Keyness general theory reconsidered in the context of the japanese economy

Part I Reconsideration of The General Theory 1 Analyzing the Structure of The General Theory References 2 Analyzing Book I of The General Theory 2.​1 Introduction 2.​2 Involuntary Unempl

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Masayuki Otaki

Keynes’s General Theory Reconsidered in the Context of the Japanese Economy

Masayuki Otaki

Institute of Social Sciences, The University of Tokyo, Tokyo, Japan

Research Institute of Capital Formation, Development Bank of Japan, Tokyo, Japan

ISSN 2191-5504 e-ISSN 2191-5512

ISBN 978-4-431-55913-9 e-ISBN 978-4-431-55915-3

DOI 10.1007/978-4-431-55915-3

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lessons from this period of unprecedented economic events I believe that Japan has produced toolittle lively debate and too few valuable studies about its difficult experiences It is my hope that thisnew booklet series will address these deficits and thereby benefit society not only in Japan but also inother economies facing similar challenges.

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on an integration of our myriad resources, including those mentioned above, with the aim of providingyou an access to the fruits of our research as well as other intellectually stimulating content

Masaaki Komiya (The Research Institute of Capital Formation of Development Bank of Japan

Inc.)

In this book, I reconsider Keynes’s The General Theory of Employment, Interest and Money ( The General Theory ) from the perspective of modern microeconomic dynamics It comprises two parts: (i) the reconsideration of The General Theory and (ii) the applications of the extended theory derived

from such reconsideration to the current Japanese economy There are two prominent issues in Part I,which deals with the reconsideration The first is that I clarify that Keynes has surely succeeded in

proving the existence of involuntary unemployment without an ad hoc price rigidity assumption by

using the method of comparative statics although the way in which the nominal wage is determinedremains an open question Namely, Keynes shows that there are some involuntarily unemployed

workers for any given nominal wage to the extent that effective demand is insufficient The second

issue asserts the inseparability of effective demand and liquidity preference theories I shall show thatunless the flow aspect of an economy (the effective demand theory) depends on the stock aspect (theliquidity preference theory), Say’s law is upheld To the extent that any firm maximizes its marketvalue, this implies that industries overall are only surrogates for the savings of individuals

Accordingly, capital investment is always equal to the saving In order to the sustain Keynes’s theory,the existence of an alternative investment opportunity other than capita, namely money is essential.Part II explores the theoretical relationship between Japanese radical quantitative easing (QE)

monetary policy and prolonged stagnation As will be discussed in Part I, since the flow and stockaspects of an economy are inseparable, a change in the nominal money supply immediately affects theequilibrium condition of the fund market (or equivalently, the aggregated goods market) The real rate

of return for money should be increased against that of real capital to equilibrate the fund market

whenever money is rapidly injected into the economy by a radical QE monetary policy As such, aradical QE monetary policy advances disinflation/deflation although such consequences seem to beunpredictable for the monetary authority Moreover, the heightened rate of return for money raises theopportunity cost of capital investment Accordingly, a radical QE monetary policy possibly slowsdown the economy

Part I Reconsideration of The General Theory

1 Analyzing the Structure of The General Theory

References

2 Analyzing Book I of The General Theory

2.​1 Introduction

2.​2 Involuntary Unemployment and the Stability of Society

2.​3 The Existence Proof of Involuntary Unemployment

3.​3.​1 Definition of forced saving

Appendix 1:​ A Solvable Case of the Aggregation Problem Regarding Total Employment Reference

4 Analyzing Book III of The General Theory

5.​3 Liquidity Preference and the Theory of Interest

Appendix 2:​ The Derivation of the Formula of the Marginal Efficiency of Investment References

6 Analyzing Book V of The General Theory

6.​1 Introduction

6.​2 Effects of Change in the Nominal Wage

6.​3 The Employment Function

6.​4 Liquidity and the Stable Nominal Wage

References

7 Analyzing Book VI of The General Theory

7.​1 Introduction

7.​2 Keynes’s View of the Business Cycle

7.​3 The Obituary to Keynes’s Predecessors

7.​4 Some Philosophical Notes

References

8 Concluding Remarks of Part I

8.​1 The Misunderstanding​ of Keynes and His Conscience as a Liberalist

Reference

Part II Developing a New Collective Intelligence from The General Theory

9 Developing a New Collective Intelligence from The General Theory

9.​1 Introduction

9.​2 Exorbitant Accumulation of Public Debt and Economic Growth

9.​2.​1 The Nature of Public Debt and Taxation

9.​2.​2 Adjustment Cost and Investment Function

About the Author

Masayuki Otaki

is a Professor of Economics at the Institute of Social Sciences at the University of Tokyo; and

Academic Advisor of the Research Institute of Capital Formation, Development Bank of Japan Hismain areas of research are macroeconomic theory, environmental economics, educational economics,and economic thought Born in 1957, Prof Otaki received a Bachelor’s degree in Economics at theUniversity of Tokyo in 1981 and a Ph.D in Economics at the University of Tokyo in 1990 He wasappointed Professor of Economics at the Institute of Social Sciences in the University of Tokyo in2001

Part I

Reconsideration of The General Theory

I am sure that the power of vested interests is vastly exaggerated compared with the gradual

encroaching power of ideas; for in the field of economic and political philosophy there are not manywho are influenced by new theories after twenty-five or thirty years of age, so that ideas which civilservants and politicians and even agitators apply to current events are not likely to the newest But,soon or late, it is ideas, not vested interests, which dangerous for good and evil (John MaynardKeynes ‘The General Theory of Employment, Interest and Money’: pp 383–384)

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© Development Bank of Japan 2016

Masayuki Otaki, Keynes’s General Theory Reconsidered in the Context of the Japanese Economy, SpringerBriefs in Economics,

DOI 10.1007/978-4-431-55915-3_1

1 Analyzing the Structure of The General Theory

Masayuki Otaki1, 2

Institute of Social Sciences, The University of Tokyo, Tokyo, Japan

Research Institute of Capital Formation, Development Bank of Japan, Tokyo, Japan

sections consist of and buttress the proposed theory This is a curious structure and makes The

General Theory one of the most difficult of the classic books to understand I suggest that Keynes may have been in a hurry to publish The General Theory and promote his ideas concerning a cure for

mass unemployment, which was the primary cause of the worldwide economic crisis that ultimately

triggered World War II I conclude that Keynes provides a concise summary of The General Theory

in Book I to ensure the efficient and timesaving transmission of his theory to avoid war

Keywords The General Theory – World War II – Mass unemployment

What makes The General Theory one of the most difficult of the classic books in economics may be

partly attributed to its structure In general, a modern academic book begins with an introduction thatclarifies the motivations of the author It then considers a survey of the literatures before provingtheorems and propositions via process of deduction The politico-economic insights of the author arenot precisely depicted until such a formal deduction process has been undertaking (or even

consciously hidden until the end in low quality and/or awkward cases)

Such a presentation style may come from natural sciences Nevertheless, the style has the form of

a kind of puzzle to which a solution has been prepared beforehand Consequently, The General

Theory seems quite bewildering or erroneous to those who are used to such an ordered approach This is because the model and conclusions of The General Theory are densely summed up in the

three chapters at the beginning (Book I), which comprises only 32 pages (pp 3–34)

Chapter 1 The General Theory

Chapter 2 Postulates of the Classical Economics

Chapter 3 The Principle of Effective Demand.

