4. Both Jen and Jack are considering a leisure good, i.e., going to a club with friends. They can do it in
one of four periods, t = 0, 1, 2, 3. The instantaneous utilities are the same for both Jen and Jack: $u_0 =$
1, $u_1 = 4/3$, $u_2 = 12/5$, and $u_3 = 19/6$. Assume that Jen and Jack have the same $\beta = 1/2$ and $\delta = 1$,
Jen's $\hat{\beta} = \beta = 1/2$, and Jack's $\hat{\beta} = 1$, when will Jen go to a club? How about Jack? Does Jen or Jack
pick the best time to go to a club (in terms of utility)?
