Suppose that two individuals, Jon and David, form a community and would like to construct a communal fort that would protect them from attacks. They both consume good X, a private good, and the protection of the fort, P. One unit of good X costs 1 unit of currency, and one unit of P costs 2 units of currency. Both Jon and David have an income of 100 and a utility function of the form: U = log(X_i) + 2 log(P_J+ P_D) The budget constraint for each is given by: X_i+ 2 P_i= 100 (a) Find the amount of protection Jon will provide as a function of how much David provides, and explain why the relationship is the way it is. (b) How much protection P will be privately provided in this case? (c) Explain the economic intuition behind this amount, and compare it to the socially optimal amount without solving for the socially optimal amount.