The General Theory of Employment, Interest and Money

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The General Theory of Employment, Interest and Money
GT Palgrave.jpg
Author John Maynard Keynes
Country United Kingdom
Language English
Genre Nonfiction
Publisher Palgrave Macmillan
Publication date
1936
Media type Print Paperback
Pages 472 (2007 Edition)
ISBN 978-0-230-00476-4
OCLC 62532514

The General Theory of Employment, Interest and Money  of 1936 is the last and most important book by the English economist John Maynard Keynes. It created a profound shift in economic thought, giving macroeconomics a central place in economic theory and contributing much of its terminology[1] – the “Keynesian Revolution”. It had equally powerful consequences in economic policy, being interpreted as providing theoretical support for government spending in general, and for budgetary deficits, monetary intervention and counter-cyclical policies in particular. It is pervaded with an air of mistrust for the rationality of free-market decision making.

Keynes denied that an economy would automatically adapt to provide full employment even in equilibrium, and believed that the volatile and ungovernable psychology of markets would lead to periodic booms and crises. The General Theory  is a sustained attack on the ‘classical’ orthodoxy of its time enlivened by frequent sallies of elegant wit (but weighed down by clumsiness and confusion in its technical passages). It introduced the concepts of the consumption function, the principle of effective demand and liquidity preference, and gave new prominence to the multiplier and the marginal efficiency of capital.

Contents

Keynes’s aims in the General Theory[edit]

The central argument of The General Theory  is that the level of employment is determined not by the price of labour, as in classical economics, but by the spending of money (aggregate demand). Keynes argues that it is wrong to assume that competitive markets will, in the long run, deliver full employment or that full employment is the natural, self-righting, equilibrium state of a monetary economy. On the contrary, underemployment and underinvestment are likely to be the natural state unless active measures are taken. One implication of The General Theory  is that an absence of competition is not the main issue regarding unemployment; even reducing wages or benefits has no major effect.

Keynes sought to do nothing less but upend the conventional economic wisdom. He mailed a letter to his friend George Bernard Shaw on New Year's Day, 1935:

I believe myself to be writing a book on economic theory which will largely revolutionize — not I suppose, at once but in the course of the next ten years — the way the world thinks about its economic problems. I can’t expect you, or anyone else, to believe this at the present stage. But for myself I don’t merely hope what I say,— in my own mind, I’m quite sure.[2]

The first chapter of the General theory  (only half a page long) has a similarly radical tone:

I have called this book the General Theory of Employment, Interest and Money, placing the emphasis on the prefix general. The object of such a title is to contrast the character of my arguments and conclusions with those of the classical theory of the subject, upon which I was brought up and which dominates the economic thought, both practical and theoretical, of the governing and academic classes of this generation, as it has for a hundred years past. I shall argue that the postulates of the classical theory are applicable to a special case only and not to the general case, the situation which it assumes being a limiting point of the possible positions of equilibrium. Moreover, the characteristics of the special case assumed by the classical theory happen not to be those of the economic society in which we actually live, with the result that its teaching is misleading and disastrous if we attempt to apply it to the facts of experience.

Summary of the General Theory[edit]

Keynes’s main theory (including its dynamic elements) is presented in Chapters 2-15, 18, and 22, which are summarised here. A shorter account will be found in the article on Keynesian economics. The remaining chapters of Keynes’s book contain amplifications of various sorts and are described later in this article.

Book I: Introduction[edit]

The first Book of the General Theory  is a repudiation of Say’s Law. The classical view for which Keynes made Say a mouthpiece held that the value of wages was equal to the value of the goods produced, and that the wages were inevitably put back into the economy sustaining demand at the level of current production. Hence, starting from full employment, there cannot be a glut of industrial output leading to a loss of jobs. As Keynes put it on p18, “supply creates its own demand”.

Stickiness of wages in money terms[edit]

Say’s Law depends on the operation of a market economy. If there is unemployment (and if there are no distortions preventing the employment market from adjusting to it) then there will be workers willing to offer their labour at less than the current wage levels, leading to downward pressure on wages and hence on prices.

The classics held that full employment was the equilibrium condition of an undistorted labour market, but they and Keynes agreed in the existence of distortions impeding transition to equilibrium.[3] The classical position had generally been to view the distortions as the culprit and to argue that their removal was the main tool for eliminating unemployment. Keynes on the other hand viewed the market distortions as part of the economic fabric and advocated different policy measures which (as a separate consideration) had social consequences which he personally found congenial and which he expected his readers to see in the same light.

The distortions which have prevented wage levels from adapting downwards have lain in employment contracts being expressed in monetary terms; in various forms of legislation such as the minimum wage and in state-supplied benefits; in the unwillingness of workers to accept reductions in their income; and in their ability through unionisation to resist the market forces exerting downward pressure on them.

Keynes accepted the classical relation between wages and the marginal productivity of labour, referring to it on p5[4] as the ‘first postulate of classical economics’ and summarising it as saying that ‘The wage is equal to the marginal product of labour’.

The first postulate can be expressed in the equation y' (N ) = W / p, where y (N ) is the real output when employment is N, and W  and p  are the wage rate and price rate in money terms. A system can be analysed on the assumption that W  is fixed (i.e. that wages are fixed in money terms) or that W / p is fixed (i.e. that they are fixed in real terms) or that N  is fixed (e.g. if wages adapt to ensure full employment). All three assumptions had at times been made by classical economists.

Keynes proposed a ‘second postulate of classical economics’ asserting that the wage is equal to the marginal disutility of labour. This is an instance of wages being fixed in real terms. He attributes the second postulate to the classics subject to the qualification that unemployment may result from wages being fixed by legislation, collective bargaining, or ‘mere human obstinacy’  (p6), none of which can be identified with the marginal disutility of labour and all of which are likely to fix wages in money terms.

Outline of Keynes’s theory[edit]

Keynes’s economic theory is based on the interaction between demands for saving, investment, and liquidity (i.e. money). Saving and investment are necessarily equal, but different factors influence decisions concerning them. The desire to save, in Keynes’s analysis, is mostly a function of income: the richer people are, the more wealth they will seek to put aside. The profitability of investment, on the other hand, is determined by the relation between the return available to capital and the interest rate. The economy needs to find its way to an equilibrium in which no more money is being saved than will be invested, and this can be accomplished by contraction of income and a consequent reduction in the level of employment.

In the classical scheme it is the interest rate rather than income which adjusts to maintain equilibrium between saving and investment; but Keynes asserts that the rate of interest already performs another function in the economy, that of equating demand and supply of money, and that it cannot adjust to maintain two separate equilibria. In his view it is the monetary role which wins out. This is why Keynes’s theory is a theory of money as much as of employment: the monetary economy of interest and liquidity interacts with the real economy of production, investment and consumption.

Book II: Definitions and ideas[edit]

The choice of units[edit]

Keynes sought to allow for the lack of downwards flexibility of wages by constructing an economic model in which the money supply and wage rates were externally determined (the latter in money terms), and in which the main variables were fixed by the equilibrium conditions of various markets in the presence of these facts.

Many of the quantities of interest, such as income and consumption, are monetary. Keynes often expresses such quantities in wage units (Chapter 4): to be precise, a value in wage units is equal to its price in money terms divided by W, the wage (in money units) per man-hour of labour. Keynes generally writes a subscript w  on quantities expressed in wage units, but in this account we omit the w. When, occasionally, we use real terms for a value which Keynes expresses in wage units we write it in lower case (e.g. y  rather than Y ).

As a result of Keynes’s choice of units, the assumption of sticky wages, though important to the argument, is largely invisible in the reasoning. If we want to know how a change in the wage rate would influence the economy, Keynes tells us on p266 that the effect is the same as that of an opposite change in the money supply.

The identity of saving and investment[edit]

The relationship between saving and investment, and the factors influencing their demands, play an important role in Keynes’s model. Saving and investment are considered to be necessarily equal for reasons set out in Chapter 6 which looks at economic aggregates from the viewpoint of manufacturers. The discussion is intricate, considering matters such as the depreciation of machinery, but is summarised on p63:

Provided it is agreed that income is equal to the value of current output, that current investment is equal to the value of that part of current output which is not consumed, and that saving is equal to the excess of income over consumption... the equality of saving and investment necessarily follows.

This statement incorporates Keynes’s definition of saving, which is the normal one.

Book III: The propensity to consume[edit]

Keynes’s propensities to consume and to save as functions of income Y.

Book III of the General Theory is given over to the propensity to consume, which is introduced in Chapter 8 as the desired level of expenditure on consumption (for an individual or aggregated over an economy). The demand for consumer goods depends chiefly on the income Y and may be written functionally as C (Y ). Saving is that part of income which is not consumed, so the propensity to save S (Y ) is equal to Y – C (Y ). Keynes discusses the possible influence of the interest rate r  on the relative attractiveness of saving and consumption, but regards it as ‘complex and uncertain’ and leaves it out as a parameter.

His seemingly innocent definitions embody an assumption whose consequences will be considered later. Since Y  is measured in wage units, the proportion of income saved is considered to be unaffected by the change in real income resulting from a change in the price level while wages stay fixed. Keynes acknowledges that this is undesirable in Point (1) of Section II. It would be possible to correct it by giving the propensity to consume a form like C (Y, p /W ) where p  is the price level, but Keynes does not do so.

In Chapter 9 he provides a homiletic enumeration of the motives to consume or not to do so, finding them to lie in social and psychological considerations which can be expected to be relatively stable, but which may be influenced by objective factors such as ‘changes in expectations of the relation between the present and the future level of income’ (p95).

The marginal propensity to consume and the multiplier[edit]

The marginal propensity to consume, C '(Y ), is the gradient of the purple curve, and the marginal propensity to save S '(Y ) is equal to 1 – C '(Y ). Keynes states as a ‘fundamental psychological law’ (p96) that the marginal propensity to consume will be positive and less than unity.

Chapter 10 introduces the famous ‘multiplier’ through an example: if the marginal propensity to consume is 90%, then ‘the multiplier k is 10; and the total employment caused by (e.g.) increased public works will be ten times the employment caused by the public works themselves’ (pp116f). Formally Keynes writes the multiplier as k = 1/S '(Y ). It follows from his ‘fundamental psychological law’ that k  will be greater than 1.

Keynes’s account is not intelligible until his economic system has been fully set out (see below). In Chapter 10 he describes his multiplier as being related to the one introduced by R. F. Kahn in 1931,[5] but the two have little in common. The mechanism of Kahn’s mutliplier lies in an infinite series of transactions, each conceived of as creating employment: if you spend a certain amount of money, then the recipient will spend a proportion of what he or she receives, the second recipient will spend a further proportion again, and so forth. Enough meaning can be extracted from Keynes’s account of his own mechanism (in the second para of p117) to see that it makes no reference to infinite series. It also differs from Kahn’s multiplier in being attached to investment rather than to spending in general, and in having a value determined by the marginal propensity to consume rather than by the marginal propensity to spend.

Book IV: The inducement to invest[edit]

The rate of investment[edit]

Keynes’s schedule of the marginal efficiency of capital

Book IV discusses the inducement to invest, with the key ideas being presented in Chapter 11. The ‘marginal efficiency of capital’ is defined as the annual revenue which will be yielded by an extra increment of capital as a proportion of its cost. The ‘schedule of the marginal efficiency of capital’ is the function which, for any rate of interest r, gives us the level of investment which will take place if all opportunities are accepted whose return is at least r. By construction this depends on r  alone and is a decreasing function of its argument; it is illustrated in the diagram, and we shall write it as Is (r ).

This schedule is a characteristic of the current industrial process which Irving Fisher described as representing the ‘investment opportunity side of interest theory’;[6] and in fact the condition that it should equal S (Y,r ) is the equation which determines the interest rate from income in classical theory. Keynes is seeking to reverse the direction of causality (and omitting r  as an argument to S () ).

He interprets the schedule as expressing the demand for investment at any given value of r , giving it an alternative name: “We shall call this the investment demand-schedule...” (p136). He also refers to it as the ‘demand curve for capital’ (p178). However it has many of the properties of a supply curve (for instance not being constrained by income). It is analogous to the curve giving the amount of gold which can be extracted from the soil at a price less than p. It is a decreasing function of r  while a supply curve is an increasing function of p  because the purchase of an investment with return r  is equivalent to the purchase of a perpetual annuity whose price is the reciprocal of r.[7] Nonetheless the schedule of the marginal efficiency of capital was a demand function in Keynes’s eyes.

For fixed industrial conditions, we conclude that ‘the amount of investment... depends on the rate of interest’ as John Hicks put it in “Mr Keynes and the Classics”.

