274 THE GENERAL THEORY OF EMPLOYMENT bk . v

then combines with his “real demand for labour”, a supplyfunction for labour. He assumes that this is a function of thereal wage and of nothing else. But, as he has also assumed thatthe real wage is a function of the number of men x who areemployed in the wage-goods industries, this amounts to assumingthat the total supply of labour at the existing real wage is afunction of x and of nothing else. That is to say, n =x(x),where n is the supply of labour available at a real wage F'(x).

Thus, cleared of all complication, Professor Pigou ’s analysisamounts to an attempt to discover the volume of actual employ-ment from the equations

x +y = <j)(x)

and n = x( x )-

But there are here three unknowns and only two equations. Itseems clear that he gets round this difficulty by taking n =x+y.This amounts, of course, to assuming that there is no involun-tary unemployment in the strict sense, i.e. that all labour avail-able at the existing real wage is in fact employed. In thiscase x has the value which satisfies the equation

( x )=x( x h

and when we have thus found that the value of x is equal to(say) y must be equal to x( n i) ~ n v ar *d tota l employment n isequal to x( n i)-

It is worth pausing for a moment to consider what thisinvolves. It means that, if the supply function of labourchanges, more labour being available at a given real wage (sothat « 1 + ^« 1 is now the value of x which satisfies the equation<f>( x ) =x( x ))> the demand for the output of the non-wage-goodsindustries is such that employment in these industries is boundto increase by just the amount which will preserve equalitybetween <j>(n 1 + dn^) and + The only other way in

which it is possible for aggregate employment to change isthrough a modification of the propensity to purchase wage-goods and non-wage-goods respectively such that there is anincrease ofy accompanied by a greater decrease ofx.

The assumption that n=x+y means, of course, that labouris always in a position to determine its own real wage. Thus,the assumption that labour is in a position to determine its ownreal wage, means that the demand for the output of the non-wage-goods industries obeys the above laws. In other words, itis assumed that the rate of interest always adjusts itself to theschedule of the marginal efficiency of capital in such a way as to