To What Degree Did Keynes Approach the General Theory in 1933? ― Searching for a Theory of Employment ―

For the HES Annual Meeting, 9 June 2007, George Mason University

To What Degree Did Keynes Approach the General Theory in 1933?

― Searching for a Theory of Employment ―

 Toshiaki Hirai#

I. Introduction

The aim of the present paper is to examine Keynes’s developmental stage as of 1933. The year stands between A Treatise on Money (hereafter the Treatise) and the General Theory of Employment, Interest and Money (hereafter the General Theory).  

  We need to begin our story with roughly summarizing how we understand his theoretical development from the Treatise up to the end of 1932, which was examined elsewhere.         

We argue that the Treatise theory consists of two parts, one of which addresses the determination of variables relating to consumption goods (Mechanism 1) and investment goods (Mechanism 2) in ‘each period’. The other part is formulated in such a way as entrepreneurs expand (contract) output in the next if they make a profit (loss) in the current period (we call this the TM supply function).

  The Treatise theory can thus be expressed as Mechanisms 1 and 2 working through Mechanism 3.¹This interpretation sees the Treatise theory as a dynamic process of price levels and volumes of output.

  Keynes defended his dynamic theory until around October 1932, stressing the TM supply function. This can be shown through examination of the manuscript “The Monetary Theory of Production” (JMK.13, 381-396), his controversy with Hawtrey, Robertson, the “Cambridge Circus”, etc.²

At the end of 1932, however, Keynes put forward a simultaneous equations system in the manuscript, “The Parameters of Monetary Economy” (JMK.13, pp.397-405), which took the equality of investment and saving for granted, and adopted the liquidity preference theory, a theory similar to the multiplier theory, and the first postulate (though he retained some doubt about this last).

  Although Keynes still clings to the idea of the TM supply function, this manuscript nevertheless marks a turning point from the Treatise toward the General Theory.

  We might say that Keynes’s abandonment of the function shook the foundations of his theory up to mid-1932, and the main components of the General Theory were to be built as a consequence.³

Many interpreters of Keynes hold the view that in 1933 he established the foundations of his theory of employment in the General Theory. We can not categorize those views, to which we will refer in the notes concerned, so easily, for they stand on different grounds which include their evaluation of the relation between the Treatise and the General Theory. What is clear, however, is that sufficient time and space has not been spent on studying the materials concerned.

 What we will aim at is to examine these materials in detail, and to elicit the features of the real situation.   

In this paper we will introduce two new concepts which seem to be essential in understanding the three manuscripts in a consistent way ― “the pseudo-TM supply function” and “the pseudo-TM supply function mk2” (to be explained below).

What matters here lies in our analysis of how Keynes formulated his theory of employment or income, while still sticking to his pet idea to the effect that the volume of output is determined based on the profits earned.

To show the basic line of our results beforehand, we recognise that Keynes stepped into the road which would lead to the General Theory, for he put forward several models for determining the level of output or employment together with some important concepts which were to comprise the General Theory.

We would like to emphasise, however, that Keynes’s models suffer from several theoretical inconsistencies. By examining them, we can show that Keynes in 1933  struggled to formulate a new employment theory. In that sense we can safely say that his theoretical framework is still far from completion.

 

This paper proceeds as follows. In Section II we will deal with what he was writing for the projected book in 1933. For this, we have three fragmentary manuscripts and three tables of contents. They are dealt with, respectively, in Section II and Section IV. In between (Section III), we would examine how Keynes argued his theory in the Michaelmas Terms.

In Section V, we would examine the relationship, in terms of theory, between Robertson, Hawtrey and Keynes. The present paper ends with the conclusion (Section VI). 

II. Three Manuscripts

  The manuscripts we shall be looking into here are: “The Monetary Theory of Employment” (JMK.29, 62-66. Hereafter the First Manuscript); “The General Theory of Employment” (JMK.29, 63, 66-73, 87-92, 95-102. Hereafter the Second Manuscript); and the manuscript with the same title as the Second Manuscript (JMK.29, 76-101 and JMK.13, 421-422. Hereafter the Third Manuscript).

 

1. The First Manuscript

  The First Manuscript is part of Chapter 6, “A Summary of the Argument So Far”, and is assigned to the First Table of Contents. Two points are particularly noteworthy ⁴: the system of equations leading to the GT’s Chapter 3, and the “accounting period”.

A. A System of Equations

The earliest system of equations determining the level of employment is formulated here. It should be kept in mind that Ohlin (Patinkin=Leith, 1977, p.153) stated that in 1933 (or in the latter half of 1932) economists began to treat output as a central variable in a monetary theory.

  Keynes argues:

Thus the amount of employment will be determined by a set of simultaneous equations which relate together employment (N), prospective investment (I) and prospective consumption (C), … :

            N = f₁ (Q)             (1)

                E = f₂ (N)             (2)

              C = f₃ (D) ⁵            (3)

                D = E + Q = I + C       (4)

where f₁ … may be called the Supply Function, f₂ the Cost Function, and f₃ depends on the propensity to save ....

If … we suppose the entrepreneur firms to know … f₁, … f₂, … f₃ and … I, then … N which they will offer will be determinate (JMK.29, 65).

 In his letter to Robertson (20 May 1933. JMK.13, pp.307-308), Keynes tried to persuade Robertson that Robertson’s ‘hoarding’ equals Keynes’s ‘saving – investment’, which Robertson rejected (here ‘saving’ in the Treatise). Keynes also referred to “[o]ld-fashioned saving” equal to investment. Judging from this, we estimate that the First Manuscript must have been drawn up subsequent to the letter, which has an expression: “my affection for the concept I – Q [=S]” (p.308).

 (a) The Components

  Equation (1) differs from the TM supply function as follows (the former concerns equation (1); the latter the TM supply function):

  We understand the Treatise theory as a dynamic process composed of Mechanism 1 (which determines the price level of consumption goods) and Mechanism 2 (which determines the price level of investment goods) working through the TM supply function.⁶ The TM supply function is defined as the behaviour of entrepreneurs is such that, if they make a profit (take a loss) in the current period, they expand (contract) output in the next.

(i) Q and N belong to the same period: Q to the current period and N to the next;

　(ii) N is determined by the system of equations: N by a single equation;

(iii) Q and N are variables: Q and an increment in output are variables;

  (iv) Q is expected by entrepreneurs: Q is realized.

