Te
je

PONTIFICIAE ACADEMIAE SCIENTIARVM SCRIPTA VARIA - 28

where g=(I - hp’)c and h=p-"b. By combining (V. 4) and
(V. 6), we see that

(V. 7) FhE'p<(L+F)E®s - FR*+15s - Fe

Sixth, we should probably wish to ensure a minimum level
of consumption in each year of the transitional period. This
can be expressed as

(V. 8)

Ew
>u*

where p* denotes a preassigned minimum level. Alternatively,
we might prefer to ensure that consumption did not fall during
the transitional period, in which case p* in (V.8) would have
to be replaced by E®! p.
Finally (V. 1), (V. 2), (V. 5), (V. 7) and (V. 8) form constraints
 which limit any short-run policy; the outstanding
question is what policy to pursue. Since the terminal conditions
ensure that the long-run policy can be realised at the end ot
the transitional period, the obvious course is to maximise the
utility of consumption during the transitional period subject to
the above constraints. If we denote the utility of consumption
in year ® by Ev, then

V. 9)

ESu = & [IN (Ef es — cg)'t]

where D denotes an arbitrary monotonic function and § denotes
the typical commodity. Thus we should have to maximise

(V. 10)

+1
2
—-0)

T-1
Edu=S ® [ll (ES e; — c's]
8-0 =

1] Stone - pag. 78