## 656. J. M. Keynes to Harrod

, 12 April 1937[a],[1]

[Replies to 652 and 653 , answered by 657 ]

I have undoubtedly misunderstood you and there is no question of an arithmetical slip. But the odd thing is that, having invented so interesting a theory, you should not have mentioned it in the book! For I do not see how I could possibly have understood what you were driving at in the passage where I accuse you of an arithmetical slip. Indeed, I should doubt whether any reader who has not talked or corresponded with you could be aware that the whole of the last half of the book was intended to be in relation to a moving base of steady progress. [2] Moreover, it is not as though your theory was a simple one which only had to be mentioned in a sentence. It seems to me to involve important and difficult considerations about the relation of the rate of progress with the Multiplier and the Relation. Finally, you put your readers off the track by calling your book "The Trade Cycle", and arguing as though your thesis principally related to that. For it seems to me that your theory has little or no bearing on the trade cycle, though none the less interesting for that. The phase of the boom is most certainly not a phase of steady growth. Yet you seem to be assuming that it is when you are considering the transition from the boom to the slump. However, having said so much, let me return to the main issue.

The following are the first ideas which occur to me:--

1. It is necessary to explain whether by steady growth you mean steady growth of capital or steady growth of income. For the two are only the same on the assumption that the Relation is constant. In what follows I assume that you are dealing with a steady rate of growth of capital; the rate of growth of capital being designated by y.

2. If M is the Multiplier and R the Relation, the fundamental equation [3] is

Thus a steady rate of growth is impossible unless MR is constant; and even on this assumption it does not follow that the rate of growth, though steady, will be one which is compatible with full employment.

3. It is only by a miracle or by careful design that the values of M and R will be such as to be consistent at the same time with steady growth of capital and full employment.

4. If a position of steady growth is once established, a change in the rate of growth is impossible so long as MR is unchanged; and a per saltum change cannot occur unless it is associated with suitable changes in R and M.

5. Steady growth with a constant value for the Relation implies a constant Multiplier. Now M in the above is the average Multiplier, not the marginal Multiplier. One ordinarily assumes that, as wealth increases, the marginal Multiplier declines. It follows that a constant Multiplier is very unlikely with increasing growth; the natural assumption would be that with increasing growth there is steady decline in the average Multiplier.

6. Consequently, if we are to have steady growth, then, assuming that M is all the time declining, R must be all the time rising, i.e. interest must fall fast enough for the rise in R to offset [b] the fall in M.

7. You complain that I assume a static definition of R. [4] I do not know what your definition is. But, unless there is a fall in the rate of interest, I see no reason why there should be any steady movement in R one way or the other in conditions of steady growth.

8. So far, we have excluded the possibility of changes in expectations. In fact, however, the rate of investment does not depend on current consumption, but on expectations (though the latter are, of course, influenced, perhaps unduly, by current consumption). Thus, unless expectations are of a constant character, one would anticipate short-period changes in the Relation. Apart from other difficulties, there will only be a motive to increase capital at the same rate at which consumption is changing, if expectations are of a particular character.

9. Thus the system has several degrees of freedom. For example, one might have (a) steady growth of consumption and steady growth of investment with unsteady expectation offset by unsteady interest, or (b) steady growth of consumption and unsteady growth of investment offset by an unsteady Relation and an unsteady Multiplier.

10. Since in fact the growth of population and the growth of technique are not steady, there is no presumption in favour of steady growth, although probably there has been one in recent conditions in favour of growth. If there is continuous full employment, then there will be as high a rate of (unsteady) growth as is compatible with other factors, though different institutions involving a different Multiplier and a different rate of interest in conditions of full employment might have led to a somewhat more rapid rate of growth.

11. Thus steady growth and full employment are different criteria of policy. Full employment may require unsteady growth and steady growth may involve unsteady employment.

12. You have shown, I think, that steady growth can only occur as the result of a miracle or intense design. But this is essentially a long-period problem, and steady growth a long-period conception. As I have said above, I do not see that the theory has any application worth mentioning to the trade cycle. The maintenance of steady growth is at all times an inherent improbability in conditions of laissez-faire. Your argument seems expressed, however, as though the conditions of steady growth were satisfied during the boom and the inherent improbability or impossibility only came into existence with the end of the boom. Both the boom and the slump, that is to say the whole of the cycle, are characterised, I should have thought, by none of the conditions of steady growth which you are assuming as being present.

