  The economy described in equation (5) consists of a non-deteriorating piece of cake, of size \(K(0) \gt 0\) at the initial date. It is obvious that every consumption stream \(\{C(t)\}\) satisfying equation (5) tends to zero in the long run. Formally, \(C(t) \rightarrow 0\) as \(t \rightarrow \infty\).