The Eve of the General Theory Toshiaki Hirai[*]

For the ESHET Annual Meeting, 5-7 July 2007, Louis Pasteur University, France

<Draft>

　　　　　　　　　　　　　　　

The Eve of the General Theory

Toshiaki Hirai[*]

I. Introduction

The aim of the present paper is to examine the large advances Keynes made in 1934 towards the formulations we find in the General Theory.

As we saw in Hirai (1997-1999, Chapter 11), by the end of 1933 Keynes had already developed the theoretical system explaining the level of employment, as well as the consumption function, the fundamental psychological law, the theory of liquidity preference, the concept of the marginal efficiency of capital, and the multiplier theory.

To explore how Keynes further developed these fields in 1934 we look first at two manuscripts: (i) a typescript entitled “The General Theory of Employment, Interest and Money”, written probably in the spring of 1934 (JMK.13, pp. 423-456; hereafter “The General Theory”) (Section II); and (ii) a revised version of Chapters 8 and 9 of this, written in the summer of 1934 (JMK.13, pp. 471-484; hereafter “The Summer Manuscript”) (Section III). Then, in Section IV we will look at the Michaelmas lecture of 1934, which were delivered on the basis of a manuscript we will refer to as “First Galley I”.

Although Keynes put forward the system determining the level of employment, it remained incomplete. This incompleteness was very clear in the examinations we made of the system of equations in the First Manuscript (1933) and the argument by means of “effective demand” in the Third Manuscript (1933)¹.

Although in “The General Theory” Keynes puts forward a new model to explain how the level of employment is determined, his argument as we shall see still lacks precision. This is also true of the Summer Manuscript. It is very important to bear in mind that in the area of employment theory, Keynes’s endeavours to coherently explain the workings of the economy were to continue right up to the General Theory, and that in this area, even the General Theory itself still lacks precision.

The General Theory was an epoch-making work which revolutionised macroeconomics by providing a system explaining how the level of employment is determined. The book’s theoretical inconsistencies do not undermine this achievement, but do deserve close attention.

By early 1934 Keynes’s thinking had gone far beyond the world of the Treatise and had plunged deeply into that of the General Theory. Thus our attention will naturally focus on the relations of the manuscripts to the General Theory, rather than on their relations to the Treatise. This tendency will become progressively more pronounced as we approach the General Theory itself.

　　　　　　　　　　　 II. “The General Theory”

  Of the twenty-seven chapters (divided into five “books”) listed in the table of contents of this manuscript, only Chapters 6 to 12 survive. (Chapter 12, “The State of Long-Term Expectation (or Confidence)”, has not only almost the same title as Chapter 12 of the General Theory, but is also “the final printed version with very few changes”.²)

The manuscript has two features particularly relevant to our concern here: (i) the way in which the concept of “effective demand” and the theory of employment are discussed; (ii) the way consumption theory and investment theory are argued out. Point (i) is full of ambiguities, reflecting the struggle Keynes was going through in his search for a new theory of employment, while point (ii) is very similar to the argumentation in the General Theory. This is the most salient characteristic of “The General Theory”.

As we saw elsewhere, ambiguities in the concept of “effective demand” and in the theory of employment were to be seen in the three 1933 manuscripts³, while establishment of the consumption and investment theories was a noteworthy feature of the two undated manuscripts.⁴ Taken together, they constitute a forerunner of “The General Theory”.

However, our manuscript is the first to include all the above-mentioned elements (the concept of ‘effective demand’ and the theory of employment, with their ambiguities, the consumption theory, and the investment theory), and was to have some influence on the formation of the theoretical structure of the General Theory.⁵

Here we will examine Chapters 6 to 11, focusing on three points: (i) the ambiguities in the concept of “effective demand” and the inconsistency of the employment theory; (ii) the consumption theory; and (iii) the investment theory. We then touch on some other fundamental concepts.

  1. Effective Demand and an Employment Theory

  Let us begin with Chapter 6, “Effective Demand and Income”, and Chapter 9, “The Functions Relating Employment, Consumption and Investment”, which are concerned with the sphere with which GT’s Chapter 3, “The Principle of Effective Demand” deals.

  They are interesting on two counts. Firstly, they show the state of development of Keynes’s employment theory. Here we need to pay attention to the ambiguity in the concept of ‘effective demand’. Secondly, the employment theory contains the same sort of inconsistencies as the General Theory in respect of the relations⁶ between the first postulate and the employment function, and between the arguments of Chapters 6 and 9.

   

  (A) Effective Demand

  In “The General Theory”, “effective demand” is defined as the “present value of the expected sale proceeds” (JMK.13, p. 425). This is different from the version presented in “The Third Manuscript”, where it was defined “by reference to the expected excess of sale proceeds over variable cost”. Also differing from “The Third Manuscript” definition, moreover, effective demand does not seem to be related to the stability of the equilibrium level of employment.

  We first examine the relations between, and definitions of, some key concepts in “The General Theory”, including effective demand, income, and quasi-rent, and then show that the effective demand in this manuscript partially corresponds to the “aggregate supply price” concept of the General Theory.

