Question

Please solve this

2. 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.

Answer 1