National defense is a good that is nonexcludable and nonrival in consumption. Suppose that instead of national defense being paid for with tax dollars national defense is paid for by voluntary contributions from (potentially) all individuals within Latvia. Cedric, who is a Latvian citizen, must decide whether he wants to contribute to the national-defense budget. Further, suppose that there are a total of 10 citizens, including Cedric. For the optimal amount of safety, each citizen should pay $10$10 . Every $1$1 contributed (by anyone) to the national defense leads to increased security, which each person values at $0.20$0.20 . This means that every dollar spent on defense is worth $2.00$2.00 to Latvia as a whole. How much does Cedric personally value the increase in national defense when he contributes $10$10 to the defense fund? Cedric's personal value: $ If contributions are voluntary, and assuming people rationally maximize their utility, what is the total contributed to national defense? total contributed voluntarily: $ Suppose that instead of relying on voluntary contributions the government simply levies a tax of $10$10 on each person to pay for national defense. How much better or worse off would Cedric be if everyone (including himself) were taxed $10$10 instead of contributing voluntarily? If Cedric is worse off, be sure to put a negative sign in front of the number. Cedric's gain or loss under tax: $