[We shall] call the actual sale proceeds income and the present value of the expected sale proceeds effective demand.⁷ … and it is the effective demand which is the incentive to the employment of equipment and labour. The difference between the two we shall call entrepreneur’s windfall - profit or loss, …;

The following notation will be used.

Y  for Yncome

D  for effective demand

F  for entrepreneur’s windfall [here, not F_ubut F is used]

These expressions are in terms of money. Income and effective demand in terms of the wage unit will be written Y_wand D_w.

The quasi-rent (Q) from a given output of finished goods we have already defined … as being the excess of the expected sale proceeds of the goods over their prime cost (NW) [N denotes employment, and W the money wage]. Thus … D = Q + NW (JMK.13, pp.425-426).

  From this, the following equations can be extracted:

  　　　　　　　　　　　　　　 F_u= Y- D　      (1)

　　　　　　　　　　　　　　　 D = Q + NW       (2)

  Two characteristics are to be noted. Firstly, quasi-rent, which is the difference between D and the prime cost (NW), means normal profit. This can be proved as follows. From these equations we obtain:

  　　　　　　　　　　　　　　Y - NW = F_ｕ+ Q   (3)

  The left-hand side is the actual sale proceeds minus the prime cost, so that it represents the realized profit, while F_ｕis windfall profit. Therefore Q is normal profit.

  Secondly, as shown in equation (1), excess profit (or windfall profit) is defined as the difference between the actual sale proceeds and the expected sale proceeds.  

 These two points are not found in the formulations in the three 1933 manuscripts. In those manuscripts, the difference between the expected sale proceeds and the prime cost (the sum of normal profit and excess profit) was defined as effective demand, and quasi-rent, Q, was defined as including excess profit.

  Thus effective demand D is equal to the sum of normal profit (= Q) and the prime cost, so that it corresponds, in terms of the General Theory, to the “aggregate supply price” rather than the “aggregate demand price”.

  Thus the argument centring around effective demand in “The General Theory” differs from that in the three 1933 manuscripts, not only in definition, but also in theory. Moreover, as we will see later, this argument needs to be considered in connection with the fact that Chapters 6 and 9 of “The General Theory” are theoretically inconsistent.

　(B) The Employment Theory

  Prior to “The General Theory” Keynes did not explicitly adopt the method of supply-demand equilibrium.⁸ The Treatise envisions a world in which the TM supply function plays a dynamic role and the price level of consumption goods is determined by the demand side, given the volume of output supplied. It is only in Investment Price Theory (1) that the method of supply-demand equilibrium is adopted.

In the PMT manuscript this method is adopted only in the liquidity preference theory. In the area of the commodity market, it appeared for the first time in the First Manuscript of 1933. Thereafter, Keynes progressively came to adopt a supply-demand equilibrium approach.

However, there are certain ambiguities in the way he uses it. This is typically seen in the argument concerning the “employment function”.

  <1> The Employment Function

  The employment function, which makes its first appearance in “The General Theory”, is conceived as follows:

D_w= F(N) is the employment function, where an effective demand equal to D_wleads to N units of labour being employed (JMK.13, p. 440).

  Preceding this is Keynes’s explanation of its inverse function.

The above [the first postulate] is, of course, subject to the qualification that different classes of enterprise do not … respond equally … to equal changes in the effective demand for their product, since they are not all working under the same conditions of supply. Thus the same aggregate effective demand may correspond to different levels of employment according to the way in which it is distributed between different classes of enterprise. This will be a matter for subsequent discussion …. But at the present stage of the argument I shall … assume that all firms have similar employment functions, so that aggregate employment is a simple function of the aggregate effective demand measured in terms of the wage unit (JMK.13, pp. 427-428).

  On the one hand the employment function seems to be (i) a supply concept, and on the other (ii) an equilibrium concept.

We have two reasons for point (i).

First, Keynes puts forward the employment function in relation to the first postulate of classical economics, and, moreover, with the assumption that “all firms have similar employment functions”, he considers that “aggregate employment is a simple function of the aggregate effective demand”. This suggests that he understands the employment function as a supply concept in the whole economy, as well as in the individual firm or industry.⁹

Second, as we saw in (a) above, he puts forward “effective demand” D as, in the terminology of the General Theory, the aggregate supply price, and as will be shown in <2> below, in the equation determining the level of employment, Keynes puts the employment function on the left-hand side, placing the sum of the propensity to spend and the propensity to invest on the right.

  But the employment function seems to be an equilibrium concept as well. Keynes tries to obtain aggregate employment given the distribution ratio of aggregate effective demand between industries.¹⁰ When he refers to “the effective demand for their product”, he seems to be using it as representing the demand side, for he argues in such a way as to have it determining the level of employment in each industry together with the “conditions of supply” (the first postulate). Therefore, the effective demand in each industry is not only a demand concept but also an equilibrium concept. The employment function is obtained by aggregating, on the one hand, the effective demand in each industry, and, on the other, the level of employment in each industry. Therefore, the employment function shows a functional relation between the aggregate effective demand (an equilibrium value) and the aggregate employment (an equilibrium level).

  Looking at the employment function from a different angle, it is, as it were, merely a signal indicating the level of employment which corresponds to the aggregate effective demand, for the aggregate effective demand depends on the implicit and arbitrary assumption that its distribution between industries is given. “The aggregate effective demand” per se has to be determined by some other mechanism.

