Keynes’s Theoretical Development
1. Introduction
How can we track down Keynes’s theoretical development from A Tract on Monetary Reform (December 1923; hereafter the Tract or TMR) to A Treatise on Money (October 1930; hereafter the Treatise or TM)? Few serious studies have so far been made on it, and the aim of this paper is to analyze this development, using as much primary material as is available.
In Sections 2 and 3, the framework of the Tract and of the Treatise are outlined respectively, while Section 4 looks into the intermediate process. Since Keynes rewrote his manuscripts several times, however, we are faced with a complicated process. Our investigation might make some contribution to disentangling it.
2. A Tract on Monetary Reform
The Tract stresses the importance of the stability of the value of money and the role of the central bank in creating this stability. It also bears the message that if each country could stabilize its currency value, the foreign exchange would also be stabilized, and the Gold Standard would become more of a hindrance than a help.
The Tract begins by arguing that changes in the value of money have harmful effects on society. Inflation redistributes wealth in a way that penalizes the investing class, with the result that “inflation [destroys] the atmosphere of confidence which is a condition of the willingness to save” (TMR, 29). Deflation, on the other, leads to impoverishment of both the wage-earning and the business classes, by causing the latter to restrict production and employment.
Keynes then goes on to deal with the changes in the value of money brought about by printing money — a method of taxation. He warns that this runs the risk of destroying the money system by changing the public’s use of money, and recommends a capital levy.
A. The Fundamental Equation
Keynes puts forward the theory of the domestic value of money and advocates a monetary policy to attain a stable price level. His “fundamental equation”, based on the Marshall-Pigou type quantity theory1, is:
n = p (k + rk΄)
where n denotes cash in circulation, p the price of a consumption unit, k the consumption units equivalent to what the public desire to keep in cash, k΄ the consumption units equivalent to the public’s bank deposits, and r the proportion of their liabilities, k΄, that the banks keep in cash.
The crux here is that ‘the price level [p] … is the resultant of [bankers’ and depositors’] decisions and is measured by the ratio of the volume of the cash balances created [n] to that of the real balances created [k + rk΄]’ (TM.1, p.201).
Based on this equation, he argues as follows. The duty of the monetary authority is to keep the price level stable. Both n and r are under its control, while k and k΄ depend partly on the wealth of the community, partly on its habits — “fixed by its estimation of the extra convenience of having more cash in hand as compared with the advantages to be got from spending the cash …” (TMR, 64).
Price stability can be attained (i) by stabilizing k and k΄ directly; or (ii) by manipulating n and r in such a way as that the fluctuations of k and k΄ are cancelled.
Although the bank rate influences k΄ and k to a degree, Keynes doubts “whether bank rate … is always a powerful enough instrument” (TMR, 69); instead, he chooses policy (ii).2
Based on the equation, Keynes distinguishes three kinds of inflation/deflation: cash inflation/ deflation based on an increase/decrease in n; credit inflation/deflation on a decrease/increase in r; and real balances inflation/deflation on a decrease/increase in k and k΄.
Keynes criticizes the quantity theory that a change in n influences p only. In the long run this is probably true, but what really matters occurs in the short run. The quantity theory, he says, should be expressed in such a way that changes in n also influence k, r, and k΄.
B. The Purchasing Power Parity Theory
Keynes then goes on to consider the role of the “purchasing power parity theory” in accounting for the foreign exchange3:
“...the essence of the … theory [lies] in its regarding internal purchasing power as being ... a more trustworthy indicator of a currency’s value than the market rates of exchange” (TMR, 71).
Keynes stresses the internal purchasing power rather than the foreign exchange in maintaining the stability of a currency’s value. On this basis Keynes develops his policy views:
(i) A devaluation policy offers the possibility of “stabilising the value of the currency somewhere near its present value” (TMR, 117);
(ii) When the stability of the internal price level is incompatible with that of its foreign price level, the former should have priority;
(iii) Restoration of the Gold Standard would threaten the stability of the internal price level, while it would bring about foreign exchange stability only if all other countries were to accept it.
The Tract ends with a method for regulating the supply of foreign exchange in order to avoid temporary fluctuations between the internal and the external price levels. Keynes suggests that the US
3. A Treatise on Money
The Treatise was published after “seven years off and on”. Its core is composed of “Keynes’s own theory” and “Wicksellian theory”, both of which are dynamic and monetary in nature. After taking a look at his evaluation of various theories, we will explain the core and his policy view.
A. Various Theories
If we are to grasp the aim of the Treatise we must have an understanding of Keynes’s views on bank rate theories, and investment/saving.
(a) Bank Rate Theories
Keynes identifies four bank rate theories so far developed, variously regarding the bank rate as;
(i) the means of regulating the quantity of bank money (Marshall, Pigou, and Hawtrey). According to Keynes, something essential is missing from such accounts.
