2013년 1월 12일 토요일

[Some excerpts on] Keynes's “widow's cruse” & “Danaid jar” in his Treatise on Money


※ 케인스 화폐론의 해당 구절 인용:

“There is one peculiarity of profits (or losses) which we may note in passing, because it is one of the reasons why it is necessary to segregate them from income proper, as a category apart. (1) If entrepreneurs choose to spend a portion of their profits on consumption (and there is, of course, nothing to prevent them from doing this), the effect is to increase the profit on the sale of liquid consumption goods by an amount exactly equal to the amount of profits which have been thus expended.  This follows from our definitions, because such expenditure constitutes a diminution of saving, and therefore an increase in the difference between [the cost of production] and [saving].  Thus, however much of their profits entrepreneurs spend on consumption, the increment of wealth belonging to entrepreneurs remains the same as before.  Thus profits, as a source of capital increment for entrepreneurs, are a widow's cruse which remains undepleted however much of them may be devoted to riotous living. (2) When, on the other hand, entrepreneurs are making losses, and seek to recoup these losses by curtailing their normal expenditure on consumption, i.e. by saving more, the cruse becomes a Danaid jar which can never be filled up; for the effect of this reduced expenditure is to inflict on the producers of consumption goods a loss of an equal amount.  Thus the diminution of their wealth, as a class, is as great, in spite of their savings, as it was before.”   (the Treatise on Money, Vol. 1, p. 139.)


자료 1. [구글도서] Making of Keynes's General Theory (R.F. Kahn, Cambridge University Press,1984)

(불완전한) 차례:
OF WHICH: IV. Fourth Lecture: From the 'multiplier' to the General Theory (1. The 'multiplier' 2. The Cambridge 'Circus' 3. From the 'Treatise' to the 'General Theory')

1. The 'multiplier' (p. 91) 

2. The Cambridge 'Circus'
(p. 105) 
The publication of the Treatise on 31 October 1930 led almost immediately to a group of younger Cambridge economists getting together to discuss the basic issues, stimulated by the knowledge that Keynes would shortly be embarking on a new book. It operated during the academic year 1930-31. It consisted of James Meade, Joan and Austin Robinson, Piero Sraffa and myself. In addition to discussions among ourselves, we held a seminarㅡmembership of this was severely restricted but it included strudents in their third (final) year.
(... 생략: 이론적인 내용, 전혀 없음 ...)

(p. 106)
To anybody who did not know Keynes, it is astonishing that he was willing, week after week, to discuss with me, acting as the group's spokesman, the problems which had arisen and their implications. He could so easily have requested us to submit a comprehensive draft memorandum for his consideration. Austin Robinson has referred to Keynes' 'extraordinary magnanimity'.[1: Austin Robinson, Keynes and his Cambridge Colleagues, p.35.]

And:
At no moment in his life, I think, did Keynes' greatness of character appear more strongly than at this time [...] Keynes never even appeared to hesitate. He was off with the rest of us in pursuit of truth with as enthusiastic a zest as if he were demolishing the work of his worst enemy.[2: Austin Robinson, 'John Maynard Keynes, 1883-1946', Economic Journal, March 1947, p. 40.
The age of each of us under 34; Keynes was 47 years old.

