Continuous lexicographic preferences

Under what conditions are lexicographically representable preferences continuously representable? This question is actually two questions, since there are two natural definitions of continuity for lexicographic representations. A complete answer is given for one of these questions, and the other is answered for two dimensional lexicographic representations.     

Continuous mean demand functions derived from non-convex preferences

In this paper we show that for a large subset of utility functions in the space of all C¹ utility functions and for all prices the mean demand of those consumers whose taste is represented by a given utility function in that subset is uniquely determined. This implies that for a large set of economies mean demand is a continuous function. Our analysis uses derivatives of first and of higher order. The result is essentially a consequence of the multijet transversality theorem.     

Continuous representation of Von Neumann–Morgenstern preferences

This paper considers a continuous representation of preference relations satisfying Grandmont's (1972) Expected Utility Hypothesis. We equip the preferences with the topology of closed convergence, then we show the existence of a jointly continuous expected utility function and consider its uniqueness. Furthermore, we construct an embedding map of the preferences into the set of expected utility functions.     

Euclidean preferences

This note is devoted to the question: how restrictive is the assumption that preferences be Euclidean in d dimensions. In particular it is proven that any preference profile with I individuals and A alternatives can be represented by Euclidean utilities with d   dimensions if and only if d≥min?(I,A−1)$d\ge \min ?(I\text{,}A-1)$. The paper also describes the systems of A points which allow for the representation of any profile over A alternatives, and provides similar results when only strict preferences are considered. These findings contrast with the observation that if preferences are only required to be convex then two dimensions are always sufficient.     

Quantification of preferences in markets

In this paper we quantify agent preferences in a market. In our framework every agent has a utility level associated with each transaction, and we assume that the probability of a feasible market transaction increases with an increase in total utility. It is surprising to observe that this simple behavioral principle induces a usually unique probability measure that can be constructed by a fast numerical algorithm. This unusual combination of a rigorous model and a fast numerical algorithm makes it possible to construct a well-defined set of preferences that implies a set of observed commodity prices.     

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.     

Homothetic preferences on star-shaped sets

This paper describes properties of homothetic preferences on a subset X of a vector space which is star-shaped with respect to 0 (e.g., a cone). We prove that a preference relation on X is homothetic, greedy and calibrated if and only if there exists a positively homogeneous function that represents it. This function is unique up to a strictly increasing and positively homogeneous transformation. As a corollary, we find that, if X is contained in a topological vector space, then œ is homothetic and continuous if and only if there exists a positively homogeneous and continuous function that represents it.     

Inequity-averse preferences in general equilibrium

We study the stability with respect to the introduction of opportunity-based inequity aversion à la Dufwenberg et al. (2011) of three welfare properties satisfied by competitive equilibria in self-regarding economies: (i) Pareto efficiency may not be a stable property; (ii) undomination with respect to income redistribution is a stable property whenever the marginal indirect utility of income has no extreme variations; and (iii) generically (endowment-wise) market-constrained efficiency is a stable property.     

Threshold preferences and the environment

In this article we study the implication of thresholds in preferences. To model this we extend the basic model of John and Pecchenino (1994) by allowing the current level of environmental quality to have a discrete impact on how an agent trades off future consumption and environmental quality. Thus, we endogenize the semi-elasticity of utility based on a step function. We find that for low (high) thresholds, environmental quality converges to a low (high) steady state. For intermediate levels it converges to a stable p-cycle, with environmental quality being asymptotically bounded below and above by the low and high steady state. As policy implications we study shifts in the threshold. Costless shifts of the threshold are always worthwhile. If it is costly to change the threshold, then it is worthwhile to change the threshold if the threshold originally was sufficiently low. Lump-sum taxes lead to a development trap and a proportional income tax should be preferred.     

Rank-dependent preferences without ranking axioms

A key feature of the rank-dependent model for decision making under risk is that the weighting of an outcome depends on its relative rank. This theory received numerous axiomatizations, however, all these sets of axioms need to make an explicit reference to the ranking of the outcomes. This situation is unsatisfactory, as it seems to be desirable to get the ranking property of this model as a consequence of the model, rather than as an assumption. [Yaari, M.E., 1987. The dual theory of choice under risk. Econometrica 55, 95–115] offered a special version of this model (called dual theory), where the utility function is linear. This paper offers a set of axioms implying Yaari’s dual theory without making any reference to the order of the outcomes. The main axiom is called semi betweenness, which, unlike the usual case, is made on random variables rather than on distribution functions.     

