653. Harrod to J. M. Keynes , 7 April 1937 [a]

[Follows on from 652 , answered by 656 ]

51, Campden Hill Square, W. 8. #

7 April 1937

Dear Maynard

Many thanks indeed for your comments and letting me see the lecture notes and for all the trouble you have taken. I am so glad you found the book interesting. I still hope that you will derive that extra bit of profit from it that acceptance of its main thesis entails.

The essential point is that once the rate of increase of income slows down by more than a microscopic amount, the absolute amount of investment must fall: and this in turn leads to a decrease of income: and that to a fall of investment to zero aside from long period planning.

I quite see why you were worried by my assumption that the stock of capital and investment were increasing at the same rate. I am right in saying that they must be increasing at the same rate if the increase in the stock of capital is steady. Nor is there anything unrealistic about the idea that they will increase at the same rate except in the revival. Here of course the increase of investment is greater, which entails that the increase of stock is accelerating. I did not want to trouble the reader's head with acceleration, when I was trying to get across unfamiliar stuff about rate of growth. (I notice that you define the Relation in your notes in a most undesirably static way. It makes me feel about you slightly as you feel about critics of the General Theory!--namely that you wont re-orient your mind to the dynamic point of view.)

But the main point is that even if the rate of increase of investment exceeds the rate of increase of stock throughout the boom, this still makes no difference to the point that once the increase of consumption and so of stock required slows down, investment is no longer required to increase at all. Your arguments do not invalidate this in the slightest degree, or therefore my theory of the inevitability of recession to the bottom.

Yours

Roy

1. I quite agree with what you say about the necessity of supposing that forces operate upon both the Relation and the Multiplier to distort them from normal in boom and slump. So far as the Multiplier is concerned, I have referred, as you recognize, to the shift to profit. But I have not assumed the Relation constant either. cf. p. 59 [1] where I have referred to 2 forces, viz. changes in interest rate, and changes in relative prices of goods (on which you lay stress in your paper) tending to alter the Relation. And I refer anyhow to the first of these in the subsequent argument.

2. 1 I have already commented on what you say about my alleged slip. I suggest that you will have to give further thought to my problem of the Relation, before you can traverse my account on the lines you attempt. Trying to interpret what would happen on the supposition [b] you made on p. 4 top, [2] I supposed the rate of increase of consumption (and of stock of capital goods) to change from 2% to 2.2% and showed that this meant a per saltum increase of investment of 10% with a steady increase thereafter of 2.2%.

I now try a different interpretation. What you have actually written is obscure. "Let investment now increase by l0 per cent." You do not say at what rate it was increasing before. I assume 2%. You do not say whether you mean a per saltum increase and a relapse to the old level, or a maintained increase at the new rate. In the following figures I assume you mean the latter. You will perceive that you are wrong in supposing the stock of capital goods to increase by 2.2%. It increases first by less and then by more. On your assumption the stock of capital and consumption no longer increase steadily at any rate at all, but at an accelerating pace. The figures in the last line are the data and the others are worked backwards from that. Your change is introduced in column 4. 2

Period

1

2

3

4

5

6

Stock of capital = index of level of consumption 3

1. Absolute amount

100

102

104.04

106.284

108.7524

111.46764

2. Percentage increase

2

2

2.157

approx.

2.32...

2.48...

Investment

1. Absolute amount

2

2.04

2.244

2.4684

2.71524

2. Percentage increase

2

10

10

10

If the increase of investment exceeds the increase of the stock consumption must be increasing at an accelerating pace.

I grant that the picture given in my book is only a rough sketch: I merely claim that you cannot refute me on the lines you suggest.

3. Top of page 5. [3] "If it cant be prevented, it is difficult to see how it can be mitigated." "Concession required by common sense in the face of faulty logic." My position is twofold. (i) If you have sufficient public works to maintain a given rate of increase of consumption (the multiplier) you can prevent the slump. (ii) If you cant do this, you cant prevent a recession to the "bottom" (zero saving). What you may be able to do, however, is to raise the level of the bottom. Saving wont be quite zero, owing to inventions etc. A fall in the rate of interest may be a little help.

