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PONTIFICIAE ACADEMIAE SCIENTIARVM SCRIPTA VARIA - 28 
of the equations of the model is 
2.1) 
K,_, = oY, 1 
where p is the capital-income ratio, which is assumed to be 
constant over time. Let C, be consumption and x, the savings 
ratio in vear ?: 
‘2 
2) 
C,=(1-x)Y, 
Furthermore, we use two identities: 
t 
‘2. 
>) 
(2.4) 
C,+1=Y, 
K.=K, ,+1,, 
where I, is net investment in year ¢£. Finally, we need an equa- 
tion describing the development of the population : 
(2.5) 
N.=(1+v,)N,_, , 
where N, is the mid-year population size and v, its rate of in- 
crease. 
In what follows we shall be interested particularly in the 
rate of increase of per capita consumption, C,/N,. Using (2.2), 
(2.1) and (2.5) we find: 
Ci 1—a, Ke 
N, 2 (1+v)N,_, 
and hence: 
a C/N 
(2.6)... - CoN 
K, 
— 9 
K, 1 
7 4_1 + 
“, 
71 Theil - pag. 4