In this sense, The General Theory is not a work that represents a puzzle-solving pastime.

The General Theory comprises six books After a concise description of his original theory at the

beginning (Book I), Keynes progresses a precise explanation of the constituents of his theory (Book II

to Book IV) An overall view of his theory is provided again in Chap 18 of Book III, although theoriginal model is transformed rather the static Indeed, compared with Book I, most readers may havedifficulty in determining how the price mechanism works in the model Hicks-Samuelson’s

interpretation (i.e., IS-LM analysis) originates from this chapter

Book V complements Keynes’s theory Besides the aggregation problem in a (inverse) production function (Chap 20), Keynes considers the relationship among prices, nominal wages, andliquidity (Chaps 19 and 21) Consequently, Book V is indispensable to understanding Keynes’s view

macro-on the mmacro-onetary ecmacro-onomy (not the barter ecmacro-onomy that falls within the scope of standard

I illustrate the structure of The General Theory in Fig 1.1

Fig 1.1 Structure of The General Theory

It is clear that the first three books of The General Theory take the inverse form of our

accustomed academic approach: the general equilibrium model is provided before the building

blocks of the model are introduced This suggests Keynes’s declaration in the preface:

This book is chiefly addressed to my fellow economists I hope that it will be intelligible to

others But its main purpose is to deal with difficult questions of theory, and only in the secondplace with the application of this theory to practice

As such, The General Theory is burdensome for half-hearted economists Keynes placed greater

importance on persuading subtle and influential economists of his days rather than making his theory

prevail With this mind, it may have seemed to Keynes that such a structure for The General Theory

would be effective and efficient, although his attempt caused many unnecessary misunderstandingsthat were contrary to his intentions Needless to say, he probably foresaw such trouble as the prefaceindicates:

Those, who are strongly wedded to what I shall call ‘the classical theory’, will fluctuate, I

expect, between a belief that I and quite wrong and a belief I am saying nothing new It is for

others to determine if either of these or third alternative is right

However, why did Keynes consider that such an inverted and/or complicated structure is

effective? In this regard, it seems necessary to take the prevalent political background and economic

situation into consideration The General Theory was first published in 1936 This year was not

merely in the midst of the worldwide profound recession that originated from the Great Depression of1929; it was also the time at which Germany, Italy and Japan, which were all totalitarian countries ,were heading toward World War II

The causes that prompted these countries toward war originated partly from the reparation

problem and the resultant hostility created in Germany as Keynes had prophesied in his book ‘The Economic Consequences of Peace’ in 1919, but ultimately from the appalling economic stagnation inthe totalitarian countries, which was so harsh that the existing social orders entirely collapsed or

were overturned Since Keynes loved Edmund Burke’s books, especially ‘Reflections on the

Revolution in France’ (1790), it is natural to think that he was as well aware of the reality that

serious economic impoverishment and/or income disparity significantly disrupts the social order of anation

It is also worth noting that the first translation of The General Theory is in Germany and the

second was in Japanese Both translations were published in 1936, the same year as the original waspublished, and appeared before French version of 1939 This may be mere coincidence However,

from my perspective, the publication of The General Theory in two major totalitarian countries

suggests something other than coincidence

In sum, Keynes seemed to hasten the publication of The General Theory, and targeted the book at

professional economists From one perspective, his enthusiasm, which originates from the success indeveloping a new theory, may have motivated him This seems undeniable Nevertheless, I believethat there is another side to the story

In the eyes of Keynes, it was clear throughout the writing process of The General Theory that the

next world war was inescapable Following the devastating experiences of World War I, Keynes mayhave concentrated on avoiding the next disastrous war However, he lacked sufficient time to

mobilize the decisive public opinion in order to hinder the coming war.1

As aforementioned, prevalent mass unemployment among the developed countries is a significantfactor that makes the world tilt toward war The most efficient and feasible way to avoid war is toelucidate to benevolent and outstanding economists across borders why such an appalling situation isprovoked In addition, considering the imminence of war, such an enlightenment process should becommunicated concisely Thus, assuming that my insight is close to reality, it is clear why Keynes

adopted the inverted structure of The General Theory as illustrated by Fig 1.1 and hastened

publication

The remainder of this chapter comprises a new interpretation of each Book of The General

Theory In Chap 2, I clarify the basic model of The General Theory proposed in Book I I

specifically emphasize that the interpretation of Keynes’s treatment of the second postulate of

classical economics is vital in order to understand The General Theory Contrary to the commonly

held interpretation, I emphasize that the assumption concerning the fixed nominal wage is inessential

to Keynes’s theory In Chap 3, I review the contents of Book II and show how conscious Keynes isabout the aggregation and index problems, which are both peculiar problems in macroeconomics InChap 4, I adopt the perspective of current economic theory and consider Book III, in which

properties of the consumption function are discussed

In Chap 5, I analyze Book IV by using not only current investment function theory but also

corporate governance theory The theory of liquidity preference first appears in Book IV; however,

this theory neglects the effect of money inflow on the asset markets and asserts that the nominal

interest rate is determined so as to equilibrate the existing stock of money and its demand I shall

show that if the inflow of money to the markets is not taken into consideration as Keynes assumes,Say’s law is revived to the extent that the ownership of a firm is entirely monopolized by

stockholders This is because an employer is only a faithful agent of stockholders, and individuals’saving opportunity is confined to stocks The implication here is that the aggregate saving must

always equal aggregate capital investment Thus, Say’s law still survives if we accept Keynes’s

liquidity preference theory intact Accordingly, some refinement of the theory is necessary and

inevitable in order to reestablish Keynes’s theory with a rigorous microeconomic foundation

In Chap 6, I consider Book V, which restates the place of price theory in The General Theory I

pay particular attention to the frequent enactment and revision in Britain of regulations on the

monetary wages and prices (e.g., see Trevelyan 1944) These historical facts apparently affect

Keynes’s discussion In addition, I analyze the relationship between confidence about the value of

money, which is akin to the concept of liquidity, and the stability of nominal wages This relationship

is specific to a monetary economy and does not necessarily exist in a barter economy This

consideration may also be useful whenever one analyzes hyperinflation

In Chap 7, I focus on Keynes’s politico-economic thoughts depicted in Book VI In particular, thestrain between religious and economic thought, which culminated during the life of unfortunate

Hobson, is considered In Chap 8, I present the concluding remarks of Part I

References

Burke, E (1790) Reflections on the revolution in France London: J Dodsley (Reprint, 2009 Oxford: Oxford University Press) Carr, E H (1939) The twenty year’ crisis, 1919–1939: An introduction to the study of international relations London: Macmillan

(Reprint, London: Palgrave Macmillan, 2001).

