4. Let's consider two goods: x1 = pizza and x2 = beer. Tim's utility function over these two goods is U (x1, x2) = x1 + x2.

(a) Given prices, p1, p2, and income m, write down the Lagrangian and the first order conditions.

(b) Derive the optimal choices x1 and x2 in terms of the given parameters of the problem.

(c) What share of income does Tim spend on each good?

(d) Scott's utility function is U (x1, x2) = 50x1 + 50x2. Go through the same steps (parts b-d) for solving Scott's constrained maximization problem.

(e) Are Tim and Scott's choices different? Why or why not?