Mr Harrod points out that if the make-up of consumption is unchanged, so that the amount of capital employed is strictly proportioned to the amount of consumption, consumption and capital must necessarily increase in the same ratio. This principle of connection he calls the "Relation". On the above assumption as to the constant make-up of consumption (which Mr Harrod does not, perhaps, sufficiently emphasise) net investment is a function, not of the absolute amount of consumption, but of the increase in consumption. If consumption is constant, then net investment will be zero. Thus large proportional changes in net investment will correspond to small proportional changes in consumption.
The above is on the assumption that there is no surplus capital equipment. Thus it does not apply in the earlier phase of a recovery from depression. For as consumption increases, the demand can be met by bringing existing equipment into use. At this stage the recovery will be sustained, apart from the specific increase in investment which is the primary impulse to the recovery, by the increase in working capital; since the stocks of unfinished goods will increase roughly in proportion to the increase in employment. In my own discussions of the Trade Cycle I have emphasised the importance of this factor, namely the re-investment in working capital, particularly the possible reactions of the decline in net investment from this source as soon as employment ceases, as it must sooner or later, to increase still further. But I have been too apt to assume that the surplus labour and the surplus equipment when the recovery begins are more or less proportioned to one another and will be absorbed into employment pari passu.
Mr Harrod's theory corrects the inadequacy of this tacit assumption. He points out that at the end of a depression the surplus labour is likely to be proportionately much larger than the surplus equipment. Indeed he might have emphasised this even more than he has done. If population is increasing, the total labour supply will be greater than it had been at the peak of the previous boom; whilst much of the capital equipment will be declining all through the depression through its being unprofitable and indeed useless to maintain it intact by replacing completely losses through wear and tear and obsolescence. If no other factor comes to the rescue, recovery will begin precisely because, on account of wastage, some kinds of capital are no longer in surplus supply. Thus we need to consider the second phase of the recovery, when, broadly speaking, capital equipment is fully employed but there is still a surplus of labour; though there is, in fact, no sharp division between the two phases, since some kinds of equipment will be in short supply from the start and the increased demand will bring into use old equipment of gradually declining efficiency. Broadly, however, we can distinguish between the situation where most kinds of goods can be supplied at no great increase of price in terms of wage units and the situation where there is a famine in many kinds of goods, and adequate increase in the supply of which in response to demand is for the time being a physical impossibility, even though there is still a surplus of labour. It is to this phase of the recovery that Mr Harrod's considerations particularly apply.
The next stage of his argument is to consider the combined effects of the above and of the Multiplier. Here, however, it appears to me that he is in error. There is, indeed, an important result to be obtained along his lines, but not the same result which he reaches himself.
According to the Theory of the Multiplier, there is an arithmetical relation between the level of consumption and the level of net investment, so that, other things being equal (i.e. nothing having occurred to change the value of the Multiplier) consumption and net investment rise and fall in the same proportion. Now this is in manifest contradiction to Mr Harrod's "Relation", according to which net investment must (as soon as existing equipment is fully employed) fluctuate in a much greater proportion than consumption. How is this contradiction to be resolved?
Mr Harrod's own solution is vitiated, if I have understood it rightly, by a straight-forward slip in arithmetic. The critical passage is to be found at the top of p. 91 where he writes:--"Therefore consumption will increase in the same proportion as net investment increases, that is, in the same proportion as the stock of capital goods increases".  (my italics) The error creeps in with the words which I have italicised. For a moment's consideration will show that the proportion in which the stock of capital goods increases has nothing to do with the proportion in which net investment increases. For let us suppose that the stock of capital goods is 100 and net investment is 2 per cent per annum of the existing stock. Let net investment now increase by 10 per cent. Obviously the stock of capital goods does not increase by 10 per cent, but by 2.2 per cent.
The result of Mr Harrod's mistake is to lead him to believe that for the time being all is well and that the stock of capital goods can increase fast enough to reconcile the Relation and the Multiplier. This satisfactory state continues, he argues, so long as the rate of net investment is increasing by however small an amount. But obviously this cannot continue indefinitely. A point will come when the rate of net investment will cease to increase, and the effect of this (through the Multiplier) on consumption will be, he argues, such as to make even a steady rate of net investment untenable (through the Relation). Thus, as soon as the rate of net investment ceases to increase, a slump is inevitable. 1 There are many passages in which he maintains that this situation, whilst it can be mitigated, cannot be prevented;--though, if it cannot be prevented, it is difficult to see how it can be mitigated, and I suspect that his admitting the possibility of mitigation is a concession required by common sense in the face of faulty logic. The consequences of the original slip appear particularly plainly in a passage on p. 97:--"When the rate of increase of consumption begins to slow down, what is required in net investment is not merely a slowing down in its rate of increase but a decrease."  Or again on page 119:--"If any given rate of advance is to be maintained in perpetuity, it must be limited to the rate of growth of population and efficiency. This means that any excess of the stock of unemployment over the stock of redundant capital capacity not obsolete can never be taken up." 