(ii) the means of protecting a country’s gold reserves (Goschen and Bagehot). Keynes evaluates and uses it in his open system.
(iii) a psychological influence on price levels (Pigou). Keynes criticizes this for failing to explain the original effect of the change in the bank rate on the price level.
(iv) influencing investment and savings. Keynes regards this as expressing the essence of the bank rate. Wicksell (1898) represents this understanding and comes close to his own “fundamental equation”4:
Some explanation is required. First, although the bank rate plays a pivotal role in Keynes’s theory, the role of money supply also has a part to play. This may have to do with the fact that Wicksell constructs his theory in an “organized credit economy”, and with Keynes’s criticism that Wicksell does not succeed in “linking up his theory of bank rate to the quantity equation” (TM.1, 167). Second, the “fundamental equation” should be the second fundamental equation. He also regards Mises and Hayek as representing perspective (iv).
On the other hand, Keynes criticizes Marshall
Keynes calls his own theory — an extension of perspective (iv) — the “General Theory of Bank Rate”, which is explained as follows:
(i) Suppose, for instance, that the market rate of interest rises above the natural rate. A rise in the market rate causes the demand price of capital goods (therefore, of investment goods), to fall (Profit Deflation), as a result of which the volume of investment decreases. On the other hand, it causes savings to increase, though not by an equal amount. Thus the decrease in investment is greater than the increase in savings.
(ii) (a) A fall in the price level of investment goods causes production to decrease (as a result of which the value of investment decreases); (b) In addition, since an increase in savings means a decrease in consumption, the price level of consumption goods decreases.
Thus, the price level as a whole falls.
(iii) When producers incur losses, they cut the level of employment at the existing rate of earnings. If this continues, unemployment increases until the rate of earnings is reduced (Cost Deflation. TM.1, 171).
Keynes argues (i) with the second fundamental equation in mind. The first point in (ii) is based on the TM supply function (to be explained later) in the investment goods sector, the second on the first fundamental equation.
Here the second fundamental equation occupies a central position, and the first fundamental equation a relatively minor one, but the true order in the Treatise theory is the reverse, as will be explained below. The two equations and the TM supply function are used here somewhat loosely.5
(b) Investment and Saving
According to Keynes, the distinction between investment and savings was clarified by Mises (1912)6, and introduced into the Anglo-Saxon world by Robertson (1926. hereafter BPPL).
Keynes’s understanding of saving and investment runs as follows. The income of society is partly spent on consumption, the rest being saved. Saving is a passive act of individuals while investment is a positive act on the part of entrepreneurs. Keynes grasps investment from the supply side, which reflects the fact that the Treatise lacks an investment theory.
Keynes stresses that investment is not usually equal to savings, offering two reasons: one that those who determine the division of the total output are not the same as those who determine the division of the total income, the other that earnings and savings do not include entrepreneurs’ profits (or losses), while the value of investment does.
(c) The Quantity Theory of Money
Keynes criticizes the quantity theory7 with two convictions in mind. One is that unless the influence of the bank rate upon investment and saving and the distinction between earnings and profits are introduced into analysis, the dynamic process of price formation cannot be captured. The other is that any analysis which fails to distinguish between various kinds of transactions will cause confusion.
Keynes arrived at the former conviction to assert an advantage of the "fundamental equations” theory over the quantity theories:
“...we are compelled ... to discard the [quantity theories] when we ... attempt to analyse the actual monetary problems... because...they are … ineffective for handling the [most important] elements” (TM.1, 198-199).
The “[most important] elements” should be the bank rate, the distinction between investment and saving, and the distinction between income and profits.
Keynes classifies the demand for money in terms of people’s motives and explains the determination of the price level of investment goods in terms of the relation between savings deposits and equities.8
In Chapter 14 he examines three versions of the quantity theory: the Tract version, the Marshall-Pigou version, and the Fisher version.
Although he subjects each version to particular criticism, the following observations apply to all three:
(i) They only deal with the various kinds of ambiguous price levels;
(ii) They fail to distinguish between income, business, and savings deposits, so that disturbances arising from changes in the relative proportions of different deposits cannot be explained.
(iii) They cannot analyze a dynamic process in which the disturbance of the price level arises from a divergence between saving and investment.
In contrast to the other Wicksellians, Keynes analyzes the relationship between bank rate and quantity of money, as we see in Chapter 13. He offers two reasons for giving priority to the bank rate over the quantity of money.9
(i) A change in the bank rate influences various factors such as the volume of output, the rate of profits and so forth, so that it is impossible to estimate the quantity of money related to any one of these factors.
(ii) The direction of causation runs in such a way that changes in the bank rate cause the market rate of interest to shift relative to the natural rate, which in turn causes the quantity of money, and consequently the price level, to move.