 Our argument that the employment function has the appearance of an equilibrium concept may be explained as follows:

  　　　　　　　　　　　　　　 Z_w= F(N)　　　　 (4)

  　　　　　　　　　　　　　　 D_w=  Z_w         (5)

  Suppose that equation (4) shows some concept representing the supply side, while D_wrepresents the demand side. Then equation (5) equilibrates supply with demand.¹¹From these we obtain:

  　　　　　　　　　　　　　　 D_w= F (N)         (6)

  Therefore, we can suppose that equation (6) (the employment function) indicates an equilibrium of commodity markets.

  The dualitycharacterising the employment function emerges in the General Theory.

  <2> The Employment Function in Relation to the Determination of the Level of

 Employment

  In “The General Theory”, determination of the level of employment is conceptualized as follows:

Both C_wand I_ware to be interpreted … as the expected rates of consumption and investment. Hence it follows that D_w= C_w+ I_w. Thus the level of employment, given the propensities to spend and to invest, is given by the value of N which satisfies the equation¹²

　　　　　　　　　　　　F(N) = f₁(N, r, E) + f₂(N, r, E)

(JMK.13, pp. 441-442. r denotes the rate of interest, E the state of long-term expectation, f₁the propensity to spend [or consume], and f₂ the propensity to invest.)

  The employment function here represents the supply side, and does not depend on profit. This is in marked contrast with the position in “The First Manuscript” of 1933 (where the system determining the level of employment was first developed), in which the “supply function” (the pseudo-TM supply function) is formulated as a function of profit. Keynes’s affirmative attitude toward the first postulate and the change from the pseudo-TM supply function to the employment function might well be closely related.

 On the other hand, the employment function here is in substance the same as the employment function¹³of the General Theory, except that the former is the inverse of the latter. We can interpret both as equilibrium concepts. In the General Theory, the employment function is measured in wage units and defined as the inverse of the aggregate supply function Z = f(N), which corresponds to equation (4). However, the actual argument proceeds by means of an equation similar to equation (6); that is, not N = F^-1(Z_w), but N = F^-1(D_w). D_win the General Theory is effective demand which is defined as the value of the aggregate demand price at the point where the aggregate demand function intersects the aggregate supply function. Again we are faced with the ambiguous nature of the employment function.

  (C) The First Postulate                              

  In “The Second Manuscript” of 1933¹⁴, Keynes accepted for the first time the first postulate and rejected the second. He maintained this view thereafter.

  The relation between profit and the first postulate in “The General Theory” is worth noting. Normal profit Q contributes, together with the first postulate, to determination of the level of employment. However, so far as the extant sources are concerned, we find no discussion of windfall profit (F_u), nor of the stability conditions for the level of employment, as distinct from “The Second Manuscript” and “The Third Manuscript” of 1933. Thus Keynes’s emphasis on the maximization of quasi-rent in the first postulate comes to the foreground:

Under normal assumptions of competition etc. the condition of maximum quasi-rent will be satisfied by a volume of employment such that the prime cost of the marginal employment will be equal to the expected sale proceeds of the resulting increment of product. ...

Furthermore, in the normal case we must assume decreasing returns for a given capital equipment (JMK.13, p. 426).

  The notion of the “condition of maximum quasi-rent [normal profit]” might indicate some development in Keynes’s theory. In “The Second Manuscript” and “The Third Manuscript”, despite acceptance of the first postulate, Keynes assumed “normal profit” to be constant, and did not incorporate the idea of profit-maximizing entrepreneurs¹⁵into his system. Consequently, the first postulate was incompatible with the main theoretical system. In “The General Theory”, on the other hand, Keynes repeatedly emphasizes maximization of quasi-rent¹⁶, and confines profit to quasi-rent.

  (D) Two Theoretical Difficulties

  There are two elements in particular that do not sit happily in “The General Theory”: (i) the relation between the first postulate and the employment function is unclear; (ii) the relation between the argument of Chapter 6 and that of Chapter 9 is unclear.

 The same kind of theoretical inconsistency persists in the General Theory: between the consumption theory of Book III and the investment theory of Book IV, on the one hand, and Chapter 3, “The Principle of Effective Demand”, on the other.

  <1> The First Postulate and the Employment Function

   The relation between the first postulate and the theory determining the level of employment is taken up seriously for the first time in “The General Theory”. In the First Manuscript, the supply side was represented by the sum of the cost function and the inverse of the “supply function”. Here the supply side is represented by the employment function, which is connected with the first postulate. Keynes states:

… the employment function tends to approximate to a straight line drawn at a constant angle, which … would be in the neighbourhood of 45°, between the axes of the quantity of employment and the effective demand measured in wage units (JMK.13, p. 446).

  We can begin by expressing the first postulate as follows:

                          ΔO /ΔN = W / P      (7)

where O denotes the level of output, P the price, and ΔX an increment in X.

  From equation (7):

                          Δ(P.O /W) =  ΔN      (8)

  And using the definition equation P.O = D, we obtain:

ΔD_w/ΔN  = 1        (9)

  This means that the slope of the employment function D_w= F(N) is 1.

