A reformulation of the theory of demand by compensated demand functions

We present a formal approach to consumer demand by compensated demand functions. In accordance with the integrability theory or with the theory of revealed preference, we do not require the existence of a utility function, but we do assume certain hypotheses concerning functions describing rational behavior. In view of their properties, these functions can be interpreted as compensated demand functions. According to traditional neoclassical consumer theory, Shephard's lemma and the symmetry and negative semidefiniteness of the Slutsky-Hicks matrix can be shown. We shall also see that a convex, continuous, and monotonic preference ordering, which is representable by income compensation functions, can be introduced. It can also be shown that the existence of a compensated equilibrium can be derived within this approach by compensated demand functions. In order to obtain the existence of a compensated equilibrium under less stringent conditions we finally generalize the axioms assuming that a compensated demand correspondence is given.     

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.     

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.     

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.     

The role of money demand functions in one-sector growth models

This paper shows that the assumption made regarding the functional form of the demand for money has a crucial role in determining the effect of the rate of inflation on the steady-state capital intensity in a one-sector monetary growth model. It is also indicated that by introducing money into a growth model, which assumes a fixed coefficient technology production function and a homogeneous savings function, a long-run instability problem can be avoided, irrespective of the form of the money demand function.     

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.     

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.     

The Marxian schemes of reproduction and the theory of effective demand

The paper deals with some theoretical and analytical issuesraised by a recent book by Trigg on Marx's schemes of reproduction.The paper presents a generalized model of expanded reproductionand concentrates on the attempt to develop Marx's schemes alongKeynesian lines. Trigg tries to develop a Keynesian interpretationof the schemes without significant changes to Marx's originalapproach; the paper argues that the abandonment of some of Marx'shypotheses, in particular that of free competition, is necessaryto allows us to provide a Marxian determination of underemploymentequilibria and to use a Marxian version of the Keynesian conceptof multiplier. In considering Marx's and Keynes's analyses ofcapitalist economies, the paper also emphasizes their similaritieswith respect to the importance of money and the capitalists'liquidity preference in the process of reproduction and growth.     

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.     

The theory of rational random behavior and its application to demand analysis

The author's theory of rational random behavior is developed, which distinguishes between the planning and the implementation stage of the decision-maker. Under the assumption of a quadratic loss function and decision variables with an unrestricted range, that theory implies normally distributed disturbances of behavioral equations with a covariance matrix that is known up to a scalar multiple. Those results have to be extended asymptotically by Barbosa for restricted decision variables and a more general loss function. The approach is applied to both the Rotterdam and the linear expenditure demand models: using U.S. postwar data for the former, the author finds that a likelihood ratio test accepts the theory at the 10 percent significance level.     

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.      

Endogenous timing in a mixed oligopoly under demand uncertainty

This paper analyzes a Hotelling-type game in a mixed oligopoly, where firms can either enter the market in period 1, facing demand uncertainty, or postpone their entry, in order to acquire complete information. It is shown that, for a high (low) level of uncertainty, there is a pure (mixed)-strategy equilibrium. Moreover, the standard result in the literature—that uncertainty is a differentiation force, is only possible when the degree of uncertainty is small. An increase in the degree of uncertainty could force firms to delay their entry and lead to a socially optimal outcome.     

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.     

Specification and testing of count data recreation demand functions

This article examines the effects of alternative formulations of count data recreation demand models on parameter estimates, model selection, and consumer surplus. The results indicate that large parameter and consumer surplus differences exists across the various count model formulations. More importantly, the results show that distributional assumptions, heteroscedastic functional forms, and overdispersion can have a substantial effect on consumer surplus estimates.     

The demand functions that satisfy the weak axiom of revealed preference and generalized monotonicity

We prove that the individual demand function satisfying the Weak Axiom of Revealed Preference and the excess demand function satisfying the Wald’s Axiom are pseudomonotone_*⁺, a new class of generalized monotonicity. With this new concept, we refine the characterization of Zhou for the individual demand function. In particular, a full characterization for the excess demand functions satisfying the Wald’s Axiom is derived.     

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.