Interest and liquidity preference[edit]

Keynes proposes two theories of liquidity preference (i.e. the demand for money): the first as a theory of interest in Chapter 13 and the second as a correction in Chapter 15. His arguments offer ample scope for criticism, but his final conclusion is that liquidity preference is a function mainly of income and the interest rate. The influence of income (which really represents a composite of income and wealth) is common ground with the classical tradition and is embodied in the Quantity Theory; the influence of interest had also been noted earlier, in particular by Frederick Lavington (see Hicks’s “Mr. Keynes and the Classics”). Thus Keynes’s final conclusion may be acceptable to people who question the arguments along the way. However he shows a persistent tendency to think in terms of the Chapter 13 theory while nominally accepting the Chapter 15 correction.

Chapter 13 presents the first theory in rather metaphysical terms. Keynes argues that:

It should be obvious that the rate of interest cannot be a return to saving or waiting as such. For if a man hoards his savings in cash, he earns no interest, though he saves just as much as before. On the contrary, the mere definition of the rate of interest tells us in so many words that the rate of interest is the reward for parting with liquidity for a specified period.[8]

To which Jacob Viner retorted that:

By analogous reasoning he could deny that wages are the reward for labor, or that profit is the reward for risk-taking, because labor is sometimes done without anticipation or realization of a return, and men who assume financial risks have been known to incur losses as a result instead of profits.[9]

Keynes goes on to claim that the demand for money is a function of the interest rate alone on the grounds that:

The rate of interest is... the “price” which equilibrates the desire to hold wealth in the form of cash with the available quantity of cash...[10]

which, as Frank Knight commented,[11] seems to assume that demand is simply an inverse function of price. The upshot from these reasonings is that:

Liquidity-preference is a potentiality or functional tendency, which fixes the quantity of money which the public will hold when the rate of interest is given; so that if r  is the rate of interest, M  the quantity of money and L  the function of liquidity-preference, we have M  = L(r ). This is where, and how, the quantity of money enters into the economic scheme.[12]

Chapter 15 looks in more detail at the three motives Keynes ascribes for the holding of money: the ‘transactions motive’, the ‘precautionary motive’, and the ‘speculative motive’. He considers that demand arising from the first two motives ‘mainly depends on the level of income’ (p199), while the interest rate is ‘likely to be a minor factor’ (p196).

Keynes treats the speculative demand for money as a function of r  alone without justifying its independence of income. He says that...

what matters is not the absolute  level of r  but the degree of its divergence from what is considered a fairly safe  level...[13]

but gives reasons to suppose that demand will nonetheless tend to decrease as r  increases. He thus writes liquidity preference in the form L1(Y ) + L2(r ) where L1 is the sum of transaction and precautionary demands and L2 measures speculative demand. The structure of Keynes’s expression plays no part in his subsequent theory, so it does no harm to follow Hicks by writing liquidity preference simply as L (Y,r ).

The money supply is treated as fixed and exogenous. This was the normal assumption made by economists at the time and is almost explicit on p200. At no point does Keynes mention ‘repercussions’ on the supply of money or credit arising from changes elsewhere in the economy.

Keynes does not put a subscript ‘w ’ on L or M, implying that we should think of them in money terms. This suggestion is reinforced by his wording on p172 where he says “Unless we measure liquidity-preference in terms of wage-units (which is convenient in some contexts)... ”. But seventy pages later there is a fairly clear statement that liquidity preference and the quantity of money are indeed “measured in terms of wage-units” (p246).

The Keynesian economic system[edit]

Keynes’s economic model[edit]

In Chapter 14 Keynes contrasts the classical theory of interest with his own, and in making the comparison he shows how his system can be applied to explain all the principal economic unknowns from the facts he takes as given. The two topics can be treated together because they are different ways of analysing the same equation.

Keynes’s presentation is informal. To make it more precise we will identify a set of 4 variables – saving, investment, the rate of interest, and the national income – and a parallel set of 4 equations which jointly determine them. The graph illustrates the reasoning. The red S  lines are shown as increasing functions of r  in obedience to classical theory; for Keynes they should be horizontal.

Graphical representation of Keynes’s economic model, based on his own diagram at p180 of the General Theory.

The first equation asserts that the reigning rate of interest   is determined from the amount of money in circulation   through the liquidity preference function and the assumption that L ( ) = .

The second equation fixes the level of investment   given the rate of interest through the schedule of the marginal efficiency of capital as Is ( ).

The third equation tells us that saving is equal to investment: S (Y ) = . The final equation tells us that the income   is the value of Y  corresponding to the implied level of saving.

All this makes a satisfying theoretical system.

Three comments can be made concerning the argument. Firstly, no use is made of the ‘first postulate of classical economics’, which can be called on later to set the price level. Secondly, Hicks (in “Mr Keynes and the classics”) presents his version of Keynes’s system with a single variable representing both saving and investment; so his exposition has three equations in three unknowns.

And finally, since Keynes’s discussion takes place in Chapter 14, it precedes the modification which makes liquidity preference depend on income as well as on the rate of interest. Once this modification has been made the unknowns can no longer be recovered sequentially.

Keynesian economic intervention[edit]

The state of the economy, according to Keynes, is determined by four parameters: the money supply, the demand functions for consumption (or equivalently for saving) and for liquidity, and the schedule of the marginal efficiency of capital determined by ‘the existing quantity of equipment‘ and ‘the state of long-term expectation’ (p246).

Adjusting the money supply is the domain of monetary policy. The effect of a change in the quantity of money is considered at p298. The change is effected in the first place in money units. According to Keynes’s account on p295 (offered as an simplification), in a condition of full employment the wage unit and prices will increase in exact proportion to the money supply; hence there will be inflation but no change in the real economy. But ‘an increase in the quantity of money will have no effect whatever on prices, so long as there is any unemployment’, with the result that for as long as unemployment persists, a change in the money supply will carry through into wage units.

We can then analyse its effect from the diagram, in which we see that an increase in   shifts   to the left, pushing   upwards and leading to an increase in total income (and employment) whose size depends on the gradients of all 3 demand functions. If we look at the change in income as a function of the upwards shift of the schedule of the marginal efficiency of capital (blue curve), we see that as the level of investment is increased by one unit, the income must adjust so that the level of saving (red curve) is one unit greater, and hence the increase in income must be 1 / S' (Y ) units, i.e. k units. This is the explanation of Keynes’s multiplier.

It does not necessarily follow that individual decisions to invest will have a similar effect, since decisions to invest above the level suggested by the schedule of the marginal efficiency of capital are not the same thing as an increase in the schedule.

The equations of Keynesian and classical economics[edit]

Keynes’s initial statement of his economic model (in Chapter 14) is based on his Chapter 13 theory of liquidity preference. His restatement in Chapter 18 doesn’t take full account of his Chapter 15 revision, treating it as a source of ‘repercussions’ rather than as an integral component. It was left to John Hicks to give a satisfactory presentation.[14] Equilibrium between supply and demand of money depends on two variables – interest rate and income – and these are the same two variables as are related by the equation between the propensity to save and the schedule of the marginal efficiency of capital. It follows that neither equation can be solved in isolation and that they need to be considered simultaneously.

The ‘first postulate’ of classical economics was also accepted as valid by Keynes, though not used in the first four books of the General Theory. The Keynesian system can thus be represented by three equations in three variables as shown below, roughly following Hicks.

Three analogous equations can be given for classical economics. As presented below they are in forms given by Keynes himself (the practice of writing r  as an argument to V  derives from his Treatise on money[15]).

Classical Keynesian
y' (N ) = W / p The first postulate Y / ∂N  = 1 / p
is (r ) = s (y (N ),r ) Determination of the interest rate Is (r ) = S (Y ) Determination of income
= P ·y (N ) / V (r ) Quantity theory of money = L (Y ,r ) Liquidity preference
y, is , s  in real terms; in money terms Y, Is , S , , L in wage units

Here y  is written as a function of N, the number of workers employed; p  is the price (in money terms) of a unit of real output; V (r ) is the velocity of money; and W is the wage rate in money terms. N, p  and r  are the 3 variables we need to recover. In the Keynesian system income is measured in wage units and is therefore not fully determined by the level of employment (since it will also vary with prices). The first postulate is written in a form which is only admissible if one allows prices to be represented by a single variable. Strictly it should be modified to take account of the distinction between marginal wage cost and marginal prime cost.[16]

The classics took the second equation as determining the rate of interest, the third as determining the price level, and the first as determining employment. Keynes believed (perhaps incorrectly: see wage unit) that the last two equations could be solved together for Y  and r, which is not possible in the classical system. He accordingly concentrated on these two equations, treating income as ‘almost the same thing’ as employment (p247).

Chapter 3: The principle of effective demand[edit]

The theoretical system we have described is developed over chapters 4–18, and is anticipated by a chapter which – amidst a proliferation of symbols – interprets Keynesian unemployment in terms of ‘aggregate demand’.

The aggregate supply Z  is employers’ outlay when they employ N  workers, written functionally as φ(N ). The aggregate demand D  is their expected proceeds, written as f (N ). In equilibrium Z  = D. D  can be decomposed as D1 + D2  where D1  is the propensity to consume, which may be written C (Y ) or χ(N ). D2  is explained as ‘the volume of investment’, and the equilibrium condition determining the level of employment is that D1 + D2  should equal Z  as functions of N. Presumably we should identify D2  with Is (r ).

The meaning of this seems to be that in equilibrium the total demand for goods must equal total income. Total demand for goods is the sum of demand for consumption goods and demand for investment goods. Hence Y = C (Y ) + S (Y ) = C (Y ) + Is (r ); and this equation determines a unique value of Y  given r.

Samuelson’s Keynesian cross is a graphical representation of the Chapter 3 argument.[17]

Dynamic aspects of Keynes’s theory[edit]

Expectation as determining output and employment[edit]

Chapter 5 makes some common-sense observations on the role of expectation in economics. Short-term expectations govern the level of production chosen by an entrepreneur while long-term expectations govern decisions to adjust the level of capitalisation. Keynes describes the process by which the level of employment adapts to a change in long-term expectations and remarks that:

the level of employment at any time depends... not merely on the existing state of expectation but on the states of expectation which have existed over a certain past period. Nevertheless past expectations, which have not yet worked themselves out, are embodied in to-day’s capital equipment... and only influence [the entrepreneur’s] decisions in so far as they are so embodied...[18]

Expectation as influencing the schedule of the marginal efficiency of capital[edit]

The main role of expectation in Keynes’s theory lies in the schedule of the marginal efficiency of capital which, as we have seen, is defined in Chapter 11 in terms of expected  returns. Keynes differs here from Fisher[19] whom he largely follows, but who defined the ‘rate of return over cost’ in terms of an actual revenue stream rather than its expectation. Keynes was certainly correct in this, and the point has a particular significance in his theory.

The schedule of the marginal efficiency of capital as influencing employment[edit]

Keynes differed from his classical predecessors in assigning a role to the schedule of the marginal efficiency of capital in determining the level of employment. The classics regarded this, as they regarded other supply curves, as simply influencing the allocation of resources. But here too, even from a classical point of view, Keynes can be seen to be correct, at least assuming fixed wage rates. The classics (who had written little about unemployment) had not taken account of Lavington’s observation[20] that interest is the opportunity cost of holding money. They should have reasoned that an increase in the marginal efficiency of capital leads to an increase in the interest rate which increases the cost of holding money and therefore leads to faster circulation; that this has the same effect on prices as an increase in the money supply; and that higher prices at a given wage level lead to higher employment. They might have thought this to be a weak effect, but they could not with consistency have denied its existence.

On the other hand Keynes may have considered the effect to be larger than it really is. He defines his multiplier k  as 1 / S '(Y ), and this gives the response of income to a change in the schedule of the marginal efficiency of capital for a given interest rate. However the interest rate is not given, and Keynes should have looked at the income component of the joint response of income and interest rate to a change in the schedule using his Chapter 15 model of liquidity preference.

In his ‘restatement’ of Chapter 18 (pp248f) he again treats the interest rate as given and discusses the effect of ‘an increase in the rate of investment’, concluding that ‘the ratio... between an increment of investment and the corresponding increment of aggregate income... is given by the multiplier’. He then mentions the ‘repercussions’ arising from changes in liquidity preference due to an increase in employment, thereby treating the role of interest in determining liquidity preference as primary and the role of income as a secondary correction separate from the main analysis. Hansen comments:

But this is wrong. His mistake follows from the fact that he often, perhaps generally, made the rate of interest depend exclusively on liquidity preference and the quantity of money.[21]

Keynes compounds this error when he writes in his reply to Viner that...