  However, this method does not run through “The General Theory”. The employment function presupposes a certain distribution of aggregate effective demand between different classes of firms, and the industry as a whole is divided into two sectors. Consequently the first postulate cannot be directly connected with the employment function.¹⁷

  <2> The Arguments of Chapters 6 and 9

  In Chapter 6 the entrepreneur’s windfall profit is defined as the difference between income and effective demand, while in Chapter 9 income Y finds no place in the equation which determines the level of employment:

                        F(N) = f₁(N, r, E) + f₂(N, r, E)

  Certainly, effective demand D [D_w= F(N)] can be determined with this equation. However, it is not clear how the windfall profit is determined or how it is considered to work. No concept corresponding to the pseudo-TM supply function mk2 of “The Second Manuscript” appears here. If the arguments were susceptible to being interpreted along lines similar to our interpretation of “The Second Manuscript”, we could resolve the inconsistency between Chapters 6 and 9. The definitions of normal profit and windfall profit in “The General Theory” differ from those in the three 1933 manuscripts, and we can conclude that the equation F_u = Y - D corresponds to our equation (7) in Chapter 8. Moreover, we presume that “The General Theory” is devoid of anything like Chapter 8’s equation (8) (the pseudo-TM supply function mk2¹⁸), though we cannot completely rule out the possibility of its appearance in the missing part.

  Thus we can understand the arguments of Chapters 6 and 9 in a manner which makes them consistent by considering that Keynes puts forward the stability of the equilibrium level of employment in Chapter 6, and the determination of the equilibrium level of employment in Chapter 9. If so, the three 1933 manuscripts might lead, by way of these two chapters of “The General Theory”, to Chapter 3 of the General Theory.

  2. The Consumption Theory

  The consumption theory in “The General Theory” adopts that of “The First Undated Manuscript”. It deals with both the “subjective” and the “objective” factors, and possesses the same theoretical framework as the consumption theory of the General Theory (Chapters 8 and 9). It is discussed mainly in Chapter 10, “The Propensity to Spend”.

  (A) The Subjective Factors

  Concerning the subjective factors, the argument here is, in style, very similar to that of the General Theory. It is therefore fairly safe to suppose that in the missing pages Keynes would have referred to items corresponding to the sixth, seventh and eighth – namely, “(vi) To secure a masse de manoeuvre to carry out speculative or business projects; (vii) To bequeath a fortune; (viii) To satisfy pure miserliness” –  in the General Theory (p. 108), and the first, second and third of the four saving motives of governments and firms: “(i) The motive of enterprise... (ii) The motive of liquidity...and (iii) The motive of improvement ...” (pp. 108-109).

  In Section IV of Chapter 8, “Investment and Saving”, of “The General Theory”, Keynes almost completes an argument to the effect that “financial provision” for the future becomes an obstacle to employment. Keynes treats the financial provision in such a way that it is added to the subjective factors.

 This section is succeeded by Sections I - III of Chapter 8, “Investment and Saving”, of “The Summer Manuscript” (see Section 2 below), into which Keynes incorporated Colin Clark’s statistical data for the British economy. This is further developed in Chapter 9, “The Meaning of Investment”, of “The First Galley I” (see Hirai (1997-1999, Chapter 11)), and finally leads to GT’s Chapter 8, IV (which mainly deals with the financial provision). In “The General Theory”, Keynes treats the financial provision in such a way that it is added to the subjective factors, although he ceases to do so after First Galley I.

 (B) The Objective Factors

  The objective factors also appear for the first time in “The General Theory”. The discussion here corresponds to GT’s Chapter 8, II and III, but there are some notable differences.

 In “The General Theory” Keynes lists the following: (a) the quantity of employment as determining the aggregate current rate of real income; (b) the rate of interest; and (c) the state of “confidence” or long-term expectation (JMK.13, p. 444).  

 In the General Theory the following are given: (i) a change in the wage-unit; (ii) a change in the difference between income and net income; (iii) windfall changes in capital-values not allowed for in calculating net income; (iv) changes in the rate of time-discounting; (v) changes in fiscal policy; and (vi) changes in expectations of the relation between the present and the future level of income.

 Items (b) and (iv) are very similar in style, while (c) and (iii) share something in common, in that both take into account the influence which changes in capital-values have upon consumption.

In “The General Theory” the quantity of employment is regarded as the most important, and is referred to at the point where the consumption function is considered in relation to the fundamental psychological law, whereas in the General Theory it is not regarded as an objective factor at all. So far as the other factors are concerned, there is no similarity between the two texts.

  The above argument must be understood in the following context: as far as the consumption theory is concerned, the theoretical framework in “The General Theory” is the same as that in the General Theory. Among the factors which determine the propensity to spend (consume), Keynes defines those factors which do not change in the short period to be the “subjective” factors, and those which do change in the short period as the “objective” factors. He also puts forward the consumption function in relation to the fundamental psychological law. Compared with these similarities, the differences between “The General Theory” and the General Theory in the items named as objective factors are of only secondary importance.

  3. The Investment Theory

  In “The General Theory” Keynes improves on the investment theory of “The Second Undated Manuscript” and formulates the theory that would be enshrined in the General Theory.