The most important issue discussed by the Circus was that Austin Robinson called the ‘“widow's cruse” fallacy’[3] and the ‘Danaid jar’ fallacy.[4] The reference is to the following passage in Volume I of the Treatise:
There is one peculiarity of profits (or losses) which we may note in passing, because it is one of the reasons why it is necessary to segregate them from income proper, as a category apart. (1) If entrepreneurs choose to spend a portion of their profits on consumption [...] the effect is to increase the profit on the sale of liquid consumption goods by an amount exactly equal to the amount of profits which have been thus expended. [...] Thus, however much of their profits entrepreneurs spend on consumption, the increment of wealth belonging to entrepreneurs remains the same as before. Thus profits, as a source of capital increment for entrepreneurs, are widow's cruse which remains undepleted however much of them may be devote to riotous living. (2) When, on the other hand, entrepreneurs are making losses, and seek to recoup these losses by curtailing their normal expenditure on consumption, i.e. by saving more, the cruse becomes a Danaid jar which can never be filled up.[1: Keynes, vol. v, p. 125. 케인스, 화폐론 제1권 p. 139.]
※ 케인스의 해당 문단을 좀 더 길게 복원한 인용은 칼도어의 다음 소론(Alternative Theories of Distribution) 내 각주, 그리고 아래 자료 3에서 볼 수 있다.
[3] Holy Bible, 1 Kings XVII; Austin Robinson, ^Keynes and his Cambridge Colleagues^, p. 34.
[4] In Greek lengend, Argos, founded by Danaus, suffered every summer from a drought. In the lower world the fifty daughters of Danaus (the Danaides) had to carry water in broken vases.
The complaint of the members of the Circus was that Keynes was here implicitly assuming a fixed output of consumption goods. [:]
If entrepreneurs responded to the abnormal profits by increasing the output of consumption-goods, the price-level of consumption-goods would progressively fall, and abnormal profits would fall, until either entrepreneurs earned no more than normal remuneration or some barrier was encounteredㅡfull-capacity utilization or full employment of labour.
Donald Moggridge suggests that a 'fixed national output' is implied.[2] I can se no evidence for this. It would have been quite out of keeping with other part of the Treatise, to which I am about to refer.

Keynes gave no reason for choosing any particular level of total output, O, and he did not attempt any explanation of the division of O between R, the sales of consumption-goods, and C, the output of capital-goods plus the increment of working capital and stocks.

Keynes could easily have explained that he was examining one point of time during a process of change. Towards the end of Section I of Lecture III, on the ^Treatise^, I described the Fundamental Equations as representing 'a remarkable breakthrough', in drawing a distinction in price-determination between 'money-costs per unit of output' (in an equilibrium situation) and abnormal or subnormal profits.

But the text of my present Lectures was not available to the members of the Circus; and I like to suppose that my own thinking has advanced in the course of half a century.

The astonishing thing about the ' "widow's cruse" fallacy' is that a considerable section of the two volumes of the Treatise are devoted to fluctuations in the rate of investment and the credit cycle. For example, Chapter 20 is 'An Exercise in the Pure Theory of the Credit Cycle'ㅡ
an essay in the internal mechanics of the price-wage-employment structure during the course of a cycle which represents a recovery in the volume of employment from a preceding slump which has reached an equilibrium between prices and costs of production, but is still characterised by unemployment.[1: Keynes, vol. v, p. 274]
(This chapter comprises an elaborate sequence analysis. It explains why some economists regard the ^Treatise^ as ㅡin some respectsㅡsuperior to the ^General Theory^.)

I do not see how weㅡmembers of the Circusㅡcould have attributed to Keynes the assumption of inelastic supply, and I am completely mystified by the questions:
a) why we did not see this for ourselves;
b) why it did not come out in the course of the discussions between Keynes and me, on one of the occasions when I reported on difficulties which had arisen in discussions at the Circusㅡthe upshot of which I would have reported back to the other members of the Circus.
The mystery is enhanced by Moggridge's discovery of a memorandum enclosed in a letter from Keynes to Ralph G. Hawtrey dated 28 November 1930, ten weeks after Keynes had completed the ^Treatise^ and less than a month after publication.[2] Keynes was dealing in the form of a nine-page memorandum with a large number of criticisms by Hawtrey of the proofs which Keynes had not had time to deal with before publication.
The question ^how much^ reduction of output is caused [...] is important, but not strictly a monetary problem. I have not attempted to deal with it in my book, though I have done a good deal of work at it. I am primarily concerned with what governs ^prices^.[3]
And finally the following even more astonishing passage:
I repeat that I am not dealing with the complete set of causes which determine volume of output. For this would have led me an endlessly (...)

(... pp. 109-110 ...)
(p. 111)
(During the Circus period Keynes, apart from his normal heavy load, and apart from coping with a host of critics of the ^Treatise^, with the Circus and with preparing the Harris Foundation lectures, was helping to draft the Macmillan Report, including Addendum I, which was signed on 23 June 1931.)

