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The Technique of Comparative-Static Analysis in Whewell's "Mathematical Exposition"

The Technique of Comparative-Static Analysis in Whewell's "Mathematical Exposition" “[Whewell] regards questions in economy as little more than sums in arithmetic.”1 This “contemptuous verdict,” as Joseph Schumpeter (1954, 146 n) disapprovingly called it, was seldom disputed until the 1960s. But we now could cite James L. Cochrane (1970) and Giuliana Campanelli (1982), who praised Whewell ([1831] 1968) for the first mathematical formulation of fixed capital. John Creedy (1989) refers to Whewell’s “second memoir” (Whewell [1850] 1968) as “a genuine pioneer attempt to produce a general equilibrium model of international trade.” In addition, James Henderson (1996) has published a book on Whewell’s mathematical economics that covers various aspects including the “first mathematical formulation of the elasticity concept.” Nevertheless, there remains an aspect yet to be appreciated. It is that Whewell, in his 1829 essay, conducted a comparative-static analysis using differential calculus. He set out eight equations that implicitly but completely defined the functional relation between eight endogenous variables and one exogenous variable. He then successfully solved the equation system to deduce the implicitly defined functions, and he exactly calculated their derivative to obtain a linear approximation of each function. Surprisingly or not, this remarkable aspect of Whewell’s mathematical economics has so far been disregarded. As a result, the http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png History of Political Economy Duke University Press

The Technique of Comparative-Static Analysis in Whewell's "Mathematical Exposition"

History of Political Economy , Volume 33 (4) – Dec 1, 2001

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Publisher
Duke University Press
Copyright
Copyright 2001 by Duke University Press
ISSN
0018-2702
eISSN
1527-1919
DOI
10.1215/00182702-33-4-843
Publisher site
See Article on Publisher Site

Abstract

“[Whewell] regards questions in economy as little more than sums in arithmetic.”1 This “contemptuous verdict,” as Joseph Schumpeter (1954, 146 n) disapprovingly called it, was seldom disputed until the 1960s. But we now could cite James L. Cochrane (1970) and Giuliana Campanelli (1982), who praised Whewell ([1831] 1968) for the first mathematical formulation of fixed capital. John Creedy (1989) refers to Whewell’s “second memoir” (Whewell [1850] 1968) as “a genuine pioneer attempt to produce a general equilibrium model of international trade.” In addition, James Henderson (1996) has published a book on Whewell’s mathematical economics that covers various aspects including the “first mathematical formulation of the elasticity concept.” Nevertheless, there remains an aspect yet to be appreciated. It is that Whewell, in his 1829 essay, conducted a comparative-static analysis using differential calculus. He set out eight equations that implicitly but completely defined the functional relation between eight endogenous variables and one exogenous variable. He then successfully solved the equation system to deduce the implicitly defined functions, and he exactly calculated their derivative to obtain a linear approximation of each function. Surprisingly or not, this remarkable aspect of Whewell’s mathematical economics has so far been disregarded. As a result, the

Journal

History of Political EconomyDuke University Press

Published: Dec 1, 2001

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