An individual of type x is assumed to live for L(x) years for certain, at which time they
receive utility (which is a function of wealth at the time of death) from the legacy they
leave their dependants. Each individual is assumed to discount future periods exponentially
with a rate of time preference equal to the interest rate5 and contributes towards
societal expenditures with a constant amount .e over their remaining lifespan6 , where this equals