  Keynes, however, tends to regard the two as playing a similar role, for he takes the view that entrepreneurs determine the level of output (and that of employment) based on profit⁷:

The aggregate amount of employment offered will depend ... on the amount by which the sale proceeds of output … are expected to exceed their variable cost (JMK.29, 64).

  Keynes seems to think that equation (1) works for the determination of the level of employment in the same way as equations I΄ = C΄ (Q₂) and R = H′(Q_１) do in  “The Parameters of a Monetary Economy” manuscript (JMK.13, 403. Hereafter the PME manuscript)⁸. This, however, is not the case, for Q and N in equation (1) belong to the same period:

... we are basing our conclusions about employment on the proper criterion, … whether the result of spending money on employment and of selling the output is expected to result in a larger net sum of money at the end of the accounting period than if the money had been retained (JMK.29, 66).

  Keynes compares the “proper criterion” with “other criteria”:

Other criteria, such as the relation between the real output which a given employment will yield and the disutility … of that employment [the second postulate], or the relation between the real wages of a given employment and the amount of its marginal output [the first postulate] ... are not appropriate to the actual nature of business decisions … (JMK.29, 66).

  Thus, rejecting the two postulates⁹, Keynes retains the idea that entrepreneurs determine the level of output based on profit. Given the difference from the TM supply function, and yet the perceived continuity, let us call equation (1) the ‘pseudo-TM supply function’.

  Equation (2) may be interpreted, following the explanation in Section I (2 (B)), as E = N.W (W denotes the money wage).

  Equation (3) is the consumption function formulated for the first time.¹⁰

  Equation (4) may look like the equations Δ Q =Δ D - Δ E or Δ Q =Δ I +ΔF - ΔE of the MTP manuscript. However, it is not so much an equation determining profit as one equalising supply and demand.¹¹

                                              

  Given I, the system determines the level of employment.¹²

 (b) The Position of the System

  Let us examine the position of this system in the light of Keynes’s theoretical development.

  (i) The First Manuscript maintains the idea that equilibrium of investment and saving determines the amount of employment, so that equation (4) follows equation (4) of the PME manuscript.

  (ii) In the Treatise profit and prices are simultaneously determined, while the volume of output changes with one time lag. In the MTP manuscript a time lag between profit and the volume of output is assumed, without reference to prices. In the PMT manuscript prices, the volume of output, and profit are simultaneously determined. In the First Manuscript, the level of employment (the volume of output) and profit are simultaneously determined without reference to prices.¹³

  (iii) The TM supply function virtually disappears in the First Manuscript, albeit a version of I΄= C΄(Q₂) and R= H′(Q₁) of ‘Model 2’ of the PME manuscript is retained. However, it does not work in the way he intends.

  (iv) The “aggregate demand function”, D = f (N) = X (N) + D₂, where X (N) is the expected volume of consumption and D₂ the expected volume of investment, of the GT is fundamentally the same as the equation, D = f₃ (D) + I, obtainable from equations (3) and (4):

 

The following, on the other, can be derived from equations (1) and (2):

          E + Q = f₂ (N) + f₁^-1 (N) = H (N)

where f₁^-1 is an inverse function of f₁.

  The function H (N) describes entrepreneurs’ economic activities corresponding to the “aggregate supply function”, Z= f (N), of the GT. Strictly speaking, it is not the same because of rejection of the first postulate. Moreover, the system does not have a single concept such as H (N). Thus we have some difficulty in establishing a link, and yet the system might well be the first precursor of GT’s Chapter 3.

  B. The “Accounting Period”

  In the First Manuscript Keynes defines the accounting period as the span of time during which capital equipment remains constant, and analyzes the economy in terms of it. It corresponds to the Marshallian short run, and Keynes might implicitly have used this in Model 1 of the PME manuscript.

  Two points in particular are worth noting here.

Firstly, while seemingly static, his analysis is in fact dynamic. The values of the variables determined by the system belong to the current period. Given the renewed values of the exogenous variables, the values of the variables in the next period are determined in the same way. In each period ‘a snapshot’ is taken, and the economy’s dynamic process is depicted as a series of snapshots¹⁴:

The commencement of the next accounting period will find the firms … [with] a different capital equipment, modified … by wastage and obsolescence … and the new investment …. [A]t any given time the productive processes … are decided in relation to the then existing capital equipment. … [Thus] we are … in the closest possible contact with the facts and methods of the business world …; and … we have transcended the awkward distinction between the long and the short period (JMK.29, 65-66).

  Secondly, the First Manuscript assigns the role of connecting the current period with the next to capital equipment, while the manuscripts up to the MTP manuscript attribute this part to the TM supply function (and profit). Hitherto he had not shown any particular interest in capital equipment (the Treatise had emphasized working capital, entrusting fixed capital to Schumpeter’s theory), but now, with the accounting period, he had the opportunity to reconsider capital and investment.

2. The Second Manuscript

  This manuscript consists of three fragments: one with no heading fragment, and two respectively bearing the headings “Some Fundamental Equations”, and “Definitions and Concepts Relating to Capital”. According to Moggridge, they belong to Chapters 1, 5, and 8, respectively, of the Second Table of Contents (to be examined below).

  In the Second Manuscript, Keynes emphasizes the accounting period. He also uses equation (4) and the equation E = N.W ─ a variant of equation (2). Thus the Second Manuscript stands on essentially the same ground as the First.

  The features not recognizable in the First Manuscript are:

                                                  

 (i)  a function similar to, but a little different from, the pseudo-TM supply function;

 (ii)  suggestion of the stability of the system;

 (iii)  acceptance of the first postulate;

 (iv)  heterogeneity of goods;

 (v)  two kinds of period concept.

  (i) and (ii) are theoretically important and related to Chapter 3 of the General Theory, while the others are methodologically important and related to Chapter 2 ((iii)), Chapter 4 ((iv)) and Chapter 5 ((v)) of the General Theory.

  A. The ‘Pseudo-TM Supply Function mk2’

  What characterizes the Second Manuscript is a function¹⁵ resembling the pseudo-TM supply function. This seems to be obtained by differentiating equation (1). However, this is not the case, for it is excluded from the system determining the level of employment, and relates to a stability condition. Let us call it the ‘pseudo-TM supply function mk2’.

