The theory of mixed demand functions

The properties of Samuelson's mixed demand functions, which express demand as a function of a mixed set of prices and quantities, are derived. By analyzing compensated (or substitution) effects and uncompensated effects, the relationships between mixed demand functions and conditional (or rationed) demands are examined. This provides insights on the behavioral implications of consumer theory for alternative demand specifications.     

Continuous utility functions for noninferior demand functions

Summary It is shown that if a demand function with no inferior goods satisfies the Slutsky conditions and has a convex range, then it is generated by a continuous utility function. The same conclusion holds when the Slutsky conditions are replaced by the strong axiom of revealed preference.     

On the characterization of excess demand functions

Summary. In this paper, we give the necessary and sufficient conditions that characterize the individual excess demand function when it depends smoothly on prices and endowments. A given function is an excess demand function if and only if it satisfies, in addition to Walras law and zero homogeneity in prices, a set of first order partial differential equations, its substitution matrix is symmetric and negative semidefinite. Moreover, we show that these conditions are equivalent to the symmetry and negative semidefiniteness of Slutsky matrix, Walras law and zero homogeneity of Marshallian demand functions.Received: 25 November 2002, Revised: 11 March 2004, JEL Classification Numbers: D11.Marwan Aloqeili: I would like to thank an anonymous referee for helpful comments.     

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.     

A reformulation of the foundations of welfare economics

Neoclassical welfare economics takes an outcome-oriented approach that uses Pareto optimality as its benchmark for welfare maximization. When one looks at the remarkable improvements in economic welfare that have characterized market economies, most of those improvements in welfare have been due to economic progress that has introduced new and improved goods and services into the economy, and innovations in production methods that have brought costs down, leading to higher real incomes. Pareto optimality is only peripherally related to actual economic welfare, and no economist would argue that people are materially better off today than a century ago because the economy is closer to Pareto optimality. After analyzing the actual factors that lead to improvements in welfare, this paper suggests a reformulation of the foundations of welfare economics to replace the almost irrelevant outcome-oriented concept of Pareto optimality as the benchmark for evaluating welfare with a process-oriented benchmark based on factors that generate economic progress. The paper then explores some implications of this reformulation.

A general theory of demand for information about product quality

The purpose of this paper is to construct a general theory—analogous to the neoclassical theory of consumer demand—of demand for information about product quality. The model proposed here introduces uncertain product quality by assuming that commodities possess attributes which consumers desire and that an uncertain commodity possesses are unknown quantity of some attribute. It is assumed that information about the quality of uncertain products is available. The consumer's utility function of information is derived and his information demand function is obtained.Partial analogues of the neoclassical theorems are proved for information demand. Roughly, we find that the Slutsky matrix is symmetric and that a submatrix is negative definite. The negative definite submatrix contains those terms which measure the effect of (income compensated) changes in information prices on information demand.The analysis employed to obtain these results parallels—with some important modifications—the neoclassical analysis of commodity demand. The method used to obtain expressions for the Slutsky substitution terms is an extension of the approach introduced by McKenzie [10] and later used by Hurwicz and Uzawa [6]. This approach uses an “income compensation” function to arrive at an “income compensated” demand function.     

Learning to consume – A theory of wants and the growth of demand

The theory of economic growth takes little notice of what is happening on the demand side of the markets so that ever more goods and services can be sold. In order to make progress, this paper revives a classical notion in economics, the concept of wants, and re-casts it in terms of a behavioral theory. Hypotheses are discussed concerning the wants people pursue, the changes in these wants, and the corresponding consumption knowledge. The implications derived focus on why, in spite of the historically unique growth of per capita income in the modern economies, consumption has not been altogether satiated. In the suggested explanation, increasing variety of consumption items offered in the markets and increasing specialization of the consumers in their demand activities play a key role.     

Engel curves and systems of demand functions

The functional forms of the Engel curves implied by several popular complete systems of demand functions are discussed. Among the systems are those generated by generalized quadratic indirect utility (the translog system, the generalized Leontief system, etc.), the linear and quadratic expenditure systems, and Deaton and Muellbauer's PIGL and AIDS. A new system, which can produce the Engel curves of all these systems as special cases, is suggested. The different Engel curves are tested against data from a Norwegian survey of consumer expenditure. This is done both in a complete system of Engel curves for eight commodities and commodity by commodity.     

Characterizing stochastically monotone functions by multiattribute utility theory

The research of Peter Wakker has been made possible by a fellowship of the Royal Netherlands Academy of Arts and Sciences.     