Keynes, J M (1919) The economic consequences of the peace New York: Harcourt Brace.

Keynes, J M (1936) The general theory of employment, interest and money London: Macmillan.

Trevelyan, G M (1944) English social history: A survey of six centuries, Chaucer to Queen Victoria (Reprint, London: Book Club

Associates, 1973).

This is evident from Carr’s ( 1939 : pp 218–219) following remarks:

‘Employment has become more important than profit, social stability than increased consumption, equitable distribution than maximum production.’

© Development Bank of Japan 2016

Masayuki Otaki, Keynes’s General Theory Reconsidered in the Context of the Japanese Economy, SpringerBriefs in Economics, DOI 10.1007/978-4-431-55915-3_2

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2 Analyzing Book I of The General Theory

Masayuki Otaki1, 2

Institute of Social Sciences, The University of Tokyo, Tokyo, Japan

Research Institute of Capital Formation, Development Bank of Japan, Tokyo, Japan

Masayuki Otaki

Email: ohtaki@iss.u-tokyo.ac.jp

Abstract

Book I is the core of The General Theory I clarify that Keynes has succeeded in proving the

existence of involuntary unemployment, which is incurable by reduction of nominal wage while manystandardized textbook tells us that rigidity in the nominal wage is the crucial assumption that upholdsKeynes’s proposition What is acutely important is the interpretation of the incentive for labor supply(i.e., the interpretation of the second postulate of classical economics) Indeed, Keynes denies that themarginal disutility of labor is equalized to the real wage However, one would surely find that

Keynes also emphasizes that the real wage exceeds the corresponding marginal disutility of labor if

one reads The General Theory carefully enough It is a plausible assumption since, if such a relation

is upheld, all workers are incentivized to participate Whenever an economy faces a shortage of

effective demand and labor demand contracts, the equilibrium real wage becomes costly because themarginal product of labor remains at a high level In such a case, excess supply may possibly exist inthe labor market, and such unemployment can be deemed involuntary

Keywords Involuntary unemployment – Second postulate of the classical school – Change in the

nominal wage principle of effective demand

2.1 Introduction

As discussed in Chap 1, Book I of The General Theory is a concise but intensive summary of the

theory developed throughout the work I now proceed to show that in contrast to the current

understanding of The General Theory, Keynes succeeds in proving the existence of involuntary

unemployment that is associated with the rational behavior of workers (the incentive compatibility of

labor supply) The vital point that induces this conclusion is that Keynes does not deny the secondpostulate of neoclassical economics (Keynes calls neoclassical economics classical economics), butrather extends that postulate

2.2 Involuntary Unemployment and the Stability of Society

As will be elucidated by this chapter, what Keynes asserts in The General Theory is that he had

succeeded in the radical extension of traditional theory (neoclassical economics) and established a

new theory that proves the existence of involuntary unemployment that originates from a shortage of

effective demand

However, before advancing the discussion, some preparatory considerations are necessary in

order to understand the historical legitimacy and background of The General Theory First, I must

draw attention to the tradition of the poor law in Britain According to Trevelyan (1944, pp 112–113),

Gradually, a proper system of Poor Relief, based upon compulsory rates, and discriminating

between various classes of the indigent was evolved in England, first of all the countries of

Europe It was soon found that the whipping of ‘sturdy beggars’ was by itself no solution Thedouble duty of providing work for the unemployed, and charity for the impotent was graduallyrecognized by Tudor England as incumbent not merely on the Church and the charitable, but onsociety as a whole In the reign of Henry VIII some great towns, like London and Ipswich,

organized the administrative relief of their poor At the end of Elizabeth’s reign and under Stuartkings, it had become a duty prescribed by national legislation, enforced upon the local

magistrates by a vigilant Privy Council, and paid for by compulsory Poor Rates

Thus, the necessity of saving unemployed workers from poverty by providing work was markedlyrecognized even from the end of the fifteenth century in England However, such a social safety netoften suffers from a type of moral hazard behavior on the part of poor individuals Trevelyan (1944:

p 278) argues:

According to George King over one million persons, nearly a fifth of the whole nation, were inoccasional receipt of alms, mostly in the form of public relief paid by the parish The poor-ratewas a charge of nearly £800,000 a year on the country and rose to a million in the reign of Anne.There was seldom any shame felt in receiving outdoor relief, and it was said to be given with amischievous profusion Richard Dunning declared that in 1698 the parish dole was often threetimes as much as a common labourer, having to maintain a wife and three children, could afford

to expend upon himself; and that persons once receiving outdoor relief refuse ever to work, and

‘seldom drink other than the strongest ale-house beer, or eat any bread save what is made of thefinest wheat flower.’ The statement must be received with caution, but such was the nature of thecomplaint of some ratepayers and employers about the poor-law

Even in the nineteenth century,

The condition of the agricultural labourer, particularly in the South, was often very wretched inthe thirties and ‘hungry forties,’ when even the farmer who employed him was suffering from thebad times And on the ‘labouring poor’ in field and factory, fell the heavy weight of the New

Poor Law of 1839, when outdoor relief was abolished (not indeed quite universally) and the

‘workhouse test’ was imposed on applicants for public alms Such was the remorseless

utilitarian logic of the Poor Law Commissioners, to whom the Act gave power It was a harshremedy for a terrible disease: the Speenhamland policy of granting the poor-rate in aid of wageshad pauperised even the employed workman and kept wage down; moreover, it was now ruiningthe ratepayers An operation was necessary to save society, but the knife was applied withoutanaesthetics The need to make life in the workhouse less attractive than employment in field andfactory was the principle on which the Commissioners worked, and as they could not in that era

the attractiveness of employment by enforcing a minimum wage, they felt obliged to lower the

standard of happiness of the workhouse (Trevelyan p 538)

The foregoing quotations suggest the risk that too much compensation paralyzes an individual’sdiscipline Moreover, this unwanted propensity seriously aggravates the fiscal conditions of a

society Accordingly, as insurance theory tells us, social security payment should be significantlylower than the minimum wage Nevertheless, since diligence differs across individuals and is

unknowable, some individuals are possibly unemployed voluntarily.

