803. N. Kaldor to Harrod , 9 August 1938 [a]

[Replies to 802 ]

Sedge Copse, Burley Street, New Forest, Hants.

9 August 1938

My dear Harrod,

Thank you for your interesting letter. I am afraid I still do not agree with it but I now again begin to hope that our controversy may yet end in agreement.

I very much regret that you found my letter so difficult. This worries me all the more because I am now writing a paper in which most of this stuff comes in; [1] & if you find it difficult, the "representative reader" may find it quite indigestible. [2] However, the difficulty may have been partly due to the fact that several things discussed & defined in previous letters (e.g. "marginal real wages") were not re-defined; & of course, you couldn't remember all I wrote in letters written a [b] long while ago.

(1) As to the way of measuring capital. There are two reasons why it cannot be done in terms of "real waiting", as you suggested. [3] First, that the average duration of the productive process can only be determined [c] in very special cases of productive technique, & we cannot confine our analysis to such cases (Cf. a paper of mine, of which I send you a reprint [4] ). Second, in an analysis of the equilibrium of the firm we must choose our unit in a way as to conform to the actual scale of choice the firm is confronted with. Land can be measured in physical units, because it is bought & sold in acres. Similarly labour in "man-hours". But capital, rather "capital-disposal" is not bought & sold in units of waiting, & consequently a "supply curve of funds" cannot be drawn if measured in that way. The problem I am interested in, is [d] what happens when e.g. the supply curve of labour to the firm changes, the supply curve of capital being given. If we measured capital in your way, this supply curve could not be regarded as given, but would have to be re-drawn (since the marg. cost of borrowing, for the same amount of real waiting, would no longer be the same.) Even in the purest of pure analysis, the quantity of capital invested must be measured in units of product invested--since, ultimately it is that which is invested; the product foregone--or, if [e] there is more than one kind of product, in terms of that product--which serves as a "numeraire". Measuring it in terms of the product, or the numeraire, is of course the same thing as measuring it in money. (Not entirely. For measuring it in money we can distinguish between a rise in product prices--i.e. a shift in the demand curve to the right--or a fall in wages--i.e. a shift in the supply curve of labour to the left. Measuring it in product, or in terms of wage-units, they come to the same thing. The most convenient thing is to follow Keynes & measure it in wage-units [5] ) If there is any a-symmetry here--between the way labour is measured & capital is measured--I am afraid it is in the nature of the problem & cannot be disposed of. (The trouble about measuring a unit of capital as a "unit of labour invested for a unit of time" is that [f] the "unit of time" relevant here is not real time--hours--but something which itself varies with the rate of interest. But this is a very involved problem which cannot be gone into here).

(2) You say the assumptions in my cases [g] 1) & 2) are not symmetrical--because I couple the possibility of a rising supply curve of labour with a falling demand curve, but not with a rising supply curve of capital. [6] I disagree. What matters here is the price-relation between output & input for successive units of capital, on the one side, the cost of successive units of capital on the other. Question is: is this price-relation constant (i.e. independent of the scale of investment) or is the cost of borrowing constant. If the price-relation is not constant, it doesn't matter in the least--for the problem in hand--whether this is due to a falling curve of output-prices, or a rising curve of input prices, or both.

Put differently: the question is, is the marginal efficiency curve falling, and the marg. cost of borrowing constant, or vice-versa? The marginal efficiency curve will be falling if either (a) the demand curve for the product is falling; or (b) the supply curve of labour is rising; or (c) one is falling, the other is rising. The analysis will be exactly the same in all these cases. (This should be obvious if we measured capital not in money but in wage units. In that case all 3 cases reduce themselves to the first, i.e. of a falling demand curve)

In fact, the case I had in mind is that of a falling demand curve (imperfect comp. in the product market) versus that of a rising supply curve of capital (a kind of imp. comp. in the capital market.) I only included the case of a rising supply curve of labour, which is very unimportant in practice, in order to be "inclusive." (& since it has the same effect of that of a falling demand curve.)

