Whewell, William
Whewell, William
William Whewell (1794–1866), English mathematical economist, was born in Lancashire. He was educated at Trinity College, Cambridge, and remained there as a fellow and tutor. In 1841 he was appointed master of the college. He served from 1828 to 1832 as professor of mineralogy and from 1838 to 1855 as professor of moral philosophy.
Whewell was primarily a philosopher and a mathematician, and he published his major works in these fields. He was also, however, one of a small group of British authors, which included Samuel Turner, T. Perronet Thompson, Denis G. Lube, and the anonymous “E.R.,” who made contributions to the early development of mathematical economics. Whewell’s contribution was contained in a paper, “Mathematical Exposition of Some Doctrines of Political Economy,” delivered before the Cambridge Philosophical Society in 1829. In this paper, he pointed out that some parts of the science of political economy could be presented in a more systematic and connected form, and also more clearly and simply, by the use of mathematical language.
To illustrate his argument, Whewell used mathematics to discuss Ricardo’s theory of the incidence of a tax on wages. Ricardo had argued against Adam Smith’s view that a tax on wages would ultimately be borne by the employer of labor. Such a supposition, Ricardo asserted, would lead to the absurd conclusion that, as a rise in the prices of goods due to a rise in wages would again operate on wages, the action and reaction first of wages on goods and then of goods on wages would continue “without any assignable limits” (Ricardo [1817] 1962, p. 301).
Whewell showed in his 1830 paper that if Ricardo had considered the mathematical implications of his theory, he would have found that a limitless rise in prices and wages was not only absurd but impossible. To demonstrate this, he assumed that wages would rise by the whole amount of the tax, which would be, say, 1/10. On the assumption that only a part, say 1/2, of the value of goods is wages, the rise in the price of manufactured goods would be 1/20. And on the assumption that only 1/2 of the laborers’ consumption is manufactured goods, the resulting rise in wages due to the rise in price would be 1/40, and so on. The whole rise in wages would then be
and the whole rise in the price of goods would be
Whewell concluded that as both these geometrical series have limits, Ricardo’s argument about quantities with no assignable limits is not valid. A similar argument can be found in T. Perronet Thompson’s An Exposition of Fallacies on Rent, Tithes, etc. (see 1826, pp. 39–40).
Whewell also sought in his paper to make a distinction between the moral axioms of political economy and the conclusions that might be deduced from them, a task for which mathematics could be of considerable help.
Using certain axioms as a foundation, Whewell discussed the difference between those who, following Ricardo, maintained that all taxes on the produce of land were ultimately paid by the consumer and those who maintained that most such taxes were paid by the landlord. He showed that the tax would fall solely on rent only in the absence of marginal soil. The existence of marginal soil, however, would mean that the tax would not only fall on rent but also lead to a diminution of the return on capital and an increase of price.
In a second memoir to the Cambridge Philosophical Society in 1831, Whewell presented a mathematical exposition of Ricardo’s doctrines and in a third memoir in 1850, an examination of questions of demand, supply, price, and international exchange.
Whewell was more than a translator of existing doctrine into mathematical language, as he has sometimes been described. His contributions to mathematical economics and, especially, his first approximation to a solution of the problem of the dynamic stability of equilibrium, in the discussion of the effect of a tax on wages, are really noteworthy.
WORKS BY WHEWELL
(1819) 1847 An Elementary Treatise on Mechanics. 7th ed. London: Whittaker.
1823 A Treatise on Dynamics, Containing a Considerable Collection of Mechanical Problems. Cambridge:Deighton.
1830 Mathematical Exposition of Some Doctrines of Political Economy. Cambridge Philosophical Society, Transactions 3:191–230.
1831 Mathematical Exposition of Some of the Leading Doctrines in Mr. Ricardo’s Principles of Political Economy and Taxation. Cambridge Philosophical Society, Transactions 4:155–198.
1832 An Introduction to Dynamics, Containing the Laws of Motion and the First Three Sections of the Principia. Cambridge: Deighton.
(1837) 1890 History of the Inductive Sciences, From the Earliest to the Present Time. 3d ed., with additions. New York: Appleton.
(1840) 1847 The Philosophy of the Inductive Sciences, Founded Upon Their History. 2 vols. A new edition, with corrections and additions, and an appendix containing philosophical essays previously published. London: Parker.
1850 Mathematical Exposition of Some Doctrines of Political Economy. Cambridge Philosophical Society, Transactions 9, part 1:128–149; part 2:1–7.
SUPPLEMENTARY BIBLIOGRAPHY
Ricardo, David (1817) 1962 Principles of Political Economy and Taxation. London: Dent; New York: Dutton. ? A paperback edition was published in 1963 by Irwin.
Robertson, Ross M. 1949 Mathematical Economics Before Cournot. Journal of Political Economy 57:523–536.
Schumpeter, Joseph A. (1954) 1960 History of Economic Analysis. Edited by E. B. Schumpeter. New York: Oxford Univ. Press.
Theocharis, Reghinos D. 1961 Early Developments in Mathematical Economics. London: Macmillan.
Thompson, T. Perronet (1826)1832 The True Theory of Rent, in Opposition to Mr. Ricardo and Others, Being an Exposition of Fallacies on Rent, Tithes, etc. 9th ed. London: Heward. ? First published as An Exposition of Fallacies on Rent, Tithes, etc. Containing an Examination of Mr. Ricardo’s Theory of Rent….