Pigou’s Theory of Unemployment

January 7, 2020

Pigou makes the volume of employment to depend on two factors:

1. The real rates of wages for which workpeople stipulate

2. The shape of the Real Demand Function for Labour

His work determines the shape of the latter function.

The fact that workpeople in fact stipulate, not for a real rate of wages, but for a money-rate, is not ignored; but, in effect, it is assumed that the actual money-rate of wages divided by the price of wage-goods can be taken to measure the real rate demanded.

The equations which, as he says, “form the starting point of the enquiry” into the Real Demand Function for Labour are given in his Theory of Unemployment, p. 90.

Since the tacit assumptions, which govern the application of his analysis, slip in near the outset of his argument, I will summarise his treatment up to the crucial point. Professor Pigou divides industries into those “engaged in making wage-goods at home and in making exports the sale of which creates claims to wage-goods abroad” and the “other” industries= which it is convenient to call the wage-goods industries and the non-wage-goods industries respectively. He supposes x men to be employed in the former and y men in the latter. The output in value of wage-goods of the x men he calls F(x); and the general rate of wages F’(x). This, though he does not stop to mention it, is tantamount to assuming that marginal wage-cost is equal to marginal prime cost.[1]

Further, he assumes that x + y = φ(x), i.e. that the number of men employed in the wage-goods industries is a function of total employment. He then shows that the elasticity of the real demand for labour in the aggregate (which gives us the shape of our quaesitum, namely the Real Demand Function for Labour) can be written Er = (φ’(x)/φ(x)) . (F’(x)/F’’(x)) So far as notation goes, there is no significant difference between this and my own modes of expression. In so far as we can identify Professor Pigou’s wage-goods with my consumption-goods, and his “other goods” with my investment-goods, it follows that his (F(x)/F’(x)), being the value of the output of the wage-goods industries in terms of the wage-unit, is the same as my Cw. Furthermore, his function φ is (subject to the identification of wage-goods with consumption-goods) a function of what I have called above the employment multiplier k'.

For Δx = k’Δy , so that φ’(x) = 1 + (1/k’) . Thus Professor Pigou’s “elasticity of the real demand for labour in the aggregate” is a concoction similar to some of my own, depending partly on the physical and technical conditions in industry (as given by his function F) and partly on the propensity to consume wage-goods (as given by his function φ); provided always that we are limiting ourselves to the special case where marginal labour-cost is equal to marginal prime cost. To determine the quantity of employment, Professor Pigou then combines with his “real demand for labour”, a supply function for labour. He assumes that this is a function of the real wage and of nothing else.

But, as he has also assumed that the real wage is a function of the number of men x who are employed in the wage-goods industries, this amounts to assuming that the total supply of labour at the existing real wage is a function of x and of nothing else. That is to say, n = χ(x), where n is the supply of labour available at a real wage F’(x). Thus, cleared of all complication, Professor Pigou’s analysis amounts to an attempt to discover the volume of actual employment from the equations x + y = φ(x) and n = χ(x) . But there are here three unknowns and only two equations. It seems clear that he gets round this difficulty by taking n = x + y. This amounts, of course, to assuming that there is no involuntary unemployment in the strict sense, i.e. that all labour available at the existing real wage is in fact employed.

In this case x has the value which satisfies the equation φ(x) = χ(x) ; and when we have thus found that the value of x is equal to (say) n1, y must be equal to χ(n1) - n1, and total employment n is equal to χ(n1). It is worth pausing for a moment to consider what this involves. It means that, if the supply function of labour changes, more labour being available at a given real wage (so that n1+dn, is now the value of x which satisfies the equation φ(x) =χ(x)), the demand for the output of the non-wage-goods industries is such that employment in these industries is bound to increase by just the amount which will preserve equality between φ(n1 + dn1) and χ(n1+dn1). The only other way in which it is possible for aggregate employment to change is through a modification of the propensity to purchase wage-goods and non-wage-goods respectively such that there is an increase of y accompanied by a greater decrease of x.

The assumption that n = x + y means, of course, that labour is always in a position to determine its own real wage. Thus, the assumption that labour is in a position to determine its own real wage, means that the demand for the output of the non-wage-goods industries obeys the above laws. In other words, it is assumed that the rate of interest always adjusts itself to the schedule of the marginal efficiency of capital in such a way as to preserve full employment. Without this assumption Professor Pigou’s analysis breaks down and provides no means of determining what the volume of employment will be. It is, indeed, strange that Professor Pigou should have supposed that he could furnish a theory of unemployment which involves no reference at all to changes in the rate of investment (i.e. to changes in employment in the non-wage-goods industries) due, not to a change in the supply function of labour, but to changes in (e.g.) either the rate of interest or the state of confidence. His title the “Theory of Unemployment” is, therefore, something of a misnomer.

