Problems of operationalizing the concept of a cost-of-living index



be maximised, a household6 must have preferences (predilections and dislikes)
and a preference order of quantity vectors
q (or combinations of quantities
q of N commodities). Unlike a utility function f (q) the more fundamental
“preference order” only provides a ranking of commodity combinations in
ascending order of desirability (preference) where not yet numerical values
of the amount of utility
и are assigned to vectors q/ = [q1... qN] as it is the
case in a utility function
и = f (q). In order to provide a consistent ranking
the commodity combinations have to meet criteria that are anything but self
evident, viz. completeness (the ranking ought to comprise all possible com-
binations), transitivity (permitting a one dimensional order), non-satiation7
and continuity which in turn requires “homogeneous” goods (infinite divisi-
bility where quality remains constant). As to preference formation it is as-
sumed that a household feels desires and satisfaction independently of other
households, so that all sorts of imitation and emulation behaviour (as often
observed) are ruled out.

Moreover it is assumed that the household decides over quantities in a
rational and consistent manner. Maximisation of utility (under budget con-
strains) presupposes

1. the ability and willingness on the part of consumers to collect the nec-
essary informations about prices, availability in suitable outlets) and
to make the required changes in the consumption in response to chang-
ing relative prices (reaction is immediate and well informed, ideally the
information about the
given supply is complete and always up to date) ;

2. the existence of a utility function (indifference surface) which in turn
requires that certain mathematical conditions are met, and also

3. the existence of a budget constraint (isocost plane) where again some
assumptions are implicitly made and finally it is important to note that
the COLI model assumes, that

4. the utility function is constant over time and that households make
(possibly infinitely small) changes in their consumption
solely in re-
sponse to changing relative prices
and not, for example because of

6It only later turns to the more complex COLI theory of many-households which is of
course closer related to the scope of a national CPI than the single household case.

7This means that for any combination of commodities there must exist at least one
other combination which is preferred to it.



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