Finance:Keynes’s theory of wages and prices

Keynes’s theory of wages and prices is contained in the three chapters 19-21 comprising Book V of the General theory. Chapters 20 and 21 are particularly difficult to read, and all three chapters have generally been given a subordinate role in presentations of Keynesian theory.

The role of Book V in Keynes’s theory

Kahn describes 9 chapters out of 24 (all in the first four books) as comprising the ‘real kernel’ of the General Theory, but then adds that they should be read ‘together with’ Chapters 19 and 21.

Chapter 19 discusses the question of whether wage rates contribute to unemployment. Keynes’s views and intentions on this matter have been vigorously debated, and he does not offer a clear answer in this chapter. The concept of the Keynes effect arises from his attempts to resolve the issue.

Chapter 20 covers some mathematical ground needed for Chapter 21. Keynes himself advises that “those who (rightly) dislike algebra will lose little by omitting the first section of this chapter” (p280), a dispensation which has been gratefully siezed but which conceals a pitfall since a critical assumption is buried in one of the formulae.

Chapter 21 considers the question of how a change in income resulting from an increase in money supply will be apportioned between wages, prices, employment and profits. No conclusive result is obtained nor should one be expected, since the consequences depend on the exogenous behaviour of the workforce and on the shapes of various functions.

Similar considerations arise within the body of Keynes’s theory since an increase in income due to a change in the schedule of the marginal efficiency of capital will have an equally complicated effect. When the topic arose in Chapter 18 Keynes did not mention that a full analysis needed the methods of Book V; instead he rather misleadingly asserted that ‘the amount of employment’ was ‘almost the same thing’ as the national income (p247). They are different things but under suitable assumptions they move together. Schumpeter and Hicks appear to have taken Keynes’s comment more literally than it was meant, concluding from it that the General Theory  analysed a time period too short for prices to adapt, which deprives it of any interest.

Brady and Gorga view Chapters 20 and 21 as providing belated elucidation of the ‘mumbo-jumbo’ of aggregate demand presented earlier in the book, particularly in Chapter 3.

See the General theory for an outline of the main components of Keynes’s theory as set out in Books I-IV.

Chapter 19: Changes in money wages

§I: The classical theory

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’. 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...’ ) 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 the three equations of classical macroeconomics.

§II, III: The Keynesian analysis

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.

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.

He embarks on a lengthy catalogue, comprising seven items, of ‘repercussions’ arising from a reduction in money wages. 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. 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...

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. 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...

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.

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.

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’.

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...

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.

Appendix: Professor Pigou’s ‘Theory of unemployment’

Pigou’s book was an influence on Keynes, whose opinion of its merits has been subject to debate. It is generally considered ‘immensely convoluted and tedious’  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...

Chapter 20: The employment function

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, which indeed is implicit in the ‘first postulate’. An important difference is that when competition is not perfect, “it is marginal revenue, not price, which determines the output of the individual producer”. The microeconomic background can be found in a textbook such as Samuelson’s and in Wikipedia articles starting from Supply (economics) and Elasticity (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 made explicit.

Output for a single industry (fixed wages)

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 y_r  in real terms, the marginal cost curve shows the cost per additional unit of output for the industry (in real terms). The first task in this analysis is to determine how profits and wages for the industry will vary when output changes. So suppose that the level of supply is initially y_r  at a money price p_r, 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:

• [math]\displaystyle{ \Delta \textrm{(profit)} = y_r \Delta p = y_r \Delta y \frac{\textrm d p}{\textrm d y} = \epsilon_r p_r \Delta y \qquad }[/math]where[math]\displaystyle{ \qquad \epsilon_r = \frac{\textrm d p}{\textrm d y}\frac{y_r}{p_r} }[/math]  is the supply elasticity of price.

[math]\displaystyle{ \epsilon_r }[/math] is the reciprocal of the commoner price elasticity of supply.

