The relationship between revealed preference and the Slutsky matrix

This paper presents a method of calculating the utility function from a smooth demand function whose Slutsky matrix is negative semi-definite and symmetric. The calculated utility function is the unique upper semi-continuous function corresponding with the demand function. Moreover, we present an axiom for demand functions. We show that under the strong axiom, this new axiom is equivalent to the existence of the corresponding continuous preference relation. If the demand function obeys this axiom, the calculated utility function is also continuous. Further, we show that the mapping from the demand function into a continuous preference relation is continuous, which ensures the applicability of our results for econometrics. Moreover, if this demand function satisfies the rank condition, then our utility function is smooth. Finally, we show that under an additional axiom, the above results hold even if the demand function has corner solutions.     

Measuring utility from demand

This study presents a new method to calculate a preference relation from a demand function. Our method works well under the weak axiom and can calculate a smooth utility function if the demand function obeys the strong axiom. Further, if the demand function is derived from a customary utility function, our method restores the original preference. Our method provides a complete and rigorous proof of Samuelson’s conjecture. In addition to these results, we guarantee the recoverability: i.e., the uniqueness of the preference relation corresponding to a demand function.     

Menu-dependent self-control

The literature on self-control problems has typically put forth models that imply behavior that is consistent with the weak axiom of revealed preference (WARP). We argue that when choice is the outcome of some underlying internal conflict, the resulting choices may not be perfectly consistent across choice problems: an agent’s ability to resist temptation may well depend on what alternatives are available to him. We generalize Gul and Pesendorfer (2001) so that self-control weakens in the presence of temptation. To model choices from menus explicitly, we consider a choice correspondence as well as a preference over menus and relax both the Independence axiom for the preference and the WARP condition for the choice correspondence. The model is shown to unify a range of well-known findings in the experimental literature on choice under risk and over time within a single specification.     

Afriat’s theorem for indivisible goods

We identify a natural counterpart of the standard GARP for demand data in which goods are all indivisible. We show that the new axiom (DARP, for “discrete axiom of revealed preference”) is necessary and sufficient for the rationalization of the data by a well-behaved utility function. Our results complement the main finding of Polisson and Quah (2013), who rather minimally modify the original consumer problem with indivisible goods so that the standard GARP still applies.     

Revealed preferences: A topological approach

The purpose of this paper is to study the relationship between the axiomatic foundations of revealed preference theory and the continuity properties of choice. The main result of this paper shows that the continuity of a set-to-point choice function is equivalent to the weak axiom of revealed preference and openness of the strict revealed relation, provided that the collection of budget sets is endowed with a topology used widely by economists.     

The existence of equilibrium when excess demand obeys the weak axiom

This paper gives a non-fixed point theoretic proof of equilibrium existence when the excess demand function of an exchange economy obeys the weak axiom of revealed preference.     

Non-Archimedean preferences over countable lotteries

We prove a representation theorem for preference relations over countably infinite lotteries that satisfy a generalized form of the Independence axiom, without assuming Continuity. The representing space consists of lexicographically ordered transfinite sequences of bounded real numbers. This result is generalized to preference orders on abstract superconvex spaces.     

Reexamination on updating Choquet beliefs

Eichberger et al. (2007)  characterize the full Bayesian update rule for capacities. This paper shows that a conditional preference relation represented by the Choquet expected utility with respect to the updated capacity through the rule does not satisfy the axiom of Conditional Certainty Equivalence Consistency. A counterexample is provided and it is proved that a relaxation of the axiom maintains their results.     

Demand properties of concavifiable preferences

The purpose of the present paper is to clarify the relation between choice theory for individual consumers, i.e., the observed demand behavior, and the preference ordering ?$?$ of that individual. Specifically, we study how concavifiability (i.e., representability of ?$?$ by a concave utility function) is expressed by quantities (cross-coefficients) appearing in revealed preferences theory. We present a sequence of rather explicit necessary conditions for concavifiability. All these conditions are quantitative asymptotic strengthenings of the strong axiom of revealed preference. The results and concepts are illustrated by means of examples in which an expenditure data is defined by providing its generating utility function.     

Closure and preferences

We investigate the results of Kreps (1979), dropping his completeness axiom. As an added generalization, we work on arbitrary lattices, rather than a lattice of sets. We show that one of the properties of Kreps is intimately tied with representation via a closure operator. That is, a preference satisfies Kreps’ axiom (and a few other mild conditions) if and only if there is a closure operator on the lattice, such that preferences over elements of the lattice coincide with dominance of their closures. We tie the work to recent literature by Richter and Rubinstein (2015).     

Evaluating intergenerational risks

Climate policies have stochastic consequences that involve a great number of generations. This calls for evaluating social risk (what kind of societies will future people be born into) rather than individual risk (what will happen to people during their own lifetimes). We respond to this call by proposing and axiomatizing probability adjusted rank-discounted critical-level generalized utilitarianism (PARDCLU) through a key axiom ensuring that the social welfare order both is ethical and satisfies first-order stochastic dominance. PARDCLU yields a new useful perspective on intergenerational risks, is ethical in contrast to discounted utilitarianism, and avoids objections that have been raised against other ethical criteria. We show that PARDCLU handles situations with positive probability of human extinction and is linked to decision theory by yielding rank-dependent expected utilitarianism—but with additional structure—in a special case.     

