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Violation of the Law of Demand

Forthcoming, Economic Theory

30 Pages Posted: 1 Nov 2011 Last revised: 13 May 2013

Yakar Kannai

Weizmann Institute of Science - Department of Theoretical Mathematics

Larry Selden

Columbia Business School - Finance and Economics; University of Pennsylvania - The Wharton School

Date Written: January 25, 2012

Abstract

Following the classic work of Mitjuschin, Polterovich and Milleron, necessary and sufficient as well as sufficient conditions have been developed for when the multicommodity Law of Demand holds. However, far less attention has been focused on the nature and properties of violations. To address these questions, the existing sufficient conditions although simpler in form are of little value unless they are also necessary. We show when the widely cited Mitjuschin and Poterovich sufficient condition also becomes necessary. Using this result, violation regions for the very popular Modified Bergson (or HARA (hyperbolic absolute risk aversion)) class of utility functions, are fully characterized in terms of preference parameters. For a natural extension of the CES member of the Modified Bergson family that is neither homothetic nor quasihomothetic, we create the first simple, explicit example of which we are aware that (i) fully characterizes violation regions in both the preference parameter and commodity spaces and (ii) analyzes the range of relative income and price changes within which violations occur.

Keywords: Law of demand, Monotonicity, Violation region, Minimum concavity point

Suggested Citation

Kannai, Yakar and Selden, Larry, Violation of the Law of Demand (January 25, 2012). Forthcoming, Economic Theory. Available at SSRN: https://ssrn.com/abstract=1952088 or http://dx.doi.org/10.2139/ssrn.1952088

Yakar Kannai

Weizmann Institute of Science - Department of Theoretical Mathematics ( email )

Rehovot 76100
Israel
972-8-934-2957 (Phone)
972-8-934-4122 (Fax)

Larry Selden (Contact Author)

Columbia Business School - Finance and Economics ( email )

3022 Broadway
New York, NY 10027
United States

University of Pennsylvania - The Wharton School

3641 Locust Walk
Philadelphia, PA 19104-6365
United States

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