Now since the rate of increase in the stock of capital will, in fact, be, not the same as, but much smaller than the rate of increase in net investment, the correct conclusion is that an unchanged Relation is incompatible with an unchanged Multiplier from the very moment when the existing capital equipment has become fully employed. The explanation lies, of course, in the fact that in such circumstances neither the Relation nor the Multiplier can remain unchanged.
Let us begin with the Relation. Those articles of consumption, plant for production of which is temporarily in short supply, will rise in price relatively to those articles which can be produced more readily either because there is still surplus plant to produce them or because they use so little plant that it can be rapidly augmented to the necessary extent. This change in relative prices will proceed to whatever length is necessary to divert consumption into the channels where it can be satisfied, or, if need be, to postpone consumption. It begins in particular cases very early in the recovery,--as soon, indeed, as there is any form of capital equipment in short supply. Its progress can be measured by the gradual rise in any representative index of commodity prices in terms of the wage-unit. But we can reckon, roughly speaking, that the second phase of the recovery has begun when supply becomes much less elastic in the sense that a small increase in employment is accompanied by a substantial rise in commodity prices in terms of the wage-unit. Mr Harrod points out that this is likely to occur when there is still a good deal of unemployment of labour. This is important because a change in policy may well be indicated as advisable when this phase is entered. In effect, this was, indeed, the burden of my recent articles in the Times.  And the peculiarity of the recovery in the United States which culminated in 1929 was the fact that a very high level of output was reached without entering this second phase, presumably because the pace of recovery during the previous four or five years happened to be suitably adjusted.
Thus the change in the relative prices of different consumption-goods has the effect, firstly of prolonging the period during which equipment is still in surplus by diverting consumption to the equipment which is most readily available; and secondly of changing the Relation between the rate of consumption and the stock of capital by diverting consumption to the types which require relatively less capital plant to produce them. In short, the public must consume what it can get. The price mechanism will at the same time insure this and provide a stimulus for the production of plant which in due course will allow the public to consume what it would like better. The case of house-room, which is a particularly capitalistic kind of consumption, is an obvious illustration. As the income of the public increases, they would like to spend more of it on house-room than is for the time being practicable. The price mechanism (modified, perhaps, by controls) serves both to curb present demand and to augment further supply. In the meantime the Relation has to suffer such temporary change as is required by the prevailing conditions of short-period supply and demand. There is no warrant for treating the Relation as immutable at all phases of the Cycle.
Next as regards the Multiplier. Here again forces come into play, as they obviously must, to produce the necessary adjustments. In the first place, the rise in the price of output in terms of the wage-unit causes what Mr Harrod conveniently describes as a "shift to profit", which reduces the propensity to consume. In the second place, apart from the reduced propensity to consume resulting from a redistribution of incomes in favour [c] of the entrepreneurs, the fact that consumers cannot at the moment get just what they want will cause them to "save up" until they can. Those who would like to spend their increased income on furnishings and house-room will wait until these commodities can be obtained at a more reasonable price; and prices will necessarily rise (in terms of the wage-unit, be it noted) until a sufficient number of prospective purchasers are persuaded that it is worth while to wait.
Finally, the rise in prices may have some effect in curbing the inducement to invest. For unless the rise in prices in terms of the wage-unit is expected to be permanent (which only a foolish person could expect), a point comes when it is not worth while to pay present prices for equipment, the fruits of which will be sold at corresponding prices only during a portion of its life.
Thus one way and another, the growth of investment and the corresponding growth of consumption must necessarily be adjusted to one another, so that for the time being both the rate of investment and the stock of capital bear a less than normal ratio to the level of consumption. Moreover, an arithmetical example will show what very moderate changes are required to produce an adjustment. Let us suppose that consumption is 100 and the stock of capital in use is 400, so that the "Relation" is 4; that, in the above circumstances, the marginal multiplier is reduced to 2, so that an increase in income is divided equally between consumption and investment. In such circumstances a further increase of 5 per cent in output and employment will only require a temporary [d] reduction in the Relation from 4 to 3.9, even before allowing for mitigations due to depletion of stocks, the bringing into use of inefficient and obsolete equipment, the overtime employment of efficient equipment and the expansion of those kinds of plant which can be rapidly and cheaply expanded. Thus the problem of temporary adjustment is far from insoluble.