The increase in revenue, which is the sum of the pale blue and yellow areas, is therefore equal to [math]\displaystyle{ (1\!+\!\epsilon_r ) p_r \Delta y }[/math], so

• [math]\displaystyle{ \Delta \textrm{(profit)} = \frac{\epsilon_r}{1\!+\!\epsilon_r} \Delta \textrm{(revenue)}. }[/math]

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 y_r – he designates it output  and writes it O_r, whereas when it is expressed in wage units he designates it effective demand  and writes it D_wr (as has to be inferred from the equation O_r.p_wr = D_wr, e.g. near the bottom of p284). In money terms it is D_r.

His e_or is the elasticity of output in real terms with respect to output in wage units, i.e. of O_r with respect to D_wr, 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 [math]\displaystyle{ 1/(1\!+\!\epsilon_r) }[/math].

The second task in this analysis 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 [math]\displaystyle{ \epsilon_r }[/math]) 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)

Keynes now turns to look at ‘industry as a whole’. We can decompose the price [math]\displaystyle{ p(y) }[/math] (equal to the marginal cost) into a component [math]\displaystyle{ \nu(y) }[/math] denoting the increment of manpower required to produce a further unit of real output ([math]\displaystyle{ \nu(y) = 1 / y'(N) }[/math]) and a component [math]\displaystyle{ W(y) }[/math] representing the money wage rate: [math]\displaystyle{ p(y) = \nu(y) W(y) }[/math].

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 [math]\displaystyle{ \Delta p }[/math] (i.e. of [math]\displaystyle{ \Delta(\nu W) }[/math]) 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 [math]\displaystyle{ W }[/math] the status of a new independent variable because if there is more than one independent variable then the derivatives defining Keynes’s elasticities become meaningless through not being partial. Therefore if we are not to regard [math]\displaystyle{ W }[/math] as constant we must look at the economy as a whole and write [math]\displaystyle{ W }[/math] as [math]\displaystyle{ W(y) }[/math], 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:

• [math]\displaystyle{ \epsilon_\nu = \frac{\textrm{d} \nu(y)}{\textrm{d} y} \frac{y}{\nu(y)}\qquad \epsilon_W = \frac{\textrm{d} W(y)}{\textrm{d} y} \frac{y}{W(y)} }[/math].

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 [math]\displaystyle{ \epsilon }[/math], the supply elasticity of price for the economy as a whole, as [math]\displaystyle{ \epsilon= \epsilon_\nu + \epsilon_W }[/math], 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 D_w, written as e_e and equal to [math]\displaystyle{ y \nu(y)/\bigl(N(1\!+\!\epsilon_{\nu})\bigr) }[/math].
2. The elasticity of output in real terms  with respect to output in wage units, i.e. of O  with respect to D_w. This is written e_o 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 [math]\displaystyle{ 1/(1\!+\!\epsilon_{\nu}) }[/math].
3. The elasticity of price in wage units  with respect to output in wage units, i.e. of p_w with respect to D_w, 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 [math]\displaystyle{ \epsilon_{\nu}/(1\!+\!\epsilon_{\nu}) }[/math].
4. The elasticity of price in money units  with respect to output in money units, i.e. of p  with respect to D , written e_p 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). [math]\displaystyle{ e_p = (\epsilon_{\nu}+\epsilon_W)/(1+\epsilon_{\nu}+\epsilon_W) }[/math].
5. The elasticity of wages in money units  with respect to output in money units, i.e. of W  with respect to D , written e_w 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 [math]\displaystyle{ \epsilon_W/(1+\epsilon_{\nu}+\epsilon_W) }[/math].

Several properties follow immediately from these definitions.

Legal range of values

If [math]\displaystyle{ \epsilon_{\nu} }[/math] and [math]\displaystyle{ \epsilon_W }[/math] are both positive (which isn’t guaranteed) then all of Keynes’s elasticities except e_e must lie between 0 and 1.

Relations between elasticities

It is true as before that [math]\displaystyle{ e'_p + e_o = 1 }[/math]. Keynes interprets this as showing that “effective demand spends itself, partly in affecting output and partly in affecting price” (p285).

