## 512. Harrod to J. E. Meade

, 14 January 1936[a]

[Replies to 510 , follows on from 511 , answered by 515 ]

51 Campden Hill
Square, W.8.* #*

On further thought I begin to suppose that your second objection [1] is not so weighty as I first feared that it was. I confess I have not had much time to think about it, and to-day I have to go off to the funeral of an uncle in Surrey. So I am jotting this down for your consideration now, in a rough sort of way.

Were you not really thinking of a case in which marginal costs were rising from the origin? But suppose we take the normal relation thus: [fig. 1]

(I shall have certainly to explain this in a footnote to meet a possible objection along your lines. [2] )

Would not the [b] marginal cost curve have to behave in a very peculiar way to the right of x for my proposition not to be true. E.g. somehow this:--[fig. 2]. Would not the second differential have to become negative at some point to the right of x? In that case I think one could say boldly that the condition for my proposition not holding good is a very improbable one.

I am sorry to make my point in such a scrappy way and without demonstration. None the less I am hoping to get your assent to it.

P. S. Let us take MC rising from origin. The condition that is constant is that MC is a straight line (2nd differential = 0). If 2nd differential > 0, is rising and if < 0, is falling. Starting from x if MC is a straight upward-sloping line is rising. For not to rise 2nd differential must stand below zero by more than a certain amount. When MC begins to rise (normal figure) 2nd differential is positive. I suggest that a change from positive to negative in this range would represent a very abnormal condition.

- 1. Letter
510 , Note II,
beginning on [jump
to page] .