...there is always a formula, more or less of this kind, relating the output of consumption-goods which it pays to produce to the output of investment-goods; and I have given attention to it in my book under the name of the multiplier.[22]

This relates the multiplier to the ‘output of consumption-goods’ rather than the output of all  goods and ignores the ‘repercussions’. In fact a different multiplier κ can be defined to relate changes in income to changes in the schedule of the marginal efficiency of capital under the Chapter 15 model of liquidity preference. If the schedule of the marginal efficiency of capital increases by a small unit in the region of the equilibrium position, then income increases by κ units where:

Here 0 ≤ κ ≤ k. The lower bound is attained under a pre-Lavington classical model in which interest  has no effect on liquidity preference, and the upper bound under the Chapter 13 theory in which income  has no effect; in general the position of κ between the extremes will depend on the relative magnitudes of the two influences.

The effect on employment of a change in a single parameter can be analysed only on the assumption that the others remain constant, or that they vary in a determinate way. Keynes is never precise about what assumptions he’s making about the wage rate. It would be rash to assume that it is constant over a trade cycle, but even so his theory may be indicative of behaviour in more realistic circumstances; for instance it may help us to understand the consequences of wages underadapting to changes in the real economy.

Animal spirits[edit]

Chapter 12 discusses the psychology of speculation and enterprise.

Most, probably, of our decisions to do something positive, the full consequences of which will be drawn out over days to come, can only be taken as a result of animal spirits – of a spontaneous urge to action rather than inaction, and not as the outcome of a weighted average of quantified benefits... Thus if the animal spirits are dimmed and spontaneous optimism falters, leaving us to depend on nothing but a mathematical expectation, enterprise will fade and die.[23]

Keynes’s picture of the psychology of speculators is less indulgent.

In point of fact, all sorts of considerations enter into the market valuation which are in no way relevant to the prospective yield... The recurrence of a bank-holiday may raise the market valuation of the British railway system by several million pounds.[24]

(Henry Hazlitt examined some railway share prices and found that they did not bear out Keynes’s assertion.[25])

Keynes considers speculators to be concerned...

...not with what an investment is really worth to a man who buys it ‘for keeps’, but with what the market will value it at, under the influence of mass psychology, three months or a year hence...

This battle of wits to anticipate the basis of conventional valuation a few months hence, rather than the prospective yield of an investment over a long term of years, does not even require gulls amongst the public to feed the maws of the professional;– it can be played by professionals amongst themselves. Nor is it necessary that anyone should keep his simple faith in the conventional basis of valuation having any genuine long-term validity. For it is, so to speak, a game of Snap, of Old Maid, of Musical Chairs – a pastime in which he is victor who says Snap neither too soon nor too late, who passed the Old Maid to his neighbour before the game is over, who secures a chair for himself when the music stops. These games can be played with zest and enjoyment, though all the players know that it is the Old Maid which is circulating, or that when the music stops some of the players will find themselves unseated.

Or, to change the metaphor slightly, professional investment may be likened to those newspaper competitions in which the competitors have to pick out the six prettiest faces from a hundred photographs, the prize being awarded to the competitor whose choice most nearly corresponds to the average preferences of the competitors as a whole; so that each competitor has to pick, not those faces which he himself finds prettiest, but those which he thinks likeliest to catch the fancy of the other competitors, all of whom are looking at the problem from the same point of view. It is not a case of choosing those which, to the best of one’s judgment, are really the prettiest, nor even those which average opinion genuinely thinks the prettiest. We have reached the third degree where we devote our intelligences to anticipating what average opinion expects the average opinion to be. And there are some, I believe, who practise the fourth, fifth and higher degrees.

The trade cycle[edit]

Keynes proposed a theory of the trade cycle in Chapter 22 of the General Theory , basing it on ‘a cyclical change in the marginal efficiency of capital’ induced by ‘the uncontrollable and disobedient psychology of the business world’ (pp313, 317).

The marginal efficiency of capital depends... on current expectations... But, as we have seen, the basis for such expectations is very precarious. Being based on shifting and unreliable evidence, they are subject to sudden and violent changes.[26]

Optimism leads to a rise in the marginal efficiency of capital and increased investment, reflected – through the multiplier – in an even greater increase in employment until ‘disillusion falls upon an over-optimistic and over-bought market‘ which consequently falls with ‘sudden and even catastrophic force’ (p316).

There are reasons, given firstly by the length of life of durable assets... and secondly by the carrying-costs of surplus stocks, why the duration of the downward movement should have an order of magnitude... between, let us say, three and five years.[27]

And a half cycle of 5 years tallies with Jevons’s sunspot cycle length of 11 years.

The writing of the General Theory[edit]

Keynes drew a lot of help from his students in his progress from the Treatise on Money  (1930) to the General Theory  (1936). The Cambridge Circus, a discussion group founded immediately after the publication of the earlier work, reported to Keynes through Richard Kahn, and drew his attention to a supposed fallacy in the Treatise  where Keynes had written:

Thus profits, as a source of capital increment for entrepreneurs, are a widow’s cruse which remains undepleted however much of them may be devoted to riotous living.[28]

The Circus  disbanded in May 1931, but three of its members – Kahn and Austin and Joan Robinson – continued to meet in the Robinsons’ house in Trumpington St. (Cambridge), forwarding comments to Keynes. This led to a ‘Manifesto’ of 1932 whose ideas were taken up by Keynes in his lectures.[29] Kahn and Joan Robinson were well versed in marginalist theory which Keynes did not fully understand at the time (or possibly ever),[30] pushing him towards adopting elements of it in the General Theory. During 1934 and 1935 Keynes submitted drafts to Kahn, Robinson and Roy Harrod for comment.

There has been uncertainty ever since over the extent of the collaboration, Schumpeter describing Kahn’s “share in the historic achievement” as not having “fallen very far short of co-authorship” [31] while Kahn denied the attribution. However, there is a magical element which strikes readers of Kahn’s multiplier or of Robinson’s Introduction[32] which Keynes steers away from in Book IV, taking him closer to the neo-classical interpretation of John Hicks.[33]

Keynes’s method of writing was unusual:

Keynes drafted rapidly in pencil, reclining in an armchair. The pencil draft he sent straight to the printers. They supplied him with a considerable number of galley proofs, which he would then distribute to his advisers and critics for comment and amendment. As he published on his own account, Macmillan & Co., the ‘publishers’ (in reality they were distributors), could not object to the expense of Keynes’ method of operating. They came out of Keynes’ profit (Macmillan & Co. merely received a commission). Keynes’ object was to simplify the process of circulating drafts; and eventually to secure good sales by fixing the retail price lower than would Macmillan & Co.[34]

The advantages of self-publication can be seen from Étienne Mantoux’s review:

When he published The General Theory of Employment, Interest and Money  last year at the sensational price of 5 shillings, J. M. Keynes perhaps meant to express a wish for the broadest and earliest possible dissemination of his new ideas.[35]

Chronology[edit]

Keynes’s work on the General Theory  began as soon as his Treatise on Money  had been published in 1930. He was already dissatisfied with what he had written[36] and wanted to extend the scope of his theory to output and employment.[37] By September 1932 he was able to write to his mother: ‘I have written nearly a third of my new book on monetary theory’.[38]

In autumn 1932 he delivered lectures at Cambridge under the title ‘the monetary theory of production’ whose content was close to the Treatise except in giving prominence to a liquidity preference theory of interest. There was no consumption function and no theory of effective demand. Wage rates were discussed in a criticism of Pigou.[39]

In autumn 1933 Keynes’s lectures were much closer to the General Theory, including the consumption function, effective demand, and a statement of ‘the inability of workers to bargain for a market-clearing real wage in a monetary economy’.[40] All that was missing was a theory of investment.

By spring 1934 Chapter 12 was in its final form.[41]

His lectures in autumn of that year bore the title ‘the general theory of employment’.[42] In these lectures Keynes presented the marginal efficiency of capital in much the same form as it took in Chapter 11, his ‘basic chapter’ as Kahn called it.[43] He gave a talk on the same subject to economists at Oxford in February 1935.

This was the final building block of the General Theory. The book was finished in December 1935[44] and published in February 1936.

Observations on its readability[edit]

Keynes was an associate of Lytton Strachey and shared much of his outlook. According to Hazlitt his “reputation as a great economist rested from the beginning on his purely literary brilliance”,[45] but this quality was belied by the General Theory, which in the words of Étienne Mantoux attained “a degree of obscurity without precedent in his past work”.[46] Frank Knight, another hostile critic, commented on “the exasperating difficulty of following his exposition”.[47]

More significant is the view of writers sympathetic to Keynes. Michel DeVroey comments that “many passages of his book were almost indecipherable”.[48]

Paul Davidson wrote that...

...even after reading the General Theory in 1936, [Paul] Samuelson, perhaps reflecting [Robert] Bryce’s view of the difficulty of understanding Keynes’s book, found the General Theory analysis “unpalatable” and not comprehensible.[49]

Hazlitt quotes Samuelson as saying:

It bears repeating that the General Theory is an obscure book so that would-be anti-Keynesians must assume their position largely on credit unless they are willing to put in a great deal of work and run the risk of seduction in the process.[50]

He declares himself surprised by “Samuelson’s implication that the very obscurity of the book is an embarrassment, not to the disciples of Keynes, but chiefly to his critics”.[51]

Raúl Rojas dissents, saying that “obscure neo-classical reinterpretations” are “completely pointless since Keynes’ book is so readable”.[52]

Differences of interpretation[edit]

Keynes had been an outspoken and iconoclastic commentator on economic policy during the early 1930s, often dissenting from the views of more classically minded figures such as Ralph Hawtrey and A. C. Pigou. In the General theory  he was able to provide a more theoretical justification for the views he had been expressing. In the course of writing it his views matured, and inconsistencies can be seen which may be attributed to their changing in the course of his writing it, or his wishing to maintain continuity with his earlier position, or a desire to be provocative, or (possibly) simple confusion.

Generally the later statements in the book (mostly in Book IV) are less radical than the reader expects from the earlier chapters. For exegetical purposes the later statements need to be given precedence (because these are the ones Keynes supports by considered arguments) but economists are free to interpret the book along the lines they find most satisfactory. The main axis of disagreement between Keynesian interpreters lies in the relative weights they give to Books I and IV. Joan Robinson may be taken as the archetypal Book I Keynesian: she preferred Kalecki to Keynes,[53] ignored the Book IV inducement to invest in her Introduction to the theory of employment, and described Chapter 11 – the point of divergence – as needing to be completely rewritten.[54] John Hicks occupied the opposite extreme, basing his interpretation on Book IV in “Mr Keynes and the classics”, and thereby for the first time making this part of the General theory  intelligible to other economists. He was a relatively faithful interpreter of selected elements of Keynes’s theory while also bringing Keynes close to previous orthodoxy. His reading has been severely criticised by partisans of the more radical elements of Keynes’s thinking. Even Hicks nudges the Book IV doctrine in the direction of Book I.

Both Hicks and Robinson sought to build consistent theories from the discordant elements of the General theory. Alvin Hansen saw no discordance,[55] and Paul Samuelson syncretically combined Books I and IV with ‘classical’ economics without ensuring consistency.[56]

A reason for being influenced by Book I rather than Book IV, besides doctrinal preference, lies in the difficulty of reading the General theory : each part of it has been less influential than its predecessor as readers’ stamina falls away.

Italian Wikipedia contains a Book I interpretation of the Teoria generale.

The demand for investment[edit]

Keynes’s principle of effective demand asserts that only for a particular equilibrium income will demands for saving and investment be equal. The classics had considered that ‘an act of individual saving inevitably leads to a parallel act of investment’ and that the associated demands were therefore essentially the same thing. Keynes declared the classical view to be ‘crude’ [57]  and ‘absurd’ [58]  without explanation and Hazlitt flatly contradicted him saying that ‘normally an act of saving is  an act of investment’ with an equal lack of argument.[59]

The little that Keynes said to clarify his view is summarised below. At least six different accounts (not always mutually exclusive) have been proposed of the gap between the demands for saving and investment.

Explanation based on hoarding[edit]

A natural explanation is that saving can find an outlet in hoarding (the increase in one’s holdings of money) whose demand is not a demand for investment. This was the line pursued by Jacob Viner, who wrote of Keynes that:

He finds fault with the “classical’ economists for their alleged neglect of the gulf between the desire to save and the desire to invest, i.e., for their neglect of “liquidity preferences”... It was a shortcoming of the Ricardian wing of the classical school that... they steadfastly adhered to their position that hoarding was so abnormal a phenomenon as not to constitute a significant contributing factor to unemployment...[60]

Viner quite reasonably doubted that hoarding could play the role he thought Keynes assigned to it. Keynes, in his reply, did not seem to understand why Viner had imagined hoarding to be an important part of his theory.[61] In fact his model of liquidity seems to allow no scope for either the supply or the demand for hoarding: the quantity of money is fixed and each individual person desires to hold a static amount. This may seem surprising given how closely the demand for hoarding matches the properties Keynes attributes to saving, but it would make no sense to include the demand for hoarding in a model without allowing it to be satisfied by a supply; and if both are present, the likely result is that the supply will be balanced against the demand leading to a flow of banknotes from printing presses to stockpiles leaving other economic aggregates untouched.

