Consider an economy with n consumers. The utility function of each consumer i is Ui = 2log(xi) + log(G3) and her income is $100.xi is the private good and total public good G = ni=1 gi while g is symmetric and price of each unit of public good and private good is $1.

1,Calculate the private provision of public good equilibrium.

2,Calculate the social optimum for the welfare function.

3, What happens to the ratio of the optimum and the equilibrium, Go/Ge, if the population increases.