  We need to point out a change in the definition of profit. In the Treatise profit was defined as exclusive of normal profit, but profit here includes it:

… the excess of earnings over consumption corresponds to … Saving (S) in [the Treatise]. It is not identically the same concept, since it does not include the normal return to capital equipment … (JMK.29, 69).¹⁶

  Along with this, the concept “economising” appears, referring to “the excess of earnings over consumption”, while “saving” is taken to mean “income minus consumption”.

  In the Treatise, earnings include normal profit, and consumption is assumed to be effected out of earnings. Saving is the difference between earnings and consumption.

  Contrastingly, “profit” in the Second Manuscript is composed of normal and excess profit. It comprises income together with earnings. Consumption is assumed to be effected out of income.

  Thus, the definition of profit differs between the two.¹⁷ Nevertheless, the idea that entrepreneurs determine the level of output (and the level of employment) based on  profit is retained:

… Δ N [an increment of employment] and Δ Q [an increment of quasi-rent or profit] have the same sign. Further, since Δ Q = Δ I - Δ S΄ [I is investment; S΄ economising], ...  Δ N and Δ I - Δ S΄ have the same sign (JMK.29, 70).¹⁸

... the fluctuations of aggregate quasi-rent ... lead to fluctuations in employment (JMK.29, 71).

  Thus the concept relating profit to the level of employment might reasonably corresponds to N = f₁ (Q) in the First Manuscript:

Our first fundamental proposition, namely

              N and Q have the same sign,

can then be expressed: –– the quantity of employment and the expectation of quasi-rent during the employment [accounting] period increase and decrease together (JMK.29, 76).

  Profit and the level of employment are considered to change within the same accounting period.

  B. Suggestion of the Stability of the System

  Although the Second Manuscript has not the system of equations of the First Manuscript, it has the same ground as the First manuscript. Considering this and the pseudo-TM supply function mk2, Keynes possibly used the pseudo-TM supply function mk2 similarly. If so, contrary to Keynes’s intention it would not work for determining the level of employment

Therefore something like the following solution would be required: the pseudo-TM supply function mk2 could be separated from the system for determining the level of employment and used for the stability condition.

  An argument for the stability of the system might then be suggested in terms of the pseudo-TM supply function mk2:

… fluctuations in employment will primarily depend on fluctuations in aggregate expenditure relatively to aggregate costs. This is the essential feature of an entrepreneur economy (JMK.29, 90-91).

  This proposition indicates the stability of the system, since adjustment is assumed to be made within each employment period. The pseudo-TM supply function mk2 might be interpreted as adjusting the system.

  However, Keynes develops his analysis ambiguously as he deals with normal and excess profit. This, together with a change of profit in definition and no systematic analysis, makes it difficult to reconstruct the original model. Nevertheless, confining changes to a minimum, we might formulate the pseudo-TM supply function mk2 as follows:

Q_i = I + C - (E + Q_n)       (7)

Δ N =ψ (Q_i)           (8)

ψ΄(Q_i) > 0            (9)

ψ (0)  = 0           (10)

where I denotes investment, C consumption, E variable costs, Q_n normal profit, Q_i excess profit, N employment, and ψ (･) the pseudo-TM supply function mk2.

  In equation (7), excess profit Q_i is defined as the difference between aggregate expenditure, I+C, and aggregate costs, E+Q_n (Keynes in fact regards E only as aggregate costs).

Equation (8) is the entrepreneurs’ behavioural function (actually Keynes uses the sum of normal and excess profit, and uses the total level of employment¹⁹). As excess profit increases, increase in the level of employment accelerates (equation (9)), while when excess profit falls to zero increase in the level of employment comes to a halt (equation (10)).

  The stability conditions for the system are:

             If N < N^*, then I + C > E + Q_n

             If N > N^*, then I + C < E + Q_n

where N^* is the equilibrium level of employment.

  If we call the function relating the difference between aggregate expenditure and aggregate costs to the level of employment the ‘excess demand price function’, the stability condition is that the excess demand price is a decreasing function of the level of employment (equilibrium is attained at the point where excess profit is zero):

d{(I + C) - (E + Q_n ) }/ dN < 0    (11)

  To complete the model, we need a system for determining the level of employment. This can be expressed as

I + C = E + Q_n        (12)

D = I + C          (13)

E = W.N           (14)

C = f₃ (D)            (15)

　　　　　　　　　　　

　                    Q_n = Q(ー)_n               (16)

  In the Second Manuscript, the “fundamental equation” is formulated as

              Y = E + Q = C + I = D          

where Y denotes income, E earnings, Q quasi-rents, and D disbursement.

  The Second Manuscript has equation (14). Albeit not being in the Second Manuscript, equation (15) is verbally expressed. With regard to equation (16), we read that “‘normal’ [return] is constant for a given capital equipment” (JMK. 29, 69).

 Excess profit is excluded from the right-hand side of equation (12), and is defined as the difference between I + C and E + Q_n. So defined, it becomes zero at the equilibrium point. Thus, given W, Q_n, and I, the level of employment is determined.²⁰

  C. The First Postulate

  Keynes accepts this postulate for the first time.

In his letter to Robertson dated 10 September 1933 (JMK.13, pp.310-313; GTE/1/132) which contained criticism of Pigou (1933), Keynes called it the “fundamental postulate of employment theory” approvingly.²¹

... the value of the marginal product is equal to its variable cost... (JMK.29, 72).²²

  D. The Heterogeneity of Goods

  In the Second Manuscript this is emphasized:

                  

...the concept of an average price per unit of output ... raises precisely the same difficulties as to a quantitative measure of a non-homogeneous complex, as does the measurement of real output itself. …

  I find it, however, a matter of considerable intellectual satisfaction that these partly insoluble difficulties of quantitative description do not arise in our causal analysis, which is strictly logical … and is subject, in practice, not to essentially insoluble difficulties … (JMK.29, 73).

  The unit measurement should be understood in connection with the fact that Keynes, well-versed in the index problem, tries to avoid the ambiguities of the general price level and output as a whole, finding new concepts appropriate for the theory of employment. GT’s Chapter 4 (II) originates from this, apart from the concept of “complexes” in the PME manuscript.

E. Two Kinds of Period Concept

  In the Second Manuscript two kinds of period concept are compared: the “production” (“investment”) period; and the “accounting” (“employment”) period:

The first forecast [covering the investment period] is that which … [an entrepreneur] has to make when he decides to spend money on setting up a capital equipment … The second forecast [covering the accounting period] is when, being in possession of a capital equipment, he decides how much variable cost to incur in working it … (JMK.29, 73-74).

