Since both Jon and David will spend all their income , substitute from the budget constraint into the utility function so everything is in terms of P...
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35.

# Since both Jon and David will spend all their income, substitute from the budget constraint into the utility function so everything is in terms of

P. Jon solves the following problem:Max U= log(100 - 2PJ) + 2log(PJ+ PD)The first order condition from this maximization problem is given by:-2/(100 - 2PJ) + 2/( PJ+ PD) = 0a. Solving this for PJ, one finds the following:PJ = 100/3 – 1/3PDb. Solving these two equations for the two unknowns, we find that PD= PJ= 25. So thetotal amount of protection P provided is 50 units. c. This amount of protection will be less than the socially optimal amount of protection caused by the existence of the free-rider problem, resulting in an underprovision of the public good.

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