In your other notes you observe that my argument implies that entrepreneurs are only influenced by immediate prospects. This criticism is quite sound. In so far as they take a longer view, the cycle is mitigated. The investment based on the longer view is maintained. Thus Public Works, even if not properly timed, may help--the more so, the larger proportion of total investment that they contribute.

4. "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'." [4] This is perfectly right and I cant think why you suppose that the alleged "slip" makes any difference.

As a matter of fact it is not perfectly right. A very small decrease in the rate of increase of consumption would not command a decrease of net investment. But as we were so soon coming to a state in which consumption ceased to increase at all, it did not seem necessary to bother with these very small minutiae. Thus:--

(i) On my assumption. Increase of investment = increase of stock in first 3 columns.

Periods

1

2

3

4

Stock = index of consumption

100

102

104.04

106.08

Per cent increase of same

2%

2%

1.97%

Investment

2

2.04

2.04

Per cent increase of same

2%

0

Thus a fall in the rate of increase of consumption from 2% to 1.97% (column 4)--a trifling matter--wipes out the increase of net investment. Any greater fall would require a decrease.

(ii) But now take your assumption, with investment increasing more quickly than stock in first 3 columns

Periods

1

2

3

4

Stock

100

102

104.2

106.4

Per cent increase

2

2.157

2.11

Investment

2

2.2

2.2

Per cent increase

10%

0

Here a fall of the increase of consumption from 2.157 to 2.11--again a trifling matter--wipes out the increase of investment.

To satisfy my mind I take a very strong case of investment doubling in quantity. It still only takes quite a small decline in the rate of increase of consumption to knock it all out. Thus

1

2

3

4

100

102

106

110

2%

3.92%

3.77%

2

4

4

100%

0

Thus a decline in the rate of increase of consumption of about 4%--not a decline of consumption!--knocks the increase of investment out. Yet presumably people will save more from an income of 110 than from one of 106 and so the depression sets in.

Nor do I see why you object to the quotation from p. 119. [5] It is quite right and has no direct relation to my objectionable assumption that the increase of investment is not greater than the increase of stock.

Mind you I dont at all object to your point that the increase of investment is in fact greater than the increase of stock in a boom; I merely object to your thinking that it makes a material difference to my argument.

5. Towards bottom. [6] "An unchanged relation is incompatible with an unchanged multiplier." Not necessarily. For instance:--

1

2

3

4

100

102

104.2

106.447

2%

2.157%

2.156%

2

2.2

2.247

10%

2.156%

Here multiplier is the same in column 4 as in col[umn] 3. = . This does not of course mean that the multiplier is . It may be much less, e.g. 1/4 or 1/5 of this.

If the increase of consumption could be held at 2.156% approx. and the multiplier did not increase, a consistent advance could be maintained. Both rates of increase would remain stationary at 2.156%. The increase of investment could not of course be maintained at your 10%; but that would not matter so long as the volume continued large. (The ratio of the volume of investment to the size of income does not of course appear in all these calculations.) The trouble in fact is that the rate of increase of consumption cannot be maintained and the multiplier will fall. But there is nothing inconsistent in the assumption of a steady increase with relation and multiplier constant.

6. P. 9, top. [7] This seems rather a tall order if you are already working to full capacity. Suppose the normal increase is 3% and 12% of income saved. You suppose 5% on top of this, with only an extra % saved. Some might argue that this would mean a change in the Relation not from 4 to 3.9 but from 4 to . One cannot jigger around with the pre-existing capital. One can do something by working overtime: one might get this extra 5% once over I dare say, but not a second time. 4

Not that I am in general opposition to your notion that the Relation and the Multiplier are flexible. On the contrary, I agree with that.

I quite agree with your last 3 pages. [8]

7. I dont suppose you want to hear me say much on the miscellaneous notes. I could not help feeling in your comments on ch. 1 that you were "thinking in" saving and investment questions all the time. [9]

Of course in the dynamic system the static conditions have to be fulfilled: that was the object of the separate analysis.