In conclusion, there is a point of interest which Moggridge brings to light.[1] During the summer of 1931 Joan Robinson was working on her 'Parable on Saving and Investment', in which she dealt with some of the problems which had arisen at the Circus.[2] In the article she recorded that, as to the widow's cruse, Keynes had admitted the case against him. The proofs were not available to enable her to submit them to Keynes until 9 April 1932. Keynes encouraged her to publish without amendment. On the ‘“widow's cruse” fallacy’, he wrote on 14 April 1932:
I think you are a little hard on me as regards the assumption of constant output. It is quite true that I have not followed out the consequences of changes of output in the earlier theoretical part [...] I shall be doing it in my lectures; though that does not absolve me from be criticised for not having done it in my Treatise. But in my Treatise itself, I have long discussion with [?of] the effects of changes in output [...] Surely one must be allowed at a particular stage of one's argument to make simplifying assumptions of this kind.[3]
(... ...)

자료 2: WIDOW’S CRUSE

출처: International Encyclopedia of the Social Science (2nd edn), vol. 9

※ 항목 기술자: Marc Lavoie

The term widow’s cruse was first used in economics by John Maynard Keynes (1930, p. 139) in the presentation of his fundamental equations. Keynes argued that enterprise
macroeconomic profits, as he defined them there, or what we would now call “business retained earnings,” moved up one-to-one with increases in investment and increases in consumption out of profits. Thus, Keynes argued that “however much of their profits entrepreneurs spend on consumption, the increment of wealth belonging to entrepreneurs remains the same as before. Thus profits, as a source of capital increment for entrepreneurs, are a widow’s cruse which remains undepleted however
much of them may be devoted to riotous living” (p. 139). Keynes was then making a reference to the Old Testament story (1 Kings 17) in which a widow was assured that her
barrel of meat and jar of oil would never be depleted.

The analogy was later picked up by Nicholas Kaldor (1956), when he presented his Keynesian theory of income distribution and growth. Both Keynes (1930) and Kaldor (1956) assumed full employment. For both of them, lower propensities to save would lead to an increase in prices relative to costs, and this would entail higher profits in the static case of Keynes and higher profit share and profit rates in the dynamic case of Kaldor.
In the meantime, another version of the widow’s cruse was put forward by Micha≠ Kalecki (1942), without the full-employment assumption, based on adjustments through quantities (real output and employment) rather than prices. Kalecki’s equation reads that Profits = Investment + Consumption Out of Profits, under the classical assumption that wages are all spent. Taking the public sector into account, government deficit should be added to the right-hand side. Kalecki’s equation has given rise to the aphorism—attributed to Kalecki, but which can be found in Kaldor (1956, p. 96)—that “capitalists earn
what they spend, and workers spend what they earn.” This aphorism shows the asymmetry in capitalist relations:
Capitalists can always decide to spend more (provided banks accept to finance additional investment), whereas workers cannot decide to earn more, because this depends on the employment they are offered by entrepreneurs.

Modern versions of this quantity-adjusting theory can be found in the so-called Kaleckian models of growth, which show that a decrease in the propensity to save leads to higher rates of output growth and higher rates of profit.

The widow’s cruse is the price-adjusting equivalent of
the quantity-adjusting paradox of thrift. With output
adjusting through the multiplier, the short-run version of
the paradox of thrift asserts that individual efforts to
increase saving will be useless, and that, instead, output
will fall, as was outlined by Keynes in 1936. But this is
simply the quantity analogue of the mechanisms he was
describing in 1930 as the “Danaid jar,” which can never
be filled up, or the “banana parable,” whereby a thrift
campaign in a banana-producing economy will lead only
to rotten bananas, heavy business losses, large unpaid
bank loans, and destroyed wealth.
The widow’s cruse is just as relevant now as it was at
the eve of the Great Depression. Mainstream economists
and right-wing think tanks are still chanting the virtues of
household savings and government budget surpluses,
without realizing that household expenditures have sustained
the U.S. economic boom and that government
deficits add to business profits. The issue of public pension-
funds finance is also related to the widow’s cruse,
which implies that such funds can only be financed as a
pay-as-you-go redistribution mechanism: If one attempts
to save too much, the savings will vanish like the rotten
bananas.
BIBLIOGRAPHY
Kaldor, Nicholas. 1956. Alternative Theories of Distribution.
Review of Economic Studies 23 (2): 83–100.
Kalecki, Micha≠. 1942. A Theory of Profits. Economic Journal 52
(June–September): 258–267.
Keynes, John Maynard. 1930. The Treatise on Money. Vol. 1.
London: Macmillan.


