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Necessary conditions in overlapping generations model (OLG)
The consumer at each period maximizes
\begin{equation}
\displaystyle\sum_{i=1}^{I}\beta^{i-1}U(c^i_{t+i},l^i_{t+i}) , t=0,1,2,3,...
\end{equation}
subject to
\begin{equation}
(1+\eta_t)c^{i}_t+...
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