## 830. Harrod to J. Marschak

, 7 September 1938[a]

[Replies to 822 , continues at 831 ] [1]

The Old Hall, Snettisham, Norfolk

I havent yet thanked you for your very interesting comments on my paper. It was very good of you to take so much trouble. I shall have to think a lot about them. I have already incorporated a number of your detailed suggestions; [2] I am now only taking up one small point. I am sure I am right! But it is the sort of pricking point about which a commentator's dissent makes one feel uncomfortable.

My footnote on C. [3] You say that it is sufficiently obvious and even throw doubt on whether it is necessary. And yet you add at the end "on line 2 a misprint: 1 instead of 12". [4] If it ought to be 12 the whole thing is not obvious but wrong! But I hope you will agree that 1 is right. I give you the footnote in full:

"If a month is the unit, the number of shoes added per period is 1, if a year 144. The value of G per annum is 12 times as great as that of G per month. [5] The number of machines added per month is 1 48 shoes = 48 units of increment of output. The number of machines added per year is shoes. Thus the value in shoes of the annual increment of capital required to produce an annual increment of 144 shoes is units. Therefore C per annum of C per month". 1

It is
essential that the number of shoes added per month should be 1 not
12! If you increase output by 1 pair a month, the annual increment is
144 pairs. The annual increment measured in units is 12* 2*
times the monthly increment;
[6] the annual increment measured as a fraction of
existing output (rate of growth) is 12 times the monthly increment,
because the denominator of the fraction, i.e. existing output, is 12
times as great if you take an annual period as it is if you take a
monthly period. In view of this complication, you will not perhaps
think the footnote so "obvious". Indeed the
reason why I inserted it was that a mathematical student who came to
my lectures was absolutely convinced that I had got my dimensions in
the fundamental equation wrong, and it took me about 3 weeks'
correspondence to shake him.
[7]

- 1. An
autograph note by Marschak states: "Ans. to both letters 1.X.38"
(the second being letter
831 ). His reply, however, was not found in Harrod's papers.
2. The corrections introduced in order to meet Marschak's comments are listed in the editorial notes to the first draft of the "Essay in Dynamic Theory" ( 1939:7 ), here reproduced as essay 19 .

3. Essay 19 , footnote [i] to [jump to page] .

4. Letter 822 , [jump to page] .

5. In this statement and in what follows Harrod is sometimes forgetting that growth follows exponential rather than linear laws. This generated some confusion in the time dimension of his equation.

6. It is not clear how Harrod came to use this formula, which is clearly wrong: if each month one pair of shoes is added to the previous month's production, in absolute terms the yearly addition is 12 times the constant monthly addition, as Marschak pointed out (letter 822 , [jump to page] ).

7. No such correspondence was found among Harrod's papers. This statement suggests that Harrod expounded his theory during his lectures or his tutorials before he announced to Keynes (on 13 June: letter 778 , [jump to page] ) that "the fundamental dynamic equation" was "formulated as neatly as may be" and before he wrote it out (letter 789 to Robertson of 5 July, [jump to page] ).