3

PONTIFICIAE ACADEMIAE SCIENTIARVM SCRIPTA VARIA - 2%

year; let x denote the capacity added in the year as a result
of new plant coming into operation; and let s denote the capacity
 subtracted through the scrapping of old plant. Then

(IV. 14)

Av=x-s

Correspondingly, let Al denote the increase in employment;
let » denote the labour added to man the new plants; and let #
denote the reduction in employment due to plant retirements.
Then
(IV. 15)

Finally, let p denote the net output price, which is equal to
the cost of labour and capital per unit of output, and let w
denote the wage rate. Then if we multiply (IV. 14) by b and
(IV. 15), by w and subtract, we obtain

(IV. 16) pAy—wÂl =(px—wn)—(ps—wr)
= (px —wn)

if plant is scrapped when it ceases to earn a return, that is
when ps=wr. |
Now let us define the initial rate of return, #*, as the gross
rate of return to capital embodied in new plant in the first year
of its operation. Then, denoting gross investment in new plant
by v¥,

(IV. 1
7)
y*

= (px - wn)/u*
(pÂv - wAÂl)/v

from (IV. 16), on the assumption that plant is scrapped when it
ceases to earn a return. Equation (IV. 17) can be rewritten
either as

dV. 15)

oF 3 gdh Le

'1] Stone - pag. 48