838. J. M. Keynes to Harrod , 19 September 1938 [a]
[Replies to 829 and 834 , answered by 840 ]
Tilton, Firle, Lewes. #
19 September 1938
Thanks for your revised version. I will send it to the printer in due course. You have got some extremely interesting ideas and material in it, as I said before. But, reading it again, I feel even more strongly that, from the reader's point of view, you have not done justice to them, and I doubt whether the ideas will have the full impact on the reader which they deserve. I still find the exposition half-baked and prolix, and I have found it practically impossible to work things out for myself in terms of your symbolism, which is so contrived as to lose sight of the dimensions of the quantities, which makes it very difficult to handle. I hope I am not too much influenced in saying this by the editorial preference for something short! If I were to print this in December, I should have given you something like a quarter of the whole of the space in the Journal available for articles in the second half of this year, which would scarcely be fair to the innumerable other authors pressing on me. But do not bother about the article any further at the moment. Better put it on one side and look at it again in a month or two's time. If you are then still satisfied with it, it shall be printed as it stands in the March issue.
On matters of substance as distinct from exposition, I have only been making one fundamental criticism in this correspondence, and that too is really a criticism of proof and exposition rather than of substance. It may be that I am under a misapprehension. But if there is anything at all in what I am trying to say, it would be quite out of place in a footnote.  What I am trying to call attention to is what seems to me to be the fundamental presupposition of the whole story, without which it would fall to the ground and without knowledge of which the reader's intuition will be completely at a loss. I am not saying that the assumption in question is an unreasonable one to make. I think it entirely reasonable. But, to my thinking, it is the fundamental fact in the world of experience which lends significance to your whole theory. At the risk, therefore, of being tiresome, I will repeat it, this time avoiding all the very muddling symbolism and express the point in terms of a numerical example.
The trouble begins on page 15 of your MS, where you say "the consequence will be that the actual increase of capital goods falls below that which is desired".  This is the crux of the whole theory, from which the rest follows. But you have not made the faintest attempt to prove it. You simply state it as an obvious fact. Now, it is not obvious. It is extremely difficult to prove with your notation, and the proof requires a vital assumption which you have not made.
Let us take your convenient simplification that only consumption goods are produced and that capital consists in an appropriate proportion of liquid stocks. Let us assume that the period of production is a year. Let the entrepreneurs then decide to increase annual output by 10 consumption units beyond the warranted output. Let us assume that saving is at the constant proportion of 1/10th of income. To begin with, let us suppose that there is a time lag of one week in consumption and saving, i.e. that they are governed by the previous week's income. This, being a short period relatively to the period of production, can be neglected. The result is that during the year liquid stocks will fall by 9 consumption units, but at the end of the year the new output will not only replenish this fall but will increase the stocks by one unit.
Before considering the consequences of this, let us, in order to check the argument, consider the case where the consumption time-lag is a year instead of a week. In this case stocks will not fall during the year, and they will be reduced at the end of it by 10 units, 9 of which, however, will be required to look after the delayed consumption, so that, as before, the genuine increase of stocks is by one unit. Thus, the length of the consumption time-lag does not seem to matter materially.
We now have to consider what proportion normal stocks are of a year's income. Let us begin by supposing that normal stocks are one-tenth of last year's income. In this case the increase of stocks by one unit is just enough to maintain stocks at their normal, since income had increased by 10 units. We have, therefore, a position of neutral equilibrium. If normal stocks are the same proportion of the year's income as saving is, any rate of output is warranted.
But let us suppose next that normal stocks are one-eleventh of a year's income. In this case stocks will be excessive at the end of the year and equilibrium is stable in the sense that the excess of output over the warranted will tend to be corrected.
Finally, let us suppose that normal stocks are one-ninth of a year's income. In that case stocks at the end of the year will be deficient, and the position will be unstable in the sense that an expansion beyond warranted output provides a stimulus to a further increase of output.
Thus the position is in neutral, stable or unstable equilibrium according as normal stocks are the same, a smaller or a greater proportion than saving of the income of a period equal to the period of production.
Entrepreneurs do not, of course, have to wait until the end of the year for making new decisions. The particular train of production which they have set in motion we can regard as irrevocable. But a week later they can make new decisions as to the rate of current input. This seems to me, however, not to make any material difference. If indeed we are to suppose them to know that stocks were falling, but not to know that current output is on a sufficient scale to replenish them, this might make a difference. But if we suppose that each entrepreneur knows that the fall in his stocks is temporary and will be made good by his own existing decisions by the end of the year, the question of there being or not being a stimulus to further output remains what we have already said.
It is worth noticing that this is all equally true on static assumptions, which are simply a special case where saving and the warranted increase are normally zero.
On the secondary point as to whether it is marginal or average saving which is significant,  I agree with you that it is average saving and not marginal saving which is important when you are calculating the warranted rate of output. On the other hand, it is the marginal rate of investment, i.e. the additional investment corresponding to additional income, which is significant. Also, as soon as we leave warranted output and consider excess over warranted, it is marginal saving that matters. It is a question, not of average saving, but of the marginal saving corresponding to an increase in income beyond warranted income.
J M Keynes
R. F. Harrod Esq., Christ Church, Oxford.
2. Harrod, "An Essay in Dynamic Theory", preliminary draft, here reproduced as essay 19 , [jump to page] .
3. Letter 821 , [jump to page] , and letter 834 , [jump to page] .
- a. TLS with autograph corrections, six pages on six leaves, numbered from the second, in HP II-88; CcI in JMK EJ/1/5/326-31. Printed in Keynes, Collected Writings, vol. XIV, pp. 339-42. Reproduced by kind permission of the Provost and Scholars, King's College, Cambridge.
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