[Comments on the "Essay in Dynamic Theory"]


See accompanying letter


Page 1, last line but one: "that demand is equal supply"--demand of what? If, as I think, you mean "the supply of savings is equal to the demand", it will be clearer to say so. [3]

Page 4: Your introduction of the phrase "warranted" is very good. [4] I shall certainly adopt it. It is most helpful and fills a felt want.

Page 6: You are wrapping up the influence of the rate of interest in the state of technology, and you do in passing mention this. [5] This is certainly convenient so far as the long period trend of the rate of interest is concerned, though not so convenient when applied to short period interest changes. I suggest, however, that it would be advisable to emphasise more clearly what you are doing. Moreover, you are making no reference to the "state of confidence". Presumably that also is wrapped up in the state of technology. But that is not nearly so convenient, since it is essentially a short period phenomenon. On the whole, my preference would be not to wrap up the rate of interest and the state of confidence in the state of technology, but simply to say that you were, at this stage of the argument, taking them for granted and that the influence of changes in the rate of interest or the state of confidence have to be superimposed on the present argument. Changes only really have to be brought in just in the same sort of way as you have brought in a change in the propensity to save on page 16. If you are to get your own specific point clear, it is better to segregate changes in all these factors. ( On page 16, by the way, the first sentence should run more strictly speaking "Suppose an increase in the propensity to save which means that the values of s are increased for all levels of income"). [6]

A further reason for segregating the rate of interest is the fact, which you do not, I think, mention, that a sudden change in the long term rate of interest is capable of causing a technological change, which means a large increase in the demand for capital which can only gradually be taken up. Thus the effect of changes in the rate of interest is quite a large subject, mainly distinct from your specific topic. To use a term I introduce below, a lasting change in the long-term rate of interest causes the temporarily warranted rate to exceed the normally warranted rate for a considerable period of time. [b]

Page 8: After "G is the rate of increase" add "in total output". [7]

Page 9: C is most certainly not ex-ante strictly speaking. [8] Ex-ante C is the investment the entrepreneurs actually plan to make. Your C is the addition they ought to plan to make. C is the planned investment which would equate ex-ante and ex-post investment. Since ex-ante now has quite a distinct meaning, I suggest that it would be much better not to bring it in here in a different sense, but to continue calling C the "warranted investment".

Page 10: [9] Your interpretation of my Treatise here is very happy. I am not sure that your interpretation would work out quite consistently all through. But what you say is certainly what I had confusedly in mind.

Page 12: Ex-ante saving is surely a chimera, which it is much better not to mention. [10] Moreover you are certainly not dealing with the chimera in question. You are concerned, not with ex-ante saving, but with the time-lag in ex-post saving before ex-post saving fully adjusts itself to change. Here again I should stick to the phrase "warranted". What you are dealing with is the difference between warranted and actual saving.

You are decidedly on the right track on the last paragraph of this page.

Page 15: [11] I come here to my first substantial comment. It seems to me that what you have in mind is substantially different from what you have said, and that your argument requires premises which you have not explicitly introduced. Moreover, I would retort, in return for what you have said about my Treatise, that you have here discarded too much of your previous work, which may nevertheless be influencing the background of your thought, but has disappeared from the text.

Perhaps my point can be best brought to a head by asking the question: what is "excessive output"?

If A w is the warranted current output of consumption industries and DI w of investment industries, whilst A and DI are the respective actual outputs, then presumably output is excessive if A + DI > A w  + DI w .

Let , where t is given by technology; [12] and = s, where s is given by the marginal propensity to save.

Now unwarranted output may mean

Now, for all you have said to the contrary, excessive output is compatible with any of these types of mistakes or with a combination of either of the first pair with either of the second pair. Assuming that entrepreneurs proceed by trial and error on the basis of results in the previous period, (ii) and (iii) are expansive alone or in combination; (i) (iv) are depressive alone or in combination; (i) accompanied by (iii) or (ii) accompanied by (iv) are equivocal. I could continue this argument further, but it would probably be a [c] waste of time to do so, since I fancy that the above is not at all what you have in mind. At any rate what your argument requires seems to me to be to start, not with excessive output in general, but output of investment goods beyond what is warranted. You are then tacitly bringing in the assumption that s is smaller than t. In this case an increase in investment beyond what is warranted causes, for multiplier reasons, an increase in consumption greater than the new investment can provide. Thus you get your point that the position is unstable and your paradox that an increase in investment beyond what is warranted leads to a simultaneous shortage both of investment goods and of consumption goods.