For a start, the marginal efficiency of capital here is virtually the same as in the General Theory¹⁹:

                                              

Given this series of annuities [the prospective yields] ... there is some rate of interest on the basis of which the present value of the series of annuities will be equal to the supply price of the investment. The rate thus arrived at we may call the marginal yield (or efficiency) of capital (JMK.13, p. 453).

  Secondly, what we call Investment Theory (1) of the General Theory is put forward:

... new investment will be pushed to the point beyond which the marginal yield of capital would fall short of the current rate of interest  (JMK.13, p. 453)

  Thirdly, what we call Investment Theory (2)²⁰ of the General Theory is also put forward:

The series Q_r, which can be called the prospective yield of the investment, depends on the state of long-term expectation E; whilst the series d_r[the present value of ₤1 deferred r years] is given by the rate of interest. The two together determine the schedule of effective demand for investment; and, finally, the supply from this for investment goods fixes the amount of employment which will be actually directed towards investment corresponding to any given effective demand(JMK.13, pp. 452).

  Here the demand schedule for investment to be used in Investment Theory (1) of the General Theory appears in the area belonging to Investment Theory (2). In the passage quoted, Keynes argues that the schedule of effective demand for investment is determined by the prospective yield of the investment and the rate of interest, and argues that the schedule of effective demand for investment and the “supply” determine the amount of employment which is directed toward investment, though it is not clear what the coordinate axes on which that schedule is measured are, nor how it relates to the “supply”.

  4. Some Other Fundamental Concepts

  In Chapter 8 of “The General Theory” Keynes examines some fundamental concepts, centring his attention on “(gross) investment” and “(gross) saving”.²¹This part of the discussion is the predecessor of Chapter 8, “Investment and Saving”, of “The Summer Manuscript” and “The Pre-First Proof Typescript” (see Hirai (1997-1999, Chapter 11)), which are the origins of Chapter 6, “The Definition of Income, Saving and Investment”, and Sections I-III of Chapter 7, “The Meaning of Saving and Investment Further Considered”, of the General Theory.²²

III. The Summer Manuscript

  Keynes sailed to America on 9 May 1934 to participate²³in a ceremony at Columbia University, staying there until 8 June.

He resumed work on the General Theory immediately after his return to England. The texts of five chapters written in this period survive.

 Chapter 8, “Investment and Saving”, and Chapter 9, “The Functions Relating Employment to the Independent Variables of the System”, are revisions (centring on “effective demand” and the employment theory), respectively, of Chapters 8 and 9 of “The General Theory” (JMK.13, pp. 471-485).

 The other three are Chapter 5, “The Units of Quantity”, Chapter 4, “Expectation”, and Chapter 11, “The Propensity to Invest”, and the “first versions of what were to become Chapters 4, 5 and 11 [respectively]” (JMK.13, p. 471) of the General Theory. Because the last three are close to the General Theory, we shall defer discussion of them until the next chapter (Hirai, 1997-1999, Chapter 13).

  1. Effective Demand

 The viewpoint seen in the “General Theory” which stresses gross investment and gross saving as the fundamental quantities in economic analysis is succeeded here. The appearance of the concept of “user cost” renders the relations between various concepts in this manuscript different from those in “The General Theory”. The concept of user cost here is, rather, akin to depreciation, and differs from the concept that appears in the General Theory:

Effective demand ... is gross of user cost, being equal to the gross proceeds of current output, i.e. to consumption plus investment plus the user cost of current output (JMK.13, p. 472).

[The entrepreneurs] sell their output for C + I + U [C denotes consumption, I investment, and U user cost] … Their own return Q is the excess of these sale proceeds over E, their outgoings to the other factors of production. Thus C + I + U = E + Q....

Their aggregate income Y is made up of the income of the earners E and the income of the entrepreneurs Q - U; and they [the public] spend their income on current consumption C or retain it as savings S for the acquisition of capital assets …. Thus

　　　　　　　     E + Q - U = Y = C + S²⁴    (JMK.13, pp. 477-478).

  Two points are worth noting here.

 First, effective demand is defined as the user cost plus income. Income here is treated as not a gross but a net concept. Effective demand here corresponds to “income” in “The General Theory”, which is regarded as a gross concept.

Second, gross profit disappears in “The Summer Manuscript”. In “The General Theory”, excess profit (entrepreneur’s windfall profit) appeared explicitly. However, in “The Summer Manuscript”, profit (Q) is defined as including user cost, and the sum total of excess profit and normal profit equal the difference between profit and user cost.

The argument about effective demand and income in “The Summer Manuscript” shows that Keynes has yet to find a new theory in this area, and the change in the definition of profit leads us to reconfirm that profit ceases to play the role it had previously held in his thinking.

  Let us summarize the formulation in “The Summer Manuscript”:

  　　　　　　　　　　　　　　　Y = C + I          (10)

　　　　　　　　　　　　　　　　Y = C + S          (11)

　　　　　　　　　　　　　　　　Y = E + (Q - U)     (12)

where Y denotes (net) income and I (net) investment.

