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.

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