- John Stuart Mill's Equilibrium Terms of Trade:A Special Case of William Whewell's 1850 Formula
Chapter 18 of book 3 of John Stuart Mill's Principles of Political Economy is famous for setting out the law of international values in terms of the reciprocal demands of two countries for each other's products:
The produce of a country exchanges for the produce of other countries, at such values as are required in order that the whole of her exports may exactly pay for the whole of her imports. . . . So that supply and demand are but another expression for reciprocal demand: and to say that value will adjust itself so as to equalize demand with supply, is in fact to say that it will adjust itself so as to equalize the demand on one side with the demand on the other.( 1920, 592-93)
Starting with the third edition of 1852 (Principles was first published in 1848), Mill added to chapter 18 three new sections (6 to 8) that became the subject of much controversy. After describing chapter 18 as "great" and "stupendous," Francis Y. Edgeworth (1894, 609) went on to criticize the three new sections: "The splendid edifice of theory constructed in the first five sections is not improved by the superstructure of later date which forms the latter part of the chapter. This second story does not carry us much higher." He clarified his pun by arguing that the material [End Page 609] found in the "superstructure" was already contained in the previous sections. This negative verdict, which Charles Bastable had expressed before him, was subsequently echoed by Alfred Marshall, J. Shield Nicholson, Jacob Viner, George Elliott, Lloyd Metzler, and Robert Mundell.1 Before 1965, only Joseph Schumpeter (1954, 608) mildly approved of the new sections, stating "I cannot quite share either opinion [of Bastable and Edgeworth]." In his classic survey of the theory of international trade, John Chipman (1965, 484, 486) denounced this "monotonous chorus" of disapproval and argued that
it is time to reverse Edgeworth's judgment: for [section] 7 of the "great chapter" contains a convincing proof (admittedly for a special case) of the existence of equilibrium; not only that, it does so in terms of what can today be recognized as an ingenious and correct solution of a problem in nonlinear programming. . . . In its astonishing simplicity, [Mill's law of international values] must stand as one of the great achievements of the human intellect; and yet it has passed practically unnoticed for over a hundred years, if only because it was so advanced for its time.
In the first paragraph of section 6, Mill ( 1920, 596) commented that "intelligent criticisms (chiefly those of my friend Mr. William Thornton), and subsequent further investigation, have shown that the doctrine stated in the preceding pages, though correct as far as it goes, is not yet the complete theory of the subject matter." The words in parentheses were inserted only in the sixth edition of the Principles of 1865, thirteen years after the three new sections had been added, and pose a lingering puzzle, since Thornton's writings were not directed at international trade issues.2 One of the controversies that have surrounded the added sections of chapter 18 is whether the "intelligent criticisms" that Mill received were not instead inspired by a memoir of the Cambridge philosopher William Whewell, his second on economic subjects, titled Mathematical Exposition of Some Doctrines of Political Economy (1850). Although their significance has been questioned by some [End Page 610] commentators,3 Whewell's memoirs, which include the first mathematical version of the Ricardian model dated 1831, rank among the earliest contributions to mathematical economics. His second memoir was designed to solve mathematically Mill's unresolved problem of the determination of the terms of trade in the two-country, two-commodity setting. It was distributed widely by him among economists before being published in the Transactions of the Cambridge Philosophical Society in 1856. Since Mill is the economist who would have been primarily interested in it, it is almost certain that he was acquainted with it.
As shown below, Mill's assumption that demand elasticities are unitary...