Annexe: G. Haberler to E. Lindahl , 1 November 1934 [c]
1 November 1934
Dear Mr. Lindahl,
I have studied carefully your Note on the Dynamic Pricing Problem. It seems to me an extremely interesting piece of analysis and it has stimulated my appetite for the rest of your book.
There is one point where I should like to offer some criticism. When I read your paper I first stuck on page 3 where you have the equation  .  My first objection was this: If anybody saves and the sum which he saves disappears somewhere (say in the banking system), no investment corresponds to this act of saving (unless this deficit is compensated from some other source; but you exclude [d] this possibility by assumption.) I asked myself how it is in this case possible, from the ex post standpoint, that savings are equal to investments. In order to find out, I turned to equation system (2), from which the equality of and is derived and, I believe, I was able to detect the point of confusion. On the right hand side of your first equation you have: , that is income spent on consumers' goods. This income is taken over from the preceding period. Part of it is spent on consumers' goods. The other part ( ) is saved. The second column of your equation system is: , which you sum up to . This is the income realised or earned during the given period. These two incomes you put as [e] equal and therefore they cancel out and becomes equal to .
This procedure is, however, unjustified. If a part of (or, if you like, a part of the first ) is hoarded, the second becomes smaller than the first. This possibility is so important that a theory which excludes it (especially a theory which calls itself dynamic) deprives itself of much of its value.
It could perhaps be answered that, if we take the period in question a little longer, it can be assumed that the income spent during this period has also been realised during this same period. (This is surely not your answer, because you say on page 1 that the periods "must be fairly short, for example a day";  --but I have heard such objections.) This answer is, however, not sufficient. A long period can always be split up into short periods and if you add up the realised and spent incomes for the successive sub-periods, the intermediate links cancel out and the difference between the first and the last link remains.
I am not sure whether this objection against treating income realised as equal to income spent, does not also hold for the D's in your equations.
I am convinced that this is an important matter, which you should carefully consider. You will be aware that it is basically the same point which was made by Mr. Robertson in his article on Hoarding in the Economic Journal not long ago.  I think it would be useful to send a copy of your paper to Mr. Robertson (and also to Mr. R.F. Harrod, Christ Church, Oxford) [f] :
I shall be much interested to hear what you think of this.
With kind personal regards,
Yours very sincerely,
G. Haberler [typed]
P.S. In order to forestall a possible misunderstanding I should like to add, that "income spent" means the total income taken over from, or earned in, the preceding period. A part of this is spent on consumers' goods, another part is "saved", i.e. directly invested, put into a bank, or--hoarded. In [g] the last case, it is not spent at all, therefore "income spent" is not a good expression. I should say: "Income available for spending = income earned or realised during the preceding period."
Eric Lindahl, Esq., Handelshögskolan, Göteborg. Sweden. [h]
2. R. G. Hawtrey, The Art of Central Banking, London: Longmans, 1932, pp. 343-44.
3. Haberler explicitly referred to Hawtrey's criticism to the Treatise on Money in his own criticism to the multiplier in "Mr. Keynes' Theory of the `Multiplier': A Methodological Criticism", Zeitschrift für Nationalökonomie VII, 1936, pp. 299-305.
4. Letter 388 , [jump to page] .
5. Harrod discussed indeed the matter with Marschak: see letter 398 , [jump to page] . There is no indication as to whether Harrod had exchanges with Opie on the subject.
6. E. Lindahl, "A Note on the Dynamic Pricing Problem", later published in O. Steiger, Studien zur Entstehung der Neuen Wirtschaftslehre in Schweden. Eine Anti-Kritik, Berlin: Duncker & Humblot, 1971, pp. 204-11 (also in Keynes, Collected Writings, vol. XXIX, pp. 123-29). The paper was actually sent to Harrod: his copy of the four-page Ts is in HCN 10/11/1.
On 12 November, Haberler sent to Lindahl part of his correspondence with Harrod (CcTLS, in GH Box 66). Lindahl interpreted the debate as follows:
It is very easy for me to follow your reasoning, if I interpret your terms as ex ante amounts. I can then also agree with Robertson, as the ex ante amount of saving for the next period under certain assumptions can be regarded as equal to the realized saving for the foregoing period (if the individuals expect the conditions to continue). [...]
In the same way I can follow Harrod and other economists who hold the opposite view, if I interpret the concepts as ex post amounts. I will not deny that other definitions ex post are possible that do not lead to equality between the terms. But I think it is most natural to take the position that they may be equal. If the total income is defined as the whole net produce during the period, calculated ex post, then that part of this produce that is taken over by the consumers can be defined as consumption and the other part, containing the net increase of capital, that is taken over by the investors, even if it should be unvoluntary (f. ex. unsold stocks), can be regarded as investment.
So much as regards the terminological aspect of the question. Regarding the underlying differences as to methods, I am more on your side, in so far as I think the ex ante concepts have greater importance than the ex post concepts, when one has to explain the causal development. (Lindahl to Haberler, 20 November 1934, TLS, in GH Box 66).
7. In Lindahl's symbolism,
stands for ex-post investment, defined as the increase of capital employed by the firm, calculated at the end of the period. is ex-post total saving. is the sum of all net incomes, also calculated at the end of the period in question. is the expected depreciation of the capital stock, occasioned by the delivery of products during the period, minus the appreciation of the same stock that is expected to take place; the term is based on the estimations of the entrepreneurs at the end of the period. The subscripts a, b, ... n indicate the different stages of the productive process: the stage a contains the production of services and non-durable goods which are sold to the consumers, the stage b the production of capital goods which are sold to the producers in stage a, and so on.
8. "If savings and investment both are calculated at the end of the period, they are thus identical" (Lindahl, "Dynamic Pricing Problem", in Studien zur Entstehung ..., p. 208, or in Keynes's Collected Writings, vol. XXIX, p. 127).
9. Lindahl, "Dynamic Pricing Problem", in Studien zur Entstehung ..., p. 204, or in Keynes's Collected Writings, vol. XXIX, p. 124.
10. D. H. Robertson, "Saving and Hoarding" (1933).
- a. TLS with autograph corrections, two pages on two leaves, in HP IV-395-422. Cc in NKP NK/3/5/15-16.
b. Harrod's address was written at the bottom of the first page.
c. TS, carbon copy, two pages on two leaves; in HP IV-395-422. Further Cc, together with the copies of the Harrod-Haberler correspondence, in NKP NK/3/5/17-18.
d. Ts: «but exclude».
e. Ts: «put equal».
f. The sentence in brackets was added as an afterthought, and was typed directly on the leaf Harrod received.
g. The last two sentences are directly typed on the leaf Harrod received.
h. Lindahl's address was written at the bottom of the first page.
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