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Suppose you are the State's new Premier. The people in your state are of two types: cheerful people and mournful people (there are equal numbers of...
Suppose you are the State's new Premier. The people in your state are of two
types: cheerful people and mournful people (there are equal numbers of each
type). You are trying to decide how to divide 100 units of public services (X)
between the people in your State, i.e. XC + XM = 100.
Cheerful people have utility functions UC = 2XC0.5.
Mournful people have utility functions UM = XM0.5.
a) Suppose you decide to split the 100 units of X in a way that maximises an
additive social welfare function: W = UC + UM. How many units of X do the
cheerful people get and how many units do the mournful people get? i.e. find
XC and XM that maximises W, subject to the constraint.
b) Suppose, instead, you have a Rawlsian perspective with a social welfare
function: W = min(UC,UM). How many units of X do the cheerful people get and
how many units do the mournful people get?
c) Finally, suppose you are a Libertarian so care about having a process rather
than considering the outcome. How many units of X do the cheerful people get
and how many units do the mournful people get?
