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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 equation
 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 increase.


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