The following paragraph quoted from Pigou (1933) indicates that an argument about the existence

of involuntary unemployment remained even in the midst of the Great Depression :

But in a period of depression, when all available vacancies are filled, the fact that these men donot desire employment does not cause them to act otherwise than they would do if they did theydesire it; and, since it is impossible to look directly into people’s minds, there are, therefore, nomeans of discovering or enumerating them

As such, the deliverance from poverty, which stems from unemployment, is, in principle, a

double-edged sword On the one hand, such deliverance improves the wellbeing of workers who areinvoluntarily unemployed On the other hand, some idle individuals are subsidized by social securitypayments that are financed by taxing the employed and employers To the extent that information isimperfect and one can hardly identify who would commit such malpractice as Pigou discusses, themorale of workers is affected and labor productivity slows down This in turn harms social welfare.Accordingly, whether or not deliverance from poverty due to unemployment can contribute to a

society is a genetically statistical problem in the sense of the number of individuals who are

involuntarily unemployed on average.

Besides such an empirically difficult problem, there is another problem regarding economic

theory: does involuntary unemployment really exist? It is an elementary task to show the existence ofvoluntary unemployment If the real wage is lower than the disutility of labor of an individual, he orshe would rather choose leisure than consumption This implies that such an individual is voluntarilyunemployed When one applies this logic to the overall structure of an economy, unemployment isnever a serious economic problem

Nevertheless, it is hardly tenable to insist that not less than 30 % of workers are coincidentlydisincentivized to work in an emergency as observed in the Great Depression Pigou’s (1933)

insistence is precarious because it endangers the social order of a society As Thomas More depicts

in his Utopia (1516), a community in which the constituents cannot be thankful for living there is

doomed eventually The significant income disparity due to involuntary unemployment, if it exists,and the resultant poverty cause the distaste for one’s nation The most devastating consequence of

such a misfortune is a ‘revolution’ as Burke (1790) severely warns about and criticizes In substance,

a revolution is an internal war that leaves nothing but mutual and irreducible disgust among the

residents of nation In general, a revolution can never contribute to improvement in the economicefficiency of a nation, indeed, it seriously aggravates the overall well-being of the residents as thepresent situations in North Africa and the Middle East markedly indicate

As Arendt’s ‘The Origins of Totalitarianism (1951)’ suggests, distilled distrust and disgust amongresidents is, if not indicative of interwar periods, an embryo of totalitarianism because people losethe ability to express their free will owing to the fear of violence If once violence is adjoined to a

society in such a vacuum where humans mind are enslaved, a totalitarian society ensues As Arendthad correctly understood, Keynes also regarded socialism as a variation of totalitarianism.

Moreover, in the 1930s, it was widely believed that the economic performance of the Soviet Unionand the totalitarian countries was no less successful than that of capitalist countries Accordingly,even in Britain, the threat of totalitarianism was deemed to be serious, and hence, Keynes would be

acutely conscious of the way to overcome mass involuntary unemployment To summarize, the

stability or cohesion of a nation depends significantly on whether the nation can save its economyfrom mass involuntary unemployment Nevertheless, there are two serious constraints on achievingthe desired result: how to finance the related government expenditure, and how to incentivize therecipient of social security payments so that he or she participates in work

As aforementioned, because economists up until Keynes’s era could not provide an appropriatetheory to explain involuntary unemployment, Keynes felt that he should construct such a theory thatwas compatible with microeconomic theory The results are concisely and intensely depicted in BookI

In addition, one should note that the aggregate demand management policy that Keynes proposed

is in accord with the conventional wisdom that the history of Britain had gradually built up In thissense, Keynes’s effective demand theory belongs indeed not to heretical thinking but to orthodoxbeliefs What we must consider is why his theory in itself is not properly understood and why hispolicy recommendations are hardly implemented The first question is dealt with separately in thischapter (regarding the theoretical aspects in economics) and Chap 7 (regarding the philosophicalaspects)

2.3 The Existence Proof of Involuntary Unemployment

This section reconsiders whether or not the assumption of stickiness of the nominal wage is crucial for the essence of The General Theory in which the existence of involuntary unemployment is proved.

The essential problem is what stickiness means If this concept implies that the nominal wage is

treated as an exogenous variable in Keynes’s model, it is consistent with appropriate line of thought.However, if the concept is used to mean that workers are irrational because they are prone to be

fooled by an increase in wage-goods prices, such a thought is adrift from the essence of The General Theory.

In Chap 2 (The Postulates of the Classical Economics) of The General Theory, Keynes classifies

the assumptions about labor market conditions The first postulate of classical economics is

concerned with the aggregate labor demand; the second postulate of classical economics relates to theaggregate labor supply schedule The first postulate, with which Keynes agrees, is the profit

maximization condition of a representative firm under perfect competition, wherein the marginal

product of labor should be equalized to the real wage Namely,

(2.1)where is the aggregate supply price (short-run aggregate production function); N is total employment; and w and p are the nominal wage and the price level respectively Since the marginal

product of labor diminishes together with an increase in total employment, the total demand for alabor force is a decreasing function of the real wage as illustrated by Fig 2.1

Fig 2.1 Labor demand function

What is provocative is Keynes’s interpretation of the second postulate In general, especially inhalf-baked and bulky textbooks, there is an assertion that Keynes offhandedly treats the nominal wage

a simply exogenously given However, when one invokes the following remarks in The General Theory, one finds that the matter is not so simple:

Thus, it is fortunate that the workers, though unconsciously, are instinctively more reasonableeconomists than the classical school, insomuch as they resist reductions of money-wage, whichare seldom or never an all-round character, even though the existing real equivalent of these

wages exceeds the marginal disutility of the existing employment; whereas they do not resist

reductions of real wages, which are associated with increases in aggregate employment and

leave relative wage unchanged, unless the reduction proceeds so far threaten a reduction of the real wage below the marginal disutility of the existing volume of employment (pp 14–15:

Italics by the author)

It is clear from this description that Keynes never neglects the existence of the second postulate

Furthermore, in The General Theory , Keynes asserts:

But we have thrown the second postulate, a decline in employment, although associated with

labour’s receiving a wage equal value to a large quantity of wage-goods, is not necessary due to

a large labour’s demanding a large quantity of wage goods; and a willingness on the part of

labour to accept lower money-wages in not necessarily a remedy for unemployment (p 18)