13. The central idea which you have brought forward seems to me to be the incompatibility of steady growth with such values and such fluctuations in M and R as will exist in conditions of laissez-faire, but you have not shown that steady growth is a more desirable criterion than full employment. Nor, if it were, have you shown that design is theoretically incapable of maintaining values of M and R compatible with it. What you have shown is that, if conditions of steady growth exist, the smallest fluctuation in the value of MR will cause those conditions to break down.

Turning to small points, I still do not understand why you call those forces stabilisers which, we agree, are those which cause prices to fluctuate. However, I am not really quarrelling here with anything except a lack of explanation as to what you have in mind. I still do not follow what I am meant to understand from page 123. [5]

I have just been reading your review of Joan. I quite agree with what you say about her treatment of the effect of inventions. [6] Your line of approach seems to me to be the right one. I am not quite sure what assumptions the elasticity of substitution method requires, but I think they would be found to be inappropriate.

P.S. The enclosed is a spare copy, so that I return it, although, of course, it needs much amendment in the light of your reply.

I have adopted the above schematism so as to try to follow out your theory. But I don't much like it; for the use of R brings in a false suggestion that the rate of new investment relatively to consumption must normally be such as to maintain the Relation constant.

A passage in your reply implies that a short-period change in the Relation involves "jiggering round with the pre-existing capital". [7] But this is not so. It merely means a change in the relative proportions of different kinds of consumption. [c]

R. F. Harrod Esq., Christ Church, Oxford.

- 1. Some rough
notes survive (housed in JMK CO/3/97-99), which Keynes obviously
used while preparing this letter:
where y is rate of growth of capital

- Thus the rate of steady growth
with y constant and R constant is given by the value of the
multiplier and this rate it is not necessarily compatible with
full employment.
1) But there will be one value of M which will allow the <+>

2) If M and R unchanged, a change in the rate of growth is impossible. Thus per saltum change impossible unless <some other> changes in R and M.

3) Steady growth with constant relation implies constant multiplier, i.e. average M = marginal

But if M falls with progress, R must rise for steady progress, i.e. interest must fall.

5) In general steady progress requires MR constant

6) Moreover in fact rate of investment does not depend on current consumption but on expectations (though the latter is influenced by current consumption). This means that the relation will change (i.e. character of competition changes).

Thus one might have steady consumption and steady investment with unsteady expectations offset by unsteady interest, or steady consumption and unsteady investment offset by unsteady relation and unsteady multiplier. System with several degrees of freedom.

[7]) But since growth of population [and of] technique are not steady there is no presumption in favour of steady growth. But if there is full employment, then there will be as high a rate of (unsteady) growth compatible with other factors; though different institutions leading to a different multiplier, leading to a different rate of interest in conditions of full employment might lead to a more rapid rate of growth.

[8]) Steady growth and full employment are different criteria. Full employment may require unsteady growth.

But theory of steady growth has no application worth mentioning, I should have thought, to the Trade Cycle. Essentially a long period conception.

- Thus the rate of steady growth
with y constant and R constant is given by the value of the
multiplier and this rate it is not necessarily compatible with
full employment.

- 2. Before
reading The Trade Cycle, Keynes had been instructed by Robertson
that Harrod was, "of course, trying to [...] lay down the
conditions for a `steady advance'" (Robertson to Keynes,
undated--but end of January 1937--, in JMK CO/3/47), and that he
was "chiefly interested in a growing economy" (Robertson to
Keynes, undated--February or March 1937--, in JMK CO/3/50).
3. The following calculations survive (JMK CO/3/99), leading to the fundamental equation:

where y is rate of growth

Consistently with the notation Keynes used in commenting on letter 647 (see note 8 ), C stands for the stock of capital goods.

4. Letter 653 , [jump to page] .

5. Letter 653 , [jump to page] .

6. Harrod, "Essays in the Theory of Employment" ( 1937:9 ), pp. 328-29.

7. Letter 653 , [jump to page] .

- a. TLS
with autograph corrections, formula and addition, seven
pages on seven sheets, numbered from the second, in HP
II-72. Cc including the autograph additions in JMK
CO/3/86-92. Printed in Keynes, Collected Writings, volume
XIV, pp. 170-74. Reproduced by kind permission of the
Provost and Scholars, King's College, Cambridge.
b. Ts: «off-set» (in the next occurrences of the word as well).

- a. TLS
with autograph corrections, formula and addition, seven
pages on seven sheets, numbered from the second, in HP
II-72. Cc including the autograph additions in JMK
CO/3/86-92. Printed in Keynes, Collected Writings, volume
XIV, pp. 170-74. Reproduced by kind permission of the
Provost and Scholars, King's College, Cambridge.