  This argument is the origin of GT’s Chapter 5. The first and second forecasts correspond to the short- and long-term expectations respectively.

 Keynes emphasizes the accounting period because “all decisions to employ labour depend on expectations covering this period (JMK.29, 74). This corresponds to GT, 50-51 where he stresses that the volume of employment is “determined by the producer’s short-term expectations”.

  He also stresses the importance of distinguishing the accounting period from the investment period, for failure to do so causes confusion:

[The investor’s] forecast relates to the hire which he expects to get during each accounting period until the goods are worn out …. It leads…to a great confusion to … regard the whole period from the first employment of labour until the goods are finally worn out as constituting a single period of production. … its appearance of logical completeness is illusory … (JMK.29, 75).

     Keynes clearly criticizes Hayek’s (1931) theory in which consumer goods and intermediate products differ only in production stage.²³

  F. The Second Postulate

  The Second Manuscript rejects it along with the argument of the First:

[According to] the Classical Theory …, given the amount of capital equipment and the supply schedule of labour in terms of output, the volume of output and hence the ratio of aggregate quasi-rent [Q] to the price of output [P] tends to be constant ... [This] … must … [follow] from the second postulate. Output will be pushed to the point at which the utility of the marginal product is equal to the disutility of the marginal employment … only when we waive [it] … [,] … [Q/P] can be supposed to fluctuate … (JMK.29, 70-71).

  This can read as follows. If the postulate is accepted, the economy reaches full employment. Applying this to the equation O = NW/P + Q/P ─ a variant of the equation in the Second Manuscript (see JMK.29, 71) ─, given O and NW/P, Q/P is kept constant. Unless Q/P fluctuates, output (and employment) cannot fluctuate.

  Besides these, the Second Manuscript contains various other points of considerable significance, including:

(i)  Stress on fiscal policy (first appearance in Keynes’s manuscripts) and low interest rate policy;

(ii)  Support of a protectionist policy;

(iii) Keynes’s persistent theme²⁴, based on equations (7) - (10), that unless effective demand increases, entrepreneurs cannot protect themselves from losses either by increasing the volume of output²⁵, or by reducing money wages²⁶;

(iv) The definitions of some central concepts, leading to an argument in GT’s Chapter 6 (II).

3. The Third Manuscript

  The Third Manuscript, dated December 1933, has Chapter 2, “A Difference between a Cooperative Economy and an Entrepreneur Economy”, and Chapter 3, “The Characteristics of an Entrepreneur Economy”, both being assigned to the Third Table of Contents.

The Third Manuscript is similar to the Second. Here we focus on two concepts: effective demand and the entrepreneur economy. Effective demand is closely related to the pseudo-TM supply function mk2, and the argument for effective demand corroborates our interpretation of the stability of the system (It has no passage arguing the determination of the level of employment).

  A. Effective Demand

  The Third Manuscript develops an argument based on the pseudo-TM supply function mk2, focusing on “effective demand”.

Although the term first appears in the Second Manuscript (JMK.29, 97), the argument for effective demand appears here. The definition, which is made in relation to the pseudo-TM supply function mk2, differs from that in the General Theory.

Effective Demand may be defined by reference to the expected excess of sale proceeds over variable cost ... [It]fluctuates if this excess fluctuates, being deficient [excessive] if it falls short of [exceeds] some normal figure … [I]n an entrepreneur economy the fluctuations of effective demand may be the dominating factor in determining the volume of employment (JMK.29, 80).

  Comparison is made between sale proceeds and variable cost. The difference is defined as “profit” in the 1933 three manuscripts. By subtracting “some normal figure [profit]”, “excess profit” is obtained.²⁷ Then, the phrase “it falls short of some normal figure” refers to excess loss. Effective demand is defined in relation to excess profit, moving in the same direction.

If we take into consideration that “[an entrepreneur] will increase his output if by so doing he expects to increase his money profit” (JMK.29, 82), the passage can read: if excess profit is negative [positive], effective demand is deficient [more than sufficient], so entrepreneurs will reduce [increase] the volume of output (and the level of employment); if excess profit is zero, effective demand is in equilibrium, so entrepreneurs will keep the volume of output constant.

  Here Keynes does not argue how the level of employment is determined, but discusses its stability condition.

  In the Third Manuscript effective demand is discussed solely in terms of sale proceeds and variable costs, which suggests that Keynes is only using a concept representing the aggregate demand side.

  Keynes criticizes Say’s Law, presenting an alternative proposition:

… the classical economists have taught that supply creates its own demand; … For [that] proposition, I shall substitute the proposition that expenditure creates its own income …. (JMK.29, 80-81).

  These, together with a quotation from Marshall (1879), are the starting point for GT’s Chapter 2 (VI).

  In the Third Manuscript, Keynes endorses Marx’s view²⁸, quoting from McCracken (1933):

The nature of production in the actual world is not ... a case of C - M - C΄ … the attitude of business … is a case of M - C - M΄ (JMK.29, 81).

  Keynes divides the economists advocating this view betwee those asserting “the inevitable excess of M΄” (e.g. Marx) and those asserting “the inevitable excess of M” (e.g. Hobson) (JMK.29, 82). This is closely related to GT’s Chapters 3 (III) and 23 (VII).

  B. The “Entrepreneur Economy”

  Keynes regards “fluctuations of effective demand” as the crucial feature of an entrepreneur economy (see JMK.29, 85).

  He examines the relationship between the entrepreneur economy and “money”:

[A]nything in terms of which the factors of production contract to be remunerated, which is not and cannot be a part of current output and is capable of being used otherwise than to purchase current output, is, in a sense, money. If so, … the use of money is a necessary condition for fluctuations in effective demand (JMK.29, 86).

  Money defined as something used as a means of payment and of storing wealth is a necessary condition for the fluctuations in effective demand. Although money alone does not cause the fluctuations, no economic fluctuations would occur but for money.

  In the monetary system, argues Keynes, deficient effective demand occurs more frequently than the opposite:

… the money … will ‘keep’ more readily than the output …(JMK.29, 86).

  Keynes points out the difference in property between goods and money. This, although only “carrying cost” is mentioned, leads to GT’s Chapter 17:

... it is a characteristic of finished goods, … that they incur substantial carrying charges for storage, risk and deterioration, so that they are yielding a negative return … ; where such expenses are reduced to a minimum … in the case of money (JMK.29, 86).

