785. N. Kaldor to Harrod , 25 June 1938 [a]

[Replies to 784 , answered by 802 ]

Mecklenburgh Sq., [London] W.C.1

25 June 1938

My dear Harrod,

I quite agree that we ought to begin in a new way to secure agreement.

1) I agree, of course, with your point (1).

2) You claim under (2) that "if an entrepreneur is seeking the way of mixing labour (which stands for all factors other than waiting) and waiting in such a way as to produce any number n of units of the commodity in the cheapest way, he can determine this unequivocally if he knows the supply schedule of waiting {my italics} and quite regardless of the price of labour ..." "Per contra if he knows the price of labour but does not know the cost of successive units of waiting, he is quite unable to determine the cheapest method". I can only agree to these propositions under two (alternative) assumptions (i) If the supply schedule of capital is infinitely elastic, & hence the marg. cost of borrowing is the same for all outputs, & whatever the level of wages; (ii) if the "supply schedule of waiting" is so constructed, that the marg. cost of waiting for any given output is the same, irrespective of the level of wages, i.e. if under given supply schedule you mean that the marg. cost of waiting for the nth unit of output is given, irrespectively of [b] how much "money" capital is involved in the same amount of "real" waiting. I meant under supply schedule of capital the supply price of so many £'s invested, or--in so far as we can take the price of the product in terms of money as given--of so much product invested, using the term the supply schedule in this latter sense, you have already admitted that a change in wages will change the marg. cost of borrowing for a given output--if the supply schedule of capital is not infinitely elastic--, & will change also the marg. cost of borrowing for the new equilibrium level of output; and this is all I need for my symmetry-argument.

Unless there is something in your argument which I completely failed to get hold of, I would say that your proposition only holds in the particular case where the supply curve of capital is infinitely elastic.

But may I set out my position, so that you could see why I stick to my view--that there is no asymmetry.

I. We both appear to agree that a fall in interest [c] involves a rise in wages, & vice versa (i) for the system as a whole, assuming constant returns; (ii) for the individual firm, if all demand and all supply curves are horizontal, and independent of one another & there are no economies or diseconomies of scale. As you say, disagreement begins when these assumptions are relaxed. In the following I shall deal with the individual firm, examining the consequences of removing these assumptions, one by one.

II. Different types of conditions for the individual firm.

(1) . Falling demand curve (for the product) or rising supply curve (of labour) or both. Constant supply price of capital (horizontal supply curve for capital). [d] Constant physical returns to scale. [fig. 1] The marginal cost of borrowing is the same, irrespective of scale. Hence the marg. rate of return (and marg. real wages ) are always the same, in a state of [e] equilibrium. The effect of a change in "real wages" (i.e. a shift in the demand curve, relative to the supply curve of labour, or vice versa) will be merely to change the scale of output (in such a way, as to re-establish, in the new equilibrium, the same value for marginal real wages, as obtained before).

In this case therefore, the method adopted depends entirely on the rate of interest (= supply price of capital); while real wages determine the scale of operations. A change in real wages will exclusively affect the scale & leave the method adopted unaltered.

(2) Horizontal demand curve for the product & supply curve for labour. Rising supply curve of capital. Constant physical returns to scale. [fig. 2]

In this case, marg. real wages, & hence the marg. rate of returns, is the same, irrespective of scale. Hence the marg. cost of borrowing is always the same, in a state of equilibrium. The effect of a change in the "rate of interest" (i.e. a shift in the supply curve of capital, to the right or to the left) will be merely to change the scale of output (in such a way as to re-establish, in the new equilibrium, the same value for the marg. cost of borrowing as obtained before).

In this case therefore the method adopted depends entirely on real wages (i.e. the price ratio between factor & product); while the rate of interest merely determines the scale of operations. A change in the rate of interest will exclusively affect the scale & leave method unaltered.

(Please note the complete symmetry in assumptions, analysis, conclusions, in the two cases).

(3). Falling demand curve and/or rising supply curve for labour. Rising supply curve for capital. Constant physical returns to scale. [fig. 3] This is a combination of (1) and (2) & could be regarded as the "general case". In this case, as I argued before, [1] both a change in the "rate of interest", and a change in "real wages", will have an influence on method. Which of the two will have the predominant influence, depends on whether "marg. real wages" or the "marg. cost of borrowing" are more nearly independent of the scale of output. In other words if the demand curve for the product and/or the supply curve of labour are elastic relatively to the supply curve of capital, it will depend more on real wages, & less on the rate of interest, & vice versa. In so far as the influence of either on method is small, its influence on scale will be relatively large, & vice versa.

III. You can claim that in all these cases a given "method", i.e. a given degree of roundaboutness will be uniquely associated with a given value of the marg. cost of borrowing, in a state of equilibrium. I can claim, on the other side, that in all these cases a given "method" will be uniquely associated with a given value of "marginal real wages", in a state of equilibrium. In other words, equilibrium involves a unique interrelation between marg. cost of borrowing and marg. real wages; whichever of them is more nearly independent of scale will force the other to conform to the standard set by it [f] , in the state of equilibrium. There is perfect symmetry therefore between both of these factors.

I am willing to concede to you however one point. The proposition that method will be uniquely associated with a given value of marg. real wages, assumes constant physical returns to scale. The proposition that it will be uniquely associated with a given value of the marg. cost of borrowing, is not dependent on this assumption. This does not affect the propositions (which I consider the important points) given under II.3. above. But the symmetry propositions under III. above will <strictly> only be valid if constant physical returns to scale are assumed.

I should be grateful if you could indicate where exactly our views depart, so that we can concentrate on those points. Sorry that this letter became so long.

Yours

N Kaldor

  1. 1. See, in particular, letters 765 and 767 .
    1. a. ALS, eight pages on four leaves, in HP IV-669-688. Photocopy in NKP NK/3/30/86/119-26. Written on paper with the London School of Economics letterhead, crossed out from the front page.

      b. Ms: «irrespectively how».

      c. Ms: «fall interest».

      d. Ms: punctuation missing.

      e. Ms: «of of».

      f. Ms: «it it».


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