On the theory of monopolistic competition under demand uncertainty

Establishing a model of a monopolistically competitive industry in which risk-averse Cournot firms act under demand uncertainty and in which the output of individual firms and the number of firms in the industry are both endogenously determined by free entry and exit, this paper attempts to investigate the effects of demand uncertainty on the market equilibrium of a monopolistically competitive industry. It is assumed, for calculus simplification, that the firms are identical in the sense that they have the same monopolistic power and the same production technology. The paper presents some interesting and useful comparative statics results which are contrary to those proposed in the existing papers.This is a revised version of my paper which was firstly presented to the annual meeting of the Japanese Association of International Economics held in 1988 and then included partially in my book published in 1989. I am indebted to professors D. Bös, S. Fujino, M. Ohyama, M. Nishijima, to the members of the Public Economics Research Seminar in Bonn, and to two anonymous referees for their helpful discussions and useful suggestions. Any remaining errors, however, are my responsibility.     

The equilibrium manifold keeps the memory of individual demand functions

Summary. It is shown that the property that the equilibrium manifold keeps the memory of the individual demand functions holds true if every individual demand function satisfies the following three properties: 1) It is a function of commodity prices and of consumers income; 2) Consumption belongs to the nonnegative orthant of the commodity space; 3) Walras law. Neither differentiability nor continuity are necessary. In addition, the demand functions do not have to be utility maximizing subject to budget constraints.Received: 2 September 2003, Revised: 26 January 2004, JEL Classification Numbers: D50, D51.A preliminary version of this paper was released in October 1999 under the title Deriving individual demand functions from the equilibrium manifold. I wish to thank an anonymous referee for thoughtful comments.     

Characterizing C2 aggregate excess demand functions

Summary. We integrate and sharpen two characterizations of aggregate excess demand functions: we obtain Mas-Colell's (1977) equilibrium invariance, and strengthen Geanakoplos' (1984) weakly concave utility functions to strictly concave ones. Our proofs modify and extend Geanakoplos' utility-construction. We note two applications: a sharper characterization of equilibrium price sets (cf. Mas-Colell (1977)), and a basis for the studies of computable economies (Richter and Wong (1996)). Received: July 29, 1996; revised version: February 20, 1997     

Homothetic preferences and community excess demand functions

It has recently been shown that microeconomic theory imposes almost no restriction on community excess demand functions besides Walras' Law, if the economy contains no more commodities than consumers.It is shown that the same result is true if the preferences of the consumers are further restricted by the seemingly strong requirement that they be homothetic, even when the distribution of initial endowments is a set of independent points in commodity space fixed in advance except for a scaling factor which is common to all consumers.     

A systematic analysis of the links amongst the Marshallian,Hicksian, and Frischian demand functions: A note

Three types of demand functions are central to contemporary consumer theory: the Marshallian, the Hicksian, and the Frischian demand functions. This paper presents a systematic definition of the analytical relationships amongst these demand functions under the maintained hypothesis that the decision maker is a profit maximizer.     

Estimating money demand functions for South Asian countries

In this paper, we estimate a money demand function for a panel of five South Asian countries. We find that the money demand and its determinants, namely real income, real exchange rate and short-term domestic and foreign interest rates are cointegrated both for individual countries as well as for the panel, and panel long-run elasticities provide robust evidence of statistically significant relationships between money demand and its determinants. Our test for panel Granger causality suggests short-run causality running from all variables, except foreign interest rate, to money demand, and we find evidence that except for Nepal money demand functions are stable.      

Samuelson and Davidson on ergodicity: A reformulation

The concept of ergodicity in economics seems to have the qualities of a shibboleth—a word or saying used by adherents of a party, sect, or belief, and usually regarded by others as empty of real meaning. It is in use by both neoclassical economics—after Samuelson (1965 Samuelson, P. A. “Proof That Properly Anticipated Prices Fluctuate Randomly.” Industrial Management Review, 1965, 6 (2), 41–49.[Web of Science ®] , [Google Scholar], p. 43), who used the term in his paper on what later became a foundation of the efficient market hypothesis—and post Keynesian economics—after Davidson, who picked up the term in order to highlight methodological differences. Considering the origin of the concept in statistical physics and its use in the topology of dynamical systems, which most economists are not conversant with, the importance ascribed to ergodicity in economic debate seems mystifying. We deconstruct the meaning of the term in the major contributions of Samuelson and Davidson. We suggest an alternative to (non)ergodicity to discuss the nature of randomness in the real world. While neoclassical theory assumes stochastic randomness, post Keynesians assume nonstochastic randomness, a term developed by the mathematician Kolmogorov (1986 Kolmogorov, A.N. “On the Logical Foundations of Probability Theory.” In K. Ito, and J.V. Prokhorov (eds.), Probability and Mathematical Statistics, Moscow, 1986, pp. 467–471. [Google Scholar], p. 467). We argue that even in an ergodic world there is a problem with the idea that stochastic randomness can be dealt with by the financial system.     

Excess demand functions when new assets are introduced

We demonstrate that information on the aggregate excess demand function of an incomplete real asset market economy is not helpful toward predicting the equilibrium of a new economy to which unredundant assets are added. An innovation of assets can completely change the aggregate excess demand functions.