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 cons- 
traints 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