  2. The Employment Theory

  In “The Summer Manuscript”, the system determining the volume of employment is revised as follows:

(i) N₁ = F₁ (C_w) and N₂ = F₂ (I_w) are the employment functions for consumption and investment goods respectively, where effective demands C_wand I_wfor the two classes of goods lead to volumes of employment N₁and N₂ respectively on producing them.

(ii) C_w= Q₁ (N, r, e) is the propensity to spend, where an aggregate employment N, a rate of interest r, and a marginal efficiency of capital e lead to an effective demand C_wfor consumption goods.

(iii) I_w= Q₂ (N, r, e) is the propensity to invest, where N, r and e lead to an effective demand I_wfor investment goods.

Since N = N₁ + N₂, the volume of employment N will be determined by the equation

  　　　　　　　　N = F₁ {Q_１(N, r, e)} + F₂ {Q₂ (N, r, e)}

   (JMK.13, p. 483).

  Four points are worth noting here.

First, the employment function is expressed as the inverse function of “the employment function” in “The General Theory”.

Second, the propensity to spend and the propensity to invest are directly substituted for the employment function. This shows that the employment function is used as both a supply and an equilibrium concept. As far as this point is concerned, the formulation here is in contrast with that in “The General Theory” which seems to represent the supply side. It would appear that Keynes unwittingly uses the employment function sometimes as representing a supply concept in some cases, and an equilibrium concept in others. This ambiguity continues up to, and is apparent in, the General Theory.

  Third, the equation determining the volume of employment is derived from the constraint equation on employment, N = N₁ + N₂. This differs from the case of “The General Theory”, in which the equation determining the volume of employment is based on supply-demand equilibrium. In the General Theory the equation, N = N₁ + N₂, is not used for determining the volume of employment, but only in relation to the additivity of the individual employment functions²⁵, while the idea used in “The General Theory” is adopted as the equation determining the volume of employment.

  Fourth, the relation between the definitions of certain concepts and the equation determining the volume of employment is not completely clear. Although, for example, in the equation determining the volume of employment N = F₁ {Q₁(N, r, e)} + F₂ {Q₂ (N, r, e)}, C_wand I_wplay important roles, it is not clear how this is related to effective demand Y + U, to which Keynes attaches importance in the equation Y + U = C + I + U.

  3. Connections between the Summer Manuscript and the General Theory

  In addition to the points discussed above, there are some passages in the Summer Manuscript which are directly related to certain passages in the General Theory. Section III and part of Section I of Chapter 8, “Investment and Saving”, are linked to Section IV of Chapter 8, “The Propensity to Consume: I. The Objective Factors”, of the General Theory. Section IV of Chapter 8, in which Keynes criticises the theory of forced saving²⁶ advocated by Hayek and others, is linked to Section IV of Chapter 7, “The Meaning of Saving and Investment Further Considered”, of the General Theory, via Section II of Chapter 8, “The Meaning of Saving”, of First Galley I which is to be dealt with in the next chapter.

               IV. The 1934 Michaelmas Lectures

  Keynes started the proofreading of the General Theory at about the same time he began his lecture course for 1934²⁷. The galley of the first three chapters of “The First Galley I” (see Hirai (1997-1999, Chapter 11)) was ready on October 10. He began the lectures based on them. He subsequently sent Chapters 4 to 11 and 12 to 19 in manuscript to the publishers. The galleys of these are estimated to have come out between early December in 1934 and mid-January 1935.

  The Michaelmas lectures for 1934²⁸, entitled “The General Theory of Unemployment”, is identical to those for 1933 in the most important respect – they advance a model in which income (or the level of employment) is determined within a single period (the endogenous variables are determined simultaneously).

 In the lectures for 1934 Keynes puts forward his model under the label “Theory of Effective Demand”, which runs as follows:

  The “effective demand function” D = f (N) relates the number of men employed, N, to the expected sales of their output (= effective demand), D. The level of employment is determined at the point at which the effective demand function intersects the “employment” (or supply) function D′= F(N), which relates N to the sum which will just make it worthwhile to employ N men, or the supply price D′. Effective demand is the sum of what people are prepared to spend on current consumption, D₁, and what firms are prepared to set aside for investment, D₂.

  The consumption function is defined as D₁= f₁(N₁) (N₁ is the number of men employed in the consumption goods sector needed to meet the consumption resulting from real income). Furthermore, we have the equation N₁ = f(N) (where 0 < ΔN₁/ ΔN < 1).

 The investment function is represented as D₂ = f₂ (N₂). This means that N₂ (the number employed in the investment goods sector) will be increased up to the point at which the marginal efficiency of capital becomes equal to the rate of interest.

  To sum up, the system can be expressed as follows:

  　　　　　　　　　　　F (N) = f₁ (N₁) + f₂ (N₂)        (1)

　　　　　　　　　　　　N₁ = f (N)                   (2)

  Keynes then argues that given f₂ (N₂), N and N₁ are determined (though in this case N = N₁+ N₂ is not necessarily satisfied). The level of employment thus determined is not guaranteed to be full employment.

