Approximately rational consumer demand

Summary We define measures of violations of Slutsky symmetry and negative semidefiniteness and relate them to measures of revealed preference inconsistencies exhibited by nonoptimizing demand behavior. The degree of Slutsky asymmetry is shown to restrict the rate at which real income can rise everywhere along smooth loops in income and price space. The largest eigenvalue of the quadratic form of the Slutsky matrix is used to bound violations of the weak axiom. The sizes of the violations of either Slutsky condition are used to bound the distance between the given demand function and approximating functions that satisfy that Slutsky condition exactly.This paper was originally titled Approximate Slutsky Conditions. The authors thank W. Hildenbrand, L. Hurwicz, C. Le Van, W. Neuefeind, R. Pollak, M. K. Richter, W. Shafer and T. M. Stoker for helpful discussions and suggestions. The first author is an Alfred P. Sloan Foundation research fellow. His research was supported in part by NSF grant DMS 8514341 and a Presidential Young Investigator Award. This paper was completed while the first author was visiting the Mathematical Sciences Research Institute, Berkeley, and the second author was visiting the University of Bonn, supported by the Deutsche Forschungsgemeinschaft SFB 303 and by a SUNY Faculty Research Award. Both authors are grateful for their hosts' hospitality.     

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.     

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.      

Earnings functions: Testing for the demand side

To analyze labor market phenomena, one may simultaneously grade workers (by education) and jobs (by level of difficulty and complexity). Human capital theory predicts earnings based on only worker quality. Thurow's version of a segmented labor market theory predicts that only the job level is relevant, and the assignment theory predicts that both variables are relevant. Using three different data sets for The Netherlands, testing demonstrates convincingly the superiority of the assignment theory.     

Inverting systems of demand functions

This note gives a set of sufficient conditions under which a system of demand functions for “gross substitutes” can be inverted to obtain an equivalent system of inverse demand functions, and vice versa. These conditions also ensure that either system can be inverted to obtain a system of “mixed” demand functions, i.e., a mixture of demand and inverse demand functions. In addition, the resultant functions possess intuitive properties expected of gross substitutes.     

Nominal vs real adjustment in demand for money functions

Recently, Fair (1987) has addressd an interesting question in the areas of demand for money, namely, whether the adjustment of actual to desired demand for money is in nominal or real terms. His conclusion, based on time-seies analysis for twenty-seven countries, including a few developing countries, was that the evidence was overwhelmingly in favour of the nominal hypothesis.

The aim of this paper is to address the same issue for eleven Asian countries. In the process, a reformulation of the test procedure used by Fair is suggested. In addition, the question is also examined within the framework of the error correction model. The models are also tested for structural stability.

The scheme of the paper is as follows. The models and the tests are specified in Section I. The data and the estimation issues are dealt with in Section II. Section III presents the results. The paper is concluded with a brief summary of the major findings.     

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.     

The integrability of consumer demand functions

The purpose of this paper is to characterize the class of systems of consumer demand functions that are representable as ratios of first-order polynomial functions and are integrable. Starting from a general system of consumer demand functions representable as ratios, we impose successively the restrictions corresponding to homogeneity, summability, symmetry, non-negativity, and monotonicity. We find that the only such systems which are capable of modeling arbitrary own- and cross-substitution effects are the systems generated by transcendental logarithmic utility functions.     

Return-to-normal expectations and investment demand functions

This paper analyzes an adjustment-cost model of optimal investment behavior under return-to-normal expectations. The model yields two implications that are of interest for the interpretation of empirical work on investment behavior. One is that the model rationalizes the proposition that only permanent, as distinct from temporary, changes in expected prices will have a strong sustained effect on investment. A second is that the model provides an explanation for the humped-shaped nature of the lag distributions that have been estimated in the empirical literature.     

Tax subsidies,the rational demand for insurance and the health care crisis

An individual's optimal insurance coverage depends on balancing his gain through avoiding risk against his loss through the distortion of demand. The U.S. tax system subsidizes the purchase of excessive health insurance by excluding employer premium payments from employees' taxable incomes and by permitting the deduction of a portion of individual premiums. The current operational model of demand for health insurance shows that the tax subsidy does substantially increase insurance coverage. Since much of the rise in health care costs can be attributed to the growth of insurance, the tax subsidy is responsible for much of what is widely perceived as a health care crisis.     

Strategy-proof and individually rational social choice functions for public good economies

Summary This note is to inform about a mistake in my paper (Serizawa, 1996). In that paper, I characterized strategy-proof, individually rational, budget-balancing, non-exploitative and non-bossy social choice functions for economies with one public good and one private good. I established as Theorem 3 (page 507) that a social choice function is strategy-proof, individually rational with respect to endowment, budget-balancing, non-exploitative and non-bossy if and only if it is a scheme of semi-convex cost sharing determined by the minimum demand principle. I also exposed one example (Example 2, page 507) in order to emphasize that non-bossiness is indispensable for this characterization. I claimed that the social choice function in that example satisfies the above axioms except for non-bossiness, and is not a scheme of semi-convex cost sharing. However, the social choice function in the example is actually not strategy-proof, as shown in the simple discussion below. Therefore it is an open question whether or not a similar characterization theorem holds without non-bossiness.I thank Professor Rajat Deb, who kindly pointed out my mistake.     

Strategy-proof and individually rational social choice functions for public good economies

Summary We consider the problem of choosing an allocation in an economy in which there are one private good and one public good. Our purpose is to identify the class of procedures of choosing an allocation which satisfy strategy-proofness, individual rationality, no exploitation and non-bossiness. Any such procedure is a scheme of semi-convex cost sharing determined by the minimum demand principle.I wish to thank Professors Salvador Barbera, Matthew Jackson, Herve Moulin and William Thomson for their helpful suggestions and two anonymous referees for their detailed comments. Conversations with Professors Hideo Konishi, Shinji Oseto Ken-ichi Shimomura and Stephen Ching were helpful. This work is supported by the Japan Economic Research Foundation and Research Grants PB89-0294 and PB89-0075 from the Direcion General de Investigacion Cientifica y Tecnica, Spanish Ministry of Education.     

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.     

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.     

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.     

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