\begin{equation}
\KLevBF_{t} = \int_{0}^{1} \kLevBF_{t,i}\,\text{d}i = \int_{0}^{1} \big((1 - \pDies_{t,i})\aLevBF_{t-1,i} /\PLives\, \big)\,\text{d}i = \int_{0}^{1} \aLevBF_{t-1,i}\,\text{d}i = \ALevBF_{t-1}.   \label{eq:Ktp1}
\end{equation}
