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On the local and global comparison of generalized Bajraktarevi\'c means
Given two continuous functions such that is positive
and is strictly monotone, a measurable space , a measurable family
of -variable means , and a probability measure on
the measurable sets , the -variable mean is
defined by The aim of this paper is to study
the local and global comparison problem of these means, i.e., to find
conditions for the generating functions and , for the families
of means and , and for the measures such that the comparison
inequality
be satisfied
Measures by means, means by measures
We construct measure which determines an ordinary mean in a very natural way.
Using that measure we can extend the mean to infinite sets as well. E.g. we can
calculate the geometric mean of any set with positive Lebesgue measure. We also
study the properties and behavior of such generalized means that are obtained
by a measure
Production functions having the CES property
To what measure does the CES (constant elasticity of substitution) property determine
production functions? We show that it is not possible to find explicitely all two variable production
functions f(x; y) having the CES property. This slightly generalizes the result of R. Sato [16].
We show that if a production function is a quasi-sum then the CES property determines only the
functional forms of the inner functions, the outer functions being arbitrary (satisfying some regularity
properties). If in addition to CES property homogeneity (of some degree) is required then the (twovariable)
production function is either CD or ACMS production function. This generalizes the result
of [4] and also makes their proof more transparent (in the special case of degree 1 homogeneity)
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