## 821. J. M. Keynes to Harrod

, [29 August 1938][a]

[Replies to 819 , answered by 827 ]

[29 August
1938]* **
[1]** *

Y income or output during unit of time assumed;

s proportion of income saved during any period;

DS increment of saving for unit of time assumed

= increment of capital, corresponding to increment of income at a rate DY per unit of time, required by "normal" technological considerations.

Then the warranted proportional growth during the unit of time assumed , where t is a function of the unit of time adopted but s is not.

Suppose, however, that ex-ante growth of output exceeds the warranted growth in the assumed unit of time by an amount X, then (I say) you are assuming that

where t and s
have the same values as before, i.e. that t > s (for
that unit of time).* **
[2]** * The longer the unit of time, the less
likely is this to be true. The relevant unit of time is presumably
the interval which has to elapse before previous decisions can be
effectively revised in the light of current facts. In any likely
actual circumstances, however, there should be plenty of margin to
ensure that in fact t > s for the appropriate time unit.
Thus with the basic assumption that t > s I agree with
your conclusion as to instability. But I still insist on the
necessity of this basic assumption.

But there is a lot else to take
account of. t(DY* w* + X) must equal
s(Y + X) at the values of t and s actually prevailing. Thus
if growth is unwarranted, t and s are forced from their previous
"normal" values. The extent of the changes in t and s depends on the
marginal values of t and s for short-period (unexpected) changes in
output. Haven't you, therefore, to make some assumption as to the
readiness of t and s to respond in such
circumstances?

This is leading into deep and (probably unnecessarily) complicated water. My present point is merely that you cannot assume absolute rigidity of s and t and a departure from warranted growth. You have to make some assumption as to the changes in s and t in unwarranted conditions. Moreover in this context it is the marginal s and t that matter. The actual course of the cycle will be largely influenced by the short-period factors.

At the same time the point is important. For the actual values of t and s must always be such that

which means that ex-post the marginal value of t corresponding to the increment of output X must equal the corresponding marginal value of s. Now if (as in your numerical example [3] ) the average value of t is 50 times s, this means that the distortion of the marginal from the average values of the quantities is very violent in the event of unwarranted output. The fact is, of course, that there are large fluctuations in unused capacity (or in capacity employed below its maximum) or in inventories or in both, and (especially for very short periods) in the marginal propensity to consume. You cannot assume all these complications away and yet allow unwarranted output to occur. But you are justified in pointing out that t will only fall below its normal if the prices of investment goods rise and s will only rise above its normal if the prices of consumption goods rise or incomes are redistributed in favour of profit. [b]

Consider such a
case as this. If there is all-round surplus capacity (both plant and
inventories), the position may be stable in the sense that an
unwarranted increase in output will be followed by a relapse; for it
will increase DS without involving any increased demand for
investment. In fact there is probably no moment in the trade cycle at
which t has its "normal" value in the sense that the actual values of
C and Y are so related that C = t* 0* Y where t*
0* is the technologically "normal" value of t. Thus you are
assuming that there is no surplus capacity.
[c]

In general, you must prove your point from stated assumptions, and not merely assert it as an intuition from unstated ones--especially when the assumptions are (avowedly) unrealistic and therefore not easily supplied by the reader. The above points are not intended as fundamental--they are directed to elucidating the nature of the assumptions which you are making in your schematism. [d]

- 1. The document
is undated. However, Keynes dated 29 August 1938 the last of his
autograph additions.
2. Keynes's statement is inaccurate, as s and t are not homogeneous quantities. An explicit reference to the time interval would have clarified Keynes's thought, as the instability condition would have been

, where J stands for time: see Keynes's letter 832 of 9 September and, for a comment, D. Besomi, "From The Trade Cycle to the `Essay in Dynamic Theory': The Harrod-Keynes Correspondence, 1937-38", History of Political Economy 27:2, 1995, in particular pp. 328-29n.

3. Letter 814 , [jump to page] .

- a. TDI,
with autograph corrections, formulas and additions, three
pages on three leaves, numbered from the second, in HP
II-87. CcI, corrected, in JMK EJ/1/5/313-15. At the top of
page 1 there is the indication «R. F. H.» in type.
Printed in Keynes, Collected Writings, vol. XIV, pp. 333-35.
Reproduced by kind permission of the Provost and Scholars,
King's College, Cambridge.
b. This sentence, autographed, was added as an afterthought.

c. This sentence, autographed, was added as an afterthought.

d. This sentence, autographed, was added as an afterthought.

- a. TDI,
with autograph corrections, formulas and additions, three
pages on three leaves, numbered from the second, in HP
II-87. CcI, corrected, in JMK EJ/1/5/313-15. At the top of
page 1 there is the indication «R. F. H.» in type.
Printed in Keynes, Collected Writings, vol. XIV, pp. 333-35.
Reproduced by kind permission of the Provost and Scholars,
King's College, Cambridge.