This essentially depends, however, on s being smaller than t, as is the case in your numerical illustration, where t =  and s =  . But if these values were reversed, so that s =  and t =  the conclusions would be reversed and excessive investment, instead of being expansive, would be depressive.

Moreover, I do not see that your result follows if the excessive output takes the form of an output of consumption goods beyond what is warranted, such as may have happened, for example, in America last year. An excessive output of consumption goods is not expansive. Therefore, I say that your argument needs excessive output of investment goods rather than excessive output in general, and is essentially dependent on the relative values of s and t, a premise you have not explicitly introduced.

Let me continue the argument a stage further. Suppose that there is excessive investment in the sense that C p  > C w . Then, I have argued that if t > s there will be a shortage both of capital and of consumption goods and hence further expansion. The supply of capital, however, will cumulatively catch up, unless C p  - C w constantly increases. If this latter term constantly increases, then the ceiling of full employment will ultimately be reached. But in general an obstacle to further expansion is brought about, not by the ceiling of full employment, but by the failure of actual investment to be constantly increasing beyond the warranted investment.

If I remember rightly, I am in all the above simply repeating what you yourself have taught me on previous occasions, but it all seems to be lacking from the present text.

Page 20: [13] In some stuff which he has lately published in Australia Colin Clark has dealt with imports exactly as you deal with them here, introducing a factor of propensity to import as a function of the current local income. He has a reference to this in an article which will be published in the September Journal. [14] You are doing for theoretical reasons so exactly the same thing as he has found convenient on statistical grounds that it deserves a reference.

Page 21: [15] What I have said here with reference to page 15 is distinctly relevant. It seems to me that from this page onwards you are drifting into some confusion between short and long period equilibrium. It is not the excess of warranted rate over natural rate which normally brings to an end excess of actual rate over warranted rate.

As you say on page 24, the warranted rate of growth is itself a function of the level of employment. [16] If the warranted rate corresponding to full employment is less than the natural rate corresponding to full employment, then, of course, I agree with what you are saying to the effect that full employment cannot be sustained. But this is equally true of any level of employment. If, as one can reasonably suppose, the warranted rate corresponding to a given level of employment rises as employment rises, then a [d] long period equilibrium is found with that level of employment at which the corresponding warranted rate is equal to the corresponding natural rate. This becomes the "normal rate" of growth, and we have equilibrium at a level of employment which is less than full employment. But I repeat that there is no special virtue in full employment in this connection. Full employment only functions as a brake in the rare circumstances (apart from war) in which the excess of actual investment over warranted investment is perpetually increasing without limit.

The ideal is, of course, to establish a rate of interest, a state of confidence and a propensity to save so related to one another that the normal warranted rate of growth is equal to the natural growth corresponding to full employment. In which case, full employment becomes the equilibrium level of employment.

Page 23, paragraph 14 (i): [17] Is not there a confusion here between the normal warranted rate and an actual rate which exceeds the normal warranted?

Page 26: [18] This is all very good indeed, but rather difficult. Perhaps worth re-expressing in language without the use of any symbols. The passage is intrinsically difficult, and the difficulty is added to by the fact that the reader who is not fully familiar with the symbols has to refer back and translate.

To sum up the immediately preceding discussion, given the propensity to save, the state of confidence, the rate of interest and the state of technology, each level of output and employment has a warranted rate of expansion corresponding to it. Thus, each warranted rate of growth has a "normal" warranted (rising) level of output. The normal level of employment will be that level for which the natural rate of growth is equal to the warranted rate.

In a slump (or boom) three things happen. A level of employment is reached at which

(i) the normal warranted rate is different from before,

(ii) the temporary warranted rate is different from the normal,

(iii) the actual rate is different from the normal warranted rate and is governed by (i.e. is trying to be equal to) the temporary warranted rate.

I am here using "temporary warranted rate" for that rate which is in fact the warranted rate so long as the actual rate of investment is maintaining its excess over the normally warranted rate of investment.

