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Exercise 2. Public Goods (30 points) Two individuals i E {1, 2} get utility from the consumption of a private good x; and a public good G. The utility functions are given by u(x;, G) = In(x;) + In (G). The two individuals have an income of m; = 1 and can spend the income on the consumption of the private good and the private provision of the public good: mi = Xi + gi. The total amount of the public good is given by G = 91 + 92. (a) Determine all Pareto-efficient allocations and explain the underlying rule. (15 points) (b) Determine the equilibrium of public good provision that will arise when both individuals decide individually (non-cooperatively) how much of the public good to provide. Is this allocation efficient? (15 points)