Supporters as well as critics of Keynes have adopted hoarding explanations. Paul Davidson, after rejecting Samuelson’s reading of the General Theory, reported that a 1977 paper by ‘the perennial renegade’ F. H. Hahn had generalised monetary hoarding to ‘non-reproducible assets’:

Some forty years after Keynes, Hahn rediscovered Keynes’s point that a stable involuntary unemployment equilibrium could exist even in a Walrasian system with flexible wages and prices  whenever there are “resting places for savings in other than reproducible assets”... [since] any non-reproducible asset allows for a choice between employment inducing and non-employment inducing demand.[62]

Joan Robinson, on the other hand, rejected hoarding explanations with characteristic vigour as...

...simply an error... [which] arises, no doubt, from the desire to find where the vanished savings have got to... It is of no use to search for the non-existent savings either in “hoards” or anywhere else.[63]

Of course the mystery is not that savings themselves have gone missing, but that there is a demand to save which is neither the demand for any commodity nor the demand to accumulate money in lieu of spending it.

Explanation based on the endogeneity of money supply[edit]

Hansen suggested that adjustments to the money supply might absorb the gap between demands for saving and investment:

If expectations are favorable for investment, though funds are currently lacking, means of purchase can readily be made available in a society with an elastic money and credit system.[64]

Explanation based on lending[edit]

Lending and borrowing are two sides of the same transaction which necessarily cancel out, and which the classics therefore ignored as playing no part in the economy except in imposing the constraint that the rate of interest must be consistent with their equality. It may be that Keynes saw an excess demand for lending over borrowing as giving rise to a demand for saving which was not the same thing as a demand for investment. He says that:

So long as it is open to the individual to employ his wealth in hoarding or lending money, the alternative of purchasing actual capital assets cannot be rendered sufficiently attractive...[65]

and that:

...there is always an alternative to the ownership of real capital-assets, namely the ownership of money and debts...[66]

A more decisive, though somewhat involved, statement occurs in his discussion of the multiplier on pp128f. He says in a footnote that:

It is often convenient to use the term ‘loan expenditure’ to include the public investment financed by borrowing from individuals and also any other current public expenditure which is so financed. Strictly speaking, the latter should be reckoned as negative saving...[67]

and it is difficult to interpret this as not implying that public demand for borrowing corresponds to a demand for dis-saving – not just for the exchequer (which is immaterial to the level of employment) but for society as a whole.

Explanation based on the separation of roles[edit]

Another possible explanation of the gulf is that when money is lent, the decision to lend is made by the saver and the decision to invest by the borrower, and that these may not conform with each other. This seems to be the assumption made by Frank Knight, who commented that:

It almost seems as if the money which is saved is completely distinct from the money which is lent and borrowed, and that the former, if it ever reaches a bank, or any lending agency, is still kept entirely separate.[68]

The significance of the separation of roles is rejected every bit as forcefully by Keynes himself in §V of Chapter 7.

This explanation too had acceptance among some of Keynes’s ‘Book I’ supporters. Joan Robinson wrote:

Decisions to save and decisions to invest are taken quite independently of each other... Under a completely socialist system the government would decide how much investment was desirable... But in the system under which we live the decision to save and the decision to invest are not bound together, and the motives governing them are quite different... The individual saver has no direct influence upon the rate of investment. If entrepreneurs see a profit to be made by investment, investment will take place, and if they do not it will not. The initiative lies with the entrepreneurs, not with the savers. The savers, as a group, are helpless in the hands of the entrepreneurs...[69]

She treats the equality of saving and investment as arising not through any direct nexus but by the economy expanding or contracting to equalise the amounts (which it cannot do without a significant lag). She doesn’t tell us whether decisions to save are independent of decisions to lend, or whether savers’ decisions to lend are independent of entrepreneurs’ decisions to borrow, or whether entrepreneurs’ decisions to borrow are independent of their decisions to invest.

Hansen mostly follows the separation of roles explanation. He writes that:

Under modern conditions savers and real investors are to a high degree different groups...[70]

This observation would not have been denied by the classics, who nonetheless rejected Hansen’s conclusion. Accepting the role of lending, they saw savers as indirect purchasers of capital (or of the derived revenue streams) through banks and entrepreneurs (who are certainly different groups) in much the same way as customers purchase goods through the retail and production chain.

Explanation based on the gap between plans and reality[edit]

Schumpeter provided the following summary of Keynes’s theory:

Current saving and current investment, being identically equal, cannot determine anything. Planned (ex ante) saving and planned (ex ante) investment determine income (total net output)...[71]

He may have been influenced by Samuelson’s using the terms ‘desired’ and ’planned’ as synonymous.

G. L. S. Shackle later wrote that:

Myrdalian ex ante language would have saved the General Theory from describing the flow of investment and the flow of saving as identically, tautologically equal, and within the same discourse, treating their equality as a condition which may, or not, be fulfilled.[72]

Explanation based on Chapter 11[edit]

The vagueness of Book I is excusable from a Book IV perspective since Book I merely sets the scene. The ‘investment demand schedule’ is finally defined in Chapter 11. The definition is careful and precise, and is recognisably (although Keynes does not draw attention to the fact) the definition of a supply schedule. This leaves Chapter 3 (and the Keynes/Samuelson cross) in the position of adding consumption demand to investment supply in the belief that the sum ought to equal total income. Robinson’s aversion to Chapter 11 is intelligible.

Hicks in this matter straddles Books I and IV.[73] He acknowledges the significance of the schedule of the marginal efficiency of capital, but lets it become “the amount of investment (looked at as demand for capital)”: expressions which are not technical terms and imply more clearly than Keynes did that the schedule is a true demand function. Later he adds income as a parameter to it, justifying doing so by saying that “we can call in question the sole dependence of investment on the rate of interest, which looks rather suspicious...”. Keynes remonstrated mildly.[74]

Samuelson accepts all the elements of Keynes’s theory. He follows the definition of the schedule of the marginal efficiency of capital in some detail, calling it the ‘investment demand curve’ or ‘demand-for-investment schedule’, and unhesitatingly adds it to the true consumption demand function when presenting the Keynes/Samuelson cross.

Chapter 11 not only provides a possible explanation of the gap between demands, it also specifies the size of the gap; and the size is difficult to accommodate under some of the other explanations, especially those based on hoarding and on the ex post / ex ante  distinction.

The multiplier[edit]

Kahn’s multiplier as explained by Samuelson[edit]

The multiplier was introduced to economic theory by Richard Kahn in a 1931 paper[75] cited by Keynes in his own discussion. Kahn’s mechanism is based on the premise that spending creates employment, and concludes that a proportion of the money earned will be spent again creating more employment, and so forth. Robinson, Samuelson and Hansen include it in their accounts. Mantoux wrote “The entire demonstration, it would seem... rests on this function”.

Samuelson explained the multiplier in these terms:

Let’s suppose that I hire unemployed resources to build a $1000 woodshed. My carpenters and lumber producers will get an extra $1000 of income... If they all have a marginal propensity to consume of 2/3, they will now spend $666.67 on new consumption goods. The producers of these goods will now have extra incomes... they in turn will spend $444.44... Thus an endless chain of secondary consumption respending  is set in motion by my primary  investment of $1000.[76]

Samuelson is being arbitrary in describing secondary employment as arising from carpenters’ consumption spending but not from their investment spending, while seeing the chain as being set in motion by a primary investment rather than by primary consumption. If the carpenters spend their remaining $333.33 on housing and infrastructure, the builders of these goods too will have extra incomes; and if Samuelson had instead spent $1000 on Napa Valley wine, it is reasonable to assume that the growers would likewise have spent their revenue on consumption and investment goods giving rise to similar ‘secondary respending’.

Keynes’s multipliers[edit]

There are two slightly incompatible accounts of the multplier in the General Theory : an opaque definition followed by a satirical illustration in Chapter 10 and a perfectly lucid account of its theoretical role in Chapter 18 – the Book IV ‘restatement’. Since it is the theoretical functioning of the multiplier which matters, and since Chapter 18 makes its meaning clear, one is free to dispense with the description in Chapter 10. As we might expect, the earlier account is the more radical, the later the more classical; but in neither is there any sign of an argument based on the repeated spending of the same money as we saw with Kahn and Samuelson.

The Chapter 18 ‘investment multiplier’ simply measures the response of income to a change in a system parameter, namely the schedule of the marginal efficiency of capital. There will be an associated response for employment, and given Keynes’s use of wage units this too can be expressed as a dimensionless constant. It might reasonably be termed the ’employment mulitplier’ and one might well ‘assume (as a first approximation) that the employment multiplier is equal to the investment multiplier’ (p248).

Keynes assigns a value 1 / (1–c ) to his investment multiplier, where c  is the marginal propensity to consume. This is correct under his Chapter 13 theory of liquidity preference but he doesn’t notice that it needs to be modified in the light of his Chapter 15 theory. Kahn’s multiplier must take the value of 1 / (1–x ) where x  is the marginal propensity to spend.

Multiplier triggered by value
Kahn’s arbitrary spending 1 / (1–x )
Chapter 10 investment spending 1 / (1–c )
Chapter 18
(investment)
change in the schedule of the
marginal efficiency of capital
1 / (1–c )
Chapter 18
(employment)
change in the schedule of the
marginal efficiency of capital
no simple
formula

Keynes likewise gives the value of 1 / (1–c ) to his Chapter 10 multiplier without having mentioned liquidity preference (or the schedule of the marginal efficiency of capital) at the time. He describes the multiplier as being set in motion by an ‘increment of investment’ (p117) and gives the example of ‘increased public works’ (p116). He explicitly differentiates it from Kahn’s multiplier, which he terms the ‘employment multiplier’ but which is still not the same as the employment multiplier which might be seen as implicit in Chapter 18.

Although the Chapter 10 multiplier appears to be associated with acts of investment, Keynes also describes it as a ‘logical’ mutliplier which ‘holds good continuously, without time-lag’ [77] suggesting that it is in fact a response to the schedule of the marginal efficiency of capital. It is possible that this chapter was drafted before Keynes had completed the transition from explicit to implicit multipliers, that it was imperfectly adapted to the new theory, and that Keynes was influenced in his rewriting by the desire not to sacrifice the satirical section at the end.

The four multipliers can be summarised in a table.

Keynes makes an exception to the limitation to investment as a trigger for his multiplier in Chapter 10 by generalising this to ‘loan expenditure’ which also includes public dis-saving. The passage justifying this exception has already been quoted:

It is often convenient to use the term ‘loan expenditure’ to include the public investment financed by borrowing from individuals and also any other current public expenditure which is so financed. Strictly speaking, the latter should be reckoned as negative saving...[78]

But if dis-saving is to be included, investment funded by dis-saving should be included twice. It is impossible to say whether Keynes was justified in this generalisation – granting for the sake of argument that borrowing really constitutes net dis-saving – because of the unclarity of the Chapter 10 explanation. Dis-saving cannot play a role in Kahn’s multiplier, and autonomous decisions to invest do not play a part in Keynes’s multiplier of Chapter 18 (although autonomous decisions to save could, since they amount to changes in the propensity to save whereas decisions to invest do not constitute changes to the schedule of the marginal efficiency of capital).

Hansen’s attempted reconciliation[edit]

According to Hansen,[79] the main task of Kahn’s paper was to show that x  – the marginal propensity to spend – was less than one for a variety of reasons, of which only hoarding seems significant, and none of which was available to Keynes. Hansen tries to reconcile the various multipliers.

He recognises that Keynes’s ‘initial investment expenditure’ is not the same thing as the unrestricted initial spending of Kahn’s argument, and tries to bridge the gap by defining ‘investment expenditure’ as including ‘private-consumption outlays’. He justifies this by reference to Keynes’s generalisation of investment to ‘loan expenditure’, writing that:

Whatever the initial increase in expenditure, whether private or public investment or simply an increase in private-consumption outlays resulting from tax reduction... the effect... is the same.[80]

Case c x k
I
2
3
2
3
3
II
2
3
1
IV 1 1
V 0 0 1

But this only makes things worse because Kahn’s multiplier takes no account of how spending is funded and applies to ‘private-consumption outlays’ regardless of where the money comes from. At the same time, if the government funds its own expenditure through borrowing rather than taxation, then even if this expenditure falls legitimately under Keynes’s generalisation, it looks like double counting to also consider the private consumption of consequently untaxed income as a further instance of ‘public expenditure financed by borrowing‘.

Hansen then discusses the numerical value of Kahn’s multiplier in a laborious case-by-case analysis.[81] The third and sixth cases are based on repeated rather than one-off expenditure; the remaining four are summarised in the table on the right. Hansen draws the unexpected conclusion that Kahn’s multiplier should take the value 1 / (1–c ) rather than 1 / (1–x ).

