Chapter 20

THE EMPLOYMENT FUNCTION
 

I

In chapter 3 (Chapter 3 ) we have defined the aggregate supply function Z  = f(N), which relates the employment N with the aggregate supply price of the corresponding output. The employment function only differs from the aggregate supply function in that it is, in effect, its inverse function and is defined in terms of the wage-unit; the object of the employment function being to relate the amount of the effective demand, measured in terms of the wage-unit, directed to a given firm or industry or to industry as a whole with the amount of employment, the supply price of the output of which will compare to that amount of effective demand. Thus if an amount of effective demand D_wr, measured in wage-units, directed to a firm or industry calls forth an amount of employment N_r in that firm or industry, the employment function is given by N_r  =  F_r(D_wr). Or, more generally, if we are entitled to assume that D_wr is a unique function of the total effective demand D_w, the employment function is given by N_r  = F_r(D_w) That is to say, N_r men will be employed in industry r when effective demand is D_w.

We shall develop in this chapter certain properties of the employment function. But apart from any interest which these may have, there are two reasons why the substitution of the employment function for the ordinary supply curve is consonant with the methods and objects of this book. In the first place, it expresses the relevant facts in terms of the units to which we have decided to restrict ourselves, without introducing any of the units which have a dubious quantitative character. In the second place, it lends itself to the problems of industry and output as a whole, as distinct from the problems of a single industry or firm in a given environment, more easily than does the ordinary supply curve¾for the following reasons.

The ordinary demand curve for a particular commodity is drawn on some assumption as to the incomes of members of the public, and has to be re-drawn if the incomes change. In the same way the ordinary supply curve for a particular commodity is drawn on some assumption as to the output of industry as a whole and is liable to change if the aggregate output of industry is changed. When, therefore, we are examining the response of individual industries to changes in aggregate employment, we are necessarily concerned, not with a single demand curve for each industry, in conjunction with a single supply curve, but with two families of such curves corresponding to different assumptions as to the aggregate employment. 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.

For let us assume (to begin with) that the propensity to consume is given as well as the other factors which we have taken as given in above, and that we are considering changes in employment in response to changes in the rate of investment. Subject to this assumption, for every level of effective demand in terms of wage-units there will be a corresponding aggregate employment and this effective demand will be divided in determinate proportions between consumption and investment. Moreover, each level of effective demand will correspond to a given distribution of income. It is reasonable, therefore, further to assume that corresponding to a given level of aggregate effective demand there is a unique distribution of it between different industries.

This enables us to determine what amount of employment in each industry will correspond to a given level of aggregate employment. That is to say, it gives us the amount of employment in each particular industry corresponding to each level of aggregate effective demand measured in terms of wage-units, so that the conditions are satisfied for the second form of the employment function for the industry, defined above, namely N_r  =  F_r(D_w) Thus we have the advantage that, in these conditions, the individual employment functions are additive in the sense that the employment function for industry as a whole, corresponding to a given level of effective demand, is equal to the sum of the employment functions for each separate industry; i.e.

F_r(D_w)  =  N  =  SN_r  = SF_r(D_w).

Next, let us define the elasticity of employment. The elasticity of employment for a given industry is

              dN_r         D_wr
e_er  =  ¾¾¾¾ × ¾¾¾ ,
            dD_wr          N_r

since it measures the response of the number of labour-units employed in the industry to changes in the number of wage-units which are expected to be spent on purchasing its output. The elasticity of employment for industry as a whole we shall write

             dN           D_w
e_e  =  ¾¾¾¾ × ¾¾¾ ,
            dD_w          N_r

Provided that we can find some sufficiently satisfactory method of measuring output, it is also useful to define what may be called the elasticity of output or production, which measures the rate at which output in any industry increases when more effective demand in terms of wage-units is directed towards it, namely

              dO_r          D_wr
e_or  =  ¾¾¾¾ × ¾¾¾ ,
             dD_wr          O_r

Provided we can assume that the price is equal to the marginal prime cost, we then have

                      1
DD_wr  =  ¾¾¾¾DP_r
                 1 - e_or

where P_r is the expected profit. It follows from this that if e_or  =  0, i.e. if the output of the industry is perfectly inelastic, the whole of the increased effective demand (in terms of wage-units) is expected to accrue to the entrepreneur as profit, i.e. DD_wr  =  DP_r; whilst if e_or  =  1, i.e. if the elasticity of output is unity, no part of the increased effective demand is expected to accrue as profit, the whole of it being absorbed by the elements entering into marginal prime cost.

Moreover, if the output of an industry is a function f(N_r) of the labour employed in it, we have

   1 - e_or                N_r f"(N_r)
¾¾¾¾  = - ¾¾¾¾¾¾¾ ,
     e_er                  p_wr{f'(N_r)}²

where p_wr is the expected price of a unit of output in terms of the wage-unit. Thus the condition e_or  =  1 means that f"(N_r)  =  0, i.e. that there are constant returns in response to increased employment.

