Fuel conserving (and using) production functions
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Harry D. Saunders
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Managing Director, Decision Processes Incorporated, 2308 Saddleback Drive, Danville, CA 94506
Received 6 July 2006; received in revised form 14 November 2007; accepted 26 November 2007
Available online 5 December 2007
Abstract
This article compares eight production/cost functions used or potentially useful for exploring how
energy efficiency gains affect energy consumption. We show the practitioner's choice of function can
inadvertently pre-determine results, and make recommendations as to which functions are flexible enough
to prevent this. We also show pre-selected factor substitution elasticities can similarly pre-determine results.
To aid the comparison we decompose the energy consumption “rebound” effect into intensity and output/
income effects, which also delivers insight into the mechanisms of rebound. We conclude by
recommending practitioners restrict themselves to either the Gallant (Fourier) or the Generalized
Leontief/Symmetric Generalized Barnett cost functions as being sufficiently “rebound flexible.” The
Translog cost function may be suitable given certain conditions and a particular form of the CES (Solow)
function is a possible, but problematic, candidate. Along the way, the article provides a general
methodology for similarly examining any arbitrarily-defined constant returns to scale production or cost
function.
© 2007 Elsevier B.V. All rights reserved.
Keywords: Energy efficiency; Fuel efficiency; Rebound; Rebound flexible; Production function; Cost function; Translog;
Generalized Barnett; Generalized McFadden; Gallant; Fourier; Generalized Leontief; Cobb–Douglas; CES; Leontief;
Conservation; Global warming
1. Introduction
Energy analysts wishing to explore the relationship between engineering efficiency gains and
energy use at a sectoral or macro level almost always rely on some specification of a production
function (or its dual cost function).
Available online at www.sciencedirect.com
Energy Economics 30 (2008) 2184 – 2235
www.elsevier.com/locate/eneco
☆
This article is dedicated to the memory of Alan Manne, who died September 27, 2005.
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Tel.: +1 925 743 8400.
E-mail address: hsaunders@decisionprocessesinc.com.
0140-9883/$ - see front matter © 2007 Elsevier B.V. All rights reserved.
doi:10.1016/j.eneco.2007.11.006