532 
PONTIFICIAE ACADEMIAE SCIENTIARVM SCRIPTA VARIA - 4 
where p;, is the price of good j in period ¢ and g, , the price of 
capital-service k in period à. Substituting for x;,/x;, and 
Sp: 1/X;, rom (4) and taking logs, we may put (3) in the form 
n n 
(5) logpii— > 4; log py, — 2 bi; log ¢;1 — ay logp, s+ Gy=o0 
i= i= 
where 
(6) 
n n 
G; = log F; + 2, a; log a; + 2 6 108 6j; 
j= I= 
Let us now consider a person who has a given sum of mon- 
ey M available for expenditure. If he lends that amount to 
someone for one period at the prevailing rate of interest », he 
will enter the next period with amount (1 +7)M. Alternatively, 
he may spend M on goods; if he spends it exclusively on a 
capital good k in period £, he obtains M/p, ; units of that good. 
By letting them out hire, he receives income by the amount 
Jn,1(M/P;;) in period £, which will grow to (1+7)g,,(M/P; 1) 
at the beginning of period #+1. Although the capital goods 
he owns will be worn at a certain rate (say) d, in the process 
of production, he will still own (1 - d;)(M/p,,) units of good k 
at the beginning of period #+1, which will be evaluated as 
(x — d,)(M/Pr1)Pr141 at the price in period #+1. In equilibrium 
neither option can be advantageous over the other, so that 
(147) ME (1+7)9ne (M/An 0) + (1 —d) (M/bx) Prt +1 
By dividing both sides by M/p, ,, this may be put in a simple 
form 
7) 
(I + 7) pr, = (1 + 7) Gre + (1 — dy) Priv 
9] Morishima - pag. 4