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= iwhere



(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 money
 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