# Full text: Study week on the econometric approach to development planning

```236 ‘PONTIFICIAE ACADEMIAE SCIENTIARVM SCRIPTA VARIA
The per-worker production function f(z) is therefore represented
by a curve such as is shown in Figure 6. The curve rises from
the value f(0)=0 with a decreasing slope. In particular, any
line Az through the origin and of slope A such that O<A<f(0)
will ultimately intersect the curve and continue above it 1)
oy oan.
x > o such that o
> such that
-
: f' (0) there is
-
3
(') To obtain (11) suppose that, for some such À, f(z)=)\z for arbitrarily
large values of z. Then, by f(o)=o0 and the concavity of f, f(z)=\z for
all z>o0. Bat then, for any Z>o, (7b) and the continuity of F(Z, L) imply
7 .
‘he contradiction o=F(Z, o)=lim F(Z, L)=Ilim LF(_, 1)=Z lim Haz
>Z)>o. ts 1 —0 r=» Z
4] Koopmans - pag. 12
```

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