(20 pts) Consider aneconomy with n consumers. The utility function of each consumer i is U "' = 2log($') + 109(03) and her income is $100. a: is the private good and total public good 0' = Ze=1 g while 9 is symmetric and price of each unit of public good and private good is $1. (a) Calculate the private provision of public good equilibrium. (7 pts) (b) Calculate the social Optimum for the welfare function. (6 pts) (c) What happens to the ratio of the optimum and the equilibrium, Go/Ge, if the p0pulation increases. (7 pts)