14. A society cmsists 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 11 and :2 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 benet enjoyed by individual i from providing 1; units of the public good is given by vines) = no s12 ex.- wherei = 1,2. {a} Derive the socially optimal level of provision of the public goothi marks] {b} If every individual optimally chooses how much public good to provide, derive the total level of provision of the public good. [T marks] {c} Suppose a or 1 new.r individuals anive in the society. The net benefit en joyed by new individual j from providing 1:,- units of the public good is given by 1 tests) = is X)? 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. ['3 marks]