SEMAINE D'ÉTUDE SUR LE ROLE DE L’ ANALYSE ECONOMETRIQUE ETC. 
can be written, on the assumption that plants have a fixed life- 
span, in the form 
(IV 14 
. I2) 
2) 
y 
s£-- ll 
pa! 
st 
01 
de (T4 
a* 
JF 
x) À 
In this equation, y, and /, denote respectively the net output 
of, and labour employed by, industry s at time #; v*, is the 
investment undertaken by industry s at time t expressed in 
wage units, and r*, is the initial rate of return on plant which 
comes into operation in industry s in year t; and a*, and b*, 
are parameters. The integration spans a period of © years 
equal to the fixed life spans of the plants. 
We have already seen, when discussing SAM, that the 
assumption of fixed life-spans is not satisfactory because actual 
life-spans depend on economic conditions. We can allow for 
this by integrating over an interval which is different from 
year to year and which for each year is chosen so that a plant 
1s assumed to be scrapped only when the real wage becomes 
such that the value added by the plant would be less than the 
wage bill, even if it were operating at full capacity. This can 
be expressed by writing (IV. 12) as the functional 
(IV. 1)) 
i 
- 
* ) d= 
where R,(#) is the set of values of 7 which satisfy the no-scrap 
ping requirement at time /# in industry s. 
We are only now assembling the data necessary to estimate 
a*, b*, and R,(f). So in the preliminary estimates for 1970 
given in [5] we had to adopt a simpler approach based on [32]. 
Let us now drop the subscript s. Let Ay denote the increase 
in capacity net output in a particular industry in a particular 
[1] Stone - pag. 
47