831. Harrod to J. Marschak , 7 September 1938 [a]
[Follows on from 830 ] 
7 September 1938
I am grateful to you for suggesting a graphical method of representation,  since it helps to clarify ideas, altho' I dont think the graphical method especially well adapted to this subject.
I am afraid your graph will not do: [fig. 1]
since it seems to be using 2 ordinates simultaneously [b] , viz. rate of growth and amount of output. The ceiling of full employment is not the same as the natural rate of growth. And G throughout the revival and G w for some period must be above the natural rate of growth. It is difficult to represent the ceiling and the natural rate of growth on the same diagram. By assuming the actual rate of increase in growth to be on a straight line from zero time, one might do so as follows:--[fig. 2]
Thus how soon you hit the ceiling would depend on the [c] magnitude of the acceleration. Once the line of growth hits the ceiling it must descend to the level of the natural rate. Actually, however, one may regard the ceiling as a bit elastic and the descent not quite perpendicular.
I find it hard to depict warranted growth since it may have various ups and downs within one cycle, being high in the early revival, for instance, because of surplus capacity, and again later on because of high saving. The crucial point is that it cuts the actual rate at its turning points [figures 3 and 4].
In these figures the actual is supposed to rise above the natural by about the same amount. At its highest point the unemployed are being re-absorbed at the greatest rate. But whereas in fig. 3 [d] it rises far above normal warranted, in fig. 4 it does not go far above it.
In conditions of fig. 3 the great rise in warranted may be presumed to be due to inflation. At the point at which warranted takes off from normal warranted we may be presumed to be approaching the ceiling of full employment. On the other hand in fig. 4 there is only a slight rise in warranted. This might be due to a shock to confidence. The ceiling of full employment may still be some way to the right. Or it might be because, savings having risen back to a normal proportion, there is still an excess of unused capacity which pro tanto drives the warranted rate above its normal level. (This is my suggested explanation of the U.S. recession in 1937).
Again it is possible that there may be a boom in which the actual rate never reaches the normal warranted, if that is a long way above the natural. In the slump the warranted is abnormally depressed owing to low saving and losses.
You ask me the leading question whether my theory that there are centrifugal forces on each side of the equilibrium (warranted rate) is based on some empirical view as to entrepreneurs' probable reactions.  I do not think so. On the other hand there must be some empirical basis for my theory. This may be summarized in 2 propositions. 1. The volume of saving supplied depends mainly on the size of income. 2. A considerable part of the demand for saving depends on the rate of growth. There, I think, empiricism ends and deduction begins. 1 It seems to me that we have here an opportunity of doing some important deduction from a few very broad empirical generalizations. (Cf. static theory of value and Law of Demand). 
I expect that I shall want to discuss some more of your points but I spare you for the moment.
2. Letter 822 , [jump to page] .
3. Letter 822 , [jump to page] .
4. See letter 821 , [jump to page] ; for Harrod's reply along these lines see letter 827 .
5. Harrod is resuming here the argument he put forward in "Scope and Method of Economics" ( 1938:15 ), pp. 402-5.
- a. ALS, four pages on four leaves, in JMP 1275, Box 147, folder H.
b. Ms: «simultaneous».
c. Ms: «the the».
d. In the Ms, figures 3 and 4 were numbered 1 and 2 respectively. Numbering has been silently changed throughout.
1. ... warranted equation. ex post equation. My theory:--if G > G w , C p < C; \ there is force making G still greater. To shake this you would have to show that if G = G w + DG the presence of DG has some systematic effect on s or C, so altering their values that C p is not less than C in the new situation. I cannot imagine such a force operating on C. Keynes has suggested that with a high propensity to save at the margin, s might be sufficiently increased to upset my theory.  This can be shown to be so improbable that it can be ruled out. Let Ds be the systematic increase in s 0 , due to the presence of DG. Req[uire]d to show if it is possible for not to be less than . Suppose marginal propensity to save is 100%--hypothesis most favorable to Keynes. For ratio Ds s 0 = DG G w we may substitute 100 absolute number of units of saving previously = 100 absolute number of units of increment of output. will only not be less () than if absolute number of units of saving previously is less than absolute number of units of increments of output. But this is most unlikely unless the period taken for measuring G is far longer than is relevant to this analysis. [Harrod's footnote]
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