The Book IV multiplier[edit]

The Chapter 18 multiplier is simply an intermediate term in a calculation. Any presentation of Keynesian theory which ignores it, or simply embodies it in equations, is consistent with Keynes’s Book IV since there is no need to focus attention on a single intermediate term. Hicks’s account is a case in point: he says that ‘the third equation becomes the multiplier equation, which performs such queer tricks’ and leaves the matter there.

The role which the multiplier receives in Keynes’s presentation slightly understates its significance. The response of income to changes in the schedule of the marginal efficiency of capital is discussed qualitatively  in Chapters 14 and 22: it is essential to the reasoning of the latter chapter (on the trade cycle) that the magnitude should be appreciable, but this assumption is not stated overtly. The relevance of the multiplier to Keynes’s theory of the trade cycle is more clearly seen in his reply to Viner.[82]

Shackle regarded Keynes’s departure from Kahn’s multiplier as...

...a retrograde step... For when we look upon the Multiplier as an instantaneous functional relation... we are merely using the word Multiplier to stand for an alternative way of looking at the marginal propensity to consume.[83]

Liquidity preference[edit]

The contradictions in Keynes’s doctrine of liquidity occur within Book IV, between Chapters 13 and 15. Keynes never explains why he has two different accounts. It appears that the General Theory  was conceived on the basis of the Chapter 13 theory and that the second theory was added as an afterthought without its consequences being followed through. The ‘restatement’ of the theory in Chapter 18 is notable for its not applying the Chapter 15 correction accurately: one influence on liquidity preference (the rate of interest) is treated as an ‘independent variable’ and the other (income) as acting through a ‘repercussion’.[84] There were no serious obstacles in Keynes’s path, and Hicks showed how to handle the Chapter 15 liquidity preference correctly. What he couldn’t change is the interpretation Keynes placed on his doctrines, which never shook off the picture of the interest rate being purely monetary, with a corresponding assumption that changes in the return on capital took their effect solely on income.

Viner, Knight and Étienne Mantoux understood Keynes as advancing the Chapter 13 view; Hicks and Franco Modigliani who followed him adopted the Chapter 15 generalisation.[85] Hansen recognised that Keynes often wrote as if liquidity preference was a function of interest rate alone, but saw this as a persistent error.

Samuelson accepted ‘the classical theory of interest and capital’ which determines the interest rate from the same equation as Keynes (and Samuelson himself) used to determine the level of employment.

The effect of wage rates on employment[edit]

Resistance to monetary reductions in wages is one of Keynes’s key premises, introduced in Chapter 2. In his discussion of Pigou’s Theory of unemployment  he criticises Pigou’s view ‘that unemployment is primarily due to a wage policy which fails to adjust itself sufficiently to changes in the real demand for labour’. When considering wage rates himself he argues against the desirability of reductions in the real wage firstly  by claiming that the theory he has developed so far shows that they would bring no benefit (Chapter 19 §II), and secondly  by remarks along the lines that ‘there is no means of securing uniform wage reductions’ (ibid.). He kept the second argument ‘on reserve’ (in words attributed to Schumpeter by W. H. Hutt [86]).

Once the wage rate had been absorbed into other quantities through use of the wage unit it disappeared from sight in the General Theory. Keynes doesn’t include it among the ‘independent variables’ listed near the beginning of Chapter 18. Viner took him at his word that there was ‘no place’ for ‘unemployment due to downward-rigidity of money-wages’ in his system. Mantoux came to the opposite conclusion:

It would seem that Keynes acknowledges the necessity of reducing real wages to diminish unemployment.

Robinson denied that reductions in wages would be beneficial. Without providing an analysis (under the Keynesian or any other model) she asserted that when wages fell ‘money incomes fall as much as costs, and money demand is reduced accordingly’. Hansen viewed Keynes as ‘agnostic’ and was so himself.

Modigliani analysed the Keynesian model as developed by Hicks and concluded that ‘except in a limiting case’ it was ‘rigid wages’ which accounted for Keynesian unemployment. The limiting case was that of the liquidity trap.

Inessential chapters[edit]

Chapter 16: Sundry observations on the nature of capital[edit]

§I: Say’s Law[edit]

Keynes reiterates his denial that an act of saving constitutes an act of investment without shedding light on his grounds. The three equations of classical economics were quoted above as follows:

  • y' (N ) = W / p        is (r ) = s (y (N ),r )         = p ·y (N ) / V (r )

The role of Say’s Law in Keynes’s interpretation of them can be seen if we split the second equation into two components:

  • is (r ) = id (y (N ),r )        id (y (N ),r ) = s (y (N ),r )

the first of which asserts the equilibrium between the supply and demand for investment, and the second of which identifies the demand for investment with the desired level of saving. In rejecting the second component Keynes denies that the total demand for goods in an economy is identical with its total income – i.e. that supply creates its own demand – and is therefore able to make their equality an equilibrium condition.

To justify his position Keynes needs to argue that some earnings do not enter into the demand for any commodity (consumption or capital) and he needs to say what the earner intends to do with his or her money which does not constitute the purchase of goods. He says:

An act of individual saving means – so to speak – a decision not to have dinner to-day. But it does not  necessitate a decision to have dinner or to buy a pair of boots a week hence or a year hence or to consume any specified thing at any specified date.[87]

... an individual decision to save does not, in actual fact, involve the placing of any specific forward order for consumption, but merely the cancellation of a present order.[88]

Then he adds that:

The absurd, though almost universal, idea that an act of individual saving is just as good for effective demand as an act of individual consumption, has been fostered by the fallacy... that an increased desire to hold wealth, being much the same thing as an increased desire to hold investments, must, by increasing the demand for investments, provide a stimulus to their production; so that current investment is promoted by individual saving to the same extent as present consumption is diminished.[89]

But he makes no attempt to explain how an absurd view had become ‘almost universal’ or what error its adherents had made. In fact there do exist obvious reasons to consider it absurd, but they are of no help to Keynes. A person may be happy to lend his or her money with no concern for what use the borrower makes of it; but the classics saw lending as cancelled by borrowing (both in supply and demand) and Keynes does not say why this should not be so. Or the person may prefer to accumulate cash, and this is a genuine and serious issue which the classics had been prone to neglect, but which Keynes also excluded from his system. If the classics had wished to take account of hoarding, they might have written something like:

  • id (y ,r,...) = s (y ,r ) – ( hd (...) –   )

where hd (...) is the demand for hoarding with appropriate arguments and   is the rate of change of the money supply. One might simply assume that hoarding was a fixed proportion of saving on the grounds that “the banks keep a certain ratio (about 1 to 9) of ‘cash’ to other assets”.[90] A candidate model for   would be:

  •   = hd (...) + ξ

in which the first component counteracts any inflationary or deflationary effects of hoarding and the second represents an exogenous influence determined by national policies, e.g. inflation targeting or the price of gold.

At any rate, the classics assumed that every penny earned would be lent, spent, or accumulated; that net lending was zero; that spending was split between consumption and capital goods; and that total income was therefore equal to total demand for goods plus total demand for hoarding: and like Keynes they ignored the last factor.[91]

Keynes saw savers as having the same options but came to a different conclusion. It is in this chapter that he wrote that...

...there is always an alternative to the ownership of real capital-assets, namely the ownership of money and debts...[92]

But this is itself problematic: not all saving takes place through lending or hoarding, and the role of saving in Keynes’s theory is qua  saving, i.e. the excess of income over consumption (see above), so is unaffected by its division between lending, hoarding, and the direct purchase of capital goods. A narrower definition would have deprived him of the relation between saving and investment.

Keynes stated his own position quite trenchantly:

If... an act of saving does nothing to improve prospective yield, it does nothing to stimulate investment...[93]

from which it follows that the act of saving performed by a noted economist when he commissions a summerhouse does nothing to stimulate investment except through a possible effect on the schedule of the marginal efficiency of capital.[94]

On the same page Keynes draws attention to the error of...

... believing that the owner of wealth desires a capital-asset as such, whereas what he really desires is its prospective yield.

§ II-IV: The declining yield of capital[edit]

Keynes argues that the value of capital derives from its scarcity and sympathises with ‘the pre-classical doctrine that everything is produced  by labour ’.[95] The preference for direct over roundabout processes will depend on the rate of interest.

He wonders what would happen to ‘a society which finds itself so well equipped with capital that its marginal efficiency is zero’ while money provides a safe outlet for savings. He does not consider this hypothesis far-fetched: on the contrary...

... a properly run community... ought to be able to bring down the marginal efficiency of capital in equilibrium approximately to zero within a single generation...[96]

He asserts that...

... the position of equilibrium, under conditions of laissez-faire, will be one in which employment is low enough and the standard of life sufficiently miserable to bring savings to zero’.[97]

Here he implicitly projects the wages fixed under a positive interest rate into the indefinite future.[98] However his conclusions are not pessimistic because he postulates that steps may be taken to adjust the interest rate to ensure full employment,[99] that ‘enormous social changes would result’ and that ‘this may be the most sensible way of getting rid of many of the objectionable features of capitalism’.[100]

Chapter 17: The essential properties of interest and money[edit]

Keynes begins by defining ‘own rates of interest’. If the market price for purchasing the commitment to supply a bushel of wheat every year in perpetuity was the price of 50 bushels, then the ‘wheat rate of interest’ would be 2%. He then tries to find the property which justifies us in regarding the money rate as the true rate. His arguments didn’t satisfy his supporters[101] who accepted Pigou’s contention that it makes no difference which rate is used.[102]

Hazlitt went further, considering the very concept of an own rate of interest to be ‘one of the most incredible’ of the ‘confusions in the General Theory ’.[103]

Chapter 19: Changes in money wages[edit]

§I: The classical theory[edit]

Keynes begins with a statement that...

... the classical system has been accustomed to rest the supposedly self-adjusting character of the economic system on an assumed fluidity of money-wages; and, where there is rigidity, to lay on this rigidity the blame for maladjustment...

and he continues on the next page saying that...

... this is tantamount to assuming that the reduction in money-wages will leave demand unaffected.

He mentions that some economists might argue this from the quantity theory of money, but it would be...

... more usual to agree that the reduction in money-wages may have some  effect on aggregate demand... but that the real demand of other factors... will be very likely increased...

and he concludes:

It is from this type of analysis that I fundamentally differ.

Then, ignoring the argument from the quantity theory of money, he postulates that the classical position rests on analysing the demand schedule for a given industry and transferring this conception ‘without substantial modification to industry as a whole’.[104] Since he elsewhere criticises the classics for lacking a concept of aggregate demand (‘the theory of effective demand, that is, the demand for output as a whole, having been entirely neglected for more than a hundred years...’ [105] ) they might have felt that Keynes was putting arguments into their mouths. An alternative way of attributing a view to them would be by combining their three equations above.

§II, III: The Keynesian analysis[edit]

Let us, then, apply our own method of analysis to answering the problem. It falls into two parts. (1) Does a reduction in money-wages have a direct tendency, cet. par., to increase employment, ‘cet. par.’ being taken to mean that the propensity to consume, the schedule of the marginal efficiency of capital and the rate of interest are the same as before for the community as a whole? And (2) does a reduction in money-wages have a certain or probable tendency to affect employment in a particular direction through its certain or probable repercussions on these three factors?

The first question we have already answered in the negative in the preceding chapters. For we have shown that the volume of employment is uniquely correlated with the volume of effective demand measured in wage-units, and that the effective demand, being the sum of the expected consumption and the expected investment, cannot change, if the propensity to consume, the schedule of marginal efficiency of capital and the rate of interest are all unchanged.[106]

It is difficult to interpret Keynes’s reference to the schedule of the marginal efficiency of capital remaining unchanged given that it has always been expressed in wage units.[107]

He embarks on a lengthy catalogue, comprising seven items, of ‘repercussions’ arising from a reduction in money wages.[108] The thread of his argument is hard to follow. Keynes conflates two questions: whether unemployment may be due to money wages being higher than is consistent with full employment, and what are the possible side-effects of reducing wages from a level which was initially too high. Observations on the second point are not relevant to the first.

Modigliani later performed a formal analysis (based on Keynes’s theory, but without any certainty that Keynes would have accepted it) and concluded that unemployment was indeed attributable to excessive wages.[109] His results at least did not rely on such speculations as:

On the other hand, if the workers make the same mistake as their employers about the effects of a general reduction, labour troubles may offset this favourable factor...[110]

Of the seven items in his catalogue, Keynes finds that five do not support ‘any hopes of favourable results to employment’, and that those which need further consideration are the effects on the marginal efficiency of capital and on the interest rate.[111] Note that he refers to the ‘marginal efficiency of capital’ – a percentage yield – rather than to its ‘schedule’. He finds that it has little to offer.

