552 TRANSACTIONS OF SECTION F. 
working day. Let dm be the long-period value to the operative, when his 
income is Onda, of the leisure destroyed by the addition of the O nth 
increment of time to the working day. The curve I is the locus of the 
point m. Evidently, starting at a, it will lie throughout its length below P, 
increasingly departing from P (because leisure is subject to the law of 
diminishing utility and the value of leisure rises with income), and cut 
O X to the left of b. Apart from the satisfaction or dissatisfaction of 
working, therefore, the far-sighted operative who took into account the 
value of leisure would choose a normal day O71, which is less than Ob (the 
choice of far-sighted employers in combination). When the normal day is 
Oi the marginal value of leisure to an operative with a wage Oz ha would 
be 7 h, which equals the long-period marginal earnings attributable to the 
O ith increment of time in the working day. Now, let L indicate the long- 
y! 
period values to the operative of the effects of different lengths of working 
day on the absolute satisfaction or dissatisfaction involved in the labour 
itself, L being otherwise interpreted as I, when units of money are measured 
along OY’ as well as along OY, and the parts of the curve below OX 
indicate the prices which would be paid to escape the dissatisfaction in- 
volved in working, and the parts above O X the money value of the satis- 
faction involved in working. As some of the time devoted to production 
will probably be pleasant to the operative when the length of working day 
is most favourable to his enjoyment of work, we may assume that L need 
not le throughout its length below OX. Then the working day which 
perfectly wise operatives would choose would be On, the point n being such 
that n m = nl, the attainment of which equation is the condition under 
which the operative’s satisfaction is maximised. If, as is theoretically 
conceivable but practically impossible, L lay further above O & for the 