(3) By "real wages", I meant, in fact, wages in terms of the product of the firm, or, what comes to the same thing, the price of the product of the firm in terms of wages. It is in fact, only a short-hand method of expressing this price-relation.

By "marginal real wages" I meant the ratio of the marginal revenue of output to the marginal cost of input, at the point of equilibrium. If the price-relation between product & labour is constant, this is always the same; further, it is always the same, in equilibrium, if the marg. cost of borrowing is constant (i.e. horizontal). On this cf. further, below.

(4) Provided you agree so far, it will be much simpler to consider the effect of a shift in the demand curve of the product to the left, assuming the demand curve downward-sloping, in 2 cases:--1) when the marg. cost of borrowing is constant; 2) when it is rising. (If we contemplated a rise in wage-rates, in these two cases, the position of the (falling) demand curve being given, this I suggest, comes to the same thing, but if you don't agree to this, I am prepared to return to this case).

1) Here, [7] as you say, the shift in the demand curve will restrict output, the degree of roundaboutness remaining the same. You say the restriction of output need not go so far as to leave real wages the same as before. I didnt say it must; what I said was that marginal real wages will be the same as before. The reason for this is as follows. In equi[librium]. the marg. cost of borrowing = marg. efficiency of capital (otherwise profits are not maximized). Now a given value of the marg. efficiency of capital can only be reached, with a given value of marg. real wages. Hence if the marg. cost of borrowing is the same, in the new equi. marg. efficiency must be the same, & marg. real wages must be the same.

Real wages will also remain the same if the demand curve is a constant-elasticity curve. They will rise, if the curve is a falling-elasticity curve, & fall if it is a rising elasticity curve (falling or rising elasticity--measured as you move along the curve, from left to right).

2) Now we come to the main point, on which, I believe, you are wrong. You say [8] that in case the marg. cost of borrowing is rising, the effective marg. cost of borrowing in the new equilibrium, can be either higher or lower than in the old one, depending upon the elasticity of the demand curve. 1

This could only be true, if a shift in the demand curve of the product to the left could actually raise the marginal efficiency curve for capital (at any rate, for some amounts of capital). This, however, is impossible; the marg. efficiency curve, for any given method, must shift to the left, throughout its length. (although it will change its slope) Hence, if the schedule of the marg. cost of borrowing is rising, the effective marg. cost of borrowing must be lower in the new equi. than in the old.

You say it will be lower or higher, according to whether [h] the elasticity of the demand curve is greater or less than unity. I have not quite understood this & haven't worked out [i] how you reached this result. But even if it is true, it is not incompatible with what I said. This for the simple reason because the elasticity of demand can never be unity or less at a position of equilibrium--unless the cost of borrowing is negative. If the elasticity of demand were less than unity, the marginal efficiency curve would be negative; it would always pay the firm to restrict investment. Hence the case of unit elasticity, or less than-unity elasticity can be entirely ignored. Thus the degree of roundaboutness must be increased, if the demand curve shifts to the left, or if the supply curve of labour shifts to the left, or if both shift to the left, assuming the demand curve downward sloping & the supply curve (of labour) horizontal, or the supply curve upward sloping & demand curve horizontal, or the one downward sloping & the other upward sloping at the same time. They all come to the same thing.

Thus, I believe, the "symmetry" still stands. And in plain English I would formulate it as follows:--We might conceive that the scale of investment of the typical, or representative firm is chiefly limited by the limitation of the amount it expects to sell, or by the scarcity of funds at its disposal, according as it is one or the other, the method of production adopted will depend mainly on the rate of interest ruling, or mainly on the price-relations between labour & product. In case the influence of either factor on the method adopted will be small, its influence on the scale of investment will be large, and vice versa.

