767. N. Kaldor to Harrod , 10 May 1938 [a]

[Replies to 766 , answered by 769 ]

The London School of Economics, Houghton Street, W.C.2. #

10 May 1938

My dear Harrod,

I am afraid I am not yet contested.

You say: let output be n units. It is irrelevant what determines n, whether it is rising marg[inal]. cost or increasing marg. risk.

This, however, for the matter under discussion, is not irrelevant. In fact your proposition only holds in the case where the marg. cost of investment is constant--i.e. where the scale of operations of the individual producer is limited solely by other factors than the scarcity of capital, such as dim[inishing]. returns to scale or a falling demand curve.

This is certainly a possible case, but I doubt whether it is very appropriate. No single producer can obtain unlimited amounts of capital, in a world where uncertainty is not completely absent; and this holds equally for perfect competition as for imperfect competition. Moreover, quite apart from limitations upon borrowing, the individual capitalists' willingness to invest in a given time decreases with every increase in the amount already invested--since his degree of security is all the less, the greater the investment. Hence the marg[inal]. cost of capital, including risks of all kinds (borrowers & lenders) is rising, even if the market rate of interest is quite unaffected by individual demand for capital. (In fact it may be rising very sharply; capital can be limited by "rationing").

The position of maximum profit for the firm is determined by the equality of the marg. rate of profit & the marg. cost of borrowing. If marg costs of capital are rising, the marg. rate of interest, relevant for a given output, will depend on the amount of capital required for that output, which in turn depends on the method adopted and on real wages. Hence the proposition that method depends on real wages will hold, if marg. cost of capital is rising, even if output is limited by a [b] falling marg. efficiency curve as well.

The additional proposition, that method depends solely on real wages, will only be true under constant (value) returns to scale when output is entirely limited by the scarcity of capital. But I never claimed more: which you can see if you look up my paper. [1]

Hence I still maintain what I wrote in my last letter, which I think could be set out in a more general form:--

Let represent the schedule of the marg. efficiency of capital and its marginal supply price, including risks of all kinds (The curve of course is only definite if the method of production is given--or rather there is one such curve for each method. But assuming that all these curves follow the same direction, though they differ in slope, i.e. there [c] will be constant or dim. (value) returns to scale, irrespective of the method adopted, one such curve will suffice for our purpose). Five cases are possible:--[ fig. 1]

In each, the point of intersection gives maxi[mum]. profits. In cases 1 & 4 the optimum method depends solely on real wages, in cases 2 & 5 it depends solely on the rate of interest, in case 3 it depends on both. (How much on the one, & how much on the other, depends on the relative slopes of the two curves.)

Case 4 can be regarded as the limiting case of "capital rationing", case 5 that of "zero elasticity of demand". The dotted lines in each are "reservation prices",--such as the rate capital can earn outside, or the rate that has to be paid on borrowed capital, or the maximum amount a town is willing to pay for a bridge.

I think in my last letter I only conceded Case 5. If I did, this was an error; your proposition holds in Case 2 as well.

Yours ever

Nicholas Kaldor

  1. 1. Presumably a draft of Kaldor, "Capital Intensity and the Trade Cycle", Economica, February 1939, pp. 48-49: see note 1 to letter 765 .
    1. a. ALS, five pages on three leaves, in HP IV-669-688. Photocopy in NKP NK/3/30/86/93-97.

      b. Ms: «by falling».

      c. Ms: «<there> there».


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