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 consume both good X, a private good, and the protection from the fort, P. One unit of good X costs 1 unit while one unit of P costs 2 units. 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