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

utility function f (q) but also to same value и of this function (u = f (q)) in
both numerator and denominator of the COLI (price) index which thus is
defined as equation (1) in the introduction. It is important to note that the
assumption that households utility maximisation on the part of the house-
holds is crucial. Otherwise we could not equate p(q_s = c (p_s,u_s) and bring
the observed indices P^l and P^p into play and relate them to the unobserved
COLI. Once utility maximisation does not take place a superlative index will
no longer approximate the COLI.

Ad 3: In order to define the budget constraint (or isocost plane) it is
necessary to specify how total consumption expenditure¹⁴ M is related to
income¹⁵ and the commodity prices pɪ,.. . , p^ are generally assumed as being
determined exogenously. Households are assumed to be price takers which
means prices are given, independent of quantities purchased and the same
for all households.¹⁶ Also M is given which means that we do not explain a
household’s time allocation and labour supply on the basis of decisions over
leisure time t_L and working hours t_w with reference to a utility function
f (q, t) where t = t_L + t_w.

Along with the above mentioned regularity conditions concerning f (q)
such assumptions are needed in order to have a linear budget constraint
otherwise we would run into difficulties establishing an optimum as a unique
tangency point of the isocost plane with the indifference surface. Other
necessary assumptions are

• Due to limited resources (finite income) an important constraint is also

index respectively. The assumption of “homothetic” preferences introduced later is valu-
able as a simplification in that it then does not matter to which period the utility level
refers (so that Laspeyres-KonUs and Paasche-KonUs coincide).

¹⁴One may make a distinction between consumption (creating utility) and consumption
expenditure. The difference is not only time but also household production as many
purchases are subject to a significant amount of processing (e.g. cooking) within the
households. Use of goods must also be distinguished from acquisition of goods. It is
assumed that goods are acquired by purchases and not received as payments in kind, gifts
or so.

¹⁵The familiar assumption her is that all income is spent for purchases. This rules
out that households take care of future consumption by saving. We then have a more
comfortable single period utility maximisation problem only.

¹⁶ [14]Diewert (2000) considered at length a model in which he relaxed the assumption
that “prices are constant across households” . The resulting equations (relating a disag-
gregated Laspeyres or Paasche index to the “usual” Laspeyres or Paasche index) are quite
complicated.

10

<<   8   9   10   11   12   13   14   >>

More intriguing information