  Keynes expresses the above ideas clearly as follows:

                                  

when the propensity to invest will absorb the output of N₂ men, eq[uilibriu]m requires that agg[regate] employment should be N where N is such that, with [the] existing psych[ological] prop[ensity] to consume, this vol[ume] of employment will lead to an am[ount] of cons[umption] that will absorb the labour [of] (N - N₂) men²⁹ (Rymes [Bryce], p. C-10).

given [the] propensity funct[ions] there is only one level of employment will be consistent.... There is a level of I which leads to full employment but no reason why it should always exist.... That is, [the] marginal efficiency of capital, the rate of interest, and the propensity to consume will give us all (Rymes [Tarshis], p. K-5).

  The argument is almost identical in content to that of GT’s Chapter 3.

  The point on which the 1934 lectures differ from the lectures of 1933 is that we no longer find any argument in terms of the TM supply function (moreover, the concept of quasi-rents, Q, is dealt with as a “realized” concept).

 

Besides this, the novelties we meet with here are³⁰:

(1) The argument presented in GT’s Chapters 4 - 6, which can be traced back to the lectures of 1933, approaches completion here. Above all, the concept of “user cost”, which is the same in content as that in the General Theory, makes its first appearance, playing a central role in dealing with the relations among various concepts.

(2) Quasi-rents are defined in relation to realized profits.

(3) The “objective” factors influencing the propensity to consume make their first appearance.

(4) The “marginal efficiency of capital” makes its first appearance, and the theory of investment is constructed in flow terms.

(5) The speculative motive is made clearly dependent upon the rate of interest (in the lectures of 1933, the income, business, and precautionary motives were made dependent upon the rate of interest, while the speculative motive was made dependent upon the state of bearishness).

V. Conclusion

  In this paper we examined Keynes’s developmental state in 1934 through “The General Theory”, “The Summer Manuscript” and his Michaelmas lectures in 1934.

  “The General Theory” is the manuscript which succeeded the three 1933 manuscripts and two undated manuscripts, and was to form the theoretical backbone of the General Theory.

  Firstly, “The General Theory” possesses the same theoretical framework as the consumption theory of the General Theory. It deals with the subjective factors and the objective factors. The subjective factors are almost the same as those in the General Theory, but the objective factors which appear for the first time in “The General Theory” are, to some degree, different from those in the General Theory.

  Secondly, “The General Theory” has an improved version of an investment theory which is to be enshrined in the General Theory. The marginal efficiency of capital here is virtually the same as that in the General Theory.

 So far, so good. We see a clear improvement there. 

The third point is, however, quite different. In “The General Theory” as well as “The Summer Manuscript” Keynes puts forward new models to explain how the level of employment is determined, but his argument still lacks precision. Concerning “The General Theory” we pointed out the ambiguities in the concept of “effective demand” and the inconsistency of the employment theory (esp. the relation between the first postulate and the employment function and the relation between the argument of Chapter 6 and that of Chapter 9). In this respect, Keynes’s endeavours to explain the workings coherently were to continue right up to the General Theory, even here falling somewhat short of the requisite precision.

  In Section IV we examined the Michaelmas term lectures of 1934. They are identical to those of 1933 in that they advance a model in which income (or the level of employment) is determined within a single period.

The difference is that no argument in terms of the TM supply function is to be seen. We also pointed out five new features which were not found in the 1933 lectures.

 1) See Hirai (2007a,II, 1and 3).

  2) See JMK.14, pp. 464-470. The chapter concerned is referred to as “The Pre-First Proof Index Version” (see JMK.14, p. 351. Hereafter the Index Version) by Moggridge. Sections III to VIII of Chapter 12, “The State of Long-Term Expectation”, of the General Theory retain the original form of the Index Version, except for a few paragraphs, while Sections I and II of the same chapter appear in the form of a summary in the Index Version.

  3) See Hirai (2007a).

  4) See Hirai (1997-1999, Chapter 11, Section 2).

　5) Patinkin (1976) emphasizes the importance of “The General Theory”, for it was here that Keynes put forward the theory of effective demand. Moreover, Patinkin (1976, pp.73-79; 1977, p.24) concludes, judging from the 1933 Michaelmas Lectures, that Keynes formulated the theory of effective demand in the first half of 1933. He does not refer to the ambiguities in the concept of “effective demand” and the theoretical inconsistency of Keynes’s employment theory there.

  6) A similar problem occurs in “The Second Manuscript” in which the relation between the acceptance of the first postulate and the argument in terms of aggregate expenditure and aggregate costs is not clear. Cf. JMK.29, pp. 68-69, 72, and 90-91. See Hirai (2007a).

  7) Thereafter, however, he came to feel the difference between effective demand and income “to be of secondary importance, emphasis on it obscuring the real argument” (JMK.14, p. 181). This appears in a draft for his 1937 lectures.

  8) Cf. Patinkin (1976, p.86). 

9) This also appears in the footnote in which Keynes tries to explain why the employment function might be a straight line with a slope of 45° (JMK.13, p. 446). He says that there is “a tendency for average real prime cost to increase at about the same rate as output, as supply equipment is gradually brought into use”. This indicates the first postulate (W/P =ΔO/ΔN [where W denotes the money wage, P price, O the volume of output, N the volume of employment, ΔX an increment in X]). Patinkin (1976, p.74, Chapter 8, fn.14, pp.87-88) infers from this observation, Bryce’s notes, and others, that the employment function passes through the origin and has a slope of 45°, and that it is in fact the aggregate supply function and the production function of the General Theory (the first postulate is not used in this argumentation).