A note on pro-poor social expenditures

This study extended the concept of ‘pro-poor growth’ in terms of social expenditures that measure whether social expenditures are pro-poor or not pro-poor. Using the idea of pro-poor growth, this study examines as to what extent the poor benefited from the growth of social expenditures i.e., human development, rural development, safety nets and community services. The monotonicity axiom sets out a condition that the proportional reduction in poverty is a monotonically increasing function of the pro-poor growth. This study satisfies the monotonicity criterion relative with social expenditures and proposes a ‘poverty equivalent social expenditure rate’, which takes into account both the magnitude of social expenditures growth and how the benefits of these expenditures are distributed to the poors and the non-poors. This methodology is applied to Pakistan’s unit record household surveys during the periods of 1964–2011 (21 household surveys) and examines the interrelationship between social expenditures, inequality, and poverty. It is argued that the satisfaction of a monotonicity axiom is a key criterion for measuring pro-poor growth. The results found that the social expenditures in Pakistan are not intrinsically pro poor. Although it was strongly pro poor in the 1980s and pro poor in the 1990s, growth in the 1970s and 2000s was anti poor, if the poverty related social expenditures still remains anti-poor in the subsequent years as reflected in the years 2008–2011, there is a likelihood that these expenditures may not trickle down to the poor but instead to the non-poor. It is indicative that to achieve rapid poverty reduction, the poverty equivalent growth rate ought to be maximized rather than the actual growth rate of social expenditures in Pakistan.     

Using goal programming to determine interest group disutility for public policy choices

Within this paper a framework is developed for incorporating into the process of social choice both interest group preferences for social goals and the efficient allocation of limited resources. The social welfare function is adopted as the foundation for the framework and the goal programming algorithm is used to approximate the utility of the interest groups for their optimal policy choice. A function is defined which measures the disutility experienced by a social unit when a policy other than its optimal choice is selected. A surrogate measure of this disutility involving imposed preference weight changes for social goals is determined and its implications for use in developing the social welfare function are examined.     

协同学在汽车制造业供应链中的应用综述

协同学原理表明,任何系统的发展都遵循着一种协同学的规律。汽车制造业是个复杂的社会系统,其供应链网络结构由多级汽车供应商、汽车制造商、汽车分销商、零售商以及顾客构成,各环节都显现出一种普遍的协同规律。本文对协同学的应用领域进行了研究,具体针对协同学原理在汽车制造业供应链中各个环节的应用进行相关的介绍,最后指出了协同学更加广阔的应用前景。     

On preferences over subsets and the lattice structure of stable matchings

This paper studies the structure of stable multipartner matchings in two-sided markets where choice functions are quotafilling in the sense that they satisfy the substitutability axiom and, in addition, fill a quota whenever possible. It is shown that (i) the set of stable matchings is a lattice under the common revealed preference orderings of all agents on the same side, (ii) the supremum (infimum) operation of the lattice for each side consists componentwise of the join (meet) operation in the revealed preference ordering of the agents on that side, and (iii) the lattice has the polarity, distributivity, complementariness and full-quota properties. Received: 5 March 1999 / Accepted: 12 May 2000     

Gross substitutability of point-to-set correspondences

In this paper the notion of gross substitutability for the multi-valued case is studied. It is proved that, if in a pure exchange equilibrium model gross substitutability and some auxiliary conditions prevail, then (a) the set of equilibria is a Cartesian product of a convex set of equilibrium resource allocations and a convex cone of equilibrium prices; hence all equilibria are equiadvantageous for every trader; (b) the weak axiom of revealed preference holds in any equilibrium; (c) any equilibrium is stable with respect to reallocations of initial resources. Some situations in which Walras' law does not hold are considered as well.     

Price uncertainty and the effect of capital costs in a point in-point out inventory investment

This paper analyzes a point in-point out inventory investment under price uncertainty. The optimal quantity is determined by maximizing the expected value of the investor's risk preference function, which is a function of profit. Using an exponential risk preference function, the adjustment in the optimal quantity stemming from a change in the interest rate is investigated. The main conclusion is that the sign of the adjustment depends both on how profit is expressed and on the type of price distribution applied. Contrary to what is assumed in conventional managerial control practices, a rise in the interest rate might lead to an increase in the optimal quantity when present value serves as a measure of profit.     

A further note on arrow's impossibility theorem

For arbitrary measure spaces of agents we investigate the existence of social welfare functions which fulfill a suitable non-dictatorship axiom; it turns out that there is an essential difference between finite and σ-finite but infinite measure spaces. Furthermore the condition of universal domain of social welfare functions is weakened.     

Risk control measures in payment systems

The purpose of this paper is to make a comparative analysis of modern gross and net payment systems, emphasizing on the implications of the availability of intraday liquidity in the former and of credit limits in the latter. This allows for the comparison of both the effects on social welfare of each of the two systems and the different risk control instruments analyzed. In a numerical exercise, it is shown first, how it would be legitimate for a benevolent authority a preference for a gross system, like Fedwire, over a net system, like EURO1, for relatively high values, although plausible, of risk aversion. Second, as financial development improves, the preference for a net system shifts either to gross systems or, for some countries, to a cohabitation of both settlement modes.