I am afraid this is rather a rigmarole, but I hope you will see what I am driving at.

Page 31: Where you say that inflationary policy may be most beneficial "in the later stages" [19] --why only in the later stages? In the conditions you are considering, there is a chronic need for a lower rate of interest.

Page 32: [20] Where you speak of the actual rate, you mean, it seems to me, the temporary warranted rate. The point is that, in the first phase of the excessive investment, an actual rate in excess of the normal rate is in fact warranted, in the sense which you have given to this term, namely, that entrepreneurs will be satisfied with the results of their action. I [e] ought to have emphasised this more strongly at an earlier stage of my comments. There seems to me to be frequent confusion between an actual rate which is just a mistake in the sense that it will leave entrepreneurs dissatisfied, and an actual rate which is different from the normally warranted rate but is not different from a temporarily warranted rate and does not leave entrepreneurs dissatisfied. Entrepreneurs are not losers by the "excessive" output which they produce during a boom which cannot be permanently sustained.

What you are saying is that the normally warranted rate is unstable because a departure from it induces a temporarily warranted rate which carries the departure still further in the same direction; though this cannot be permanently sustained because the "excessive" investment is cumulative and eventually consumption cannot keep up with it; so that there occurs a reversal back to (and probably beyond) the normally warranted rate.

Page 35, Paragraphs 23 and 24: [21] All this is very good indeed.

  1. 1. Harrod, "An Essay in Dynamic Theory" ( 1939:7 ); the draft referred to is reproduced here as essay 19 .

    2. See [jump to page] .

    3. Essay 19 , [jump to page] . Keynes's suggestion was not accepted.

    4. Essay 19 , [jump to page] . Harrod, however, had some doubts about Keynes's understanding of his definition (letter 814 , [jump to page] ); Keynes agreed (letter 817 , [jump to page] ), and Harrod introduced a further specification (see note 8 to essay 19 ).

    5. Essay 19 , [jump to page] . See note 13 to essay 19 for Harrod's alterations.

    6. Essay 19 , [jump to page] . Keynes's suggestion was accepted.

    7. Essay 19 , [jump to page] . Keynes's suggestion was incorporated into the final version.

    8. Essay 19 , [jump to page] . For Harrod's amendment, see note 21 to essay 19 .

    9. Essay 19 , [jump to page] .

    10. Essay 19 , [jump to page] . Harrod met Keynes's objection by adding a footnote to p. 20 of the final version (see note 27 to essay 19 ).

    11. Essay 19 , [jump to page] .

    12. The symbol t does not appear in the draft nor in the final version of Harrod's "Essay in Dynamic Theory". Its meaning, as defined by Keynes, recalls the "Relation" in The Trade Cycle (Harrod 1936:8 ), for it refers to increases in output rather than in income. Later, however, Keynes accommodated to Harrod's definition.

    13. Essay 19 , [jump to page] .

    14. C. Clark and J. G. Crawford, National Income of Australia, Sydney and London: Angus & Robertson, 1938; C. Clark, "Determination of the Multiplier from National Income Statistics", Economic Journal, September 1938, in particular pp. 437-38. In the final version of the "Essay" Harrod did not refer to these writings.

    15. Essay 19 , [jump to page] .

    16. Essay 19 , [jump to page] : Harrod is listing the forces tending to depress the warranted rate during a depression.

    17. Essay 19 , [jump to page] .

    18. Essay 19 , [jump to page] (paragraph beginning "What precisely happens ...").

    19. Essay 19 , [jump to page] .

    20. Essay 19 , [jump to page] (section 20).

    21. Essay 19 , [jump to page] .

    1. a. TLS, one page, in HP II-84. Annexe comment: TD, with autograph corrections and initialled addition, nine pages on nine leaves, numbered from the second, in HP II-85. CcI, without some of the autograph additions, in JMK EJ/1/5/295-304. Printed in Keynes, Collected Writings, vol. XIV, pp. 321-27. Reproduced by kind permission of the Provost and Scholars, King's College, Cambridge.

      b. This autograph sentence was introduced as an afterthought.

      c. Ts: «be waste».

      d. Ts: «then long».

      e. The following specification (from this point on to the end of the next full paragraph) was inserted as an afterthought. It is autograph, initialled and dated 18 August 1938.

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