest Economic Theory and International Economics Conference, and at the 2006 Australasian Meeting of the Econometric Society for their very useful comments. I began working on this project during a year-long visit to the Central Bank of Venezuela. I gratefully acknowledge their hospitality and financial support.     

An application of the SF-6D to create heath values in Portuguese working age adults

Objectives: This study describes the health-related quality of life (HRQOL) of the Portuguese working age population and investigates sociodemographic differences.

Methods: Subjects randomly selected from the working age population (n=2,459) were assessed using the SF-36v2 and converted into the preference-based SF-6D.

Results: The mean SF-6D utility value was 0.70 (range 0.63–0.73). The mean utility value was lower for the lower educational level than for the highest. Women, people living in rural areas and older adults reported lower levels of utility values. Non-parametric tests showed that health utility values were significantly related to employment; unskilled manual workers reported utility values lower than non-manual workers. For different diseases, mean utility values ranged from 0.58 (sexual diseases) to 0.66 (hepatic conditions). Cluster analysis was adopted to classify individuals into three groups according to their answers to the SF-6D dimensions. Multinomial logit regression was used to detect sociodemographic characteristics affecting the probability of following each cluster pattern. This study yielded normative data by age and gender for the SF-6D.

Conclusions: The authors conclude that SF-6D is an effective tool for measuring HRQOL in the community so that different population groups can be compared. The preference-based measure used seems to discriminate adequately across sociodemographic differences. These results allow a better understanding of the impact of sociodemographic variables on the burden of illness perception.

A previous version of this paper was presented at the International Society for Pharmacoeconomics and Outcomes Research (ISPOR) 8th Annual European Congress held at Florence, Italy in November 2005.     

Structural change in the presence of network externalities: a co-evolutionary model of technological successions

The paper uses a two-stage, multi-agent simulation model to examine the conditions under which technological successions can occur in the presence of network externalities. Data is used to identify a robust econometric model of the probability of succession. Four key factors are identified. First, the trade-off between higher direct utility from new technology goods and the network utility of old technology goods. Second, the relative innovative performance of new and old technology firms. Third, cost (price) differentials due to increasing returns in production. Fourth, the time old (new) firms have to develop their product designs prior to entry.JEL Classification: O30, C15 Correspondence to: Paul WindrumThe authors would like to thank Richard Nelson and Uwe Cantner for their helpful comments on an earlier draft of the paper, and for the comments provided by the anonymous referees. The usual disclaimers apply. The authors gratefully acknowledge supportive funding through SEIN-Project, European Commissions Framework 4 Programme (contract# SOEI-CT-98-1107) and through the Policy Regimes and Environmental Transitions (PRET) project funded by the Dutch Scientific Research Council (NWO).     

Existence of a continuous utility function with path monotonicity: the Wold approach

Summary This paper uses the approach of Wold to prove the existence of a continuous utility function on a subset ofR ⁿ with a path monotonicity assumption. This result is then extended to a Banach space.The research for this paper was begun while visiting the University of Cambridge and the London School of Economics in 1988. I should like to thank Dr. A. Beardon, Professor M. Desai, Professor L. Foldes and Dr. A. Horsley for their hospitality. Also, I am grateful to an anonymous referee for comments that led to an improvement in the exposition.