To summarize, we can interpret what Keynes asserts as follows:

The equilibrium real wage is determined above the labor-supply schedule prescribed by the

Without interchanging the existing interpretation of labor market equilibrium in Keynesian

economics with our new interpretation, one can scarcely understand foregoing Keynes’s remarks.That is, as illustrated in Fig 2.2, the feasible labor-supply domain is the shaded area locatedabove the hypothetical labor-supply function, , which corresponds to the second postulate

Fig 2.2 Extended second postulate

Within the shaded area, in fixed employment, workers can earn a real wage, compared with thesituation in which workers behave price takers and maximize the utility Thus, the shaded feasibledomain implies a set where workers can obtain a higher utility than obtained by utility maximization

as price takers Hence, all workers wish to participate if an economy is located within this area Inturn, whenever the equilibrium of the labor market is achieved within the area, the resultant

unemployment is, by definition, involuntary.1

It is important to emphasize that Keynes presumes the stickiness of the nominal wage by referring

to the incentive compatibility of workers to participate although most textbooks state that Keynes

assumes stickiness without sufficient consideration

The bold part of the aggregate labor-demand function , which is defined by Eq (2.1), in

Fig 2.3 illustrates possible equilibria of the labor market.

Fig 2.3 Labor market equilibrium

The situation illustrated in Fig 2.3 exists partly because Keynes assumes that the first postulate isupheld (see Fig 2.1), hence, the equilibrium of the labor market should always be located on Curve

This is also because he assumes that the equilibrium real wage should be beyond the marginaldisutility of labor, which is illustrated by Curve in Fig 2.2, in order to incentivize workers.Consequently, the overall equilibrium of an economy as a whole cannot be determined solely by thelabor market equilibrium condition (i.e the supply-side of the economy) unlike neoclassical

economics

The whole structure of neoclassical economics, which presumes the first and the second

postulate, is illustrated by Fig 2.4

Fig 2.4 Neoclassical equilibrium

The first quadrant depicts the equilibrium of the labor market The equilibrium is achieved at theintersection of Curve and The equilibrium real wage is determined to equalize labor

demand to supply The fourth quadrant expresses the aggregate supply price (aggregate productionfunction) It is apparent from the figure that, to the extent that the labor market clears, the realGDP is determined only by the aggregate supply price function unrelated to the conditions of theaggregate demand

Namely, regardless of how much individuals decide to save and how much entrepreneurs plan toinvest, the equilibrium real GDP is determined only by the conditions concerning the labor market Since aggregate savings can be defined as the residue of real GDP after deducting aggregate

consumption, and real GDP is invariant in the case of neoclassical school, it is a natural consequencethat aggregate saving is always equal to aggregate capital investment

In other words, Say’s law holds, as John Stuart Mill and Alfred Marshall assert In Chap 2 of

The General Theory, using the aforementioned model, Keynes keenly criticizes both men This is

because all unemployment is voluntary since workers make their labor supply decisions optimally inthe sense that their marginal utility from consumption is equalized to the marginal disutility of labor

In this regard, Keynes declares the following in The General Theory (p 26):

If, however, this is not the true law relating the aggregate demand and supply function, there is avitally important chapter of economic theory which remains to be written and without which alldiscussions concerning the volume of aggregate employment are futile

‘‘The vitally important chapter of economic theory which remains to be written’’ is The General

Theory itself.

Chapter 3 (The Principle of Effective Demand) of The General Theory concludes Keynes’s

model by taking the conditions of the demand-side of the economy into consideration As discussed,

in contrast to neoclassical theory, the model presented in The General Theory, is not concluded only

by the aggregate supply conditions

As the conditions of aggregate demand, Keynes provides the following aggregate demand function:

(2.2)where is the propensity to consume (the aggregate consumption function), the properties ofwhich are precisely analyzed in Book II Since some part of real GDP is considered saved and

consumption increases with real GDP (total employment), it is natural to assume

(2.3)

D 2 is the real independent aggregate expenditure, which does not relate to total employment N or

real GDP This includes capital investment and government expenditure.2

Combining Eq (2.2) with the aggregate supply price , one obtains the following equilibriumcondition for the goods market:

(2.4)The complete illustration of Keynes’s model is presented in Fig 2.5 The first quadrant illustratesthe equilibrium of the goods market The total employment level and real GDP is determined at theintersection of the aggregate supply price Z and the aggregate demand D Keynes dubbed such an equilibrium aggregate demand effective demand

Fig 2.5 Keynesian equilibrium

The best and most elegant part of Keynes’s microeconomic theory is represented in the fourthquadrant Here, the first and the second postulate are illustrated as Curves and When

equilibrium total employment is determined by the principle of effective demand (the first

quadrant), the equilibrium real wage is located at Point , which is compatible with the maximization condition of the representative firm For the determined equilibrium real wage, there ispotential labor supply, which amounts to , and thus the workers, whose volume is , are

profit-involuntary unemployed as long as the level of effective demand remains at Point

As discussed, there is no incentive for employers and employees to diverge from this equilibrium.This is partly because the equilibrium real wage is compatible with the profit-maximization of therepresentative firm, and partly because this wage provides employees with higher utility than thecorresponding marginal disutility of labor This is the astute character of the labor market equilibrium

in Keynes’s model.3 This analysis contrasts with the authorized interpretation of The General Theory

by Hicks, Samuelson, and Modigliani, which entirely neglects the incentive-compatibility conditionabout labor supply

Such a prominent feature of Keynes’s model is most significant concerning the macroeconomiceffect of the reduction of the nominal wage That is, Keynes shows the following proposition:

Proposition 2.1

Suppose that the nominal wage w sags Then, as far as its indirect effects on the aggregate demand are negligible, this only results in causing a proportionate reduction of the price level In other words, the reduction of the nominal wage never rescues workers who are involuntarily

unemployed.

This proposition is evident from Fig 2.5 If the locations of D and are unchanged by the reduction

of the nominal wage w, equilibrium total employment is kept intact Accordingly, the corresponding

marginal productivity of labor should also be unchanged Thus, the real wage is invariant even

though the nominal wage w sags This implies that the price level p proportionately decreases with the nominal wage w.

