^{8}For notational simplicity we express the value function and the expected discounted value
function as functions simply of wealth and savings, but implicitly these functions reflect the entire
information set as of time t; if, for example, the income process is not i.i.d., then information on lagged income
or income shocks could be important in determining current optimal consumption. In the remainder of the
paper the dependence of functions on the entire information set as of time will be unobtrusively
indicated, as here, by the presence of the subscript. For example, we will call the policy rule
in period which indicates the optimal value of consumption . In contrast, because we
assume that the utility function is the same from period to period, the utility function has no
subscript.