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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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Two‐Stage Budgeting

Two‐Stage Budgeting

(p.19) 2 Two‐Stage Budgeting
Separability and Aggregation

W. M. Gorman (Contributor Webpage)

, C. Blackorby, A. F. Shorrocks
Oxford University Press

This paper is from an unpublished typescript (University of North Carolina, 1970), and is the first of a series of papers in Part I of the book on the general subject of budgeting––the rather vague notion that households, organizations, or governments first allocate a given total expenditure to various subsets of commodities, such as ’food’, ’recreation’, or 'saving’. Only after the allocations to these broad sectors have been specified, does the agent or organization decide how to split each sectoral expenditure among its component parts, such as the particular food commodities. The set of papers assumes that the agent or organization has a well‐defined preference ordering over all relevant commodities, and hence the problems are cast in the context of consumer theory (purely for expositional purposes). Reinterpreting the results in terms of a firm presents no special difficulties, and allows a variety of problems to be discussed. ’Two‐stage budgeting’ supposes that the correct intersector allocations have been made, and then shows that separability of that sector is necessary and sufficient for the resulting intrasector allocations to be optimal.

Keywords:   allocation, budgeting, firms, intersectoral allocation, intrasectoral allocation, sectoral expenditure, separability, two‐stage budgeting

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