Keynes concludes that only in equilibrium the quantity of money and the velocities of circulation are related to price levels (Cf. TM.1, 132-133).
B. The Core10
In our view, the most significant feature of the Treatise theory is the coexistence of a Wicksellian theory and “Keynes’s own theory”.
We designate the monetary economic tradition stemming from Wicksell and developed by several economists as the “Wicksell Connection”. Wicksell, approving of a separation between the theory of relative prices and the theory of money prices in neo-classical economics, put forward the “cumulative process” theory, while Myrdal, Hayek and Mises constructed their own brands of monetary economics by criticizing the neoclassical system per se.
The Treatise belongs to the Wicksell Connection. Putting the market rate of interest together with the natural rate at its centre, distinguishing between investment and saving, and accepting “Wicksell’s three conditions of monetary equilibrium”, the Treatise explains fluctuations of prices and output in both dynamic and monetary terms with the stability of the price level as an objective. Keynes’s Wicksellian theory, in which the second fundamental equation is used, plays an important role in TM, 2.
Keynes, at the same time, develops his own theory consisting of two parts, one of which addressing the determination of variables relating to consumption goods and investment goods in “each period” (Mechanisms 1 and 2, respectively).
(Mechanism 1) The cost of production and the volume of output are determined at the beginning of the current period. Once the expenditure for consumption goods is determined on the basis of earnings, it is automatically realized as the sale proceeds of consumption goods, and the price level and the profit amount are simultaneously determined.
It should be noted that Mechanism 1 is substantially the same as the first fundamental equation (to be explained later).
(Mechanism 2) The cost of production and the volume of output are determined at the beginning of the current period. The price level of investment goods is determined either in the stock market (bearishness function) or as the demand price of capital goods. As a result, profit is determined.
The other part of Keynes’s theory concerns the determination of variables between one period and the next.
(Mechanism 3) The TM supply function
The behavior of entrepreneurs is such that, if they make a profit (take a loss) in the current period, they expand (contract) output in the next.
Now “Keynes’s own theory” can be expressed as a dynamic process composed of Mechanisms 1 and 2 working through Mechanism 3. As a result of this process, the economy may or may not reach long-period equilibrium. This interpretation sees the Treatise theory as articulating a dynamic process inclusive of price levels and volumes of output.
C. Policy View
The Treatise emphasizes the bank (or discount) rate policy manipulated by the central bank. The policy can make the value of investment move in one direction while savings move in the other until profit disappears, and the stability of the price levels and the level of output is achieved.
“...the governor of the whole system is the rate of discount. ...the only factor...subject to ...the central authority.../ [T]he control of prices is exercised... through the control of the rate of investment. [O]ur fundamental equation has shown that, if the rate of investment can be influenced at will, then this can be brought in as a balancing factor to affect in any required degree ... the price level of output as a whole” (TM.2, 189).
The “fundamental equation” should be the second fundamental equation:
Π = E/O + (I - S)/O
where Π denotes the price level of output as a whole, E money earnings, O the total output, I the value of investment, and S the volume of savings.
In an open system, the second fundamental equation and the first fundamental equation ― P = E/O + (I΄ - S)/R ― are respectively extended as follows11:
Π = E/O + (I1 - S1)/O
P = E/O + (I1΄ - S1)/R
where P denotes the price level of consumption goods, I1 the value of home investment, I΄ the cost of investment, S1 the volume of home savings, I1΄ the adjusted cost of home investment, and R the volume of consumption goods.
The external equilibrium is defined as equilibrium of the BOP:
L = B
where L is the capital balance, and B the current balance.
Then, “complete equilibrium [internal and external] requires both that I１= S１ and I１= I1΄, and that L = B” (TM.1, 147). Keynes maintains that internal and external equilibrium are simultaneously attained through the bank rate policy.12
Keynes’s analysis of the real world is mainly based on the above analysis.13
4. Conjectural Examination Based on Various Tables of Contents
In this section we examine Keynes’s theoretical development from the Tract to the Treatise based on the materials in JMK.13, Chapter 2 of JMK.29, Chapter 2 of JMK.20, and Keynes Papers.14 On the zigzag path from the Tract to the Treatise, he continually rewrote his manuscripts, introducing new ideas. Unfortunately, little evidence of these intermediate steps is extant, apart from various Tables of Contents (hereafter TOCs), a few manuscript fragments, several pieces of correspondence and the Macmillan Committee evidence. Our examination shows that Keynes moved through the Transaction Approach (hereafter TA) on his way from the Tract theory to the Treatise theory, and that the year 1928 marked a crucial turning point.
A. The Tract Theory
How long did Keynes maintain the Tract theory? Our answer is that he held to this theory up to the TOC of 27 April 1926.
a. The Fundamental Equation
The TOC of 14 July 1924 (Tm/3/2/6), entitled “The Standard of Value”, is the earliest of the TOCs.15 Here we find terminology such as cash (m), the price level (p), the purchasing powers (k and k΄), and the relation of credit to cash (r).