  C. Shortcomings of “Classical Economics”

  The Third Manuscript criticizes the Classical theory of employment and of interest.

  In Keynes’s view, the level of employment in a co-operative economy is determined in accordance with the second postulate, but classical economics erroneously assumes that the postulate is applicable to the existing economy.

  He also attacks Fisher and Marshall’s interest theory, in particular the “real rate of interest”²⁹, arguing that the idea that fluctuations of prices cause those in the level of employment is, practically and theoretically, an error. The role of effective demand is again stressed:

... it is not the prospect of rising prices as such which stimulates employment, but the prospect of an increased margin between sale proceeds and variable costs (JMK.29, 85).

4. An Evaluation of the Three Manuscripts

   The above examination shows that the three manuscripts reveal advantageous points in his theoretical development while they expose theoretical inconsistencies.

  A. The Essential Points

  The fundamental elements can be summed up thus:

(1) In the First Manuscript, under the concept of “accounting period”, the system determining the level of employment appears for the first time, using the consumption function and expressing all the variables in terms of expected values.

(2) In the Second and Third Manuscripts, the stability conditions are argued in terms of aggregate expenditure and variable costs.³⁰

  Point (1) is important, for it leads to GT’s Chapter 3. As far as point (2) is concerned, the stability conditions are not taken into consideration as such.

                        

  B. Several Inconsistencies

The three manuscripts are flawed by several inconsistencies.

(i) Keynes tends to regard the relation between the commodity market analysis in the Treatise and in the General Theory as continuous.

  This has to do with the fact that Keynes transformed the TM supply function into first the pseudo-TM supply function, and then the pseudo-TM supply function mk2.

  This inclination is to be found in the argument of the Second Manuscript (JMK.29, 71-73), which might indicate a reversion to the Treatise world. Surprisingly enough, it appears in GT, 77-78. This comes partly from his unconscious adherence to the idea of the TM supply function.

  Nevertheless, the argument in the Second and Third Manuscripts can be properly understood only if the function in question is interpreted as the pseudo-TM supply function mk2.

(ii) In the First Manuscript, equation (1) is in an awkward position, for it contributes to determining the level of employment while it is also treated as if the TM supply function.

(iii) In the Second and Third Manuscripts, normal returns are considered to be constant, while the maximizing behaviour of entrepreneurs is acknowledged.

(iv) In the three manuscripts there exists no concept representing the aggregate supply side.

  From our investigations two clues for the interpretation of GT’s Chapter 3 can be gleaned.

  First, a Marshallian framework is adopted from the First Manuscript onwards. It is reflected in:

(i) an equilibrium analysis by means of the demand and the supply functions (although the supply side is unclear);

  (ii) the stability condition;

 (iii) the period concept.

  Second, Keynes probably thinks that “windfall profit” becomes zero at the equilibrium point determined in GT’s Chapter 3.

III. The 1933 Michaelmas Lectures

  The remarkable feature of the 1933 lectures³¹ (16 October – 4 December) is that the theoretical framework there, if not completely that of the General Theory, comes close to it.³²

In the fifth lecture Keynes states that the income and price levels are determined in such a way that Y = C + I (or I = S), which is the essential feature of the monetary system (Y is income, C consumption, I investment and S saving).

In the sixth lecture the “psychological law” makes its first appearance. Keynes then argues that given the state of expectation and the propensities to consume and invest, a set of values for Y and C is obtained which satisfy Y = C + I, criticizing the classical theory of interest. In order to increase income the state of expectation, or the propensity to consume, or the amount of investment must be changed. It was not until this lecture that the determination of income was put forward in terms of Y = C + I.

  His new model appears more concretely in the eighth lecture:³³

  　　　　　　　　　M = A (W, ρ)      (1)

                    Y = C + I         (2)

                    C =φ₁ (W, Y)     (3)

                    I = φ₂ (W, ρ)      (4)

where M is the quantity of money, A the state of liquidity preference, W the state of “news”, and ρ the rate of interest.

  Y is given by

                    Y =φ₁ (W, Y) +φ₂ (W, ρ)

  Equation (1) shows that the rate of interest is determined by the equality of the quantity of money and the state of liquidity preference.³⁴ This is essentially the same as equation (6) of the PME manuscript. In the eighth lecture Keynes explains his theory as follows: the income motive, business, precautionary motives depend on business cycle, the facility of overdrawing and the rate of deposit interest while the speculative motive on the state of bearishness.³⁵

Equation (4) shows that, given the rate of interest, the value of investment is determined. This differs from Investment Price Theory (1). From the time of the PME manuscript Keynes had maintained Investment Price Theory (2) as determining the price level of investment goods. Then, in the Third Table of Contents, the concept of the “marginal efficiency of capital” appears. Keynes seems to have distinguished, after the “Second Undated Manuscript”³⁶ (JMK.29, 111-120), this from the rate of interest, although the definition differs from that in the General Theory.

  Equation (3) and equation (2) are akin to equations (3) and (4) respectively of the First Manuscript. They share in common that given I, either the level of employment (in the First Manuscript) or the level of income (in the last lecture) is determined.

  Concerning consumption, in the fifth lecture Keynes regards it as a function of  income and “windfall appreciation”, while in the sixth of income only.

  The most significant difference between the model in the lectures and that of the First Manuscript lies in the fact that in the former the pseudo-TM supply function is not used and quasi-rent plays no role in determining the level of income, while in the latter that function is used and quasi-rent plays a role in determining the level of employment.

  In the final lecture Keynes puts forward “a better analysis” (Rymes, 1988, G34) for determining the level of employment³⁷:

M = A (W, ρ)            (1)

N₁ = f₁(N)              (5)

N₂ = f₂(ρ)              (6)

N  = f₁(N) + f₂ (ρ)³⁸     (7)

where N is the amount of employment as a whole, N₁that in the consumption goods sector, and N₂ that in the capital goods sector.

                                                 

  Thus Keynes argues that the fundamental forces determining the level of employment are the state of confidence, the propensity to consume, the state of liquidity preference, and the quantity of money. This is called “The General Law of Employment” (Rymes, 1988, G35), in contrast to “The Particular Law of Employment” of classical economics, which tells what national income will be in full employment.

