636 
PONTIFICIAE ACADEMIAE SCIENTIARVM SCRIPTA VARIA - 
7 
income, we should obtain families of curves of the following 
shapes: 
Der-capréa 
expenditure 
Se ration 
level 
r-capita 
eal income 
Fic 
Curves of type (a) are likely to fit the cases of goods which 
are absolutely necessary for physiological reasons (e.g. food), 
and curves of type (b) are likely to fit almost all other cases. 
Type (c) finally represents the typical behaviour of inferior 
goods (1). 
Of course, the relation between expenditure on each single: 
commodity and real income, represented in fig. 1, is limited 
by the two-dimensional character of the diagrams. The actual 
time-path of each single expenditure will also depend on the 
variation of the structure of prices. It is important to realize, 
however, that the shapes of the relations represented in fig. 1 
will remain unaffected. 
7. The criterion for the choice of the hvpotheses 
Before going on to considering the general dynamic model 
to which the foregoing discussion has graduallv paved the wav. 
(1) J. AITCHINSON and J.A.C. Brown (in The Log-normal Distribution, 
Cambridge, 1957, chap. 12) suggest a function based on the log-normal 
distribution, as a general function capable of fitting almost all the cases 
of ENGEL curves. The shape of the function is of the type (b) represented 
in fig. 1. 
10] Pasinetti - pag. 66