\begin{equation} \ifnumSw \label{eq:kBartp1i}
\bar{\mathbf{k}}_{t+1,i} =  \omega_{t+1,i} \daleth \left(\mathbf{a}_{t,i}\pi_{t+1,i}+\bar{\mathbf{a}}_{t,i}(1-\pi_{t+1,i})\right)/\Omega + (1-\omega_{t+1,i})0
\end{equation}
