7

Public Goods [20 points} Some analysts see the North Atlantic Treaty Organization (NATO) as a provider of a public good called "common security\" to its members. Suppose we measure security in terms of amounts of military force, units of which we represent by the variable G. Units of this military good must be jointly consumed by three member governments, A, B, and C, which have the following respective utility functions over G and total dollars left over for spending on all other goods (at): Unlm, x} = 4ln{G} + x Ualm, x] = 32[|n[4G)] + at Uclm, it] = 4662 + x where In{] is the natural logarithm function, G is the amount of iointly consumed military goods, and it is dollars spent on all other goods. Note that in the above, government (I attaches a negative utility to military goods [i.e., government C is a probably a very pacifistic government). Because of how it is dened, the dollar price per unit of): is fixed at pJlt = $1. . (10 points] Suppose that each government was to be charged the separate prices p5\