\begin{eqnarray*}
\PopE_t & = & \frac{\EmpGro^{t+1}}{\EmpGro-\erate} \label{eq:PopEt}
\\ \PopU_t & = & \frac{\urate \EmpGro^{t+1}}{(\EmpGro-\PLives)(\EmpGro-\erate)}. \label{eq:PopUt}
\end{eqnarray*} % Derivation: PopUt
