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Inequality aversion and risk aversion. (English) Zbl 1244.91029
A social welfare function can be defined as a function of individual preferences. A comparative notion of inequality aversion for certainty equivalents is easily defined. The analysis is made slightly simpler by supposing that the social welfare function operates on utilities directly; that is, it is a Bergson-Samuelson social welfare function with respect to the certainty equivalents. In this paper the author proves that for two social welfare functions which are inequality averse with respect to certainty equivalents, if one is more inequality averse for certainty equivalents than the other, the household preference induced by optimally allocating aggregate bundles according to this social welfare function is more risk averse than the other. It is also shown that the comparative static can be reversed if absolute inequality aversion is dropped and the utilitarian rule always induces the least risk averse household preference among all social welfare functions.

##### MSC:
 91B08 Individual preferences 91B15 Welfare economics 91B30 Risk theory, insurance (MSC2010)
##### Keywords:
risk aversion; inequality aversion; aggregation
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##### References:
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