Indeed these elements of "give" in the system allow for a gradually continuing recovery in the level of employment of labour during the second phase after the existing equipment has been brought fully into use. Prices (in terms of the wage-unit) will pass their peak and gradually decline; the tendency of the Relation to return to its normal figure will maintain net investment at a figure sufficient to allow a gradual increase in employment; whilst the tendency of the Multiplier to return to its normal figure may allow employment to increase even though net investment is falling away.
Provided that the rate of interest is not raised to an inappropriate figure, I see no reason why this process should not continue until the Relation and the Multiplier have both returned to their normal; since so long as either of them is below normal there is a strong inducement to new investment. It may be that this process will be completed before the whole of the surplus of labour has been absorbed. But whether this is so or not, a new problem arises at this stage or may have been gradually developing before it.
For, at this point aggregate income in terms of wage-units is not capable of increasing further at anything like the same pace as before, since it can no longer be materially augmented by bringing into use a reserve of labour previously unemployed. And we are thrown back for a stimulus to a further improvement in income on the demand for increased capital arising from either (a) an increase in population or (b) an improvement in the standard of life or (c) an increase in the ratio represented by the "Relation". Yet the theory of the Multiplier teaches us that we cannot even maintain aggregate income at the level we have reached unless the demand for new capital can be kept at the proper figure.
Thus during the recovery the potential demand for capital is excessive and has to be held back by changes in prices which temporarily modify the Relation and the Multiplier. It is when recovery is all but complete that the real problem arises--a problem which has never yet been solved--of how to prevent a relapse back again.
The problem has never been solved, even though we have had hitherto certain factors in our favour, namely a continuous and large increase in population and a continuous and large increase in output per head. These have served to moderate the extent and the duration of the decline, but no more. We can illustrate the dimensions of the problem by figures similar to those which I gave in my Galton Lecture; though the figures now to be given, whilst not unplausible, are intended only to be illustrative and hypothetical.
Let us assume that the Relation is constant in the neighbourhood of 4;--which means that the stock of capital is the equivalent of four years income. Let us suppose that population is increasing at 1 per cent per annum, and that the standard of life is also increasing at the rate of 1 per cent per annum. And let us take the average Multiplier at 10 in conditions of full employment, which means that the public is disposed to save one-tenth of its income (the marginal multiplier will, of course, be much less--more like 2 or 3 perhaps). Now these particular figures are incompatible with the maintenance of full employment. For with a constant Relation the increase in population and the standard of life require an increment of only 2 per cent per annum in the stock of capital; whereas the Multiplier demands an increment of per cent per annum for the maintenance of full employment. Thus the maintenance of a steady rate of full employment requires that we should either diminish the Multiplier by modifying the distribution of incomes or in some other way, or raise the Relation by a reduction in the rate of interest. If population ceases to increase, it is obvious that the problem is correspondingly aggravated.
Thus it is probable that a rate of interest, which could be sustained without difficulty during the process of recovery, will prove fatal to the maintenance of full recovery after it has been attained. It is for this reason that I strongly advocate not raising the long-term rate of interest during the period of recovery. But the grounds for this opinion can be further developed as follows.
If the long-term rate of interest could be controlled on short-period considerations, it would obviously be a useful weapon for regulating the pace of recovery. We could have a high long-term rate with a view to moderating the pressure whilst the mere impulse of the recovery was itself providing a sufficient demand for net investment, and a low long-term rate after recovery was complete. But it is obvious that such a policy is impracticable, indeed impossible, under a system of individualism. For the long-term rate must necessarily conform to the market's expectations of changes during the currency of the loan; so that, apart from mistakes, the long-term rate at any time can only depart by a strictly limited small amount from the expected average rate over the period in question. For this reason the long-term rate is ineligible for use as a short-period weapon. If, indeed, the short-term rate had the efficacy which Mr Hawtrey attributes to it, it would be a different matter; and the above would not apply to changes in the short-term rate for what they were worth, if it were not that this policy is liable to have an exaggerated effect on the market's confidence towards the long-term rate. I think that it is safe, therefore, to keep the long-term rate during the period of recovery only a very moderate degree higher than what will be required when the recovery is complete; and to depend on price-movements and on various indirect measures to retard investment for keeping the rate of expansion within bounds. In any case, after prices have reached their peak and there are indications that the Relation and the Multiplier are returning to normal, it is peremptorily required that the rate of interest should fall and other measures to stimulate investment be [e] brought into play. In the past, unfortunately, the peak of prices has been associated with an increased and unsatisfied demand for money which has always produced the opposite effect.
