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PONTIFICIAE ACADEMIAE SCIENTIARVM SCRIPTA VARIA - 28

by making use of a few definitions. We know from (II.11)
that each production of capital goods (X,) is composed of two

. I
parts: replacement of worn-out capacity ( T %inXn) and new
investment (a;,X,). Denoting these two parts respectively
by X,, and X,,, so that

(111.3)

Xe =X", (6) + Xx, (2) ,

we have

(111.4) x, 0= 2K, @], i=1, 2, .... (n-1).

By substituting now (III.4) into (III.2), we obtain

voy
(IIL. 5) Xp) =o [XO], i=1,2, ... (n-1).

which amounts to expressing the capacity equilibrium conditions
 in the form of equilibrium relations between the production
 of capital goods in each period of time and the rate of
change in that period of the corresponding consumption goods.
Using the (II.11) and (III.1), the (III.5) become

d :
ay; X,(0)e8 = — [ain X,(0)e#] , i=1,2,....(n-1),

D]

Ann X,(0)e8' = g a,,X,(0)e8

and finally

(111.6)

Ain = E Gin »

ey 2) vee (m=T1).

“10] Pasinetti - pag. 38