Production saving model
The Euler equation of the production saving model is
U^0 (ct)=βU^0 (ct+ 1 )f^0 (kt+ 1 ),
for the cake eating model the Euler equation is
U^0 (ct)=βU^0 (ct+ 1 ).
In the cake eating model there is no production sof(kt)=kt.From this
it is clear that the production saving model is a generalization of the cake
eating model. The cake eating model is a Örst order equation, but as the
production saving model containskt+ 1 it is a second order di§erence
equation. with boundary conditionsk 0 =a,kT+ 1 =0 which is not easy to
solve.