His book is not really concerned with this subject. It is a discussion of how much employment there will be, given the supply function of labour, when the conditions for full employment are satisfied. The purpose of the concept of the elasticity of the real demand for labour in the aggregate is to show by how much full employment will rise or fall corresponding to a given shift in the supply function of labour. Or — alternatively and perhaps better — we may regard his book as a non-causative investigation into the functional relationship which determines what level of real wages will correspond to any given level of employment.

But it is not capable of telling us what determines the actual level of employment; and on the problem of involuntary unemployment it has no direct bearing. If Professor Pigou were to deny the possibility of involuntary unemployment in the sense in which I have defined it above, as, perhaps, he would, it is still difficult to see how his analysis could be applied. For his omission to discuss what determines the connection between x and y, i.e. between employment in the wage-goods and non-wage-goods industries respectively, still remains fatal. Moreover, he agrees that within certain limits labour in fact often stipulates, not for a given real wage, but for a given money-wage. But in this case the supply function of labour is not a function of F’(x) alone but also of the money-price of wage-goods; — with the result that the previous analysis breaks down and an additional factor has to be introduced, without there being an additional equation to provide for this additional unknown.

The pitfalls of a pseudo-mathematical method, which can make no progress except by making everything a function of a single variable and assuming that all the partial differentials vanish, could not be better illustrated. For it is no good to admit later on that there are in fact other variables, and yet to proceed without re-writing everything that has been written up to that point. Thus if (within limits) it is a money-wage for which labour stipulates, we still have insufficient data, even if we assume that n = x + y, unless we know what determines the money-price of wage-goods. For, the money-price of wage-goods depend on the aggregate amount of employment. Therefore, we cannot say what aggregate employment will be, until we know the money-price of wage-goods; and we cannot know the money-price of wage-goods until we know the aggregate amount of employment. We are, as I have said, one equation short. Yet it might be a provisional assumption of a rigidity of money-wages, rather than of real wages, which would bring our theory nearest to the facts. For example, money-wages in Great Britain during the turmoil and uncertainty and wide price fluctuations of the decade 1924-1934 were stable within a range of 6 per cent., whereas real wages fluctuated by more than 20 per cent. A theory cannot claim to be a general theory, unless it is applicable to the case where (or the range within which) money-wages are fixed, just as much as to any other case. Politicians are entitled to complain that money-wages ought to be highly flexible; but a theorist must be prepared to deal indifferently with either state of affairs.

A scientific theory cannot require the facts to conform to its own assumptions. When Professor Pigou comes to deal expressly with the effect of a reduction of money-wages, he again, palpably (to my mind), introduces too few data to permit of any definite answer being obtainable. He begins by rejecting the argument (op. cit. p. 101) that, if marginal prime cost is equal to marginal wage-cost, non-wage-earners’ incomes will be altered, when money-wages are reduced, in the same proportion as wage-earners’, on the ground that this is only valid, if the quantity of employment remains unaltered — which is the very point under discussion. But he proceeds on the next page (op. cit. p. 102) to make the same mistake himself by taking as his assumption that “at the outset nothing has happened to non-wage-earners’ money-income”, which, as he has just shown, is only valid if the quantity of employment does not remain unaltered — which is the very point under discussion. In fact, no answer is possible, unless other factors are included in our data. The manner in which the admission, that labour in fact stipulates for a given money-wage and not for a given real wage (provided that the real wage does not fall below a certain minimum), affects the analysis, can also be shown by pointing out that in this case the assumption that more labour is not available except at a greater real wage, which is fundamental to most of the argument, breaks down. For example, Professor Pigou rejects (Op. cit. p. 75) the theory of the multiplier by assuming that the rate of real wages is given, i.e. that, there being already full employment, no additional labour is forthcoming at a lower real wage. Subject to this assumption, the argument is, of course, correct.

But in this passage Professor Pigou is criticising a proposal relating to practical policy; and it is fantastically far removed from the facts to assume, at a time when statistical unemployment in Great Britain exceeded 2,000,000 (i.e. when there were 2,000,000 men willing to work at the existing money-wage), that any rise in the cost of living, however moderate, relatively to the money-wage would cause the withdrawal from the labour market of more than the equivalent of all these 2,000,000 men. It is important to emphasise that the whole of Professor Pigou’s book is written on the assumption that any rise in the cost of living, however moderate, relatively to the money-wage will cause the withdrawal from the labour market of a number of workers greater than that of all the existing unemployed. Moreover, Professor Pigou does not notice in this passage (Op. cit. p. 75) that the argument, which he advances against “secondary” employment as a result of public works, is, on the same assumptions, equally fatal to increased “primary” employment from the same policy. For if the real rate of wages ruling in the wage-goods industries is given, no increased employment whatever is possible except, indeed, as a result of non-wage-earners reducing their consumption of wage-goods. For those newly engaged in the primary employment will presumably increase their consumption of wage-goods which will reduce the real wage and hence (on his assumptions) lead to a withdrawal of labour previously employed elsewhere.