자료 3. [doc] Lord Keynes and the 'Moderns' (Gunnar Tomasson, February 22, 1988)

※ 케인스 화폐론의 해당 구절 인용:
“There is one peculiarity of profits (or losses) which we may note in passing, because it is one of the reasons why it is necessary to segregate them from income proper, as a category apart.  If entrepreneurs choose to spend a portion of their profits on consumption (and there is, of course, nothing to prevent them from doing this), the effect is to increase the profit on the sale of liquid consumption goods by an amount exactly equal to the amount of profits which have been thus expended.  This follows from our definitions, because such expenditure constitutes a diminution of saving, and therefore an increase in the difference between [the cost of production] and [saving].  Thus, however much of their profits entrepreneurs spend on consumption, the increment of wealth belonging to entrepreneurs remains the same as before.  Thus profits, as a source of capital increment for entrepreneurs, are a widow's cruse which remains undepleted however much of them may be devoted to riotous living.  When, on the other hand, entrepreneurs are making losses, and seek to recoup these losses by curtailing their normal expenditure on consumption, i.e. by saving more, the cruse becomes a Danaid jar which can never be filled up; for the effect of this reduced expenditure is to inflict on the producers of consumption goods a loss of an equal amount.  Thus the diminution of their wealth, as a class, is as great, in spite of their savings, as it was before.” 
(...)

(ii) The "widow's cruse"

In the Treatise on Money, the very same incoherence took the form of the "widow's cruse" paradox. As now demonstrated, that paradox derived from the definition of “investment” in the context of the “fundamental equations” of the Treatise:
  1. Consider a market economy in which two entrepreneurs, A and B, engage in production, transforming factor services into goods for sale and consumption by the suppliers of factor services.
  2. Following Keynes' definition let "the earnings of the factors of production" be the income of any given period. [17]
  3. Now assume that [?A] sells his output at a profit before B seeks to do likewise.
  4. A will then have realized sales proceeds equal to the factor cost of his output plus a part of the factor cost of B's output.
  5. A's profits being a measure of B's prospective loss, neither entrepreneur can in principle realize profits on the sale of his output which would bring aggregate profits in the economy to a non-zero positive level.
  6. Hence, profits of A and B cannot in principle be “a source of capital increment for entrepreneurs” in the manner supposed by Keynes.
  7. However, by letting historical factor cost be the measure of the value of investment in the economy's work in process, Keynes concluded differently and created the paradox of the "widow's cruse."
(...)

Known as the "Cambridge Circus," the group's evaluation of the "widow's cruse" paradox and related issues would later be summarized as follows:
"However true [the paradox] was and remains in broad terms, regarded as a rigid and precise foundation of the process, it was evident that the widow's cruse proposition as stated assumed a fixed national output with the whole adjustment through prices. As a "general theory," rather than a statement of a particular limiting case, it was inadequate."
"Towards this conclusion," the summary continued, "and the ultimate emergence of what soon came to be known as the "widow's cruse fallacy," Richard Kahn's article on the multiplier was a primary impulse.  Conceived in the summer of 1930, it was in Keynes's hands in a preliminary form just before the actual publication of the Treatise but far too late to modify its exposition.  This article gave much greater precision to the line of thought that had already emerged in ^Can Lloyd George Do It?^, published by Keynes and Hubert Henderson in May 1929 and in a broadcast and articles in 1931." [23: Chapter 5, 'Towards the General Theory', JMK, Vol. XIII, 1973, pp. 339-340.]
(...)

자료 4. Keynes’s Fundamental Equations From The Treatise on Money




4. ..





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