# 270. Harrod to J. E. Meade , 25 November 1932 [a]

[Replies to 269 , answered by 272 ]

25 November 1932

Your note is most valuable and throws a flood of light on the matter. But I dont think it is velocity on which the beam should be concentrated. What do you say to this:--

Initially incomes in x rise by A and those in y fall by A. Suppose the rate at which a given change in incomes diffuses its effect to be the same in both spheres (your velocity, I think). Suppose that y = not-x. Suppose the proportion of incomes in x spent on imports to be i, and the proportion in y to be . This is the natural assumption if the whole world is divided into x and y.

Then the initial rise of incomes in x [b] diffuses employment in x at a rate proportional to 1 - i and in y at a rate proportional to i. While the fall of incomes in y diffuses unemployment in y at a rate proportional to and in x at a rate prop. to . Then employment in x is diffused at a rate prop. to and unemployment in y at a rate prop. to . Then the ratio of the rate at which imports into x rise to that at which imports in y fall is . Thus the gap originally caused between x's imports and exports will be filled by increased imports and reduced exports in the proportion of y to x.

Surely then differing velocities of circulation in the different spheres could be treated as a special case. Do you see any snags? I feel guilty taking up so much of your time

Yours

R. F. H.

I am not clear how far I have merely repeated what you said. Comparative size of x and y seems to be the determining factor, while equal velocities in both spheres [c] is the proper assumption.

1. a. ALS, two pages on one leaf, in MP 2/4(4). Photocopy in HP (NC).

b. From this point, Harrod changed notation and used (with one exception) capital Xs and Ys.

c. Ms: «sphere».

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