and the Harrod, Keynes, "Fundamental Relation" WARREN L. YOUNG* Introduction In a letter to Pigou on 15 June 1939, some three months after the publication of Harrod's 1939 Essay in Dynamic Theory, Keynes, among other comments on Harrod's paper and the enormous correspondence preceding its publi- cation, wrote [1, p. 320] "In the final result, I do not find myselfin agree- ment, but I do think that he has got hold of a very interesting point which, subject to the nec- essary qualifications, is of real importance." With what, then, was Keynes in "disagree- ment"-and, for that matter, with what did he agree in Harrod's attempt to "dynamise" Keynes' economics? Section I. First, let us consider Keynes' initial com- ments on Harrod's draft manuscript. In the let- ter where Keynes opens his extensive correspon- dence with Harrod (17 August 1938), Keynes points out to Harrod that the latter's treatment of the rate of interest in his "dynamic system" must be explicitly described. This, of course, follows from the fact that Harrod does not specify a relationship between his "incremental" capital-output ratio C and the interest rate, and thus, as Keynes points out, Harrod is simply "wrapping up" its influence in "the state of technology." What this means is that rather than introduce a production function into his ap- proach or, for that matter, relate the interest rate to the rate of profit, Harrod has focused on the problem of how best to operate on the in- terest rate so that, given a relation between the savings ratio and the interest rate itself, such manipulation would result in attaining a steady growth rate. This manipulation is obtained by Harrod's assumption of a constant interest rate which, along with technological neutrality as- *University of Nottingham, England. 1All correspondence cited appears in Keynes' Collected Writings [ 1, pp. 320-50]. 22 sures an unchanged capital-output ratio [2, pp. 109, 113-14]. Keynes further points out to Harrod that since over the long run interest rate changes of a sudden nature can cause "techno- logical change," in general the interest rate can be "segregated," but that Keynes personally would prefer not to include the influence of either the interest rate or the "state of confi- dence'-which he notes that Harrod does not refer to-in the "state of technology." Harrod, while not altering his treatment of the interest rate did, however, acknowledge its role in a cursory manner in the published form of the article [4, p. 47] : The value of C depends on the state of technol- ogy and the nature of the goods constituting the increment of output. It may be expected to vary as income grows and in different phases of the trade cycle; it may be somewhat dependent on the rate of interest. Interestingly enough, Keynes also pointed out to Harrod that his C was, in fact, a "war- ranted" and not a "planned" (i.e., ex-ante) value, which is how Harrod originally saw it. Simply put, according to Keynes, Harrod's C was really the addition to what investment entrepreneurs "ought to plan to make" rather than what they "actually plan to make." Harrod, however, did not heed Keynes on this point and retained the original notation in the published version of the paper. Recently, however, Harrod has changed his view regarding this issue. This can be seen in the fact that in annotating Harrod's 1939 paper, Sen notes that in the original paper, the equation relating to the determination of the warranted growth rate-Harrod's "fundamental equa- tion'-was, according to Harrod himself, in- sufficiently specified with regard to notation. Harrod now claims that his "fundamental equation" [4, p. 43] "'Equation 1 determining warranted growth G w should have both determinants subscripted to