Problem 1
Spyros has preferences expressed by a Cobb-Douglas utility function,
$U(q_1, q_2) = q_1^a q_2^{1-a}$. He wants to maximize his utility choosing his optimal
consumption of $q_1$ and $q_2$ keeping in mind he wants to spend all his
income, Y, that the price of the two goods are $p_1$ and $p_2$, respectively.
Solve for the optimal consumption of the two goods, $q_1^*$ and $q_2^*$, using the
Lagrangian method.