  10) This shows that the three features of the General Theory first appeared in “The General Theory”: (i) the four kinds of aggregate supply function; (ii) the aggregate supply function as a whole as an equilibrium concept; and (iii) “Keynes’s incompleteness” in the sense that because he assumes a fixed distribution of the amount of effective demand between different industries, his methodological standpoint which stresses “the heterogeneity of goods” and expectations is not persistently maintained. See GT, p. 286.

  11) In fact, there no distinction is made between equations (4) and (5).

  12) Keynes considers that the level of employment thus determined remains “within a modest range of fluctuation” and does not “proceed to extreme lengths”. Cf. JMK.13, p. 446. Here we see the idea of “underemployment equilibrium” in GT, p.254.

  13) See GT, p. 280.

  14) Cf. Keynes’s letter to Kahn (13 April 1934. JMK.13, pp. 422-423), and Keynes (1939).

  15) The term “maximise” (JMK.29, p. 89) means to maximize excess profit. It has no direct relation to the first postulate. (This is inconsistent with the main theoretical system of “The Second and Third Manuscripts”, where excess profit is considered to become zero in equilibrium.)

  16) See JMK.13, p. 427 and p. 436.

　17) Patinkin (1976, pp. 91-92) seems to point out the same inconsistency from a different angle.

  18) However, this is not unquestionable, because around this period Keynes clearly tries to separate the functions of profit. It would perhaps be more accurate to say that he shows no interest in the pseudo-TM supply function, rather than that the manuscript is devoid of anything corresponding to equation (8).

  19) In a letter to Harrod dated 27 August 1935, Keynes states that the discovery of the definition of marginal efficiency of capital was absolutely vital in the development of his thought. See JMK.13, p. 549. Historically speaking, Keynes’s marginal efficiency of capital follows Fisher’s “rate of return over cost” in The Theory of Interest (Fisher, 1930), a key concept in Fisher’s “principle of investment opportunities”. See GT, pp. 140-141. Fisher said that his theory of the rate of return over cost could be traced back to John Rae (1834).

  20) In Hirai (1997-1999, Chapter 7) we referred to the “duality” problem in the theory of the determination of the price level of investment goods in the Treatise. The investment theory of the General Theory is also inconsistent. Or rather, there are two investment theories, the inconsistency between which Keynes overlooks. For more on this, see A Reconstruction, pp. 195-200.

   21) Keynes’s examination of some fundamental concepts can be traced back to “The Second Manuscript” of 1933 (see JMK.29, pp. 68-69).

   22) For comparison between the table of contents of “The General Theory” and the tables of contents of the Third Manuscript of 1933 and First Galley I, II and III (see Section 1 of Chapter 13), see Hirai (2003, pp.460-467).

23) On this occasion, Keynes read the paper entitled “The Theory of Effective Demand” (JMK.13, pp. 457-468) to the American Political Economy Club. The main themes of this paper were analysis of the American economy and some suggestions on economic policy. Keynes argued that an increase in public spending through deficit financing was indispensable for the restoration of the economy, and put forward the multiplier theory in relation to the policy of public spending. Keynes wrote open letters to President Roosevelt in the New York Times of 31 December 1933 and 11 June 1934 (JMK.21, pp. 289-304; 322-329, respectively). Lippmann wrote a letter to Keynes to the effect that the former letter, Lippmann, had a great effect on the U.S. Treasury’s policy of lowering the long-term rate of interest. The latter, in which Keynes urged the government to effect emergency spending, was encouraged by Lippmann. See Hession (1984), pp. 275-276. On the relation between Keynes and Lippmann, see Wright (1973), p. 78.

  24) Immediately after this, the equation C + I = E + Q = Y = C + S appears. In view of the argument developed up to this point, this equation should have been C + I + U = E + Q = Y + U = C + S + U.

  25) Cf. GT, p. 282.

  26) As can be seen at JMK.13, pp. 104-108, Keynes himself, together with Robertson, developed the theory of forced saving in 1928. On this, see Presley (1979), pp. 79-80, and also Hirai (1997-19999, Section V of Chapter 4, and Note 36 to Chapter 5).

  27) For a close relation between the galley and the lectures, see Moggridge’s comment (JMK.13, p.485).

  28) For a chronological analysis of the 1934 Michaelmas lectures, see Hirai (2003, pp.474-484.

  29) In this quotation equation (1) is dealt with, while equation (2) overlooked.

　30) In November 1934 Keynes gave a public broadcast entitled “Poverty in Plenty: Is the Economic System Self-Adjusting?” (JMK.13, pp. 485-492), in which he stresses “a fatal flaw in that part of the orthodox reasoning [economics] which deals with the theory of what determines the level of effective demand and the volume of aggregate employment; the flaw being largely due to the failure of the classical doctrine to develop a satisfactory theory of the rate of interest” (p. 489) and emphasises the importance of increasing investment through the fall in the rate of interest rather than that of increasing consumption through the drastic social changes like an equalisation of income).

 

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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 12).