2 Public goods Suppose the production possibilities frontier for an economy that produces one public good (x) and one private good (y) is given by 100x2 + y2 = 5000 . This economy is populated by 100 identical individuals, each of whom has a utility function given by: U(x,yi) = Vxyi, where yi is the individual's share of private good production (= y/100). Notice that the public good is nonexclusive and that everyone benefits equally from its production. (a) If the market for x and y were perfectly competitive, what levels of those goods would be produced? [Hint: Consider a point of tangency between the slopes of the production possibilities frontier and a typical individual's indifference curve.] (b) What would be the typical individual's utility given the scenario in part (a)? (C) What are the socially optimal production levels for x and y? [Hint: Your solution will involve the sum of the individuals' marginal rates of substitution.] What would be the typical individual's utility in this instance? (d) How should consumption of good y be taxed to achieve the result in part (c)? (e) Explain how the private provisioning of public goods (in general) might be characterized as a type of prisoner's dilemma problem. 2 Public goods Suppose the production possibilities frontier for an economy that produces one public good (x) and one private good (y) is given by 100x2 + y2 = 5000 . This economy is populated by 100 identical individuals, each of whom has a utility function given by: U(x,yi) = Vxyi, where yi is the individual's share of private good production (= y/100). Notice that the public good is nonexclusive and that everyone benefits equally from its production. (a) If the market for x and y were perfectly competitive, what levels of those goods would be produced? [Hint: Consider a point of tangency between the slopes of the production possibilities frontier and a typical individual's indifference curve.] (b) What would be the typical individual's utility given the scenario in part (a)? (C) What are the socially optimal production levels for x and y? [Hint: Your solution will involve the sum of the individuals' marginal rates of substitution.] What would be the typical individual's utility in this instance? (d) How should consumption of good y be taxed to achieve the result in part (c)? (e) Explain how the private provisioning of public goods (in general) might be characterized as a type of prisoner's dilemma