We do not suppose the cycle to be governed by cyclical variation in the fundamental conditions (utility functions, cost functions etc.). There may be some variations there, but we neglect them. Therefore the system must be in neutral equilibrium over the range within which it swings. Therefore any one force must be equal and opposite to the resultant of all the others. The price movement is a de-stabilizer. \ the resultant of the others is a stabilizer. If the price drop required to induce a unit change in output is large, the stabilizers must be acting strongly. If I have to exert great strength to make the billiard ball move an inch over the cloth, the forces opposed to that action must be great.

You say "`when prices fall, the sooner the downward movement is called to a halt, the more powerful the stabilising forces must be ...' On the contrary, it seems to be that if costs were not plastic etc. etc. prices would always be constant, and the only thing that would change would be output." Precisely: but "on the contrary" is wrong; you repeat what I say. An infinitesimal price drop will take the billiard ball right across the table; the stabilizing forces are weak to the point of non-existence.

p. 59 top. [10] You say in addition to the causes I enumerate you would give that of your Galton Lecture. But it is there already! I say "in addition to the Net Investment required as a basis of increases of consumption ...."

I quite agree, as I have said already, that I over emphasize the influence on entrepreneurs of immediate prospects. I do. I over-explain the Trade Cycle. But isnt that rather an advantage? We can then introduce the various factors tending after all to make it not so bad.

p. 123. [11] I dont think I have confused the long term rate with the yield. Surely it is the rate, viz. the sum of money annually payable on stock divided by its present market price, that determines the cost of new capital to entrepreneurs. The fact that the market price may subsequently rise or fall and so affect the yield including capital gains and losses wont help or hinder the entrepreneur in raising new money. If a firm paying l0% wants to issue new shares, it is surely the current return of shares of similar status in the sense of dividend/market price which determines the premium which the issue house will advise.

p. 149. By home investment I mean home produced investment. I say in a footnote on p. 154 "the foregoing argument concerning net investment at home is independent of whether that is financed by domestic or foreign capital".

p. 156. [12] You are doubtful if "increased exports may so stimulate internal activity as to entail a greater increase of imports." Only of course if you take the Relation as well as the Multiplier into account. I already have a marginal note: "it should be made plain that this is dynamic." Increasing exports stimulate investment both for the production of them and also for the production of the extra home consumption consequent upon the increased income from exports through the multiplier. It is not only the increase of exports but the consequential increase of investment that goes to increase the multiplicand. And the consequent increase of income may be such as to raise imports more than exports.

R. F. H.

  1. 1. Harrod, The Trade Cycle ( 1936:8 ).

    2. Letter 647 , [jump to page] .

    3. Letter 647 , [jump to page] .

    4. Letter 647 , [jump to page] .

    5. Letter 647 , [jump to page] .

    6. Letter 647 , [jump to page] .

    7. Letter 647 , [jump to page] .

    8. Letter 647 , from [jump to page] to the end.

    9. Letter 647 , [jump to page] .

    10. Letter 647 , [jump to page] .

    11. Letter 647 , [jump to page] .

    12. Letter 647 , [jump to page] .

    1. a. ALS, three pages on two leaves, in JMK CO/3/73-75. Accompanying untitled notes, seven pages on seven leaves, in JMK CO/3/79-85. The letter is printed in Keynes, Collected Writings, vol. XIV, pp. 164-70.

      b. Ms: «supposal».

      c. Pencilled mark, probably by Keynes.


1. This paragraph to be taken in conjunction with comment already dispatched. [Harrod's note in the margin]

2. Method of calculation:--last line gives data: then third is calculated: then first: finally second. [Harrod's note in the margin].

3. These figures of course only give an index of consumption. Actual values would, on your assumption of stock = 4 years income, only be one quarter of this. Similarly in subsequent tables. [Harrod's footnote].

4. This paragraph is marked in the margin with a pencil vertical line--probably by Keynes.


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