that budget shares of all N goods ought to add up to unity (100%).
• The (linear) budget constraint is a function (in M and p) which should
be homogenous of degree zero in M and p (to ensure that no “money il-
lusion” prevails). This assumption is needed to make sure that only rel-
ative prices rather than absolute prices matter when households make
rearrangements (substitutions) in their consumption.
Ad 4: It is important to note that these substitutions are made on a con-
stant (invariant) utility function solely in response to changes in the relative
prices (over which the household has no command). To increase or decrease
one’s demand should not result from changing tastes or reacting to activi-
ties on the supply side. Ideally higher or lower income should not influence
the preferences order.17 However, in reality tastes are constantly changing
with the passage of time and they are also affected from ageing, technology
and supply. The set of goods over which quantified preferences (that is util-
ity values) are defined is varying, new goods emerge an old ones disappear
from the market. In reality changes in consumption patterns are clearly not
attributable only to decisions on the demand side of the market.
In summary all these assumptions are inherent in the COLI approach on
the basis of which also both approaches, SIA and DSA are built. It is by no
means less realistic to make the assumption of a constant (and observable)
basket of goods than to assume a constant function f (q) relating quantities
to the unobservable “utility”. Furthermore we have seen that to legitimately
call the COLI approach theoretically superior to the COGI approach depends
on the realism of the underlying theory of consumer behaviour. And this in
turn is contingent on quite a few conditions which are not likely to be met
in real situations.
2.3 Functional forms and their corresponding indices
(the SIA assumptions)
We now come to additional assumptions needed in Diewert’s SIA. The pre-
ceding section made clear that to be eligible as a utility function (and as the
corresponding cost function), or more general as an “aggregator function”
is not easy. To serve as a utility function f (q) the function rather needs to
17This refers to the issue of “homothetic” preferences we will discuss shortly.
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