Public Econ

Two individuals have identical utility functions defined on X, a private good (cookies), and F, a public good (fireworks). Define as F = F1 + F2 where Fi the contribution of individual i, and Ui = log(6Xi)+log(F1 +F2) with budget Xi + 3Fi = 120.

(a) Find the socially optimal level of contributions to the public good.
(b) Find the individually optimal level of contributions to the public good.