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

```262 PONTIFICIAE ACADEMIAE SCIENTIARVM SCRIPTA VARIA -
28
We note that, by Assumption (c), both the feasible set and
the attainable sets are convex, and that the function g(z) defined
in (36) 1s strictly concave. Since g(z) vanishes for z=o0 and for
z=2, it reaches its maximum # in a unique point #, so that
(38) (38a) æ = g(2) > 9(2) for all 22, where o<z<2,
3 A A
(38b) 9(2)>9(2)= 0 > g'(z*) whenever 0 <Cz7<2<2*<Z.
From (35 a), (36), we have
‘
a
3:
2<x,+2 = g(z,
and hence for all feasible paths, using (35 a), (37), and the
fact that g(2)>0 only for 0<z<Z ,
40)
0<2,<z for all t=o0
Here o0=2z, has been ruled out because it would not allow the
positive consumption x, for #=¢ required by (35 a).
À 4.
A BASIC INEQUALITY AND ONE APPLICATION
The concavity Assumption (e) of u(x) implies that
41) u(x)- u(x*)<u (x*)e(x-x*) for all x, x*
4]
Koopmans - pag. 38
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