213. R. F. Kahn to Harrod , 25 June 1931 [a]
[Replies to 212 ]
26 Fairtagels, London as from King's College, Cambridge
25 June 1931
Dear Mr. Harrod,
Dennis has passed on your queries, which I enclose for the purposes of reference, to me, and I must apologise most humbly for the delay in replying to them. I have had a busy term of teaching and found it difficult to match the <lucid> interval that is necessary for dealing with a thing of this kind. But I feel very ashamed of myself and apologise.
I cannot see that your and on p. I are the same as your and on p. II.  It is the latter, not the former, that seems to me to be the same as Keynes' and . But I think I have misunderstood your p. I. What are and and why do you assume that their ratio is the same as that of E - S to S? Incidentally the condition that is not sufficient for making Q equal to 0. If , then the profit on consumption-goods is zero, but total profit is zero only if I = S.
As regards p. II, you agree that
But R = O - C (R is the volume of current consumption)
but (by definition of S--see below)
The trouble--so it seems to me--is that you have forgotten Keynes' special definition of "income".  It does not include "profits", so that the profits that are spent ( ) appear as negative saving. In other words, E-S is inevitably, and by definition, the amount being spent on consumption, so that . But, of course, it all depends on the definitions.
I cannot see why you regard the widow's cruse theory as correct only if = 1. It follows from your equation that is greater than it would be if and were both zero by the amount . This is the widow's cruse theory (It is only true, of course, if output remains constant).
Your definition of savings (which is different both from Keynes' definition and from the ordinary simple-minded definitions as the difference between net receipts and expenditure) has, to my mind, the very great advantage that it gives us a quantity that is purely cause and not partly effect. (Keynes' "savings" depend on and and the simple-minded "savings" are necessarily and always equal to I, the value of investment). What your equations indicate is that, for a given value of and for a given behaviour on the part of everybody except entrepreneurs, there is an infinite series of possible pairs of values of P and . (If , in your terminology, it is given by the equation ). The problem becomes determinate only when some further condition is introduced. Such a condition is afforded by the speculative demand curve for securities. The fundamental importance of this demand curve in the logical scheme of things was gradually brought home to some of us in the <course> of the wrangles that preceded some public discussions that we held on the Treatise during the Term. The conclusions at which some of us arrived do not, as it turns out, differ from those of the Treatise, except in regard to emphasis. (The demand curve is, of course, all in the Treatise). They are not set out anywhere in writing, but, if you are interested, I could let you see a preliminary note that I circulated to the protagonists during last vacation.  It is now very antiquated and superseded, but it may possibly interest you as containing an equation rather like one of yours.
I do hope that I have succeeded in meeting at any rate some of your points, but I am not sure that I have completely understood your position. If you think that I could be of any further use, I should be very grateful if you would let me hear from you.
Richard F. Kahn.
2. "Income" is defined in Keynes, Collected Writings, vol. V, p. 111.
3. Kahn's note for the Cambridge Circus (possibly "The Price Level of Investment Goods", dated 5 April 1931, published in Keynes's Collected Writings, vol. XIII, pp. 203-6) was not found among Harrod's papers.
- a. ALS, four numbered pages on two sheets, in HP, IV-586-668.
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