652. Harrod to J. M. Keynes , 6 April 1937 [a]
[Replies to 647 , the exchange continues at 653 ]
51 Campden Hill Square, London W.8.
6 April 1937
My dear Maynard
I write this in haste, so to speak, because having glanced at your screed I perceive grave mis-understandings. You refer to the slip in arithmetic at the top of p. 91.  There is no slip. This is a matter to which I gave very long thought and reached my conclusions after much trial and error. The consequence of my reflexions was the elaboration of this technique of dynamic analysis: now you may criticize the technique itself as not fitting real conditions, but given the technique there is no slip.
The fact is that you in your criticism are still thinking of once over changes and that is what I regard as a static problem. My technique relates to steady growth.
I start with consumption. If this increases at 2%, the stock of capital goods increases at 2% if the methods of production remain the same and we are considering full capacity working. If the stock of capital increases at 2% investment increases at 2% also. I am considering, as I explain on p. 89, a geometric series viz. 100, (102/100)x100, (102/100) 2 x100 etc. If consumption increases arithmetically thus: 100, 102, 104, there is no increase in investment at all. When you explain what you take to be the slip, you say, "let net investment now increase by 10%: obviously the stock of capital does not increase by 10% but by 2.2%". Certainly for a per saltum increase of investment.
Start again with consumption. It has been increasing at 2% and begins to increase at 2.2%. Stock of capital has been increasing at 2% and now is required to increase at 2.2%. What happens to investment? It increases per saltum by 10%, but thereafter only by 2.2%. The per saltum increase of investment corresponds to the discontinuous change in the rate of increase of consumption.
Consider these figures:--
1. Steady increase of consumption:--
2. In period 3 increase of consumption rises from 2% to 2.2% and thereafter continues to increase at that rate:-- 1
2.2% will continue as the rate of increase of investment for remaining
Your 10% shows up in column 3 as a per saltum increase. 
Now you may object to my assumption of a geometric increase: but you must not accuse me of a slip in arithmetic and base your argument on that.
Why did I assume a geometric increase? The static system provides an analysis of what happens when there is no increase which entails (as in Joan Robinson's long period analysis  ) that saving = 0. Now I was on the lookout [b] for a steady rate of advance, in which the rates of increase would be mutually consistent. An arithmetic increase of income wont do, because then, with inventions neutral, no increase of saving at all is required, only the same amount each year. But that is inconsistent, on your psychological principle, with any increase of income at all.
You may suppose that population or efficiency in fact shows an arithmetic increase. That may be so. If it is we must have a cycle to allow things to get into arrears and then go forward for a time in a geometric spurt. It is in some respects the converse of the difficulty which Malthus feared, population increasing in arithmetic ratio and the means of subsistence (stock of capital) increasing in geometric ratio!
I am sorry not to be replying to your screed in greater detail. I will do so in a day or two. Meanwhile I hope you will reconsider your line of attack and dismiss the notion of the arithmetical slip!
2. The following passage was crossed out at this point of the Ms: "In 4 the increase of investment sinks almost to 2.2%, but it is a little higher, because the increase in 3 is not quite as much as it would have been if the 2.2% increase of consumption had begun one period earlier."
3. J. V. Robinson, "The Long-Period Theory of Employment", in Zeitschrift für Nationalökonomie, Bd VII:1, March 1936, pp. 74-93, reprinted in Robinson's Essays in the Theory of Employment, London: Macmillan, 1937, pp. 139-52; see Harrod's review of the book ( 1937:9 ), p. 328.
- a. ALS, three pages on three leaves, in JMK CO/3/76-78. Printed in Keynes, Collected Writings, vol. XIV, pp. 163-64.
b. Ms: «look out».
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