Public finance

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(Xi) + 2 × log(PJ + PD)
The budget constraint for each is given by:
Xi + 2 × Pi = 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.