# The geometric structure of some systems of demand equations

Article Abstract:

Demand equations have become a focus of attention among economists, and this study suggests that a demand functions system can be additively separated into prices and income using a classification first developed by Sophus Lie. This classification was first developed in 1888, and Lie groups and Lie algebra can be used in econometrics as an alternative to Gorman's conditions and notions of separate functional forms. Lie group transformations are particularly approriate to the problem of aggregate demand.

Publication Name: The Journal of Mathematical Economics

Subject: Mathematics

ISSN: 0304-4068

Year: 1993

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# A stable Nash mechanism implementing Lindahl allocations for quasi-linear environments

Article Abstract:

Lindahl allocations can be implemented in the form of Nash equilibrium, and with given quasi-linear consumer preferences there is global stability to his game form. Nash equilibrium can thus be created or reestablished following exogenous parameter shifts. There are, nevertheless, difficulties in developing a game form with local stability with a 'nice' environment, and it appears to be important to restrict the type of environment if stability of a mechanism is to be achieved.

Publication Name: The Journal of Mathematical Economics

Subject: Mathematics

ISSN: 0304-4068

Year: 1993

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# Integrability, Gorman systems, and the Lie bracket structure of the real line

Article Abstract:

Exterior differential calculus and Lie group theory are employed to address the problem of determining if individual demand behavior can be considered 'integrable.' The relationship between Lie's theory on real line groups and integrability precursors of Gorman demand systems are shown to be problematic. Gorman systems are limited by their inflexibility in price functions when they are obtained from utility maximization subdued by budget constraints.

Publication Name: The Journal of Mathematical Economics

Subject: Mathematics

ISSN: 0304-4068

Year: 1998

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