Consumer preferences and demand systems

This paper is an up-to-date survey of the state-of-the-art in consumer demand modelling. We review and evaluate advances in a number of related areas, including different approaches to empirical demand analysis, such as the differential approach, the locally flexible functional forms approach, the semi-non-parametric approach, and a non-parametric approach. We also address estimation issues, including sampling theoretic and Bayesian estimation methods, and discuss the limitations of the currently common approaches. We also highlight the challenge inherent in achieving economic regularity, for consistency with the assumptions of the underlying neoclassical economic theory, as well as econometric regularity, when variables are nonstationary.     

Agricultural arbitrage and risk preferences

A structural intertemporal model of agricultural asset arbitrage equilibrium is developed and applied to agriculture in the North Central region of the US. The data are consistent with a unifying level of risk aversion. The levels of risk aversion are more plausible than previous estimates for agriculture. However, the standard arbitrage equilibrium is rejected; perhaps, this is due to the period and the shortness of the period studied.     

Community preferences and social choice

This paper gives necessary and sufficient conditions for the aggregation of preferences, extending an earlier treatment of aggregation by Stolper, Gorman, Samuelson and Chipman. Such aggregation procedures are intended to deal with the problem of aggregating demand functions in econometrics, where the aggregate is required to be independent to the income distribution. Thus, it is usually assumed in this form of aggregation that all consumers face the same prices, but that the distribution of income is unrestricted.In order to establish the characterisation result, we present a new approach to preference aggregation which involves summing certain subsets of the graphs of the preferences, viewed as subsets of a Euclidean space. This procedure has a clear geometrical interpretation, and a number of useful applications. In particular, it enables us to analyse the possibility of aggregation when prices are not constrained to be the same for all consumers, a case of possible empirical significance. We also show that the Stolper-Gorman-Samuelson-Chipman construction of community indifference curves coincides with a special case of this procedure.Finally, this approach allows us to develop the relationship between these forms of aggregation and the preference aggregation problem as it occurs in social choice theory.     

Smooth preferences and the regularity of equilibria

To study equilibria we describe an economy by its distribution of consumers' preferences and endowments. All preferences are smooth and weakly convex. Demand of an economy need not be single valued, but there is an open dense set of economies for which demand is a C¹-function in a neighborhood of the equilibrium prices. We call an economy regular if its excess demand is transversal to zero. A regular economy has locally unique equilibria. It is shown that regular economies form an open dense set on which the equilibrium price correspondence varies continuously and the number of equilibria is locally constant.     

Diversity of preferences in an unpredictable environment

The origin of preferences was viewed as related to the dominant eigenvalue of a Leslie matrix modelling reproductive strategies. In a variable environment, however, the coexistence of varying preferences no longer requires optimality, but is identified with the mathematical property of viability: a state of the population is viable if there exists at least one solution starting from it and remaining in the set of constraints until a given time horizon (or forever).The coexistence kernel of two competitors with varying preferences is computed for the case of scalar and 2 × 2 Leslie matrices, with either measurable or differentiable preferences. The homologue of indifference curves is the regulation map, the correspondence associating the set of viable preferences to a given state of the population.Among these viable trajectories, some are also optimal in the sense of dominance discounted in time. These viable optimal solutions are obtained as specific trajectories in an auxiliary dynamic system, and the associated maximal values constitute one boundary of the viability kernel of this auxiliary system (theorem). Hence, the perpetuation of varying preferences allows the diversity of economic preferences, as shown here using the example of the comparative history of fertility from mid-nineteenth century to nowadays in France and England.     

Diversification preferences in the theory of choice

Diversification represents the idea of choosing variety over uniformity. Within the theory of choice, desirability of diversification is axiomatized as preference for a convex combination of choices that are equivalently ranked. This corresponds to the notion of risk aversion when one assumes the von Neumann–Morgenstern expected utility model, but the equivalence fails to hold in other models. This paper analyzes axiomatizations of the concept of diversification and their relationship to the related notions of risk aversion and convex preferences within different choice theoretic models. Implications of these notions on portfolio choice are discussed. We cover model-independent diversification preferences, preferences within models of choice under risk, including expected utility theory and the more general rank-dependent expected utility theory, as well as models of choice under uncertainty axiomatized via Choquet expected utility theory. Remarks on interpretations of diversification preferences within models of behavioral choice are given in the conclusion.