Now, in so far as the classical theory assumes that real wages are always equal to the marginal disutility of labour and that the latter increases when employment increases, so that the labour supply will fall off; cet. par., if real wages are reduced, it is assuming that in practice it is impossible to increase expenditure in terms of wage-units. If this were true, the concept of elasticity of employment would have no field of application. Moreover, it would, in this event, be impossible to increase employment by increasing expenditure in terms of money; for money-wages would rise proportionately to the increased money expenditure so that there would be no increase of expenditure in terms of wage-units and consequently no increase in employment. But if the classical assumption does not hold good, it will be possible to increase employment by increasing expenditure in terms of money until real wages have fallen to equality with the marginal disutility of labour, at which point there will, by definition, be full employment.

Ordinarily, of course, e_or will have a value intermediate between zero and unity. The extent to which prices (in terms of wage-units) will rise, i.e. the extent to which real wages will fall, when money expenditure is increased, depends, therefore, on the elasticity of output in response to expenditure in terms of wage-units.

Let the elasticity of the expected price p_wr in response to changes in effective demand D_wr, namely (dp_wr/dD_wr) × (D_wr /p_wr), be written e'_pr.

Since O_r × p_wr  = D_wr, we have

     dO_r          D_wr           dp_wr         D_wr
¾¾¾¾ × ¾¾¾  +  ¾¾¾¾ × ¾¾¾  =  1
    dD_wr          O_r            dD_wr         p_wr

or         e'_pr + e_or  =  1.

That is to say, the sum of the elasticities of price and of output in response to changes in effective demand (measured in terms of wage-units) is equal to unity. Effective demand spends itsell, partly in affecting output and partly in affecting price, according to this law.

If we are dealing with industry as a whole and are prepared to assume that we have a unit in which output as a whole can be measured, the same line of argument applies, so that e'_p + e_o  =  1, where the elasticities without a suffix r apply to industry as a whole.

Let us now measure values in money instead of wage-units and extend to this case our conclusions in respect of industry as a whole.

If W stands for the money-wages of a unit of labour and p for the expected price of a unit of output as a whole in terms of money, we can write e_p (= (Ddp) / (pdD)) for the elasticity of money-prices in response to changes in effective demand measured in terms of money, and e_w (= (DdW) / (WdD)) for the elasticity of money-wages in response to changes in effective demand in terms of money. It is then easily shown that

e_p  =  1  =  e_o(1 -e_w).

This equation is, as we shall see in the next chapter, first step to a generalised quantity theory of money.

If e_o  =  0 or if e_w  =  1, output will be unaltered and prices will rise in the same proportion as effective demand in terms of money. Otherwise they will rise in a smaller proportion.
 

II

Let us return to the employment function. We have assumed in the foregoing that to every level or aggregate effective demand there corresponds a unique distribution of effective demand between the products of each individual industry. Now, as aggregate expenditure changes, the corresponding expenditure on the products of an individual industry will not, in general, change in the same proportion;¾partly because individuals will not, as their incomes rise, increase the amount of the products of each separate industry, which they purchase, in the same proportion, and partly because the prices of different commodities will respond in different degrees to increases in expenditure upon them.

It follows from this that the assumption upon which we have worked hitherto, that changes in employment depend solely on changes in aggregate effective demand (in terms of wage-units), is no better than a first approximation, if we admit that there is more than one way in which an increase of income can be spent. For the way in which we suppose the increase in aggregate demand to be distributed between different commodities may considerably influence the volume of employment. If, for example, the increased demand is largely directed towards products which have a high elasticity of employment, the aggregate increase in employment will be greater than if it is largely directed towards products which have a low elasticity of employment.

In the same way employment may fall off without there having been any change in aggregate demand, if the direction of demand is changed in favour of products having a relatively low elasticity of employment.

These considerations are particularly important if we are concerned with short-period phenomena in the sense of changes in the amount or direction of demand which are not foreseen some time ahead. Some products take time to produce, so that it is practically impossible to increase the supply of them quickly. Thus, if additional demand is directed to them without notice, they will show a low elasticity of employment; although it may be that, given sufficient notice, their elasticity of employment approaches unity.

It is in this connection that I find the principal significance of the conception of a period of production. A product, I should prefer to say, has a period of production n if n time-units of notice of changes in the demand for it have to be given if it is to offer its maximum elasticity of employment. Obviously consumption-goods, taken as a whole, have in this sense the longest period of production, since of every productive process they constitute the last stage. Thus if the first impulse towards the increase in effective demand comes from an increase in consumption, the initial elasticity of employment will be further below its eventual equilibrium-level than if the impulse comes from an increase in investment. Moreover, if the increased demand is directed to products with a relatively low elasticity of employment, a larger proportion of it will go to swell the incomes of entrepreneurs and a smaller proportion to swell the incomes of wage-earners and other prime-cost factors; with the possible result that the repercussions may be somewhat less favourable to expenditure, owing to the likelihood of entrepreneurs saving more of their increment of income than wage-earners would. Nevertheless the distinction between the two cases must not be over-stated, since a large part of the reactions will be much the same in both.

