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.

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.

Economics For Today

10th Edition

ISBN:9781337613040

Author:Tucker

Publisher:Tucker

Chapter1: Introducing The Economic Way Of Thinking

Section: Chapter Questions

Problem 7SQ

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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, so the budget constraint for each is given by: Xi + 2Pi = 100. Both Jon and David have an income of 100 and a utility function of the form: U = log(Xi) + 2log(Pj + Pd) (a) How much protection, P, will be privately provided? What is optimal consumption of X, the private good? (b) What are the socially optimal amounts of protection, P, and consumption, X, of the private good? How do the socially optimal amounts compare to that privately provided? Explain why.
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