We also find that [math]\displaystyle{ e_p = 1 - e_o(1-e_w) }[/math] (again on p285). Unfortunately this last equation is subject to a typographical error in some editions of the General Theory, being written as [math]\displaystyle{ e_p = 1 = e_o(1-e_w) }[/math].

Division of revenue

Noting that [math]\displaystyle{ D_w = y \nu(y) }[/math] we see that:

• [math]\displaystyle{ \Delta D_w = y \Delta \nu(y) + \nu(y) \Delta y = (1\!+\!\epsilon_\nu)\,\nu(y) \Delta y }[/math]
• [math]\displaystyle{ \Delta (\textrm{profit}_w) = y \Delta \bigl(p(y)/W(y)\bigr) = \epsilon_\nu \nu(y) \Delta y }[/math]

Hence [math]\displaystyle{ \Delta (\textrm{profit}_w) = (1\!-\!e_o)\Delta D_w }[/math].

Constant returns to employment

The condition [math]\displaystyle{ e_o=1 }[/math] is equivalent to [math]\displaystyle{ \epsilon_{\nu}=1 }[/math] which is the definition of “constant returns in response to increased employment” (p284).

Keynes’s interpretations

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.

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 effective 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. The money supply remains constant in wage units and the rate of interest is unaffected.

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

Chapter 21: The theory of prices

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

Quantity theory and neutrality

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.

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”.

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

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...

He later retreats from this in his point (2), but there is a significant technical error which he doesn’t correct: 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

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...

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

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 posits a fifth: “aggregate or effective demand turns out to be, for all practical purposes, synonymous with the money supply”.

Some of the confusion in Keynes's writing has a simple explanation. In a 1934 draft of the General Theory  effective demand had been defined as expected aggregate demand – i.e. in accordance with what later appears to be a flirtation. The definition as the intersection with aggregate supply was adopted later in its place. Evidently some of the General Theory  still follows the old definition.

Assumptions concerning wage behaviour

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

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

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

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

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

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.

Antecedents of Keynes’s theory

Keynes’s theory bears a close (but unacknowledged) similarity to Kahn’s account in his famous 1931 multiplier paper. Kahn had made “no claims of originality”, suggesting that it was the “very obviousness” of his theory “which accounts for its being so persistently overlooked”. He had written:

The price-level and output of home-produced consumption goods, just like the price and output of any single commodity, are determined by the conditions of supply and demand.

Keynes wrote:

In a single industry its particular price-level depends partly on the rate of remuneration of the factors of production which enter into its marginal cost, and partly on the scale of output. There is no reason to modify this conclusion when we pass to industry as a whole.

Kahn assumed constant money wages (p175) and never portrayed the supply curve as a demand curve.

Asymmetry of Keynes’s assumptions

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.

Presumably he means that away from full employment wages would fall without limit, and without getting any closer to full employment.

Symbolic statement of Keynes’s theory of prices

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

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 e_p is unity. If this condition holds then it follows from the formulae for e_p and [math]\displaystyle{ \epsilon }[/math] above that [math]\displaystyle{ \epsilon_\nu+\epsilon_W }[/math] 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

Keynes begins by defining a new elasticity:

• [math]\displaystyle{ e_d = \frac{M}{D} \frac{\textrm d D}{\textrm d M} }[/math].

e_d differs from the other elasticities in not being a property of the supply curve. The elasticity of D_w – 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 I_s(). e_d is determined jointly by these things and by the elasticity of D  with respect to D_w but is not analysed here.

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

• [math]\displaystyle{ \frac{M}{p} \frac{\textrm d p}{\textrm d M} = e_p \cdot e_d\qquad\textrm{where}\qquad e_p = 1 - e_e e_o(1-e_w) }[/math].

e_p had been defined earlier and is now incorrectly equated to [math]\displaystyle{ 1 - e_e e_o(1-e_w) }[/math] when its true value has already been given as [math]\displaystyle{ 1 - e_o (1-e_w) }[/math]. 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 e_o as the elasticity of output in real terms with respect to employment  rather than with respect to output in wage units.

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

The declining yield of capital

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 with a monitory tone.

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.