I’ve searched through the site but have not found anything about solving consumption problem if we include leisure \ell alongside with c.
Can you add a relevant lecture or show how to approach that kind of problem numerically. (The notes jump right to stochastic cases, but it would be instructive to show the deterministic case first.)
\max_{c_t, \ell_t} \sum_{t = 0}^\infty \beta^t[\ln(c_t) + \gamma \ln(\ell_t)] \text{ s.t. } \begin{cases} y_t = k_t^\alpha(1- \ell_t)^{1- \alpha}\\
k_{t+1} = y_t - c_t\end{cases}
It seems to be an important topic given the role of RBC in macro textbooks.