J M K
2. Keynes annotated a number of remarks in the margin and on the last page of his copy of The Trade Cycle, which is housed in the Marshall Library of Economics in Cambridge. Some of these annotations were not elaborated into the "Miscellaneous notes":
p. 57: Keynes underlined the first line, and commented: "i.e. after full employment of existing capital."
p. 57, line 24: Keynes underlined the words "are incompletely mobile", and commented: "No need to assume this."
p. 59, line 23: Keynes underlined the words "this is right and proper", and remarked: "But not at the top of the boom."
p. 96, top: Keynes noted: "Only a fall in the rate of interest can <counter> the <+>".
p. 113, beginning of full paragraph: Keynes remarked: "If my earlier criticisms are correct, all this of course falls to the ground."
p. 121, line 4: Keynes underlined the word "fluctuate", and asked: "fluctuate or change?"
p. 144, lines 4-12: Keynes marked the passage in the margin, and wrote: "Yes."
p. 145, end of section: Keynes commented: "? if the real resources for <+> investment do not exist."
p. 148, line 7: Keynes underlined the word "unless", and commented: "but they will."
p. 153, lines 14-15: Keynes underlined the words "by a blessed chance", and wrote in the margin: "or on purpose."
On the last page of the book, Keynes wrote:
On the dust jacket, Keynes wrote:
. Thus if multiplier is greater than inflation results, which is very likely for . Various <mitigations>: (1) prices from consumption (a small change is effective) <+> capitalist (2) high prices for capital goods <bring> obsolescent plant back to <+> use (3) ditto <regards> investment since prices expect[ed] to fall (4) shift to profits lowers multiplier (5) propensity to spend <raising> saving.
3. "Some Economic Consequences of a Declining Population", originally published in the Eugenics Review, April 1937, and reprinted in The Collected Writings of John Maynard Keynes, vol. XIV, pp. 124-33. The factors affecting the demand for capital are listed on p. 126, and had already been discussed by Harrod and Keynes in letters 632 , 633 and 634 .
4. Keynes marked the passage in the middle of the page with two vertical lines in the margin, added the word "temporarily" before "justified by results", and noted: "Yes--until full employment is reached."
5. Keynes commented in the margin: "But not over the whole course of the investment."
6. On line 21, before the word "investment" Keynes inserted "home-produced". On p. 146, at the beginning of full paragraph, Keynes wrote: "At what point is this assumption <dropt>?" This passage was the subject of an exchange between Keynes and Robertson: on 19 March 1937, Keynes pointed out to Robertson that at this point Harrod was assuming that "no capital accumulation is occurring". In an undated note, Robertson replied that the assumption is removed on p. 149: "he is, after all, chiefly interested in a growing economy". On 27 March, Keynes admitted that he "had not realised that the rather obscure passage on page 149 was intended to remove the preliminary assumption", and remarked that this passage "gives the clue to where the confusion lies" (these documents are filed in JMK CO/3/49-51).
7. Keynes is here referring to the argument with Robertson on the foreign trade multiplier: see note 2 to letter 618 .
8. Keynes marked this passage with a question mark, and commented:
But §mp is not equal to §mp."
9. Keynes marked this passage with two question marks in the margin.
10. This sentence is actually on p. 114, and "slack" should be read instead of "stock". In the margin of this passage, Keynes commented: "This is the fundamentally erroneous conclusion".
11. "Borrowing for Defence: Is it Inflation", The Times, 3 and 11 March 1937.
- a. TLS with autograph correction, two pages on two leaves, in HP II-69, Cc in JMK CO/3/54-55. Annexes: "Miscellaneous notes", TD with autograph corrections, four pages on four leaves, in HP II-70, Cc in JMK CO/3/56-59; Untitled note: CcTDI, with autograph corrections, 13 pages on 13 leaves, numbered from the second, in HP II-71, Cc in JMK CO/3/60-72. Harrod pencilled on the top of the first page of his copy. "Am I right in assuming you want this back. If not, I should like it." The letter and notes are printed in Keynes, Collected Writings, vol. XIV, pp. 150-63. Reproduced by kind permission of the Provost and Scholars, King's College, Cambridge.
b. Ts: «rate».
c. Ts: «facour».
d. Ts: «remporary».
e. Ts: «investment brought».
1. E.g. p. 104. "The trouble is that, when any decline of net investment sets in, a recession to the bottom is entailed and we have to begin the climb all over again from there; an ordered change from one rate of net investment to a lower one is impossible without this interlude." [Keynes's footnote].
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