Hence:

It is, therefore, on the effect of a falling wage- and price-level on the demand for money that those who believe in the self-adjusting quality of the economic system must rest the weight of their argument; though I am not aware that they have done so... if the quantity of money is virtually fixed, it is evident that its quantity in terms of wage-units can be indefinitely increased by a sufficient reduction in wage units...

An indirect effect of wages on employment through the interest rate was termed a ‘Keynes effect’ by Don Patinkin.

We can, therefore, theoretically at least, produce precisely the same effects on the rate of interest by reducing wages... that we can by increasing the amount of money...[112]

He does not say what those effects are, but does caution that ‘wage reductions, as a method of securing full employment, are also subject to the same limitations as the method of increasing the money supply’:

A moderate reduction in money-wages may prove inadequate, whilst an immoderate reduction might shatter confidence even if it were practicable.[113]

And he summarises:

There is, therefore, no ground for the belief that a flexible wage policy is capable of maintaining a state of continuous full employment;– any more than for the belief that an open-market monetary policy is capable, unaided, of achieving this result. The economic system cannot be made self-adjusting along these lines.[114]

And having come to the view that ‘a flexible wage policy and a flexible money policy come, analytically, to the same thing’, he presents four considerations suggesting that ‘it can only be an unjust person who would prefer a flexible wage policy to a flexible money policy’.[115]

Finally:

In the light of these considerations I am now of the opinion that the maintenance of a stable general level of money-wages is, on a balance of considerations, the most advisable policy...[116]

Axel Leijonhufvud attached particular significance to this chapter, adopting the view in his 1968 book ‘Keynesian economics and the economics of Keynes’ that its omission from the IS-LM  model had pointed Keynesian economics in the wrong direction. He argued that:

His [Keynes’s] followers understandably decided to skip the problematical dynamic analysis of Chapter 19 and focus on the relatively tractable static IS-LM model.[117]

Appendix: Professor Pigou’s ‘Theory of unemployment’[edit]

Pigou’s book was an influence on Keynes, whose opinion of its merits has been subject to debate.[118] It is generally considered ‘immensely convoluted and tedious’ [119] and little read. Pigou’s theory seems to have been an analysis of the ‘first postulate’ in isolation, this equation having only a single variable if written y '(N ) = w  with w  the wage rate (assumed given) in real terms. Keynes finds Pigou to have introduced more variables than equations and sums up:

Thus Professor Pigou believes that in the long run unemployment can be cured by wage adjustments; whereas I maintain that the real wage (subject only to a minimum set by the marginal disutility of employment) is not primarily determined by ‘wage adjustments’ (though these may have repercussions) but by the other forces of the system...[120]

Chapter 20: The employment function[edit]

Chapter 20 is an examination of the supply function. Keynes makes use for the first time of the ‘first postulate of classical economics’, and also for the first time assumes the existence of a unit of value allowing outputs to be compared in real terms. He depends heavily on an assumption of perfect competition. The microeconomic background can be found in a textbook such as Samuelson’s and in Wikipedia articles starting from Supply (economics).

We will begin by looking at the supply function for a single industry on the assumption of fixed wages. This cannot be Keynes’s assumption because the elasticity of wages is one of the quantities he examines, but his model is never specified.

Output for a single industry (fixed wages)[edit]

In perfect competition the supply curve is equal to the marginal cost curve, with the qualification that the latter is normally U-shaped, and that an industry will shut down rather than produce goods under conditions in which the curve is descending, or has not yet ascended sufficiently to yield an adequate return. Since by hypothesis we are considering an industry which has not shut down, we may consider the supply curve to be the same thing as the marginal cost curve and to be increasing.

We use the identifier r  as a suffix to designate the industry under consideration, dropping it when we refer to the economy as a whole (treated as a single large industry).

The microeconomic argument of Keynes’s Chapter 20

For any level of output yr  in real terms, the marginal cost curve shows the cost per additional unit of output for the industry (in real terms). Our first task is to determine is how profits and wages for the industry will vary when output changes. So suppose that the level of supply is initially yr  at a money price pr , and that the output and price increase by Δy  and Δp  respectively. The industry moves to a new point on its supply curve. The increased revenue (in money terms) is split between a component for extra wages equal to the area of the pale blue region in the graph and a component of extra profits equal to the yellow area. Thus the increase in profits is given as:

  • where  is the supply elasticity of price.

is the reciprocal of the commoner price elasticity of supply. (For a brief description of elasticitity in general, see Elasticity (economics)).

The increase in revenue, which is the sum of the pale blue and yellow areas, is therefore equal to , so

Keynes gets a similar result near the top of p283, presenting it in confusing terminology. When the output is expressed in real terms – i.e. when it is equivalent to our yr  – he designates it output  and writes it Or , whereas when it is expressed in wage units he designates it demand  and writes it Dwr  (this meaning has to be inferred from the equation Keynes writes as Or .pwr  = Dwr , e.g. near the bottom of p284).

His eor  is the elasticity of output in real terms with respect to output in wage units, i.e. of Or  with respect to Dwr , described as “the rate at which output in any industry increases when more effective demand in terms of wage-units is directed towards it” (pp282f). Its value is .

Our second task is to see what the supply function tells us about the returns from increased employment. Suppose that the marginal cost curve is flat, i.e. that dp /dy  (or equivalently ) is zero. It follows that marginal cost per unit of output is constant, hence that marginal manpower per unit of output is constant, hence that marginal output per unit of manpower is constant, hence that “there are constant returns in response to increased employment” (p284). Keynes obtains this result in a more complicated way.

Aggregate output (variable wages)[edit]

Keynes now turns to look at ‘industry as a whole’. We can decompose the price into a component denoting the marginal increment of manpower required to produce a further unit of real output and a component representing the money wage rate: .

While Keynes evidently does not consider the wage rate to be constant, he says nothing about how it should be modelled. It makes no sense mathematically to talk of (i.e. of ) except on the assumption that W  is a function of the independent variables; and it makes no sense economically to regard the wage rate as a function of the variables representing a single industry. It would not be valid to give W  the status of a new independent variable because if there is more than one independent variable the derivatives defining Keynes’s elasticities become meaningless through not being partial. Therefore if we are not to regard as constant we must look at the economy as a whole and write as , allowing it to adapt to changes in the level of employment.

Under the decomposition we have adopted for marginal cost there are now two primitive elasticities:

  • .

The first may be described as the supply elasticity of the labour intensity of production; the second is the supply elasticity of the wage rate. We can write , the supply elasticity of price for the economy as a whole, as , and the price elasticity of supply is its reciprocal.

Keynes does not use these values, but instead defines five derived elasticities which can be expressed in terms of them (by means of standard formulae for the differentiation of compound functions). They are as follows:

  1. The elasticity of employment  with respect to output in wage units, i.e. of N  with respect to Dw , written as ee  and equal to .
  2. The elasticity of output in real terms  with respect to output in wage units, i.e. of O  with respect to Dw . This is written eo  and described as “the rate at which output in any industry increases when more effective demand in terms of wage-units is directed towards it” (pp282f). Its value is .
  3. The elasticity of price in wage units  with respect to output in wage units, i.e. of pw  with respect to Dw , written e'p  and described as “the elasticity of the expected price... in response to changes in effective demand” (near the bottom of p284). It is equal to .
  4. The elasticity of price in money units  with respect to output in money units, i.e. of p  with respect to D , written ep  and described as “the elasticity of money-prices in response to changes in effective demand measured in terms of money” (near the middle on p285). .
  5. The elasticity of wages in money units  with respect to output in money units, i.e. of W  with respect to D , written ew  and described as “the elasticity of money-wages in response to changes in effective demand measured in terms of money” (p285). This final elasticity is equal to .

Several properties follow immediately from these definitions.

Legal range of values[edit]

If and are both positive (which isn’t guaranteed) then all of Keynes’s elasticities except ee  must lie between 0 and 1.

Relations between elasticities[edit]

It is true as before that . Keynes interprets this as showing that “effective demand spends itself, partly in affecting output and partly in affecting price” (p285), which in fact is an immediate consequence of the upward slope of the supply curve, and which in turn assumes perfect competition. In practice about 90% of companies report constant or diminishing marginal costs.[121]

We also find that (again on p285). Unfortunately this last equation is subject to a typographical error in some editions of the General Theory, being written as .[122]

Division of revenue[edit]

Noting that we see that:

Hence .

Constant returns to employment[edit]

The condition is equivalent to which is the definition of “constant returns in response to increased employment” (p284).

Keynes’s interpretations[edit]

Keynes provides a little interpretation before the mathematical study we have outlined above and a larger quantity after it.

He begins the chapter by defining the ‘employment function’ F  claiming that it has certain advantages over the ‘ordinary supply curve’, including being applicable to ‘industry and output as a whole... without introducing any of the units which have a dubious quantitative character’ (p281). He also says that:

In the case of the employment function, however, the task of arriving at a function for industry as a whole which will reflect changes in employment as a whole is more practicable.[123]

The considerations he adduces to back this up do not seem to bear on the question. The employment function then disappears from sight and Keynes analyses the supply function using values measured in real terms when appropriate.

He interprets the undoubted relation between output  and employment as a causative relation between demand  and employment. He discusses what happens at full employment (p289) concluding that wages and prices will rise in proportion to any additional expenditure leaving the real economy unchanged, ignoring effects on money supply and liquidity preference.

Chapter 20 makes almost no reference to anything contained in Chapters 5–19 of the General Theory.

Chapter 21: The theory of prices[edit]

The purpose of this chapter is to examine the effect of a change in the quantity of money on the rest of the economy. Keynes does not provide a conclusive statement of his views, but rather presents an initial simplification followed by a number of corrections. Many aspects of his account present difficulties which it is best to consider at the outset.

Preliminary remarks[edit]

Quantity theory and neutrality[edit]

Keynes presents himself as criticising or correcting the quantity theory of money. In the preface to the French edition he says that the book “registers my final escape from the confusions of the Quantity Theory”. But none of his references to the quantity theory make sense if taken literally, whereas all make perfect sense if understood as referring instead to the neutrality of money, a concept which had been introduced to economics in 1931 by Hayek. The word ‘neutrality’ occurs nowhere in the General Theory. Keynes’s interest is not in how total income/output in money terms adjust to changes in money supply, but in how individual measures – prices, wages, employment – are affected. This can be seen from his dismissal of ‘crude quantity theory’ in Chapter 20:

We have reached, that is to say, a situation in which the crude quantity theory of money (interpreting “velocity” to mean “income-velocity”) is fully satisfied; for [real] output does not alter and prices rise in exact proportion to MV.[124]

In Chapter 21 itself he offers a modified version of the quantity theory, saying that it...

... can be enunciated as follows: “So long as there is unemployment, employment  will change in the same proportion as the quantity of money; and when there is full employment, prices  will change in the same proportion as the quantity of money”.[125]

Of course it is no surprise that Keynes rejected the neutrality of money, given his emphasis on contracts fixed in money terms; equally, there is no need for him to address the quantity theory in the present chapter, having already opposed his own liquidity preference theory to it.

Returns to employment[edit]

In Chapter 20 Keynes has said that ‘ordinarily’ there will be decreasing returns to employment (i.e. the marginal cost cuve will slope upwards – see p284). In the initial simplification of the present chapter he says something different:

let us... assume (1) that all unemployed resources are homogeneous and interchangeable in their efficiency to produce what is wanted... In this case we have constant returns... [126]

He later retreats from this in his point (2), but there is a significant technical error which he doesn’t redress: the ascending slope of the marginal cost curve in perfect competition owes little to workforce inhomogenity and much to the decreasing level of capital per unit of labour. In his point (2) he adds inhomogeneity of equipment as a possible cause of decreasing returns, but the changing ratio of labour to capital has nothing to do with inhomogeneity in either factor.

The multiplier[edit]

The multiplier plays a role in this chapter:

(b) the schedule of marginal efficiencies which tells us by how much a given fall in the rate of interest will increase investment, and (c) the investment multiplier which tells us by how much a given increase in investment will increase effective demand as a whole...[127]

Evidently the ‘schedule of marginal efficiencies’ is the schedule of the marginal efficiency of capital and the ‘investment multiplier’ is Keynes’s implicit multiplier of Chapter 18; but, as in the theory of the trade cycle, the correct value to use is κ rather than k.

Effective demand[edit]

Chapter 21 is one of those which make frequent use of the term ‘effective demand’, which undergoes many adventures at Keynes’s hands.