In the TOC of 9 October 1924 (Tm/3/2/8), “The Monetary Standard”, worthy of note is the heading of Chapter 4, “Prices Regarded as the Ratio of the Supply of Money Credit to the Supply of Real Credit”, which the TOCs of 30 November 192416 (Tm/3/2/12) and 21 March 1925 (Tm/3/2/13) also contain, and which the TOC of 6 April 1925 (Tm/3/2/16) contains in a similar form, but crossed-out. The supply of money credit would then correspond to n, and the supply of real credit to k plus rk΄, so that the price level p as the ratio of the two could correspond to n/(k+rk΄) in the Tract equation. This idea is closely related to Chapter 2, “The Law or Equation of Money Recapitulated”. We can safely say that these TOCs essentially belong to the Tract theory.17
In the November 1924 manuscript, “A Summary of the Author’s Theory” (Tm/3/2/63-70), two sets of conclusions are drawn. One is an argument concerning the stability of the price level, similar to that found in the Tract and apparently related to Chapter 4 of the October 9 TOC:
“I shall argue in this book … that the general price level [p] can be stabilised by giving the [BOE] a control over the volume of bank-money created [n], ..., and by using this control to cause the volume of bank-money to vary in the same proportion as that in which the volume of real balances [k and k΄] varies” (Tm/3/2/69-70).
The other set deals with the trade cycle theory, in which the stress comes on circulating capital. Judging from the absense of “circulating capital” from the TOC of 9 October 1924, the term seems to be introduced here for the first time. Moreover, the lack of reference to working capital suggests that this manuscript may have been written prior to the TOC of 30 November, in which working capital is stressed, and before the manuscript for Chapter 4, “Working Capital in Slumps and Booms” (Tm/3/2/72).
The phrase, “the fundamental equations of money”, appears for the first time in the TOC of 6 April 1925 (Tm/3/2/16). Here we find expressions like “the determination of price by the ratio of the supply of money-credit to the supply of real credit” and “the velocity of circulation” (both of them crossed out). We also see the phrase, “the fundamental equation of money”, in the TOCs from June, 1925 (13 June, Tm/3/2/18 and 30 June, Tm/3/2/21).
Noteworthy in the TOCs from 9 October 1924 to 13 June 1925 is the stress on “money credit” and “real credit”. In the Keynes-Robertson correspondence toward the end of that period (Tm/1/2/9-31), Keynes investigates the factors determining the volume of money credit and that of real credit, and distinguishes price fluctuations initiated by changes in money credit (inflation/deflation) from those initiated by changes in real credits (boom/slump). These correspond, respectively, to cash inflation/deflation and real balances inflation/deflation in the Tract. The same investigation is also to be seen in the TOCs of 30 June 1925 and 27 April 1926, in which the terms “bank money” and “purchasing power” are used.
Judging from the above, we might suppose that Keynes thought in terms of the Tract theory until the TOC of 27 April 1926 (Tm/3/2/22).
b. The Bank Rate
Keynes take a particular interest in the bank rate (or discount rate): we see the title heading, “the influence of bank rate on prices” in the TOC of 14 July 1924 and the phrase “bank rate” in the TOCs of 9 October and 30 November, followed by “the part played by the rate of discount” in the TOCs of 21 March and 6 April, 1925, and “the modus operandi of bank rate” in the TOCs from 30 June 1925 on.
This might not be an entirely new element, however, for these TOCs are argued in terms of the Tract equation.
B. New Elements
In the above-mentioned TOCs we find some new elements leading to the theory of the Treatise.
a. Working Capital
We find that working capital is stressed from the TOC of 30 November 1924 on. Working capital is argued in the manuscript, “A Summary of the Author’s Theory” (November 1924), which is closely related to Chapter 3, “Fluctuations in the Demand for Working Capital in Relation to the Trade Cycle” of the TOC of 30 November 1924. In a slump, neither the recovery of business sentiment nor the expenditure of public money raised by taxation alone are sufficient to bring about a rapid increase in employment.
“...only through the replenishment of working capital, by new savings becoming...available in liquid form, the position can be restored” (Tm/3/2/72).
Interestingly he believes that fixed capital might be an obstacle to employment by depriving working capital of current savings. Thus, he is against “the expenditure, on the production of fixed capital, of public money...raised by borrowing” (Tm/3/2/72).18
b. Bearishness Function
Although the bearishness function plays an important role in the Treatise, it is very difficult to find any traces of it in the surviving TOCs. Savings deposits (semantically preceded by “investment deposits” in the TOCs of 30 June 1925 to 2 June 1927), which are closely related to that function, appear for the first time in the TOC estimated to have been written between September 1927 and September 1928 (Tm/3/2/33). However, even in the TOC of 2 August 1929 reveals no section corresponding to “the price level of new investment goods” (TM.1, 127-131).
