14. A society consists of 2 identical individuals who derive utility from a public good. The public good can be provided at a constant marginal cost of 6. Let x1 and x2 denote the level of public good provision by 1 and 2 respectively and let X denote the total provision of the public good. The net benefit enjoyed by individual i from providing x; units of the public good is given by Ui(x;, X) = -=(10- X)2 - 6xi where i = 1, 2. (a) Derive the socially optimal level of provision of the public good. [6 marks] (b) If every individual optimally chooses how much public good to provide, derive the total level of provision of the public good. [7 marks] (c) Suppose n > 1 new individuals arrive in the society. The net benefit en- given by joyed by new individual j from providing x; units of the public good is Vi( x ; , X ) = =(9-x)2 -6x; Suppose every individual optimally chooses how much public good to provide. Does the total level of public good provision change compared to part (b) as a result of the new arrivals? Explain your answer. [7 marks]