The Employment Function
12 minutes • 2387 words
Superphysics Note
Chapter 3 defined the aggregate supply function Z = φ(N)
.
This 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
 defined in terms of hourlycommonwage.
 aims to relate the amount of the effective demand, measured in hourlycommonwage, directed to a given firm or industry with the amount of employment
 The supply price of its output is compared to that amount of effective demand.
Thus, if an amount of effective demand Dwr
, measured in hourlycommonwage directed to a firm or industry calls forth an amount of employment Nr
in that firm or industry, the employment function is:
Nr = Fr(Dwr)
Or, more generally, if we are entitled to assume that Dwr
is a unique function of the total effective demand Dw
, the employment function is:
Nr = Fr(Dw)
Nr
men will be employed in industry r
when effective demand is Dw
.
This chapter explains certain properties of the employment function.
The substitution of the employment function for the ordinary supply curve is consistent with the goal of this book for 2 reasons:

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

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 curve .
The ordinary demand curve for a commodity is based on the incomes of the public.
 It has to be redrawn if the incomes change.
In the same way, the ordinary supply curve for a commodity is based on the output of industry. It changes if the aggregate output of industry changes.
When we examine the response of individual industries to changes in aggregate employment, we are concerned, not with a single demand curve for each industry, in conjunction with a single supply curve, but with 2 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.
Let us assume that the propensity to consume is given as well as the other factors which we have taken as given in Chapter 18 above, and that we are considering changes in employment in response to changes in the rate of investment.
For every level of effective demand in terms of hourlycommonwage, there will be a corresponding aggregate employment. 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.
We also assume that a given level of aggregate effective demand has 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.
 It gives us the amount of employment in each particular industry corresponding to each level of aggregate effective demand measured in terms of wageunits. In this way, the conditions are satisfied for the second form of the employment function for the industry, defined above, as:
Nr = Fr(Dw)
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(Dw) = N = ΣNr = ΣFr(Dw)
.
Next, let us define the elasticity of employment.
The elasticity of employment for a given industry is eer = dNr/dDwr . Dwr/Nr, since it measures the response of the number of labourunits employed in the industry to changes in the number of wageunits which are expected to be spent on purchasing its output. The elasticity of employment for industry as a whole we shall write
ee = (dN/dDw).(Dw/N)
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 wageunits is directed towards it, namely eor = dOr/dDwr . Dwr/Or, Provided we can assume that the price is equal to the marginal prime cost, we then have `ΔDwr = 1/(1  eor)``. ΔPr where Pr is the expected profit.[2]
It follows from this that if eor = 0, i.e. if the output of the industry is perfectly inelastic, the whole of the increased effective demand (in terms of wageunits) is expected to accrue to the entrepreneur as profit, i.e. ΔDwr = ΔPr; whilst if eor = 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 φ(Nr) of the labour employed in it, we have[3] (1  eor)/eer =  Nrφ’’(Nr) / pwr{φ’(Nr)}2 , where pw is the expected price of a unit of output in terms of the wageunit. Thus the condition eor = 1 means that φ’’(Nr) = 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 wageunits.
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 moneywages would rise proportionately to the increased money expenditures so that there would be no increase of expenditure in terms of wageunits 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, eor
will have a value intermediate between zero and unity. The extent to which prices (in terms of wageunits) 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 wageunits. Let the elasticity of the expected price pwr in response to changes in effective demand Dwr, namely (dpwr/dDwr).(Dwr/pwr), be written e’pr. Since Or.pwr = Dwr, we have dOr/dDwr . Dwr/Or + dpwr/dDwr . Dwr/pwr = 1 or e’pr + eor = 1 .
The sum of the elasticities of price and of output in response to changes in effective demand (measured in terms of wageunits) is equal to unity. Effective demand spends itself, 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 + eo = 1, where the elasticities without a suffix r apply to industry as a whole. Let us now measure values in money instead of wageunits and extend to this case our conclusions in respect of industry as a whole.
If W stands for the moneywages 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 ep( = Ddp/pdD) for the elasticity of moneyprices in response to changes in effective demand measured in terms of money, and ew( = DdW/WdD) for the elasticity of moneywages in response to changes in effective demand in terms of money. It is then easily shown that ep = 1  eo(1  ew). [4]
This equation is, as we shall see in the next chapter, a first step to a generalised Quantity Theory of Money. If eo = 0 or if ew = 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 of aggregate effective demand there corresponds a unique distribution of effective demand between the products of each individual industry.
As aggregate expenditure changes, the corresponding expenditure on the products of an individual industry will not change in the same proportion.
partly 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 wageunits), 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 change in favour of products having a relatively low elasticity of employment.
These considerations are particularly important if we are concerned with shortperiod 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 has a period of production n if n timeunits of notice of changes in the demand for it have to be given if it is to offer its maximum elasticity of employment.
Consumptiongoods, as a whole, have 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 equilibriumlevel 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 wageearners and other primecost 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 wageearners would.
Nevertheless the distinction between the two cases must not be overstated, since a large part of the reactions will be much the same in both.[6] 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 change — unless, indeed, there is some peculiar mechanism which ensures temporary fluctuations of just the right degree in the propensity to consume. But priceinstability 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 priceinstability due to change cannot affect the actions of entrepreneurs, but merely directs a defacto 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.