As for an investment price theory, we have a fragmentary note (December 1929, Tm/1/2/7-8), where Keynes argues that the price of new investment goods, P΄, is “determined by degree of capital inflation which depends on rate of interest and bull-bear sentiment”, while the “price of old capital [P˝] determined by rate of interest and by expectations of future prices”. He then states that “P΄ will be dragged up and down by P˝”.
C. An International Monetary Standard
The TOCs from July 1924 through April 1925 show Keynes preoccupied with an international monetary standard, which suggests that his interest in writing a book was prompted by the controversy over the Gold Standard.
The TOC of 14 July 1924, “The Standard of Value”, includes an examination of managed and automatic currency systems, the automatic and the managed Gold Standard, and the controlling authority’s instruments and objectives. In the TOC titled “The Monetary Standard” (9 October), eighteen of the twenty-three chapters deal with ideal standards in some form or another, and we find an important argument relating to Chapter 38, “Problems of Supernational Management” of the Treatise, where the requirements of a standard, “short-period adjustability to the fluctuations of real balances and credit”, and “long-period stability of intrinsic value” are pointed out. Moreover, he mentions the tabular standard as an alternative intrinsic value standard.
However, as he proceeds to the TOCs of 21 March and 6 April 1925, titled “The Theory of Money with Reference to the Determination of the Principle of an Ideal Standard”, Keynes seems to be increasingly concentrating on the theories of credit money and the credit cycle.
The change of the title from October 1924’s “The Monetary Standard” to early 1925’s “The Theory of Money with Reference, etc.” suggests that his interest was moving from an ideal monetary standard to the theory of money per se. In the TOC of 21 March, only one of the nineteen chapters deals with the monetary standard, while the rest address working capital, money credit, real credit, and price fluctuations.
In fact, from the second half of 1925 up to the TOC of 31 August 1926 (Tm/3/2/27), the title “The Theory of Money and Credit” seems to have been related to the United Kingdom
D. The Development of the Fundamental Equation(s)
The most effective method of theoretically distinguishing the Tract from the Treatise is to keep track of how the “fundamental equation(s)” are dealt with, for they occupy a major position in both books.
a. The Transaction Approach
What was described in the 1926 TOCs (26 May, Tm/3/2/23; 6 August, Tm/3/2/26; and 31 August, Tm/3/2/28) as “the fundamental equation of price”19 first took “the fundamental equations of price” in the TOC of 23 May 1927 (Tm/3/2/31). What characterize them is that the equation(s) are developed along Fisher’s TA20, for the elements of the “fundamental equation” turn out to be the velocity of circulation, the proportion of investment deposits, the volume of total deposits, the volume of transactions, and so on. This is also true of “the fundamental equations”, which are enumerated as “the first and second” equations, in the TOC of 2 June (Tm/3/2/32) and 22 September 1927, JMK.13, pp. 48-50. These TOCs are entitled “A Treatise on Money”).
Fisher’s formulation is:
MV+M΄V΄= PT
where M denotes the quantity of money, V its velocity of circulation, M΄ bank deposits, V΄ their velocity of circulation.
The equation shows that if M and M΄ are, say, doubled (M΄is supposed to hold a definite relation to M), then P is doubled provided that V, V΄ and T remain unchanged.21
At the same time, however, Keynes maintains the Tract theory. We find headings such as ‘cash balances and real balances’, ‘price level as the factor which brings decisions of bankers and depositors into harmony’ (Tm/3/2/23; 26; 32).
b. The Embryo of the Fundamental Equations of the Treatise
There survive three TOCs from September 1927 to 4 September 1928 that signal the sea change in Keynes’s thinking from the TA to the idea which leads to the Treatise.22
Let us call the first two, estimated to have been written between September 1927 and September 192823 (Tm/3/2/29-30 and 33-36), TOC(1) and TOC(2).
TOC(1)24 contains headings such as “the flow of consumers’ income”, “withholding of consumption and of sales”, “quantity of money versus flow of income”, and “the fundamental equations”, though we cannot find savings and investment. TOC(2) contains headings such as “quantity of money versus flow of income”, “the fundamental equations for the purchasing power of money”, “the relation of the price-level to the rate of earnings and to the rate of employment”, and “savings and investment”. These indicate that Keynes had begun to turn his attention to the elements that were to comprise the fundamental equations of the Treatise.
In TOC(2) we see for the first time the chapter, “Alternative forms of the Fundamental Equation”, which contains three types ― the “Real Balances” quantity equation, the “Cambridge” quantity equation, and the “Fisher” quantity equation (Tm/3/2/36) ―, indicating that he is still under the influence of the Fisher type. It is interesting to compare it with the TOCs of 6 October 1928 and 2 August 1929, which contain a section dealing with the relationship between the Fisher equation and his fundamental equation (Tm/3/2/41; Tm/3/2/48).