  • In Chapter 3, aggregate demand  is defined as the demand for all goods – consumption and capital – as a function of income. There is a corresponding aggregate demand curve which crosses the aggregate supply curve (i.e. total income/output) at a particular point.
  • In the same chapter, effective demand  is defined as the common value of supply and demand at the point of intersection (p25). It is as much a supply as a demand so the term is misleading. Being the point of intersection of two curves it cannot have a curve of its own.
  • In the reply to Viner effective demand is simply a synonym for aggregate demand: “effective demand, that is the demand for output as a whole...”
  • In Chapter 20, effective demand has usually been a synonym for total output, i.e. aggregate supply. It has a curve – the supply curve – and has the Δ operator applied to it.
  • This is also its usual meaning in Chapter 21, as in the sentence quoted above concerning the multiplier.
  • On p299 of this chapter Keynes flirts with the idea that effective demand differs from total income through being an expectation: “effective demand corresponds to the income the expectation of which has set production moving, not the actually realised income...”.
  • When he comes to interpret his results, Keynes again reverts to the definition of effective demand as aggregate demand, and as causing  the level of output rather than as being the same thing: “When a further increase in the quantity of effective demand produces no further increase in output...” (p303).
  • Where Keynes has four distinct meanings for effective demand Hazlitt rather fancifully posits a fifth: “aggregate or effective demand turns out to be, for all practical purposes, synonymous with the money supply”.[128]
Assumptions concerning wage behaviour[edit]

Wages are exogenous in Keynes’s system. In order to obtain a determinate result for the response of prices or employment to a change in money supply he needs to make an assumption about how wages will react. His initial assumption is that so long as there is unemployment workers will be content with a constant money wage, and that when there is full employment they will demand a wage which moves in parallel with prices and money supply.

His corrected explanation (point (4), p301) is that as the economy approaches full employment, wages will begin to respond to increases in the money supply. Wage inflation remains a function of the level of employment, but is now a progressive response rather than a sharp corner.

Keynes’s assumptions in this matter had a significant influence on the subsequent fate of his theories.

Keynes’s initial simplification and his corrections[edit]

Keynes’s simplified starting point is now easy to summarise. Assuming that an increase in the money supply  leads to a proportional increase in income in money terms  (which is the quantity theory of money), it follows that for as long as there is unemployment wages will remain constant, the economy will move to the right along the marginal cost curve (which is flat) leaving prices and profits unchanged, and the entire extra income will be absorbed by increased employment; but once full employment has been reached, wages, prices (and also profits) will increase in proportion to the money supply. This is the ‘modified quantity theory of money’ mentioned previously.

Keynes now moves on to his corrections.

(1) Quantity theory of money[edit]

Keynes does not, of course, accept the quantity theory. “Effective demand [meaning money income] will not” – he tells us – “change in exact proportion to the quantity of money” (p296).

The correction (p298) is based on the mechanism we have already described under Keynesian economic intervention. Money supply influences the economy through liquidity preference, whose dependence on the interest rate leads to direct effects on the level of investment and to indirect effects on the level of income through the multiplier. This account has the fault we have mentioned earlier: it treats the influence of r  on liquidity preference as primary and that of Y  as secondary and therefore ends up with the wrong formula for the multiplier. However once we correct Keynes’s correction we see that he makes a valid point since the effect of money supply on income is no longer one of proportionality, and cannot be one of proportionality so long as part of the demand for money (the speculative part) is independent of the level of income.

(2) Movement along the supply curve[edit]

Keynes reminds us that the marginal cost curve is not in fact flat (while he is not quite accurate about the reasons for this).

(3), (4) Premature motion of wages[edit]

Keynes’s point (4) has also already been mentioned, stating that the response of wages to the economy reaching full employment will not be abrupt but instead graduated. He also remarks as point (3) that some classes of worker may be fully employed while there is unemployment amongst others (expressing the observation in rather vague wording which might apply to ‘specialised unemployed resources’ other than labour).

(5) Components of marginal cost[edit]

Although we have treated an employer’s marginal cost as being his or her wage bill, this is not entirely accurate. Keynes isolates user cost  as a separate component, identifying it as “the marginal disinvestment in equipment due to the production of marginal output” (p67). His point (5), which may be considered a technical detail, is that user cost is unlikely to move in exact parallel with wages.

Asymmetry of Keynes’s assumptions[edit]

Keynes mentions in §V that there is an asymmetry in his system deriving from the stickiness he postulates in wages which makes it easier for them to move upwards than downwards. Without resistance to downward motion, he tells us, money wages would fall without limit ‘whenever there was a tendency for less than full employment’ and:

... there would be no resting-place below full employment until either the rate of interest was incapable of falling further or wages were zero. In fact we must have some  factor, the value of which in terms of money is, if not fixed, at least sticky, to give us any stability of values in a monetary system.

He doesn’t say what’s wrong with a resting place at full employment.

Symbolic statement of Keynes’s theory of prices[edit]

In §VI Keynes draws on the mathematical results of his previous chapter. Money supply is now being introduced as an independent variable, and as before we must remark that if there is more than one independent variable Keynes’s definitions of his elasticities become meaningless. But this need not happen: we may regard money supply as the sole independent variable, total real output y  as varying in accordance with it, and prices, wages and employment as being related to output in the same way as in Chapter 20, allowing his previous results to hold.

Constant velocity of circulation[edit]

Keynes begins with the equation MV = D  where:

M  is the quantity of money, V  its income-velocity (this definition differing in the minor respects indicated above from the usual definition) and D  the effective demand...

and where ‘effective demand’ is quite nakedly the total output/income in money terms. This equation is useful to Keynes only under the assumption that V  is constant, from which it follows that output in money terms D  moves in proportion to M  and that prices will do the same only if they move in proportion to output in money terms, i.e. only if Keynes’s ep  is unity. If this condition holds then it follows from the formulae for ep  and above that is infinite and therefore that the price elasticity of supply is zero. Keynes gets an equivalent result by a different path using one of his relations between elasticities.

So his conclusion is that if the velocity of circulation is constant, then prices move in proportion to money supply only in conditions in which real output is also constant.

Variable velocity of circulation[edit]

Keynes begins by defining a new elasticity:

  • .

ed  differs from the other elasticities in not being a property of the supply curve. The elasticity of Dw  – i.e. of Y  – with respect to M  is determined by the gradients of the preference functions in Keynes’s theory of employment, L (), S (), and Is (). ed  is determined jointly by these things and by the elasticity of D  with respect to Dw  but is not analysed here.

Keynes proceeds to consider the response of prices to a change in money supply asserting that:

  • .

ep  had been defined earlier and is now incorrectly equated to when its true value has already been given as . This is presumably the ‘inadequate derivation of the equations on page 305’ mentioned by the editors of the RES edition on p385. The likeliest explanation is that Keynes wrote this part while working with a definition of eo  as the elasticity of output in real terms with respect to employment  rather than with respect to output in wage units.[129]

None of this gets us very far since the response of prices to money is being explained in terms of an elasticity ed  which is itself unanalysed.

The Phillips curve[edit]

Keynes’s empirical assumption of the dependence of wage behaviour on the level of employment plays only a small role in Chapter 21. He could easily have dispensed with it.

He says on p299 that “if we have all the facts before us, we shall have enough simultaneous equations to give us a determinate result” without telling us what are the facts whose absence stands in our way. Hazlitt observes: “Of course if we have all the facts we shall have all the facts”.[130] A possible, but highly conjectural, interpretation is that Keynes would have liked to set up equations with a similar flavour to those in Mr Keynes and the Classics but could not see a way to do so, and was forced into an unnecessarily concrete assumption about workforce behaviour through being unable to give his ideas a sufficiently abstract expression.

At any rate he attributes remarkable meekness to the workforce in supposing that they will be content with fixed wages in the presence of rising prices. Lerner rejected this assumption in the 40’s, after which a succession of models were constructed of wage behaviour, many associated with the Phillips curve. Since the relation between government and trades unions is viewed as an adversarial game, the adoption by one player of a simplistic model of the behaviour of the other is unlikely to lead to successful strategies.

The models needed frequent correction and the standing of Keynesian theory suffered. Geoff Tily wrote ruefully:

Finally, the most destructive step of all was Samuelson’s and [Robert] Solow’s incorporation of the Phillips curve into ‘Keynesian’ theory in a manner which traduced not only Phillips but also Keynes’s careful work in the General Theory, Chapter 21, substituting for its subtlety an immutable relationship between inflation and employment. The 1970s combination of inflation and stagnating economic activity was at odds with this relationship, and therefore ‘Keynesianism’, and by association Keynes were rejected. Monetarism was merely waiting in the wings for this to happen.[131]

The declining yield of capital[edit]

Perhaps forgetting that he had already written a section on the topic, and that he had then welcomed a decline in the return to capital as a means of “getting rid of many of the objectionable features of capitalism” (p221), Keynes devotes another section to the subject, this time doubting the possibility of taking steps “to ensure that the rate of interest is consistent with the rate of investment which corresponds to full employment” (p220).

The acuteness and the peculiarity of our contemporary problem arises, therefore, out of the possibility that the average rate of interest which will allow a reasonable average level of employment is one so unacceptable to wealth-owners that it cannot be readily established merely by manipulating the quantity of money. So long as a tolerable level of employment could be attained on the average of one or two or three decades merely by assuring an adequate supply of money in terms of wage-units, even the nineteenth century could find a way. If this was our only problem now – if a sufficient degree of devaluation is all we need – we, to-day, would certainly find a way.

But the most stable, and the least easily shifted, element in our contemporary economy has been hitherto, and may prove to be in future, the minimum rate of interest acceptable to the generality of wealth-owners... If, in conditions of tolerable average employment, this net yield [i.e. the return on capital] turns out to be infinitesimal, time-honoured methods may prove unavailing.[132]

Reception[edit]

Keynes did not set out a detailed policy program in The General Theory, but he went on in practice to place great emphasis on the reduction of long-term interest rates[133] and the reform of the international monetary system[134] as structural measures needed to encourage both investment and consumption by the private sector. Paul Samuelson said that the General Theory "caught most economists under the age of 35 with the unexpected virulence of a disease first attacking and decimating an isolated tribe of South Sea islanders."[135]

Praise[edit]

Many of the innovations introduced by The General Theory continue to be central to modern macroeconomics. For instance, the idea that recessions reflect inadequate aggregate demand and that Say's Law (in Keynes's formulation, that "supply creates its own demand") does not hold in a monetary economy. President Richard Nixon famously said in 1971 (ironically, shortly before Keynesian economics fell out of fashion) that "We are all Keynesians now", a phrase often repeated by Nobel laureate Paul Krugman (but originating with anti-Keynesian economist Milton Friedman, said in a way different from Krugman's interpretation).[136] Nevertheless, starting with Axel Leijonhufvud, this view of Keynesian economics came under increasing challenge and scrutiny[137] and has now divided into two main camps.

The majority new consensus view, found in most current text-books and taught in all universities, is New Keynesian economics, which accepts the neoclassical concept of long-run equilibrium but allows a role for aggregate demand in the short run. New Keynesian economists pride themselves on providing microeconomic foundations for the sticky prices and wages assumed by Old Keynesian economics. They do not regard The General Theory itself as helpful to further research. The minority view is represented by post-Keynesian economists, all of whom accept Keynes's fundamental critique of the neoclassical concept of long-run equilibrium, and some of whom think The General Theory has yet to be properly understood and repays further study.

In 2011, the book was placed on Time's top 100 non-fiction books written in English since 1923.[138]

Criticisms[edit]

From the outset there has been controversy over what Keynes really meant. Many early reviews were highly critical. The success of what came to be known as "neoclassical synthesis" Keynesian economics owed a great deal to the Harvard economist Alvin Hansen and MIT economist Paul Samuelson as well as to the Oxford economist John Hicks. Hansen and Samuelson offered a lucid explanation of Keynes's theory of aggregate demand with their elegant 45° Keynesian cross diagram while Hicks created the IS-LM diagram. Both of these diagrams can still be found in textbooks. Post-Keynesians argue that the neoclassical Keynesian model is completely distorting and misinterpreting Keynes' original meaning.

Just as the reception of The General Theory was encouraged by the 1930s experience of mass unemployment, its fall from favour was associated with the ‘stagflation’ of the 1970s. Although few modern economists would disagree with the need for at least some intervention, policies such as labour market flexibility are underpinned by the neoclassical notion of equilibrium in the long run. Although Keynes explicitly addresses inflation, The General Theory does not treat it as an essentially monetary phenomenon or suggest that control of the money supply or interest rates is the key remedy for inflation, unlike neoclassical theory.

Lastly, Keynes' economic theory was criticized by Marxist-oriented economists, who said that Keynes ideas, while good intentioned, cannot work in the long run due to the contradictions in capitalism. A couple of these, that Marxians point to are the idea of full employment, which is seen as impossible under private capitalism; and the idea that government can encourage capital investment through government spending, when in reality government spending could be a net loss on profits.

