In view, however, of the difficulty of obtaining reliable estimates of household income,
the analysis of demand elasticities has been based on the recorded total expenditure of the
household as the determining or independent variable.

 In order to carry out the analysis, households from the rural areas and from Kingston
were first grouped into a series of household types of constant composition in order to eli-
minate the influence of variations in size and numbers of children on the expenditure pat-
tern. The records for each of the most numerous of these groups were then analysed by
fitting for each of the major commodity groups a semi-logarithmic equation of the form

 y = a + b log x

where x represents total household expenditure expenditure and y the expenditure on the
particular product- group under investigation. The income elasticity of demand, repre-

sented mathematically by dy, is equal, in this formulation, to b/y, the average value
 y dx'
of y being taken in order to give the average elasticity for each sample. 1/ By this pro-
cedure a number of estimates of the elasticity for each product- group are obtained. These
may, in appropriate cases, be combined by suitable methods of averaging to give an over-
all estimate of elasticity for the whole population.

 The above equation is only one of a number of different equations from which estimates
of income elasticity may be derived. The choice of the equation depends on the nature of
the relationship assumed to exist between total expenditure and expenditure on a particular
item, and in particular, on the change (if any) expected to occur in the value of the elasti-
city as the income or consumption-level itself changes. In the above formulation the elas-
ticity is assumed to diminish as the income or consumption level rises, and this seems in
general a more satisfactory assumption than the hypothesis of a constant income elasticity,
especially in projecting demand from a base period in which the initial elasticity is high,
as it is for many commodities in the West Indies. The semi-logarithmic equation is not
the only type which satisfies an assumption of this kind, but it has the merit of being readi-
ly calculated and simple to apply for purposes of projection.

 After obtaining the elasticity estimates in this way, it is necessary to consider how far
they seem to give a valid representation of the demand situation in 1958 and in what re-
spects, if any, it is desirable to adjust them in projecting future levels of demand. In the
present instance it was necessary first of all to allow for the fact that only a relatively
small part of the whole survey sample could be used in the elasticity analysis, and that
the households included were of small size and had relatively few children. As would be
expected, they had considerably higher average values of total expenditure and of expendi-
ture on food per person than the whole sample. Part, but not the whole, of this difference
is due to the relatively small number of children in the households analysed. A rough es-
timate was therefore made of the difference in expenditure per equivalent adult between
the households included in the elasticity analysis and households in the whole of the sample,
and the average elasticities derived from the analysis were adjusted to the estimated aver-
age rates of expenditure in the full samples of both urban and rural households. Since the
1/ In practical computation using common logarithms b must be multiplied by logl0
 (.43429...) to obtain the estimate of elasticity.