However long the notice given to entrepreneurs of a prospective change in demand, it is not possible for the initial elasticity of employment, in response to a given increase of investment, to be as great as its eventual equilibrium value, unless there are surplus stocks and surplus capacity at every stage of production. On the other hand, the depletion of the surplus stocks will have an offsetting effect on the amount by which investment increases. If we suppose that there are initially some surpluses at every point, the initial elasticity of employment may approximate to unity; then after the stocks have been absorbed, but before an increased supply is coming forward at an adequate rate from the earlier stages of production, the elasticity will fall away; rising again towards unity as the new position of equilibrium is approached. This is subject, however, to some qualification in so far as there are rent factors which absorb more expenditure as employment increases, or if the rate of interest increases. For these reasons perfect stability of prices is impossible in an economy subject to change¾unless, indeed, there is some peculiar mechanism which ensures temporary fluctuations of just the right degree in the propensity to consume. But price-instability arising in this way does not lead to the kind of profit stimulus which is liable to bring into existence excess capacity. For the windfall gain will wholly accrue to those entrepreneurs who happen to possess products at a relatively advanced stage of production, and there is nothing which the entrepreneur, who does not possess specialised resources of the right kind, can do to attract this gain to himself. Thus the inevitable price-instability due to change cannot affect the actions of entrepreneurs, but merely directs a de facto windfall of wealth into the laps of the lucky ones (mutatis mutandis when the supposed change is in the other direction). This fact has, I think, been overlooked in some contemporary discussions of a practical policy aimed at stabilising prices.

It is true that in a society liable to change such a policy cannot be perfectly successful. But it does not follow that every small temporary departure from price stability necessarily sets up a cumulative disequilibrium.
 

III

We have shown that when effective demand is deficient there is under-employment of labour in the sense that there are men unemployed who would be willing to work at less than the existing real wage. Consequently, as effective demand increases, employment increases, though at a real wage equal to or less than the existing one, until a point comes at which there is no surplus of labour available at the then existing real wage; i.e. no more men (or hours of labour) available unless money-wages rise (from this point onwards) faster than prices. The next problem is to consider what will happen If, when this point has been reached, expenditure still continues to increase.

Up to this point the decreasing return from applying more labour to a given capital equipment has been offset by the acquiescence of labour in a diminishing real wage. But after this point a unit of labour would require the inducement of the equivalent of an increased quantity of product, whereas the yield from applying a further unit would be a diminished quantity of product. The conditions of strict equilibrium require, therefore, that wages and prices, and consequently profits also, should all rise in the same proportion as expenditure, the 'real' position, including the volume of output and employment, being left unchanged in all respects. 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 output does not alter and prices rise in exact proportion to MV.

Nevertheless there are certain practical qualifications to this conclusion which must be borne in mind in applying it to an actual case:

(1)  For a time at least, rising prices may delude entrepreneurs into increasing employment beyond the level which maximises their individual profits measured in terms of the product. For they are so accustomed to regard rising sale-proceeds in terms of money as a signal for expanding production, that they may continue to do so when this policy has in fact ceased to be to their best advantage; i.e. they may underestimate their marginal user cost in the new price environment.

(2)  Since that part of his profit which the entrepreneur has to hand on to the rentier is fixed in terms of money, rising prices, even though unaccompanied by any change in output, will redistribute incomes to the advantage of the entrepreneur and to the disadvantage of the rentier, which may have a reaction on the propensity to consume. This, however, is not a process which will have only begun when full employment has been attained;¾it will have been making steady progress all the time that the expenditure was increasing. If the rentier is less prone to spend than the entrepreneur, the gradual withdrawal of real income from the ormer will mean that full employment will be reached with a smaller increase in the quantity of money and a smaller reduction in the rate of interest than will be the case if the opposite hypothesis holds. After full employment has been reached, a further rise of prices will, if the first hypothesis continues to hold, mean that the rate of interest will have to rise somewhat to prevent prices from rising indefinitely, and that the increase in the quantity of money will be less than in proportion to the increase in expenditure; whilst if the second hypothesis holds, the opposite will be the case. It may be that, as the real income of the rentier is diminished, a point will come when, as a result of his growing relative impoverishment, there will be a change-over from the first hypothesis to the second, which point may be reached either before or after full employment has been attained.
 

IV

There is, perhaps, something a little perplexing in the apparent asymmetry between inflation and deflation. For whilst a deflation of effective demand below the level required for full employment will diminish employment as well as prices, an inflation of it above this level will merely affect prices. This asymmetry is, however, merely a reflection of the fact that, whilst labour is always in a position to refuse to work on a scale involving a real wage which is less than the marginal disutility of that amount of employment, it is not in a position to insist on being offered work on a scale involving a real wage which is not greater than the marginal disutility of that amount of employment.

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