In other words, whenever perfect competition prevails and the price is determined so that it isequalized to the marginal cost (the nominal wage), to the extent that the production volume is

constrained to remain constant, the effect of the cost reduction is entirely reflected in its output price.4

It is not wage reduction but the encouragement capital investment or the expansion of governmentexpenditure that save workers from involuntary unemployment Figure 2.6 depicts how an upward

adjustment of the aggregate demand curve caused by an increase in autonomous expenditure, D 2,affects the volume of employment

Fig 2.6 Effect of the expansion of aggregate demand

An economy initially located at Point moves toward Point E by such an expansion in

autonomous expenditure Thus, the volume of total employment increases by

One must also note that while the real wage sags because the price become dearer in accordance

with the expansion of the aggregate demand, employed workers never fall into the money illusion

The reason is that the equilibrium real wage (the marginal utility from consumption) is still higherthan the corresponding marginal disutility of labor This contrasts with the prevalent interpretation ofKeynes’s theory, which neglects the incentive mechanism of labor supply and is hardly tenable fromthe perspective of the monetarist critique that the assumption of the nominal-wage stickiness impliesthe irrational behavior of workers (i.e., money illusion)

Thus, contrary to neoclassical economics (Say’s law), in Keynes’s theory, demand creates

supply Keynes regards involuntary unemployment as an acute social injustice that the market

economy should overcome To achieve this, it is evident that some kind of social planning such as

efficient and well-founded government spending is inevitable From this point of view, in The

General Theory, Keynes criticizes neoclassical economics as follows:

That it could explain much social injustice and apparent cruelty as an inevitable incident in thescheme of progress, and the attempt to change such things as likely on the whole to do more harmthan good, commended it to authority That it afforded a measure of justification to the free

activities of the individual capitalist, attracted to it the support of the dominant force behind

authority (p 33)

Pigou, A C (1933) The theory of unemployment London: Macmillan.

Trevelyan, G M (1944) English social history: A survey of six centuries, Chaucer to Queen Victoria (Reprint, London: Book Club

Associates, 1973).

Footnotes

Mathematically, this discussion suggests that Keynes regards the labor supply schedule not as a function but as a correspondence.

When one defines the labor-supply function, which derived from the second postulate, as

, Keynes’s labor-supply feasible set is defined by

.

There is a serious theoretical problem about whether capital investment is unrelated to savings to the extent that the ultimate owners of

a firm are stockholders, and the employer is responsible to them This problem will be considered in Sect 1.5.

Keynes asserts that

(5) Hence the volume of employment in equilibrium depends on (i) the aggregate supply function, , (ii) the propensity to consume, , and (iii) the volume of investment, This is the essence of the General Theory of Employment.

(6) For every value of N there is a corresponding marginal productivity of labor in the wage-goods industries; and it is this which determines the real wage (5) is, therefore, subject to the condition that N cannot exceed the value which reduces the real wage to equality with the marginal disutility of labor This means that not all changes in D are compatible with our temporary assumption that

monetary-wages are constant Thus it will be essential to a full statement of our theory to dispense with this assumption (p.29)

This statement can be taken to mean that the equilibrium of an economy, which The General Theory considers, is confined to an underemployment economy where some workers are involuntary unemployed However, a full-employment economy, where true

inflation is associated, is also analyzed in Book V.

The following description is in The General Theory:

Now the assumption that the general level of real wages depends on the money-wage bargains between the employers and the workers in not obviously true Indeed, it is strange that so little attempt should have been made to prove or to refute it For it is far from being consistent with the general tenor of the classical theory, which has taught us to believe that prices are governed by

marginal prime cost in terms of money and that money-wages largely govern the marginal prime cost Thus if money-wages change, one would have expected the classical school to argue that prices would change in almost the same proportion, leaving the real wage and the level of employment practically the same as before,… (p.12)

© Development Bank of Japan 2016

Masayuki Otaki, Keynes’s General Theory Reconsidered in the Context of the Japanese Economy, SpringerBriefs in Economics, DOI 10.1007/978-4-431-55915-3_3

(2)

3 Analyzing Book II of The General Theory

Masayuki Otaki1, 2

Institute of Social Sciences, The University of Tokyo, Tokyo, Japan

Research Institute of Capital Formation, Development Bank of Japan, Tokyo, Japan

macroeconomics was still under development, one necessarily finds that the definition of

macroeconomic variables should be clarified before any essential discussion However, above all,the aggregation problem of the macroeconomic production function is still important and seriousbecause it questions whether a stable relationship exists between total employment and GDP Thisproblem is never self-evident because it even relates to the structure of aggregate demand function Inother words, relative prices for a given nominal wage determine the allocation of the labor forceacross industries and are affected by the structure of aggregate demand through goods market

equilibrium Accordingly, the aggregation problem in the production function is unsolvable withoutconsidering the state of aggregate demand This chapter provides an example in which such

aggregation is feasible

Keywords User cost – Definition of income and saving difficulty in aggregating production functions

3.1 Introduction

Book II comprises the following chapters and considers the definition of some macroeconomic

concepts relating to the aggregation problem It also emphasizes the meaning of the equivalence ofcapital investment to saving

Chapter 4 The Choice of Units;

Chapter 5 Expectations and Employment;

Chapter 6 The Definition of Income;

Chapter 7 The Meaning of Saving and Investment Further Consideration

Book II diverts from the essence of The General Theory (1936) Nevertheless, one should note

that there is no framework for macroeconomics (e.g., SNA statistics) when The General Theory was

published Strictly speaking, the aggregation procedure is still a serious problem in macroeconomics

In addition, there is no concordance on whether the equalization of investment to saving is a structure

equation or merely an accounting identity of Keynes’s era Book II is the preparatory considerationfor macroeconomics framework that elucidates the theory that Keynes proposed in Book I.

3.2 The Conundrum in the Aggregation Problem of Prices and

Quantities

Chapter 4 of The General Theory emphasizes the measurability of the performance of an economy in

relation to the aggregation problem While other chapters have become rather obsolete, this chapter isthe most important in Book II in the sense that the aggregation problem regarding macroeconomicproduction function is still in debate even in current macroeconomic theory although most economistsincautiously presume its existence

According to Keynes,

The fact that two incommensurable collections of miscellaneous objects cannot in themselves

provide material for a quantitative analysis need not, if of course, prevent us from making

approximate statistical comparisons, depending on some broad element of judgment rather than

of strict calculation, which may possess significance and validity within certain limits But theproper place for such thing as net output and the general level of price lies within the field of

historical and statistical description, and their purpose should be to satisfy historical or socialcuriosity, a purpose for which perfect precision—such as causal analysis requires, whether ornot our knowledge of actual values of the relevant quantities is complete or exact—is neither

usual nor necessary To say that net output to-day is greater, but the price-level lower, than tenyears ago or one years ago, is a proposition of a similar character to the statement that Queen

Victoria was a better queen but not a happy woman than Queen Elizabeth—a proposition not

without meaning and not without interest, but unsuitable as material for the differential calculus.Our precision will be a mock precision if we try to use such partly vague and non-quantitativeconcepts as the basis of a quantitative analysis (p 40)

This quotation suggests that Keynes is quite skeptical about the reliability of aggregate economicindexes such as ‘net output’ and ‘general level of price.’ Moreover, he may even dislike the avowedambiguity (or vagueness) and arbitrariness that such concepts contain Such vagueness and

arbitrariness originate from the heterogeneity of existing goods and services In reality, various goodsand services are transacted in an economy Consequently, how should we aggregate them in order toevaluate overall economic activity?

