\begin{eqnarray}
    \vFunc({m}_{t,i},\PtyGro_t) & = & \max_{\cLev_{t,i}} ~ \big\{ \uFunc(\cLev_{t,i}) + \PLives \beta
    \Ex_{t}\big[ (\PtyGro_{t+1} \pmb{\psi}_{t+1,i})^{1-\CRRA}\vFunc(\mLev_{t+1,i},\PtyGro_{t+1})\big] \big\}
    \label{eq:scaledv}
\\  & \mbox{s.t.} & \nonumber
\\ \ifnumSw  \aLev_{t,i}   & = & \mLev_{t,i} - \cLev_{t,i}, \nonumber
\\ \ifnumSw  \kLev_{t+1,i} & = & \aLev_{t,i} /( \PLives \PtyGro_{t+1} \pmb{\psi}_{t+1,i} ),  \nonumber
\\ \ifnumSw  \mLev_{t+1,i} & = & \Rprod \kLev_{t+1,i} + \Wage \pmb{\theta}_{t+1,i}.  \nonumber
\end{eqnarray}
