Suppose That Two Individuals,Jon and David,form a Community and Would

question 20

Essay

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.

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