  Keynes intends the model of equations (1) - (4) to determine its endogenous variables simultaneously, which is closely related to the following developments:

(1) Acceptance of the “first postulate”.

(2) Adoption of the marginal propensity to consume and the multiplier theory.

(3) Reference to the “fundamental psychological law”.

  Besides the above, we see several arguments which first appear in these lectures and seem to be the origins of various aspects of the General Theory:

(a) Acceptance of the first postulate and rejection of the second.

(b) A “choice of units” in terms of money value and employment.

　(c) Reference to short-period and long-period expectations.

  Although Keynes advances the above arguments moving towards the General Theory, we should not overlook that he still adheres to the argument that ΔQ, ΔO, ΔN have the same sign, using relations such as ΔQ = ΔI - ΔS′ (S′, correspondent to “saving” in the Treatise, is called the “amount of economizing”).

 It is not clear how this discourse is connected with the main argument in which income (or the volume of employment) is determined by Y = C + I. It seems to suggest a stability condition, but this role is entrusted to the “fundamental psychological law”. The connection is indeed complex. At any rate, evidently the role of quasi-rents re-defined here as an inducement in terms of short-period expectations recedes into the background as compared to his position in 1932.

IV. Comparison of the 1933 Three Tables of Contents

             

  Keynes produced three tables of contents in 1933:

(i) “The Monetary Theory of Employment” (seventeen chapters. JMK.29, 62-63. Hereafter the First Table of Contents);

(ii) “The General Theory of Employment” (nineteen chapters. JMK.29, 63. Hereafter the Second Table of Contents);

(iii) “The General Theory of Employment”, dated December 1933 (twenty-one chapters with two excurses. JMK.13, 421-422. Hereafter the Third Table of Contents).

1. The First Table of Contents

  In Chapters 3 and 4, disbursement, economising and saving might have been defined as expounded in Section I.

  In Chapter 5, the consumption function might have been expressed as equation (3).

  Chapter 6 is important because some fragments survive in which the system of determining the level of employment appears for the first time.

  Chapters 7 and 9 might have dealt with the liquidity preference theory, and Chapter 10 with the liquidity trap (no corresponding chapter in the General Theory).

  Chapter 13, “The Relation between Real Wages and Employment”, may have had to do with Keynes’s criticism of Pigou (1933)³⁹ (See JMK.13, 312).

  Chapter 14 may have argued the influence exerted the amount of employment by changes in the distribution of aggregate quasi-rent, and equation (1) in detail:

The aggregate amount of employment offered will depend … on the amount [of quasi-rent] … ― [albeit] … the nature of the distribution of the aggregate expectation of quasi-rent between different firms will probably affect the volume of employment, since the supply and cost functions ... of different firms are not uniform (JMK.29, 64).

  Chapter 15 might have argued the multiplier theory for the first time, as far as manuscripts are concerned. Judging from the fact that he developed the multiplier theory in The Means to Prosperity (March 1933. JMK.9, 335-366), the table of contents of the First Manuscript might have been written before it (and possibly before the Second Manuscript).

Chapter 16, “The Theory of Prices”, may have been related to the argument at JMK.29, 71-73.

Chapter 17 may have foreshadowed GT’s Chapter 23.

2. The Second Table of Contents

  The only differences from the First Table of Contents are found in Book I.

  Chapter 2, “The Characteristics of an Entrepreneur Economy”, deals primarily with the proposition that changes in employment depend mainly on changes in aggregate expenditure relative to aggregate costs.

  Chapter 5, “Fundamental Equations” deals with the equations Y = E + Q = C + I = D and Q = D - E = I - (E - C).

  Chapter 8 addresses the accounting period.

3. The Third Table of Contents

  The Third Table of Contents comes closer to the contents of the General Theory than the First and Second Table of Contents.

  Chapter 1, “The Postulates of the Classical Economics”, establishes the argument of the General Theory.

  The remarkable features of the Third Table of Contents are found in Book II which comprises “Quasi-rent”, “Income”, “Disbursement”, and “Saving”. Given that Keynes stresses the “Essential Feature”, the definitions of quasi-rent, income, disbursement and saving might have been the same as those in the Second Table of Contents.

  Chapter 8, “The Propensity of Spend”, Chapter 10, “The Problem of the Rate of Interest”, and Chapter 11, “The Concept of Liquidity Preference as Determining the Rate of Interest”, might have established the arguments of the General Theory.

  Chapter 12, “The Nature of Capital”, Chapter 13, “The Conditions of Stability”, and Chapter 14, “The General Theory of Employment”, are new, but with no surviving text.

  Chapter 12 might have been related either to GT’s Chapter 8 or Chapter 16 possibly the former, judging from the fact that the table of contents of “The General Theory” in 1934 (JMK.13, 423-424) has no chapter corresponding to Chapter 12.

  Chapters 13 and 14 might have developed an argument explained, respectively, in Section II (2 (B)) and in Section II (1 (A)).

  Chapter 15, “The Supply Function”, is of particular interest. The function might have been equation (1) rather than the first postulate. There are two reasons for this: firstly, Chapter 3, “The Characteristics of an Entrepreneur Economy”, deals with the “Essential Feature” (moreover, no concept corresponding to the aggregate supply function of the General Theory); secondly, quasi-rent, which disappears in the General Theory, is treated as an independent chapter.

  Chapter 16 uses the term “Multiplier” for the first time.

  Chapter 18, “The Equations of Price”, may have been related to the argument in JMK.29, 71-73.

  Excursus II uses the term “Marginal Efficiency of Capital” for the first time. The sense in which it is used differs from that in the General Theory, for even in the “Second Undated Manuscript”, which follows this table of contents, the concept differs from that in the General Theory.

V. Robertson, Hawtrey and Keynes

  In his letter to Robertson (26 October. JMK.13, 315-317), Keynes argued that Robertson’s spontaneous saving is very near to his ‘saving’ in the Treatise and he can see “no connection whatever’ between … [Robertson’s] revised meaning of hoarding and the Marshallian K and income velocity V”.

 Concerning the second remark Robertson stated that “I am prepared to assert that on any level of abstraction all forces acting on P can be expressed in terms of M, V, or R” (JMK.13, 318). The topic should be around M=KRP=RP/V. In an unpublished paper, “Saving and Hoarding” (GTE/1/164-170), Robertson argued that his revised hoarding and Keynes’s revised one are one and the same of the Cambridge quantity theory.

