On continuous utility functions derived from demand functions

In the theory of revealed preference and in the approach to integrability theory of Hurwicz and Uzawa certain conditions are proposed implying the existence of a utility function generating the given demand function. This article presents a hypothesis which, under supposition of some well-known axioms of those models, is necessary and sufficient for the existence of a continuous utility function. This hypothesis implies the existence of a utility function u with the property that all of the boundary points of the set $\text{{x|u(x)≧α}}$ for every $\text{α?}\text{R}$ are lower boundary points, being fundamental for the continuity of the utility function.     

Price-dispersed preferences and C1 mean demand

In this paper we introduce the concept of price-dispersed preferences. Moreover we state conditions under which economies with price-dispersed preference distributions have a continuously differentiable mean demand function.     

Absolute approximations to equilibrium in markets with non-convex preferences

It is by now a well-known result that non-convexity can be ‘cured’ in large markets. There exist approximations to core allocations and competitive equilibria, in these approximations the excess demand is made small relative to the size of the economy. This work is concerned with absolute approximations, that is, making the excess demand itself arbitrarily small.     

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.     

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.     

Continuous extension of preferences

We consider the problem of extending preferences from a subset of a commodity space to the entire space. It is a simple consequence of the Tietze extension theorem that continuous preferences can be extended if they are defined on closed subsets of a normal space and are representable by utility functions. We show the following: If the space is a non-separable metric space, then extension of preferences is not always possible. In fact for (path-connected) metric spaces, extension property, utility representation property, and separability are equivalent to each other.     

Economies with a mean demand function

The present paper shows one way to look at G. Debreu and W. Hildenbrand's conjecture that certain atomless economies have mean demand functions. We conclude within the continuity framework that an economy gives rise ‘in general’ to a continuous mean demand function, and that the class of all atomless economies is ‘big’ in the space of all economies with a continuous mean demand function. The same problems are reconsidered within the framework of a space of differentiable preferences at the end.     

Local disaggregation of negative demand and excess demand functions

The literature on the characterization of aggregate excess and market demand has generated three types of results: global, local, or ‘at a point’. In this note, we study the relationship between the last two approaches. We prove that within the class of functions satisfying standard conditions and whose Jacobian matrix is negative semi-definite, only n/2+1$n/2+1$ agents are needed for the ‘at’ decomposition. We ask whether, within the same class, the ‘around’ decomposition also requires only n/2+1$n/2+1$ agents.     

Index numbers and demand functions

The article proposes a method of approximating the Konüs true cost of living index, given a system of integrable demand functions. It is shown that the approximation is contained within the Staehle bounds so long as the Engle curves satisfy a weak monotonicity condition. The result is likely to be most useful where the demand functions are known-and known (or constrained) to be integrable-but the solution for the form of the direct or indirect utility function is unknown.     

Proper preferences and quasi-concave utility functions

It is shown that preferences which are continuous, convex and uniformly proper [Mas-Colell (1983)] on the positive cone of a Banach lattice can be represented by a quasi-concave utility function which is defined on a larger domain with non-empty interior. This utility function may be chosen to be either upper or lower semi-continuous on its domain, and continuous at each point of the positive cone. Conversely, any preference relation on the positive cone which is monotone and arises from such a utility function is shown to satisfy a condition which is slightly weaker than uniform properness but which (in the presence of appropriate compactness assumptions) is sufficient to establish the existence of quasi-equilibria. An example is presented to illuminate the role played by the uniformity requirement.     

The derived demand for faculty research

Estimation of the demands for many services supplied by government and charitable organizations are hampered by two practices common to the supply of these services. The suppliers often employ non‐price rationing of these services, and they price discriminate. The supply of college training, for example, is rationed on the basis of academic ability as well as willingness to pay, and more able students are typically quoted lower net prices (associated with scholarships) than less able students. This paper suggests a method for dealing with both practices in the analysis of cross‐sectional data. This methodology is used to investigate the question of why university faculty members are expected to do research as well as teach. One answer supported by our empirical work is that the customers (e.g., the students) demand it. Thus, controlling for price and non‐academic features, better students will choose to attend a university where more scholarly research is performed. Moreover, our empirical findings also support a strong negative link between faculty time devoted to teaching and the supply of research. Copyright © 2003 John Wiley & Sons, Ltd.     

Uniqueness of mean maximizers and continuity of aggregate demand

Using Mather's Multijet Transversality Theorem one obtains generic results for uniqueness of mean maximizers and continuity of aggregate demand.     

Capital,labor, and derived demand for information: Evidence from China

In this paper, information capital is considered as a separate input of production along with noninformation capital and labor. The substitution possibility among information capital, noninformation capital and labor has been estimated by nonlinear iterative algorithm using Chinese data for 1995–2017. The empirical results from the study imply that estimates of Chinese input substitution degree and productivity are underestimated without including information capital as an input separate from noninformation capital. When information capital and labor are combined, the contribution ratio of labor force may increase. Information capital interacts with noninformation capital and labor to promote economic development and production efficiency.     

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.     

Bounding quantile demand functions using revealed preference inequalities

This paper develops a new approach to the estimation of consumer demand models with unobserved heterogeneity subject to revealed preference inequality restrictions. Particular attention is given to nonseparable heterogeneity. The inequality restrictions are used to identify bounds on counterfactual demand. A nonparametric estimator for these bounds is developed and asymptotic properties are derived. An empirical application using data from the UK Family Expenditure Survey illustrates the usefulness of the methods.     

A comparative study of complete systems of demand functions

Ten models of consumer demand, including the indirect translog model, the linear expenditure system and the Rotterdam model, are applied to Swedish data and compared, using fit and predictive performance as criteria. Demand models tend to be superior to naive models, but nonadditive models are not clearly better than additive. Each model is estimated on two levels of commodity aggregation. The results show that the estimated structures depend on the level of aggregation.     

Quantile-locating functions and the distance between the mean and quantiles

Given a random variable X with finite mean, for each 0 < p < 1, a new sharp bound is found on the distance between a p -quantile of X and its mean in terms of the central absolute first moment of X . The new bounds strengthen the fact that the mean of X is within one standard deviation of any of its medians, as well as a recent quantile-generalization of this fact by O'Cinneide.