Further reading[edit]

Introductions[edit]

The earliest attempt to write a student guide was Robinson (1937) and the most successful (by numbers sold) was Hansen (1953). These are both quite accessible but adhere to the Old Keynesian school of the time. An up-to-date post-Keynesian attempt, aimed mainly at graduate and advanced undergraduate students, is Hayes (2006), and an easier version is Sheehan (2009). Paul Krugman has written an introduction to the 2007 Palgrave Macmillan edition of The General Theory.[136]

Journal articles[edit]

Books[edit]

  • Amadeo, Edward (1989). The principle of effective demand. Aldershot UK and Brookfield US: Edward Elgar.
  • Ambrosi, Gerhard Michael (2003). Keynes. Pigou and Cambridge Keynesians, London: Palgrave Macmillan.
  • Chick, Victoria (1983). Macroeconomics after Keynes. Oxford: Philip Allan.
  • Davidson, Paul (1972). Money and the Real World. London: Macmillan.
  • Davidson, Paul (2002). Financial markets, money and the real world. Cheltenham UK and Northampton US: Edward Elgar.
  • Hansen, Alvin (1953). A Guide To Keynes. New York: McGraw Hill.
  • Harcourt, Geoff and Riach, Peter (eds.) (1997). A 'Second Edition’ of The General Theory. London: Routledge.
  • Hayes, Mark (2006). The economics of Keynes: a New Guide to The General Theory. Cheltenham UK and Northampton US: Edward Elgar.
  • Hazlitt, Henry (1959). The Failure of the New Economics. Princeton, NJ: Van Nostrand.
  • Keynes, John Maynard (1936). The General Theory of Employment, Interest and Money. London: Macmillan (reprinted 2007).
  • Lawlor, Michael (2006). The economics of Keynes in historical context. London: Palgrave Macmillan.
  • Leijonhufvud, Axel (1968). Keynesian economics and the economics of Keynes. New York: Oxford University Press.
  • Markwell, Donald (2006). John Maynard Keynes and International Relations: Economic Paths to War and Peace. Oxford: Oxford University Press.
  • Markwell, Donald (2000). Keynes and Australia. Sydney: Reserve Bank of Australia.
  • Minsky, Hyman (1975). John Maynard Keynes. New York: Columbia University Press.
  • Patinkin, Don (1976). Keynes's monetary thought. Durham NC: Duke University Press.
  • Robinson, Joan (1937). Introduction to the theory of employment. London: Macmillan.
  • Sheehan, Brendan (2009). Understanding Keynes' General Theory. London: Palgrave Macmillan.
  • Tily, Geoff (2007). Keynes's General Theory, the Rate of Interest and ‘Keynesian’ Economics. London: Palgrave Macmillan.
  • Trevithick, James (1992). Involuntary unemployment. Hemel Hempstead: Simon & Schuster.

External links[edit]

References[edit]

  1. ^ Olivier Blanchard, Macroeconomics updated  (2011), p580.
  2. ^ Cassidy, Johnson (10 October 2011). "The Demand Doctor". The New Yorker. 
  3. ^ See for instance Pigou’s evidence to the 1930 Macmillan Committee cited on p194 of Richard Kahn’s, “The Making of Keynes’ General Theory ”.
  4. ^ Page numbers refer to the edition published for the Royal Economic Society as Vol VII of the Collected Writings. These appear to agree with the original edition.
  5. ^ See Kahn’s “The Making of Keynes’ General Theory”, Fourth lecture, part 1.
  6. ^ ”The theory of interest...”, p155, quoted by Keynes, p141.
  7. ^ Keynes himself remarks on the fallaciousness of ‘believing that the owner of wealth desires a capital-asset as such, whereas what he really desires is its prospective yield ’. p212.
  8. ^ pp166f.
  9. ^ “Mr Keynes on the causes of unemployment”, Quarterly Journal of Economics, 1936.
  10. ^ p167.
  11. ^ “Unemployment: and Mr. Keynes’s revolution in economic theory”, Canadian Journal of Economics, 1937, p112.
  12. ^ p168.
  13. ^ p201.
  14. ^ “Mr Keynes and the classics.”
  15. ^ Robert Dimand, “The origins of the Keynesian revolution”, p7.
  16. ^ See Appendix to Keynes’s Chapter 19.
  17. ^ P. A. Samuelson, “Economics: an introductory analysis”, 1948 and many subsequent editions.
  18. ^ p50.
  19. ^ Theory of interest.
  20. ^ Frederick Lavington, “The English capital market” (1921), cited in “Mr Keynes and the classics”.
  21. ^ Alvin Hansen, “Guide to Keynes” (1953) pp165f.
  22. ^ See below.
  23. ^ p161.
  24. ^ pp152, 154.
  25. ^ The Failure of the New Economics  (1959) p177.
  26. ^ p315.
  27. ^ p317.
  28. ^ Kahn, “The making of Keynes’ General Theory ” (1984), p106.
  29. ^ M. C. Marcuzzo, “The Collaboration between J. M. Keynes and R. F. Kahn from the Treatise  to the General Theory ”, History of Political Economy, June 2002, p435.
  30. ^ M. C. Marcuzzo, op. cit. p441.
  31. ^ “History of economic analysis”, 1954.
  32. ^ Joan Robinson, “Introduction to the theory of employment”, 1937.
  33. ^ See particularly the final sentence of §I of Chapter 18 of the General Theory, where Keynes seems to step back from claiming that the multiplier can be used to reduce unemployment. Hicks presented his interpretation in “Mr. Keynes and the classics”, reprinted in “Critical essays in monetary theory” (1967).
  34. ^ Kahn, op. cit., p171.
  35. ^ Translated in Henry Hazlitt (ed.), “The critics of Keynesian economics”, 1960.
  36. ^ Dimand, op. cit., p163.
  37. ^ Dimand, op. cit., p87.
  38. ^ Letter cited from Collected writings  by Kahn, op. cit., p112.
  39. ^ Dimand, op. cit., pp152f, 155.
  40. ^ Dimand, op. cit., pp162, 166.
  41. ^ Kahn, op. cit., p114.
  42. ^ Dimand, op. cit., p172.
  43. ^ Op. cit., chapter title.
  44. ^ Kahn, op. cit., p112.
  45. ^ “The critics of Keynesian economics”, p9.
  46. ^ “Mr. Keynes’ General Theory”, trans. in H. Hazlitt, op. cit., p97.
  47. ^ Frank Knight, “Unemployment: And Mr. Keynes's Revolution in Economic Theory”, p113, Canadian Journal of Economics, 1937.
  48. ^ “Dead or Alive? The Ebbs and Flows of Keynesianism Over the History of Macroeconomics” in Thomas Cate (ed). “Keynes’s General Theory Seventy-five years later“ (2012).
  49. ^ “Samuelson and the Keynes/Post-Keynesian revolution...” (2007), citing D. C. Colander and H. Landreth, “The Coming of Keynesianism To America”, p159.
  50. ^ “The failure of the ‘New Economics’ ” (1959), p89.
  51. ^ “The failure of the ‘New Economics’ ”, pp2f, quoting “The development of economic thought”, ed. by Henry William Spiegel, 1952.
  52. ^ “The Keynesian Model in the General Theory: A Tutorial”, (2012).
  53. ^ Joan Robinson and John Eatwell, “An introduction to modern economics”.
  54. ^ Kahn, op. cit., p256.
  55. ^ A guide to Keynes, 1953.
  56. ^ P. A. Samuelson, “Economics: an introductory analysis”, 1948 and many subsequent editions.
  57. ^ p19.
  58. ^ p210.
  59. ^ Op. cit., p220.
  60. ^ “Mr. Keynes on the causes of unemployment” in Hazlitt, op. cit., p51.
  61. ^ Reply to Viner.
  62. ^ “Samuelson and the Keynes/Post-Keynesian revolution...” (2007), citing Hahn, “Keynesian Economics and General Equilibrium Theory” in “The Microfoundations of Macroeconomics”, ed. by G. C. Harcourt. Davidson gives Hahn an erroneous middle initial. The term ‘perennial renegade’ is Gonçalo L. Fonseca’s.
  63. ^ Introduction to the theory of employment, pp15f.,
  64. ^ op. cit., p27.
  65. ^ p160.
  66. ^ p212.
  67. ^ pp128f.
  68. ^ “Unemployment: And Mr. Keynes's Revolution in Economic Theory”, in Hazlitt, op. cit..
  69. ^ pp9, 10, 13.
  70. ^ op. cit., p154; see also p32.
  71. ^ “History of economic analysis” (1954).
  72. ^ "What did the General Theory do?" (1989), in J. Pheby (ed), “New Directions in Post-keynesian Economics”.
  73. ^ “Mr Keynes and the classics.”
  74. ^ Kahn, op. cit., p160.
  75. ^ “The Relation of Home Investment to Unemployment”, The Economic Journal.
  76. ^ 16th edition consulted.
  77. ^ p122.
  78. ^ pp128f.
  79. ^ op. cit., p89.
  80. ^ p90, footnote.
  81. ^ pp90–96.
  82. ^ See above.
  83. ^ “Time in economics” (1958), cited by G. M. Ambrosi, “Keynes, Pigou and the Cambridge Keynesians” (2003).
  84. ^ Alvin Hansen, “Guide to Keynes” pp165f.
  85. ^ Hazlitt, op. cit., for Mantoux and Modigliani.
  86. ^ Hazlitt, op. cit.
  87. ^ Opening sentence.
  88. ^ p211.
  89. ^ p211.
  90. ^ Robinson, op. cit., p72.
  91. ^ See Hazlitt, Failure of the new economics, p223.
  92. ^ p212.
  93. ^ p212.
  94. ^ ‘Unemployment: is there a principal cause’ by Bernard Schmitt, in M. Baranzini and A. Cencini, eds., ‘Inflation and Unemployment: Contributions to a New Macroeconomic Approach’ (1996), p79.
  95. ^ p213.
  96. ^ p220.
  97. ^ p218.
  98. ^ Hazlitt, Failure of the new economics, p225.
  99. ^ p220.
  100. ^ p221.
  101. ^ Lawrence Klein, Ph.D. thesis, 1944 (the basis of his ‘Keynesian revolution’, 1947), p120; Hansen, op. cit., p159; Abba Lerner, ‘The essential properties of interest and money’, Quarterly Journal of Economics, 1952, cited by Hansen.
  102. ^ Review of the General Theory, Economica, 1936, cited by Klein.
  103. ^ Op. cit., p237.
  104. ^ p259.
  105. ^ Reply to Viner, op. cit.
  106. ^ pp260f. The expression ‘schedule of marginal efficiency...’ rather than ‘schedule of the  marginal efficiency...’ is presumably a typo.
  107. ^ ‘The ratio, thus determined, between an increment of investment and the corresponding increment of aggregate income, both measured in wage-units, is given by the investment multiplier.’ p248.
  108. ^ pp262-264.
  109. ^ See Mr Keynes and the Classics.
  110. ^ p264.
  111. ^ p265.
  112. ^ p266.
  113. ^ p267.
  114. ^ Id.
  115. ^ Id.
  116. ^ p270.
  117. ^ Peter Howitt, English draft of entry on Leijonhufvud’s book for the Darroz ‘Dictionnaire des grandes oeuvres économiques’.
  118. ^ See Ambrosi, op. cit.
  119. ^ Allin Cottrell “Keynes’s Appendix to Chapter 19: A Reader’s Guide,” History of Political Economy, 1994.
  120. ^ p278.
  121. ^ See cost curve.
  122. ^ The formula is incorrect in the RES edition (consulted), where it may have originated, and is not mentioned in the list of printing errors on p385 there.
  123. ^ p281.
  124. ^ p289.
  125. ^ pp296f.
  126. ^ p295.
  127. ^ p298.
  128. ^ Op. cit., p298.
  129. ^ Cf. ‘Integrating the Formal, Technical, Mathematical Foundations of Keynes’s D-Z Model...’ by Michael Brady and Carmine Gorga (2009).
  130. ^ Op. cit., p307.
  131. ^ ‘Keynes’s General Theory, the Rate of Interest and ‘Keynesian’ Economics’ (2007).
  132. ^ pp308f.
  133. ^ See Tily (2007)
  134. ^ See Davidson (2002)
  135. ^ Samuelson 1946, p. 187.
  136. ^ a b Krugman, Paul. "Introduction to the General Theory". www.pkarchive.org. Retrieved 25 December 2008. 
  137. ^ See Leijonhufvud (1968), Davidson (1972), Minsky (1975), Patinkin (1976), Chick (1983), Amadeo (1989), Trevithick (1992), Harcourt and Riach (1997), Ambrosi (2003), Lawlor (2006), Hayes (2006), Tily (2007)
  138. ^ "All-Time 100 Nonfiction Books". Time. 30 August 2011.