For example, what does real net domestic product (NDP) (‘net output’ to use Keynes’s term)

mean? To transform a monetary (nominal) value into a physical (real) one, one should divide themonetary value by the price of some assigned goods or service However, the problem is the price bywhich the monetary value should be denominated For example, is real NDP in terms of wheat a

relevant index in such an industrialized world? Such vagueness and arbitrariness is unavoidable nomatter how artificial devices are progressed

Thus, Keynes declares:

It is my belief that much unnecessary perplexity can be avoided if we limit ourselves strictly tothe two units, money and labour, when we are dealing with the behaviour of the economic

system as a whole; reserving the use of units of particular outputs and equipments to the occasion

(ii)

when we are analysing the output of individual firm or industries in isolation; and the use of

vague concepts, such as the quantity of output as a whole and the general level of prices, to

occasions when we are attempting some historical comparison which is within certain (perhapsfairly wide) limits avowedly unprecise and approximate (p 43)

That is, Keynes uses, henceforth, the nominal value of various economic variables as value

indexes and total employment as a quantity index of economic activities There are two persuasivereasons for using these measures

First, Keynes proposes that labor forces are more homogenous than goods and services Eventhough employee A has twice the ability of employee B, Keynes insists that labor force is measurable

as an efficiency unit The foregoing example shows that employee A is evaluated as though two

employees of type B exist Although it is a matter of degree, such a procedure is more modest andplausible than saying that real GDP is two by adding one apple to one orange

In reality, there may be more profound and practical reasons to use total employment as a quantityindex As discussed in Sect 2.​1, the most serious concern of The General Theory is how to deliver

workers from involuntary unemployment Accordingly, Keynes strives hard to verify the aggregation

method of labor forces Such efforts appear at the end of this chapter and Chap 20 of The General Theory although the exact aggregation method, which appears in the Appendix of this book, is not as

simple as Keynes assumes

Second, using monetary (nominal) value as an economic indicator is more reliable in Keynes’smodel This is because, as shown in Sect 2.​2, the price of wage-goods is kept constant over time inequilibrium Since there is neither inflation nor deflation, in which exchange rates between money andgoods steadily decrease or increase, evaluating economic activities in terms of money is more

convenient and easily calculable

3.3 Some Definitions

From Chaps 5–7 in The General Theory, some auxiliary arguments are provided to buttress the

model that is proposed in Book I In Chap 5 (Expectation as Determining Outputs and Employment),Keynes analyzes the role of short-term expectation in determining the total employment level Short-term expectation is expectation concerning the output price level in the near future This is distinctfrom long-term expectation, which relates to the long-run stream of profits and which Keynes

discusses in Chap 12

According to Keynes,

short-term expectation is revised gradually and steadily by the information obtained from dailybusiness activities, and

the macroeconomic environment, which surrounds a firm, scarcely changes in the short run

Thus, he induces that it is natural to assume that short-term expectation heavily depends on a

firm’s latest economic performance

Mathematically speaking, under the assumption of perfect competition, such an expectation may

be expressed by the following equation:

(3.1)where is the expected price of the next period and denotes the proportional constant thatrepresents the velocity of the adjustment of the expectation Equation (3.1) implies that short-termexpectation is renewed proportionately by the volume of the aggregate excess-demand price.1 If issmall enough (this corresponds to property (ii) of short-term expectation), it is clear from Fig 2.​5 thatsuch an adjustment process is stable and short-term expectation converges to rational expectation tothe extent that there is no additional exogenous shock

Keynes dubs such a state of an economy as long-period employment This concept may mean that

once the economy has reached such a situation, there is no incentive to change the employment levelfor a firm.2 As discussed in Sect 2.​2, the model of The General Theory presumes that an economy is

always in situation of long-period employment

In closing Chap 5, Keynes considers the relationship between short-term and long-term

expectation Capital investment relies heavily on the state of long-term expectation as discussed in

Chap 12 of The General Theory, and the amount of capital stock is fixed in the short run In addition,

equilibrium employment, which is governed by short-term expectation, is affected by existing capitalstock Consequently, the current state of short-term expectation is a function of the vector the elements

of which are past long-term expectations Thus, short-term and long-term expectations mutually

interact

Chapter 6 (“The Definition of Income, Saving and Investment’’) intends to emancipate the

relationship between capital investment and savings by using an unfamiliar concept of user cost This

chapter seems to have been necessary because the system of national accounts (SNA) was not yetdeveloped The concept of user cost is defined as the difference between the optimum monetary value

of existing capital goods, which are defined under the condition that they are preserved as furnished

as possible, and their actual depreciated value in terms of money Namely, the user cost is akin to thenet monetary depreciation value of capital Let the user cost be denoted

Keynes defines income, , as the difference of the aggregate proceeds, , and the user cost

Namely,

(3.2)

He suggests that this concept almost corresponds to Marshall’s income and Pigou’s national

dividend Income includes wage payments and rewards for entrepreneurs In addition, let be theaggregate monetary value of final goods purchased among firms for capital investment Then, theaggregate consumption becomes

(3.3)because Keynes regards user cost as dissaving (equivalent to consumption) He defines aggregate

saving, S, as the residue of aggregate income after deducting consumption Accordingly,

(3.4)However, the outputs, which are not consumed, are entirely invested Thus, the aggregate capitalinvestment, , becomes

(3.5)From (3.4) and (3.5), one obtains

From (3.4) and (3.5), one obtains

What Keynes shows in Chap 6 is that equalization between capital investment and saving is anaccounting identity While this discussion clarifies the relationship between aggregate capital

investment and saving, this provokes another dispute: can we regard the equalization of capital

investment to saving as an equation that Keynes uses in Book I? If not, Keynes himself proves Say’slaw , which he uncompromisingly negates in Book I In this sense, it is undeniable that Chap 6

contains some confusing elements However, in that era, one should note that there seems no commonand clear understanding that both capital investment and saving belong to dynamic decisions andrelate to the exchange between current and future goods

Chapter 7 (“The Meaning of Saving and Investment Further Consideration’’) buttresses the formerChapter and comprises two parts: a critique of the thesis that saving is unequal to investment, and acritique of the ‘forced saving’ hypothesis, which assumes the equalization of saving to investment as

