\begin{eqnarray}
\vFunc_{t}(\mRat_{t}) & = & \max_{\{\cFunc\}_{t}^{T}}~  \util(\cFunc_{t}) +\Discount \Ex_{t}[\PGro_{t+1}^{1-\CRRA}\vFunc_{t+1}({\mRat}_{t+1})]  \label{eq:veqn} \\
& \mbox{s.t.} &  \notag
 \\ {\aRat}_{t} & = & \mRat_{t}-c_{t}  \label{eq:smalls} \notag
 \\ {\bRat}_{t+1} & = & (\Rfree/\PGro_{t+1})\aRat_{t}  ~ = ~ \Rnorm_{t+1}\aRat_{t}  \notag \label{eq:smallb}
\\ \mRat_{t+1} & = & \bRat_{t+1}+\tShkAll_{t+1}  \notag %
\end{eqnarray}