I am sorry this letter again got so annoyingly long. I should like to come over to Cambridge, just for a day or two if I knew (a) which days are likely to be interesting; (b) whether I could get sleeping accommodation. Could you perhaps advise me as to point (a)? [9]

Yours

Nicholas Kaldor

P.S.-- I enclose a diagram [10] made some time ago (drawn accurately on the basis of a numerical example) which illustrates what I was saying under 4)2) above; & I find that it also supports your proposition on p. 2, §2 (bottom paragraph). [11]

I have chosen 2 methods of production, with a downward sloping demand curve, & a horizontal supply curve for labour, (or rather, I have taken its marginal revenue curve) & assumed a proportionate increase in marg. revenue, first I believe by 20% & then another 50 per cent. (I cannot find the paper at the moment, on which the numerical example was written out, so you must take it on trust). Method A is more capitalistic Method B is less capitalistic. As you see, a shift in the demand curve to the left, shifts the marg. efficiency curve to the left, but reduces its slope at the same time. (The curves are of course, marg. efficiency schedules; i.e. they show the marg. rate of profit for successive units of capital, without deducting interest costs. The schedule of the marg. cost of borrowing is not drawn in the diagram)

Now the elasticity of the demand curve for the product, at the level of output at which the marg. efficiency curves cut the x-axis must, of course, be greater than unity; since additional output involves additional costs, I thought, therefore, that if these curves are prolonged in the negative quadrant, & your proposition about unity-elasticity is correct, they must all meet at the same point; at the point, that is, where an output is reached where the elasticity is equal to unity. (And [j] beyond which it is less than unity). Great was my joy when I found that this, in fact, was the case; at any rate in the case of Method A; while the slight divergence in the case of Method B can be due to inaccuracy of drawing. If this is so, your prop. is undoubtedly correct; but, as I said, it would only affect my position if the rate of interest were negative.

Could you return me this diagram?

I also enclose the two previous letters, since I found that it is very helpful to have them.

  1. 1. N. Kaldor, "Capital Intensity and the Trade Cycle" (Economica, NS VI, February 1939, pp. 40-66): see note 1 to letter 765 .

    2. Harrod was not alone in finding Kaldor's argument difficult. Keynes, to whom "Capital Intensity and the Trade Cycle" was originally submitted for publication, found it "half-baked and not likely to be intelligible to more than a very small number of readers". Indeed, he preferred to accept instead "Stability and Full Employment", which was originally sent along to the editor of the Economic Journal together with "Capital Intensity and the Trade Cycle" for reference (Keynes to Kaldor, 19 September 1938, Cc in JMK EJ/1/5/229).

    3. Letter 802 , [jump to page] .

    4. Probably Kaldor, "Annual Survey of Economic Theory: The Recent Controversy on the Theory of Capital", Econometrica 5, July 1937, pp. 201-33; see in particular pp. 230-32.

    5. Keynes, General Theory (1936), chapter 4.

    6. Letter 802 , [jump to page] .

    7. Letter 802 , [jump to page] .

    8. Letter 802 , [jump to page] .

    9. Kaldor is recorded among the participants in the discussion following Keynes's paper on "The Policy of Government Storage of Foodstuffs and Raw Materials", 1938 (minutes of the meeting in BAAS 337/64).

    10. The diagram was not found among the Harrod or the Kaldor papers.

    11. Letter 802 , [jump to page] .

    1. a. ALS, six pages, numbered (with the exception of the first and last), on three leaves, in HP IV-669-688. Photocopy in NKP NK/3/30/86/128-33.

      b. Ms: «written long».

      c. Ms: «only determined».

      d. Ms: the verb is missing.

      e. Ms: «or if,».

      f. Ms: «time" that».

      g. Ms: «case».

      h. Ms: «according as the».

      i. Ms: «worked it out».

      j. Ms: «and».


1. I agree that if this were so, my symmetry-proposition would fall to the ground [Kaldor's footnote].


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