TOC(2) is also worth noting for the first appearance of a distinction between savings and investment, which has something to do with the Chapter, “Fluctuations in the Rate of Investment”, followed by the TOCs of 4 September 1928 (Tm/3/2/37-38), 6 October 1928, and 2 August 1929. In the TOC of 2 August 1929, we see expressions such as “by restoring equilibrium between saving and investment”, “by stimulating savings”, and “by changing the channels of investment” (Tm/3/2/52). These corroborate our theme that Keynes was slow in adopting the distinction between investment and saving.
The third TOC, from 4 September 1928 (Tm/3/2/37-38), includes headings such as “the fundamental equation” and “digression on savings and investment”.
The TOC of 6 October 1928 (Tm/3/2/39-45) contains headings such as “quantity of money versus flow of income”, “the fundamental equation for the purchasing power of money” (which should indicate “the fundamental equation in terms of monetary factors”), “digression on savings and investment”, and “earnings and profits”.25
The TOC of 2 August 1929 (Tm/3/2/48), which has headings such as “flow of income and quantity of money”, “the relation of the price level to the rate of earnings and to profits”, “the rate of employment”, and “earnings and profits” (all of them are crossed out), is worth noting, for Keynes distinguishes between the fundamental equation “for the purchasing power of money” and the one “in terms of monetary factors”, which might suggest two ways of expressing the price level of the consumption goods.
All the TOCs from 6 October 1928 onwards place the main emphasis on the fundamental equation in terms of monetary factors26, expressed as “the elements of the fundamental equation”. While this indicates that the TA is still dominant, we recognize the direction turning towards the equations of the Treatise. In this respect the year 1928 is crucial.
c. Thereafter
Keynes’s Michaelmas lectures of 1929 were delivered on the basis of the galley belonging to the TOC of 2 August 1929.
In his letter to Keynes (29 September 1929, Tm/1/2/42), Kahn wrote that “the modification in the treatment of the Fundamental Equations that you have now introduced...carry...big advantages”. Kahn should refer to “the modification” of the fundamental equation “for the purchasing power of money” (Tm/3/2/48), which can be corroborated with his letter to Keynes (17 December):
“I ... feel that a few simple equations involving the elements of savings and profits that are devoted to the banking system...and to new investment, would make things much clearer” (JMK.13, 121).
We also have Robertson’s letter to Keynes (5 December), according to which Keynes seems to refer to the role played by profits, an increase in investment, a rise in prices, and so forth, which indicates something like the first fundamental equation:
“...I find a certain indeterminacy about the role of profits. They first appear as a result... of the rise of P: then, ... in connection with bank-rate, as a motive-force towards the excess of investment which raises P ....” (Tm/1/2/34-35).
Taking this into consideration, the first fundamental equation possibly came into being, in some form or another, after the TOC of 2 August 1929.
The preface dated 1 September 1929 (Tm/3/2/56-60) is worth noting in comparison with the Treatise’s preface.
In the latter Keynes declares, “In Books III and IV... I propose a novel means of approach to the fundamental problems of monetary theory” (TM.1, p. xvii), while in the former he had expressed his view less clearly: “as the point of the book lies...more in its cumulative effect than in any particular part of it....the central theory of the book is to be found in chapters 9 [the fundamental equation], 10 [digression on savings and investment] and 16 [the genesis of the price level], …” (Tm/3/2/56).
The best source we can draw on to form an idea of Keynes’s theoretical situation in early 1930 is the evidence he submitted in February-March 1930 in the Macmillan Committee (JMK.20, 38-157).
In his statement concerning the fundamental equations (though these terms are not used) we see him discussing the first (see JMK.20, 74) and the second fundamental equations in broad terms, with the TM supply function behind the scene (see JMK.20, 75).
However it is also clear from Keynes’s letter to Kahn (18 arch 1930, JMK.13, 125-126) that the fundamental equations had yet to be established.
“... I am unable to arrive at any simple formula connecting the change in the value of investment with the amount of saving which goes on through the banking system...” (JMK.13, 125-126).
Subsequently, he revised the chapter on the fundamental equations, which is confirmed by his letter to Hawtrey (18 July 1930. See Tm/1/2/171).
E. Robertson’s Influences
Keynes had ongoing discussions with Robertson regarding BPPL27 in the making. Initially, as his 28 May 1925 letter to Robertson (Tm/1/2/18-20) shows, Keynes had objected to a “distinction between hoarding and forced effective abort lacking” and the idea of the admitted power of inflation to bring unused resources into use. In his 10 November 1925 letter (JMK.13, 40-41), however, Keynes had come round to essentially agreeing with Robertson's ideas as a result of Robertson’s revisions (see JMK.13, 40).
