BK. V

APPENDIX TO CHAPTER 19

273

that x +y = <f>(x), i.e. that the number of men employed in thewage-goods industries is a function of total employment. Hethen shows that the elasticity of the real demand for labour inthe aggregate (which gives us the shape of our quaesitum, namelythe Real Demand Function for Labour) can be written

So far as notation goes, there is no significant differencebetween this and my own modes of expression. In so far aswe can identify Professor Pigou ’s wage-goods with my con-sumption-goods, and his “other goods” with my investment-

of the wage-goods industries in terms of the wage-unit, is thesame as my C w . Furthermore, his function cf> is (subject tothe identification of wage-goods with consumption-goods) afunction of what I have called above the employment multi-plier k'. For

Thus Professor Pigou ’s “ elasticity of the real demand forlabour in the aggregate” is a concoction similar to some of myown, depending partly on the physical and technical conditionsin industry (as given by his function F) and partly on thepropensity to consume wage-goods (as given by his function rf>)\provided always that we are limiting ourselves to the special casewhere marginal labour-cost is equal to marginal prime cost.

To determine the quantity of employment, Professor Pigou

eluded from combining with the additional labour any additional entre-preneurship or working capital or anything else other than labour whichwould add to the cost; and we are even precluded from allowing theadditional labour to wear out the equipment any faster than the smallerlabour force would have done. Since in the former case we have forbiddenany 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-costare equal. But the results of an analysis conducted on this premiss havealmost no application, since the assumption on which it is based is veryseldom realised in practice. For we are not so foolish in practice as to refuseto associate with additional labour appropriate additions of other factors,in so far as they are available, and the assumption will, therefore, onlyapply if we assume that all the factors, other than labour, are already beingemployed to the utmost.

#(*) F'(s)

^r~ ±fj\

- <j>{x) F"to-

being the value of the output

goods, it follows that his

Ax = TAy,

so that

f(x) = i +i„

T