542 
PONTIFICIAE ACADEMIAE SCIENTIARVM SCRIPTA VARIA - 28 
where 
(26) 
Ao —=Po a(P°)—! , Be =Pe b(Q°)=! , Co = Po c(Po)-1 ; 
Let us denote the balanced growth solution to (14) cor- 
responding to the VON NEUMANN rate of interest by (1 + 7°)'x°; 
then x° is the eigen-vector x of (15) evaluated at »=#°, P,=Pe 
and Q,=0Q°. Define a vector z, as 
‘27 
2, =(1+7) "x, — x° 
We may now put (13) in the form: 
(28) 
(x°+2,)B,(1 - d) + 
+ (I+°)(X°+2,,1) (1+—A,,,—B,1—C;41) #0. 
Substitute for A,, B,, and C, from (25), and neglect higher- 
power terms such as z,P,A°, z,B°Q', etc.; in view of (16), and 
(24), we may linearize (28) as: 
(20) (I- d) (Bz + (1+)[I- (A°+B°+C°'] 2/41 + 
+ D°p, + E°p,,; + F°p,,3 0, 
where D°, E°, and F° are some n x n matrices whose elements 
are independent of z and p, and a prime applied to a vector 
(or a matrix) denotes the transposition of that vector (or that 
matrix). 
Equations (22) and (29) describe movements of prices and 
9] Morishima - pag. 14