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Consider an economy with n consumers. The utility function of each consumer i is U l = 2log(a:l) + log(G3) and her income is $100. ml is the private good and total public good G = 2;; gi while g is symmetric and price of each unit of public good and private good is $1. (a) Calculate the private provision of public good equilibrium. (b) Calculate the social optimum for the welfare function. (c) What happens to the ratio of the optimum and the equilibrium, GO/Ge, if the population increases