## 766. Harrod to N. Kaldor

, 6 May 1938[a]

[Replies to 765 , answered by 767 ]

Your analysis is not complete; you say that "receipts increase at the same rate as the amount of capital invested", [1] but then realizing that production is not infinite you put in a parenthesis but do not examine the conditions of equilibrium.

The matter may be dealt with simply thus. Let output be n units. It is irrelevant to enquire what determines n, whether it is that marginal cost rises to equalize with price owing to entrepreneurial indivisibility which you have so ably discussed elsewhere [2] or it is "increasing marginal risk" as you now suggest, though this does not seem a very appropriate notion for perfect competition. These questions are happily irrelevant to the following demonstration, which holds for all finite values of n, and I believe for infinite values also, but I am not expert on the mathematics of infinity and we need not perhaps consider the case of infinite output!

If n units are produced there is a choice of doing so with £500n or £1000n units of capital. If the yield on the extra £500n units is greater than the current rate of interest, the second method will be adopted unequivocally, regardless of the comparative average yield of the capital. Thus the case of perfect competition, together with all intermediate cases, reduces for this purpose to the case where the elasticity of demand is 0.

P.S. Since something can be had for nothing on the employment of the 2nd £500n of capital, without in the least spoiling the returns on the first £500n, and it is impossible to get the high return (=that on the first £500n) on more than £500n, the opportunity will be taken to get something for nothing on the 2nd £500n. It is, in fact, the ordinary marginal principle.

- 1. Letter
765 ,
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2. N. Kaldor, "The Equilibrium of the Firm", Economic Journal XLIV, March 1934, pp. 60-76; see in particular pp. 65-66. A draft was commented upon by Harrod in November 1933: see letter 327 .