Yet Professor Pigou accepts, apparently, the possibility of increased primary employment. The line between primary and secondary employment seems to be the critical psychological point at which his good common sense ceases to overbear his bad theory. The difference in the conclusions to which the above differences in assumptions and in analysis lead can be shown by the following important passage in which Professor Pigou sums up his point of view= “With perfectly free competition among workpeople and labour perfectly mobile, the nature of the relation (i.e. between the real wage-rates for which people stipulate and the demand function for labour) will be very simple. There will always be at work a strong tendency for wage-rates to be so related to demand that everybody is employed. Hence, in stable conditions everyone will actually be employed. The implication is that such unemployment as exists at any time is due wholly to the fact that changes in demand conditions are continually taking place and that frictional resistances prevent the appropriate wage adjustments from being made instantaneously.”[2]

He concludes (op. cit. p. 253) that unemployment is primarily due to a wage policy which fails to adjust itself sufficiently to changes in the real Jemand function for labour. Thus Professor Pigou believes that in the long run unemployment can be cured by wage adjustments;[3] 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, some of which (in particular the relation between the schedule of the marginal efficiency of capital and the rate of interest) Professor Pigou has failed, if I am right, to include in his formal scheme. Finally, when Professor Pigou comes to the “Causation of Unemployment” he speaks, it is true, of fluctuations in the state of demand, much as I do. But he identifies the state of demand with the Real Demand Function for Labour, forgetful of how narrow a thing the latter is on his definition.

For the Real Demand Function for Labour depends by definition (as we have seen above) on nothing but two factors, namely (1) the relationship in any given environment between the total number of men employed and the number who have to be employed in the wage-goods industries to provide them with what they consume, and (2) the state of marginal productivity in the wage-goods industries.

Yet in Part V. of his Theory of Unemployment fluctuations in the state of “the real demand for labour” are given a position of importance. The “real demand for labour” is regarded as a factor which is susceptible of wide short-period fluctuations (op. cit. Part V. chaps. vi.-xii.), and the suggestion seems to be that swings in “the real demand for labour” are, in combination with the failure of wage policy to respond sensitively to such changes, largely responsible for the trade cycle.

To the reader all this seems, at first, reasonable and familiar. For, unless he goes back to the definition, “fluctuations in the real demand for labour” will convey to his mind the same sort of suggestion as I mean to convey by “fluctuations in the state of aggregate demand”. But if we go back to the definition of the “real demand for labour”, all this loses its plausibility.

For we shall find that there is nothing in the world less likely to be subject to sharp short-period swings than this factor. Professor Pigou’s “real demand for labour” depends by definition on nothing but F(x), which represents the physical conditions of production in the wage-goods industries, and φ(x), which represents the functional relationship between employment in the wage-goods industries and total employment corresponding to any given level of the latter. It is difficult to see a reason why either of these functions should change, except gradually over a long period. Certainly there seems no reason to suppose that they are likely to fluctuate during a trade cycle. For F(x) can only change slowly, and, in a technically progressive community, only in the forward direction; whilst φ(x) will remain stable, unless we suppose a sudden outbreak of thrift in the working classes, or, more generally, a sudden shift in the propensity to consume.

I should expect, therefore, that the real demand for labour would remain virtually constant throughout a trade cycle. I repeat that Professor Pigou has altogether omitted from his analysis the unstable factor, namely fluctuations in the scale of investment, which is most often at the bottom of the phenomenon of fluctuations in employment. I have criticised at length Professor Pigou’s theory of unemployment not because he seems to me to be more open to criticism than other economists of the classical school; but because his is the only attempt with which I am acquainted to write down the classical theory of unemployment, precisely. Thus it has been incumbent on me to raise my objections to this theory in the most formidable presentment in which it has been advanced.

Author’s Footnotes

1. The source of the fallacious practice of equating marginal wage-cost to marginal prime cost may, perhaps, be found in an ambiguity in the meaning of marginal wage-cost. We might mean by it the cost of an additional unit except additional wage-cost; or we might mean the additional wage-cost involved in producing an additional unit of output in the most economical way with the help of the existing equipment and other unemployed factors. In the former case we are precluded from combining with the additional labour any additional entrepreneurship or working capital or anything else other than labour which would add to the cost; and we are even precluded from allowing the additional labour to wear out the equipment any faster than the smaller labour force would have done.

Since in the former case we have forbidden any element of cost other than labour cost to enter into marginal prime-cost, it does, of course, follow that marginal wage-cost and marginal prime-cost are equal. But the results of an analysis conducted on this premiss have almost no application, since the assumption on which it is based is very seldom realised in practice. For we are not so foolish in practice as to refuse to associate with additional labour appropriate additions of other factors, in so far as they are available, and the assumption will, therefore, only apply if we assume that all the factors, other than labour, are already being employed to the utmost. 2. Op. Cit. p. 252. 3. There is no hint or suggestion that this comes about through reactions on the rate of interest.