where F denotes the functional relationship between e and h. By monotonicity, it follows that for
all health profiles h,h, W(h)≥W(h) if and only if F(h)≥F(h). Hence, W and F both represent
and they must be related by a positive monotonic transformation.
The concern with inequality stems primarily from the feeling that reductions in inequality
should lead to increases in social welfare, provided that mean health remains constant. Given any
health profile h, we can define an index of inequality I(h) as the proportion of total health that can
be discarded without affecting social welfare. This is the methodology associated with Atkinson
(1970), Kolm (1969) and Sen (1973) (AKS). See Dutta (2002) for an overview. In our decision
context, this means that