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Separability and AggregationThe Collected Works of W. M. Gorman, Volume I$
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W. M. Gorman, C. Blackorby, and A. F. Shorrocks

Print publication date: 1996

Print ISBN-13: 9780198285212

Published to Oxford Scholarship Online: November 2003

DOI: 10.1093/0198285213.001.0001

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Conditions for Generalized Additive Separability

Conditions for Generalized Additive Separability

Chapter:
(p.183) 13 Conditions for Generalized Additive Separability
Source:
Separability and Aggregation
Author(s):

W. M. Gorman (Contributor Webpage)

, C. Blackorby, A. F. Shorrocks
Publisher:
Oxford University Press
DOI:10.1093/0198285213.003.0013

This paper is from an unpublished typescript (1970) and is a straightforward elaboration of a referee report on a paper by Robert Pollak that was eventually published in Econometrica (1972). In the paper, Gorman explores the restrictions on preferences arising from Pollak's notion of generalized additive separability. Pollak essentially defines a generalization of separability as a restriction on the form of the demand curves, shows that it is a true generalization, and, in some special cases, finds the corresponding restrictions on direct and indirect utility functions. This leaves open the question of the general form of preferences implied by the demand‐function restrictions, and it is this question that Gorman addresses. He determines the circumstances in which it would be optimal to make intrasector allocations that depend only upon sector‐specific normalized prices and some function of all normalized prices.

Keywords:   additive separability, additivity, demand curves, demand‐function restrictions, generalized additive separability, intrasectoral allocation, normalized prices, separability, utility functions

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