Keynes considers in The General Theory

In the first critique, Hawtrey’s inventory cycle appears According to Hawtrey , entrepreneurs aresensitive to information provided by inventory management They increase production when an

unexpected reduction of their inventory occurs, and vice versa Hawtrey asserts that an inventorycycle caused by errors of expectation is at the heart of the business cycle

Keynes admits that consumption goods markets possess such a property but capital goods market

do not Moreover, Keynes states that the impact of inventory fluctuation is negligible compared withthe produced goods overall It is a natural theoretical consequence from his discussion of short-termexpectation in Chap 5

In his second part of the first critique, Keynes advocates his discussion that appears in A Treaties

on Money, this book also assumes an imbalance between saving and investment He argues that when

saving exceeds investment, the ‘realized profits’ are below ‘normal profits,’ which suppresses

production volume Nevertheless, if capital goods are always in equilibrium as he discussed, only theconsumption goods markets are necessarily in disequilibrium This is the thesis that Hawtrey

provides, and Keynes by himself is skeptical Thus, it seems undeniable that some confusion exists inKeynes’s discussion here

The final part of the first critique is concerned with Robertson’s lag According to Robertson ,there is a substantive lag in income distribution In such a case, current income, , becomes the sum

of aggregate consumption and capital investment during the prior period Let each of them be denoted , When we define the aggregate saving as the difference between current income and

consumption, the following relationship holds:

(3.6)where is the income in the sense of The General Theory (no lag in income distribution exists).

Thus, if aggregate saving exceeds investment under a significant lag in income distribution, this

implies the downturn of business (i.e., )

The discrepancy between saving and investment emerges because current saving, , is not

affected by current income but only by income earned during the prior period, which is

predetermined Accordingly, when current investment is thwarted, saving exceeds investment

Meanwhile, income in Keynes’s sense decreases by the same amount as the reduction of investment;thus, an economy stagnates As such, Keynes agrees with the imbalance of saving and investment

when a serious lag in income distribution exists.

In the second critique, Keynes clearly defines the concept of ‘forced saving,’ which matches The General Theory in the sense both assume the equalization of saving to investment as follows.

3.3.1 Definition of forced saving

Assume that an economy already achieves full-employment equilibrium Thus, the aggregate savingfunction is only an increasing function of the rate of interest Further, the aggregate investment function

is a decreasing function of the rate of interest If the schedule of the investment function adjusts

upward, this raises the rate of interest and induces a corresponding saving increment This increment

is defined as ‘forced saving’ Figure 3.1 illustrates this phenomenon

Fig 3.1 Forced saving

As long as full-employment equilibrium is maintained, the aggregate saving function is

upward-sloping and the investment function is downward-sloping Assume that the investmentschedule adjusts to the right as because of some technological progress associated with a period

of investment growth The equilibrium moves from Point to Thus, the equilibrium rate of

interest becomes costly and this induces additional saving is the calculation of forced saving.Keynes is critical about the ‘forced saving’ theory in the following two senses First, additionalsaving is caused by individuals’ voluntary intentions, so the concept of ‘forced saving’ is misleading.Second, since the ‘forced saving’ theory cannot explain the existence of the imperfect employmentequilibrium, Keynes’s ‘principle of effective demand’ contains more generality

Besides these two critiques, around the end of Chap 7, Keynes introduces the famous saving paradox This paradox says that additional saving aggravates poverty To examine this paradox, let

us apply the principle of effective demand For simplicity, assume that aggregate investment is

exogenously given as , and that aggregate saving is proportional to income Then, from the

equilibrium condition of the goods market, one obtains the equilibrium income as

(3.7)Consider the case that individuals become cautious about their futures and save additional money,which amounts to The new equilibrium condition is

(3.8)

It is apparent from Eqs (3.7) and (3.8) that

(3.9)

holds This is the saving paradox.

Appendix 1: A Solvable Case of the Aggregation Problem Regarding Total Employment

To sum up Keynes’s critique of the aggregation problem , he cannot find significant economic

meaning in an index comprised of the different goods In order to examine this difficulty, we consider

an example of the aggregation procedure when there are multiple-types of goods

Assume that there are types of final goods, and the production function is:

(A.1)where are the volume of output and corresponding employment of jth goods Without the

loss of generality, one can regard the first goods as wage goods and assign them as the numeraire.Then, in accordance with the profit-maximization condition of a firm, one obtains

(A.2)Since total employment is defined as

if the relative price vector is kept constant, total employment is uniquelydetermined as a function of the real wage, , by the following procedure Let the inverse function of

Eq (A.2) be

(A.3)Then, there is which satisfies

(A.4)for any positive given , to the extent that the Inada condition is satisfied Because it is apparent

from Eq (A.4) that is a function of , let us denote this relationship

(A.5)Then, the aggregate supply price can be defined as

Fig 3.2 Derivation of the total employment

As this example shows, unless some affinity exists in both utility and production functions, theaggregation problem becomes unsolvable This is because the aggregate supply price in Eq (A.6)contains not only total employment but also the relative price vector , which relates to the

equilibrium condition for each goods market Although Keynes is skeptical about the concept of ‘thetotal quantity of output,’ if there is only one type of goods in an economy and a change in relative

prices can be neglected, such a concept easily revives and is definable even in the context of The General Theory In other words, without the index number theory that assumes some kind of affinity

in the utility function, tractable aggregation is unfeasible because the aggregation for obtaining a

macroeconomic production function or aggregate supply price function always contains the relative

price vector which determines the allocation of the total employment In The General Theory, Keynes

is too optimistic for this difficulty

The most familiar case in which the relative price vector is kept invariant is when the

functional form of production function is

(A.7)

In such a case, the profit-maximization condition requires

(A.8)Accordingly, in order to keep the relative price vector invariant, the output of every industryshould increase proportionately whenever the price of wage goods, , becomes costly

When the utility function of individuals is homothetic, the expenditure propensity relating to eachgoods remains unchanged and is multiplicatively separable from total expenditure, to the extent thatthe relative price vector remains invariant with the change of the aggregate demand The demandfunction of good becomes

(A.9)Thus, the demand for good also proportionately increases with the aggregate demand,

This implies

(A.10)With regard to Eqs (A.8) and (A.10), if each goods market is in equilibrium,

(A.11)holds If Eq (A.11) has a solution, , the vector is invariant thereafter Consequently, if the

labor-demand function is hyperbolic as in Eq (A.7) which means that the production functions

belongs to the family of square root functions, and the utility function from consumption is homothetic,the aggregation procedure of Keynes is validated because the equilibrium relative price vector isunaffected by the condition of aggregate demand