1. This question extends Question #3 of Problem Set 3. There are two goods, apples (A) and bananas (B), which are each sold in perfectly competitive markets with no pre-existing distortions. The supply and demand curves for apples are the same as before: P (qa) = 20 9A , P: (qa) = 4 + 9A The demand curve for bananas is identical, but unlike apples, bananas can be produced at a constant marginal cost of c = 8: PB (9B) = 20 9B , P (9B) = 8 Assume that apples and bananas are neither complements nor substitutes, so any tax imposed on one good does not affect demand for (or supply of) the other good. (a) Find the competitive equilibrium price and quantity of bananas. (b) Calculate the deadweight loss DW LB(TB) and revenue Rb(TB) generated by a per- unit tax of TB on bananas. Suppose that, as in PS3 #3, the benefit of revenue generated by taxes is B(R) $1.25 R. Now, revenue can come from taxing both apples and bananas. (c) Find the optimal tax rates (ATB) using the optimality conditions DW L'A(TA) DW LB(TB) B'(R(TA,TB) 1= R'A(TA) Rb(TB) (d) Explain, in words, why optimal commodity tax rates must satisfy the above equations. (e) Discuss how differences in the supply and demand curves for bananas (compared to applies) leads to the difference in optimal tax rates for the two goods. Now suppose banana eaters throw the banana peels on the ground, causing others to slip and fall. Neither producers nor consumers take this damage into account. As a result, the production of bananas generates a negative externality of $1 per unit. There are still no externalities associated with applies. (f) How does your answer to part (c) change in the presence of this externality? Assume that the social benefit from government revenue is still B(R) = 1.25 ~ R. 1. This question extends Question #3 of Problem Set 3. There are two goods, apples (A) and bananas (B), which are each sold in perfectly competitive markets with no pre-existing distortions. The supply and demand curves for apples are the same as before: P (qa) = 20 9A , P: (qa) = 4 + 9A The demand curve for bananas is identical, but unlike apples, bananas can be produced at a constant marginal cost of c = 8: PB (9B) = 20 9B , P (9B) = 8 Assume that apples and bananas are neither complements nor substitutes, so any tax imposed on one good does not affect demand for (or supply of) the other good. (a) Find the competitive equilibrium price and quantity of bananas. (b) Calculate the deadweight loss DW LB(TB) and revenue Rb(TB) generated by a per- unit tax of TB on bananas. Suppose that, as in PS3 #3, the benefit of revenue generated by taxes is B(R) $1.25 R. Now, revenue can come from taxing both apples and bananas. (c) Find the optimal tax rates (ATB) using the optimality conditions DW L'A(TA) DW LB(TB) B'(R(TA,TB) 1= R'A(TA) Rb(TB) (d) Explain, in words, why optimal commodity tax rates must satisfy the above equations. (e) Discuss how differences in the supply and demand curves for bananas (compared to applies) leads to the difference in optimal tax rates for the two goods. Now suppose banana eaters throw the banana peels on the ground, causing others to slip and fall. Neither producers nor consumers take this damage into account. As a result, the production of bananas generates a negative externality of $1 per unit. There are still no externalities associated with applies. (f) How does your answer to part (c) change in the presence of this externality? Assume that the social benefit from government revenue is still B(R) = 1.25 ~ R