Jump to ContentJump to Main Navigation
Separability and AggregationThe Collected Works of W. M. Gorman, Volume I$
Users without a subscription are not able to see the full content.

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

Show Summary Details
Page of

PRINTED FROM OXFORD SCHOLARSHIP ONLINE (www.oxfordscholarship.com). (c) Copyright Oxford University Press, 2020. All Rights Reserved. An individual user may print out a PDF of a single chapter of a monograph in OSO for personal use. date: 29 March 2020

Conditions for Additive Separability

Conditions for Additive Separability

Chapter:
(p.141) 11 Conditions for Additive Separability
Source:
Separability and Aggregation
Author(s):

W. M. Gorman (Contributor Webpage)

, C. Blackorby, A. F. Shorrocks
Publisher:
Oxford University Press
DOI:10.1093/0198285213.003.0011

Suppose that an agent has preferences over a finite time horizon, and that, in addition, marginal rates of substitution between adjacent time periods are independent of the level of consumption in other time periods. This means, for example, that marginal rates of substitution between commodities in periods one and two are independent of consumption in period three, and that marginal rates of substitution between commodities in periods two and three are independent of consumption in period one. Then, by the overlapping theorem, the utility function must be additive in the consumption of the three periods. A proof along these lines is presented in Sect. 4 of ’The structure of utility functions’ (Ch. 12); this paper presents an alternative proof of the same theorem. John Whitaker at the Oxford Mathematical Economics Seminar posed the problem in 1964, and Gorman submitted the paper to Econometrica in July 1965 and it was published in Econometrica 36 (1968).

Keywords:   additive separability, additive utility functions, additivity, consumption, marginal rates of substitution, overlapping theorem, separability, time periods

Oxford Scholarship Online requires a subscription or purchase to access the full text of books within the service. Public users can however freely search the site and view the abstracts and keywords for each book and chapter.

Please, subscribe or login to access full text content.

If you think you should have access to this title, please contact your librarian.

To troubleshoot, please check our FAQs , and if you can't find the answer there, please contact us .