It should be noted that throughout their correspondence Keynes did not express his new theory as explained in the present paper.

   We go to the controversy between Hawtrey (1933) and Robertson (1933). They were very critical of each other’s theory. Hawtrey criticized Robertson’s economics of lacking on (i) the lack in reality; (ii) the neglect of stock of commodities from a point of his economics of consumers’ income and outlay (See Hawtrey (1926)). Robertson (1933), in turn, criticized Hawtrey’s theory, and emphasized his theory’s advantage of “setting in high relief” analytically interesting points.

Hawtrey (1932, 279) maintained his theory of consumers’ income and outlay, arguing that the quantity theory is of no use in the state of disequilibrium. Hawtrey’s criticism of the quantity theory (see Deutscher, 1990, 36-39) is similar to Keynes’s one in the Treatise.⁴⁰

  Interestingly Keynes, who was first influenced by Robertson in the mid-1920s, was influenced by Hawtrey after the Treatise, and moved forward thereafter, while Robertson and Hawtrey retained their theories.  

                                                       

 Robertson defended Pigou (1933). See JMK.13, pp.318-319. An interesting point here has to do with the effect of a money-wage cut on employment. See GTE/1/148 (‘II Money wages and real wages’. Robertson), GTE/1/150 (2 Oct. 1933. Keynes), GTE/1/151-152 (19 Oct. Keynes), GTE/1/159-160 (26 Oct. Keynes), JMK.13, pp.316-317 (26 Oct. . Keynes), 319 (Robertson). Shove was on Keynes’s side, saying that “It [Pigou (1933)] struck me as the worst book on economics that I had read for a long time” (JMK.13, 321), and that “I have spent so much time in the course of my life in abortive attempts to invent defences for him” (JMK.13, 326).

With regard to Pigou (1933), Besomi’s Archive has four letters from Keynes to Harrod (320, 322, 337, 343). In no.320 (10 Oct.) Keynes wrote: “To solve the question of the effect of the reduction of money-wages in a most general case is hideously complex, and requires in my judgment a different technique from that which you employ.” This was to lead to his analysis in Chapter 19 of the General Theory. In no.322 (27 Oct.) he said: “my criticism is prompted by a lot of stuff I am now doing as to the inapplicability of many of the classical assumptions to a monetary entrepreneur economy. Even if I am right, I cannot expect you to agree until you have read some 100 pages or more of unpublished material. In no.337 (30 Dec.) he wrote: “…I am finding it impossible to make my points successfully without bringing in a quantity of my unpublished theorising, …”. “unpublished material”, “my unpublished theorizing” is what is examined in this paper.

      Finally Keynes opted not to write a review of Pigou (1933) in the Economic Journal, but published his observation as Appendix to Chapter 19 of the General Theory. Beveridge, who was asked to write a review of Pigou (1933) in the Economic Journal, waived the task. It was Harrod (1934) who eventually wrote the review in the Journal.

VI. Conclusion

                                      

In this paper two concepts have received particular emphasis as essential for an understanding of Keynes’s theoretical development in 1933: the pseudo-TM supply function and the pseudo-TM supply function mk2 as important for understanding the three manuscripts in a consistent way. We use the prefix ‘pseudo’ because the functions, in substance, differ from the TM supply function, while we retain the phrase ‘TM supply function’ because Keynes tends to regard them as continuous.

The three manuscripts reveal advantageous points in his theoretical development while they expose theoretical inconsistencies.

The three manuscripts constitute the origins of Chapter 3 of the General Theory. They discuss both an equilibrium condition for the level of employment and its stability condition, although no concept correspondent to the GT’s aggregate supply function makes any appearance. In the First Manuscript Keynes put forward for the first time a system determining the level of employment. This was a breakthrough. And in the Second and Third Manuscripts, the stability conditions are argued in terms of aggregate expenditure and variable costs.

Keynes’s way of formulating the system, however, suffers from certain insufficiencies or inconsistencies. Although we interpreted it as describing the stability condition for the equilibrium level of employment, the argument in terms of the pseudo-TM supply function mk2 is unclear. Among others, the argument in the Third Manuscript which stresses effective demand is unclear, because it is always made in terms of the sale proceeds and variable cost. The concept of “effective demand”, moreover, is to undergo several changes before reaching the General Theory. The arguments seen in the Second and Third Manuscripts are to disappear thereafter.

These ambiguities or inconsistencies in Keynes’s argument show him feeling his way towards a new employment theory.

The remarkable feature of the 1933 lectures is that the theoretical framework there, if not completely that of the General Theory, comes close to it. The most significant difference between the model in the lectures and that of the First Manuscript lies in the fact that in the former the pseudo-TM supply function is not used and quasi-rent plays no role in determining the level of income.

It is not clear, however, how this discourse is connected with the main argument in which income (or the volume of employment) is determined by Y = C + I. It seems to suggest a stability condition, but this role is entrusted to the “fundamental psychological law”. The connection is indeed complex. Evidently the role of quasi-rents re-defined here as an inducement in terms of short-period expectations recedes into the background as compared to his position in 1932.

  From the three tables of contents we can get some information.

(i) In the First Table of Contents, the system of determining the level of employment appears for the first time; equation (1) is argued in detail; the liquidity trap is discussed; the first appearance of the multiplier theory as far as manuscripts are concerned.

(ii) In the Second Table of Contents, the proposition that changes in employment depend mainly on changes in aggregate expenditure relative to aggregate costs is argued; the equations Y = E + Q = C + I = D and Q = D - E = I - (E - C) are argued.

(iii) In the Third Table of Contents, “The Postulates of the Classical Economics”, “The Propensity of Spend”, “The Problem of the Rate of Interest”, and “The Concept of Liquidity Preference as Determining the Rate of Interest” might establish the arguments of the General Theory; “The Nature of Capital”, “The Conditions of Stability”, and “The General Theory of Employment”, are new; “The Supply Function” might be equation (1) rather than the first postulate; the term “Multiplier” appears for the first time; the term “Marginal Efficiency of Capital” appears for the first time although it differs from that in the General Theory.

Finally, we described how different, in terms of theory, Robertson, Hawtrey and Keynes were in 1933.

1) For the theoretical framework of the Treatise, see Hirai (1997-1999, Chapter 7).

2) For this, see Hirai (2007b).

3) For this, see Hirai(2004).