The object of BPPL was “to interweave with the ...‘non-monetary’ argument of [Robertson (1915)] a discussion of the relation between saving [lacking], credit creation and capital growth” (Robertson, 1949, vii-viii). Credit-creation by the banking system plays an important role in the procurement of real capital (required for the increase of production) by entrepreneurs, which in turn induces a rise in the price level.
It was not until two years later after BPPL that a distinction between investment and saving began to make its appearance in Keynes. Moreover, Keynes dealt with “savings and investment” in the late 1928 TOCs (4 September, Tm/3/2/37, and 6 October 1928, Tm/3/2/41) and August 1929 TOC (Tm/3/2/48) only as a “Digression”.
The TOC of 2 August 1929 is the latest of the surviving TOCs, consisting of thirty-two chapters in the form of one volume with no text surviving except for Chapter 23.
We can recognize Robertson’s influence in Chapter 23, “The Part Played by the Banking System” (JMK.13, 83-113). Two points can be made in this regard.
The first concerns the stability of prices.28 Accepting Robertson’s idea that “[t]he aim of monetary policy should surely be...to permit [price increase]...necessary to ...appropriate alterations in output” (BPPL, p. 39), Keynes came to think that the correct method of achieving price stability
“must be sought...in the discovery of some means to meet the fluctuating demands for...credit without causing those reactions on the stability of the price level” (JMK.13, 90).
The second point concerns forced saving. Keynes considers “methods of adjusting the supply of working capital by means of banking policy”. One of the methods is the use of credit inflation, which induces forced saving. He allows employment and output to increase at the expense of price stability (see JMK.13, 104).
These points are recognizable in the TOCs of 6 October 1928 and 2 August 1929, which include the headings, “the ‘justification’ of credit inflation” and “by forced transfers [or transferences] of purchasing power from ‘unproductive’ consumers”.
Thereafter, however, he excluded these phrases. The divergence between Keynes and Robertson widened.29
F. The Final Stage
Keynes planned to publish a one-volume book in May 1929. He wrote to Harcourt (26 September 1928) that “I have devoted the whole of this summer to [the Treatise] … four-fifths ... is... finished” (Tm/1/3/91).
In the proofing process there survives only the first galley for Chapters 30, and 31, with “16 July 1929” and “27 July 1929” stamped on them respectively. Keynes then changed the arrangement of the Books, and wrote to Harcourt (28 August and 25 September 1929, respectively):
“the rewriting...will prove a great improvement./...the book will probably fall... into two parts of about equal length” (Tm/1/3/103).
“I have now definitely decided to make it a two volume book…” (Tm/1/3/107).
The letters around January 1930 are: Robertson to Keynes (5 December 1929; 8 January 1930; 4 March); Kahn to Keynes (29 September 1929, Tm/1/2/42; 17 December, JMK.13, 120-121; March 1930, JMK.13, 123-124; 12 March, JMK.13, 124-125); and Keynes to Kahn (18 March 1930, JMK.13, 125-126).
Keynes wrote to Harcourt on 18 February 1930;
“Since [25 September] I have been working on the book continuously. But the labour of revision and rearrangement in two-volume form has proved very heavy, and, … the end is not yet” (Tm/1/3/109).
From the third galley of the Treatise, there survive only Chapters 21 and 25, on which “4 March” and “28 May 1930” are respectively stamped.30
It was Hawtrey who appeared as a critic at this stage. On 23 April 1930 (Tm/1/2/84) Keynes sent Hawtrey a batch of the proofs, followed by “a … batch of Volume II” on 24 June (Tm/1/2/89).
Hawtrey responded to Keynes with long critical notes31 on 7 and 9 July ― the most important source showing the state of development at the end of April: we see the formulation of the second fundamental equation32 as well as the TM supply function (Tm/1/2/107; Tm/1/2/116) and the natural rate of interest (Tm/1/2/146-147; Tm/1/2/137).
We find detailed evidence of the gestation on the book as of 30 June 1930 in a letter to R.& R. Clark;
“I could let you have the proofs of the whole of Vol. I and of the first 144 pages of Vol. II, finally marked for press…” (Tm/1/3/11).
On 18 July 1930 Keynes wrote to Harcourt;
“Almost the whole of [the book] is now in type, and I am sending off sheets marked for press every few days” (Tm/1/3/115).
On 14 September 1930 Keynes wrote to his mother:
“This evening...I have finished my book. It has occupied me seven years off and on... Artistically it is a failure. I have changed my mind too much during the course” (JMK.13, 176).
5. Conclusion
The main purpose of this paper was to disentangle the zigzag process from the Tract to the Treatise, and to distinguish some important stages. Our main results are as follows:
(i) Keynes went on working out his theory along the Tract theory up to the TOC of 27 April 1926.
