2. One version of a family's common preferences utility function can be
$U(c_m, c_f) = c_m^\alpha c_f^{1-\alpha}$
Where $c_m$ and $c_f$ are the consumption of the family's product (Z) for person m and
person f, respectively.
a If the family wants to choose $c_m$ and $c_f$ to maximize their utility subject to budget
constraint $Z_{mf} = c_m + c_f$, solve for their optimal choice of consumptions.
b Using the results from Weiss's model (solved in lecture and the reading) that an
individual i's consumption of Z outside of marriage is $\frac{1}{4}w_i$, and the couple's total
married consumption is max$(w_m, w_f)$, find the gains from marriage for both parties
if $w_m - w_f = w$ (your answer will be in terms of w and $\alpha$).