4) In the three manuscripts variables are expressed in terms of expectation.

  5) Following the Second Manuscript, we interpret “D” in the First Manuscript as “disbursement”.

6) See Hirai (1977-79, Ch.7).

  7) The level of employment is presupposed to be uniquely related to the volume of output through a short-run production function.

8) C΄[H΄] denote a supply function of profit, Q_１[Q₂], in the capital [consumption] goods industry.

  9) They made their first appearances here.

  10) Keynes referred to the consumption function in “The Monetary Theory of Production” manuscript (JMK.13, pp.381-396. Hereafter the MTP manuscript), but in different sense.

  11) However, he shows some ‘hesitation’ and places equation (4), seeing it as a definition of Q, in equation (1). See JMK.29, 64. This ‘hesitation’ appears in the Second Manuscript.

  12) By solving the equation, I + f₃{f₂ (N) + f₁^-1 (N)} = f₂ (N) + f₁^-1 (N).

  13) Keynes was to tackle the problem of prices again, accepting the first postulate in the Second Manuscript.

  14) The “Economics of the Budget Constraint” follows this idea. See Christ (1968), Tobin (1980) and Turnovsky (1980).

  15) See JMK.29, 76.

  16) Following this, normal return is stated to be constant.

  17) The argument that saving is necessarily equal to investment also appears in the Second Manuscript (see JMK.29, 69). This can be traced back to the PME manuscript.

  18) Judging from the Treatise, Δ N and Q should be considered to have the same sign. Below we put forward an argument with this change. Q is interpreted as excess profit.

  19) We can consistently interpret both the equilibrium and stability of the system only by using an increment in the level of employment.

  20) For the propensity to save, see JMK.29, 100.

  21) His approval is also seen in the first Michaelmas lecture for 1933 (see Bryce notes, p.B2-B3; Salant notes, p.M1; Tarshis notes, pp.J1-J2).   

22) However, there exists no evidence showing the first postulate’s incorporation into the system of equations (7) - (16). See also JMK.29, 101-102 as the origin of GT’s Chapter 2.

  23) See GT, 76.

24) See JMK.29, 97, I and II. The same arguments are in the 1933 Michaelmas lecture.

25) For a similar argument, see JMK.13, 384 (in the MTP manuscript).

26) For a similar argument, see JMK.13, 369-370 (in the Round Table on “Unemployment as a World Problem” of June 1931.

  27) Keynes does not compare what adds “some normal value” to variable costs (i.e. aggregate costs) with aggregate expenditure. Nothing like the aggregate supply function of the General Theory appears here.

  28) See also the second lecture for his 1933 Michaelmas Term.

  29) This criticism might be directed against the “transition periods” analysis in Fisher (1911, 55-73) based on the rates of interest lagging behind prices.

30) Patinkin maintains that the Second and Third Manuscripts are revisions of the Treatise, basing this supposition on Keynes’s assumption of the TM supply function (1980, 20). Milgate (1983, 195) judges that the three manuscripts of 1933 “re-express the [Treatise’s] Fundamental Equations … in terms of different definitions”.

Amadeo (1989, 79) states, [in the Third Manuscript], “we can first identify the central elements … of the principle of effective demand”.

31) There survive the following students’ notes: Bryce (pp.61), Cairncross (pp.16), Fallgatter (pp.38), Tarshis (pp.39), Salant (pp.19), Thring (pp.18), and Douglas (pp.15).

32) Patinkin judges that in the 1933 Michaelmas lectures the effective demand theory is argued for the first time (Patinkin = Leith, 1977, 15-16). Dimand (1988, 166) states that except for an investment theory, in the 1933 Michaelmas lectures all were “in forms recognizably similar to those of the [General Theory]”, pointing out that “[b]etween the Michaelmas 1932 lectures and the 1933 lectures, Keynes dropped profits … from its central position in his theory, although it made a fleeting reappearance as A, windfall appreciation”. Clarke (1998, 95) maintains that the 1933 Michaelmas lectures “gave a more cogent account of the theory of effective demand according to the criteria of professional economists” (he thinks that the inception of the theory can be found in the 1932 lectures).

33) Kates (1998, p.140) argues that the seventh lecture is decisive, for it reveals Keynes’s reading of Malthus which made him step into the world of the General Theory. Our judgement is that the direct influence of Malthus upon Keynes’s thinking is rather limited, although he was stimulated by finding deficiency in demand as the cause of unemployment in Malthus.

  34) “This is the alternative to the two classical views [the loanable fund theory and Marshall’s circularity] already discussed and seen to be abortive” (Rymes, 1988, G33).

35) See Rymes (1988, B55).

  36) See Hirai (1997-1999, Chapter 9, Section 2).

  37) “The real tool is thought, and … [these equations] are not a substitute for it, but at most a guide …” (Rymes, 1988, G35). Also see Rymes (1988, B59, J37, N17).

  38) We see, moreover, f₂ (ρ)= f₃ (M/w) where w is a money wage.

39) Robertson defended Pigou (1933). See JMK.13, pp.318-319. An interesting point here has to do with the effect of a money-wage cut on employment. See GTE/1/148 (“II Money wages and real wages”. Robertson), GTE/1/150 (2 Oct. 1933. Keynes), GTE/1/151-152 (19 Oct. Keynes), GTE/1/159-160 (26 Oct. Keynes), JMK.13, pp.316-317 (26 Oct. Keynes), 319 (Robertson). Shove was on Keynes’s side, saying that “ [Pigou (1933)] struck me as the worst book on economics that I had read for a long time” (JMK.13, 321), and that “I have spent so much time in the course of my life in abortive attempts to invent defences for him” (JMK.13, 326).

40) The following letter to Lydia (30 Oct.) mirrors Keynes’s state of mind: One can argue with [Hawtrey] a long time on a perfectly sane and interesting basis and then, suddenly, one is in a madhouse. … I have just been having a hopeless debate with [Robertson]. His mind, though frightfully ingenious, seems to me maliciously perverse. Again it is like arguing with a madman” (Skidelsky, 1992, p.495)

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# Professor, Faculty of Economics, Sophia University, Tokyo. E-mail: hirai-t@sophia.ac.jp The paper originates in Hirai (1997-1999, Chapter 10). The earlier version was read at the International Conference on Keynes and Keynes’s Influences on Modern Economics, Sophia University, Tokyo, in March 2007. The author appreciates valuable comments there.