(ii) Keynes then adopted the TA from 26 May 1926 to 22 September 1927.
(iii) We stress the importance of the three TOCs written between September 1927 and September 1928 as pointing the way towards the fundamental equations of the Treatise, albeit with the TA still remaining dominant. These TOCs might well mark the real breakthrough on the way to the Treatise.
(iv) In the light of some letters, the preface dated 1 September 1929 and Keynes’s evidence in the Macmillan Committee, we may go as far as saying that the first fundamental equation possibly appeared after the TOC of 2 August 1929.
(v) However, as is clear from Keynes’s letter to Kahn (18 March 1930), the fundamental equations had yet to be established. He revised the chapter on the fundamental equations, as is confirmed by his letter to Hawtrey (18 July). Judging from Hawtrey’s criticism on 7 and 9 July, we see that by the end of April the second fundamental equation, the TM supply function and the natural rate of interest had made their appearance.
(vi) We see that the key elements going into the Treatise theory made their first appearance at a very late stage, which fact explains why Keynes took so long to abandon the quantity theory.
Notes
1) Keynes in (TMR, 63) states that his equation follows that in Pigou (1917), which allows for variability of its components. For the relation between the two, see Bigg (1990, 75). The Tract equation is used as explaining the short-term economic fluctuations.
2) See TMR, 34.
3) For the theory’s applicability, see TMR, 73-80. For its rejection, see TM. 1, 64-65.
4) See TM.1, 176-177. Kahn (1984, 74) denies Wickell’s influences on TM.
5) This is true of the argument at TM.1, 183-187.
6) Keynes (1914) reviews it critically, although it evaluates Part III.
7) See TM.1, 205. We find three types of interpretation: (i) TM accepts it; (ii) TM is critical of it; and (iii) TM stands in between.
8) Laidler (1990) appraises TM’s portfolio selection theory as well as Lavington’s one (1921) as making good the defect of neo-classical monetary economics.
9) See TM.1, 196-197. This shows why TM regards money supply as endogenous. For exogeneity/endogeneity in Keynes’s economics, see Moore (1988) and Graziani (2003).
10) This is examined in Hirai (1997-9, Chapters 3 and 7).
11) See TM.1, 118-119, and 145-147.
12) See TM.1, 191-192. TMR stresses the difficulty of the simultaneous attainment.
13) See TM.2, 162-169, and 338-347.
14) Cf. Skidelsky (1992, 281-285) .
15) See also Skidelsky (1992, 164). The TOC (Undated, Tm/3/2/2) of the same period survives, arguing “[t]he control of p by control of n …only requires that [k, k΄, and r] should not be linear functions of n”.
16) See Skidelsky (1992, 281).
17) Keynes, in fact, maintains it thereafter. See D (a) below.
18) Robertson stressed fixed capital. See his comment on Keynes’s draft (JMK. 13, 26).
19) The only surviving formula around this period is “P=M/(C1+WT) where …C1 [is] the real value of the investment-deposits, T the volume of transactions, and W the inverse of the “efficiency” of the money deposits” (Tm//2/350).
20) Possibly Keynes used the TA in terms of the short run rather than the long run, for he argues ‘the variability of [the equation’s] elements’ (Tm/3/2/23; 26). Keynes (1911) had criticized Fisher’s TA from Marshall
21) Beside this, Fisher has a “transitional periods” theory.
22) See Moggridge (1992, 441-442).
23) Patinkin (1976, 28-29) estimates that the fundamental equations may have appeared in the latter half of 1928.
24) Chapter 1 of Book IV seems to be related to a memo (Tm/2/342-3).
25) See also the expression, “(Earnings minus Savings)/(Output minus Investment) = Price Level” (undated, Tm/3/2/86), substantially similar to the first fundamental equation.
26) These are to be moved to Book V of TM.2, after separation from the fundamental equation. See Keynes’s “precautionary word” (TM.2, 4).
27) For “Keynesian parallels” in BPPL, see Fletcher (2000, Chapter 21).
28) See Bigg (1990, 175-176).
29) See “Notes on the Definition of Saving” (esp. JMK.13, 287-288).
30) The material which concerns the TM’s Chapter 37 survives in Tm/2/246-275.
31) For this impact on Keynes, see Deutscher (1990, 102-105). Keynes’s rejoinder was made on 28 November 1930 (Tm/1/4/14-54).
32) See Tm/1/2/102.
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# The paper originates in Hirai (1997-1999, Chapter 6). The earlier versions were read at Prof. C. Marcuzzo’s workshop, the University of Rome “La Sapienza”, Italy , in January 2004, Prof. R. Arena’s seminar, the University of Nice-Sophia , France
* Faculty of Economics, Sophia University , Tokyo
