A
PONTIFICIAE ACADEMIAE SCIENTIARVM SCRIPTA VARIA - 28
(il) « consumption expenditure at implicit prices »
I
| 2 x, dt
.
reaches its minimum, on the set of paths with utility
Uz(p) equal to or exceeding that of the path (£, 2), if
(x,, 2,)= (%X,, Z,).
(G) If (x, 5), (x, z,) ave two eligible and attainable paths,
5)
r I
Joue — dt = [late — 3) — bé, — 21) dt =
9 5
= lea, +5) (2,— 2,) ar — plan — 2,
for all finite T, and for T=oo if the integrals converge and
the last term has a limit.
Again, all three members vanish if (x,, 2,) is itself the path
(#,, 2,). The inequality in (25), rewritten as
I
[puta + 2, — Ly — 2. di
1
[ae —2ndt=o ;
4] Koopmans - pag. 22