Amold and Betty have identical marginal benefit formulas for a public good. The MBs are given...

 

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Amold and Betty have identical marginal benefit formulas for a public good. The MBs are given by: MB, = a(Y, +q,)- BQ* MB, = a(Y, +q.)- BQ* where, Q* = 9,+9, a and ß are constant positive numbers, a<1. YA, Ys, are incomes of Arnold and Betty. qa, , are purchases of the public good by Amold and Betty. The marginal cost of a unit of the public good is constant: MC=C. a. As in lecture, determine the best response functions for Armold and Betty. Suppose now that a-.5, -5, YA-Yu=200, and MC=10. b. What is the strategic equilibrium quantity of the public good that gets produced? c. What is the socially optimal quantity of the public good that gets produced? d. Claim: as the slope of the MB curve gets steeper, the difference between the strategic equilibrium and the socially optimal quantity increases. Agrec or disagree. How do the formulas help you answer the question? In words briefly explain the economics of this result. Amold and Betty have identical marginal benefit formulas for a public good. The MBs are given by: MB, = a(Y, +q,)- BQ* MB, = a(Y, +q.)- BQ* where, Q* = 9,+9, a and ß are constant positive numbers, a<1. YA, Ys, are incomes of Arnold and Betty. qa, , are purchases of the public good by Amold and Betty. The marginal cost of a unit of the public good is constant: MC=C. a. As in lecture, determine the best response functions for Armold and Betty. Suppose now that a-.5, -5, YA-Yu=200, and MC=10. b. What is the strategic equilibrium quantity of the public good that gets produced? c. What is the socially optimal quantity of the public good that gets produced? d. Claim: as the slope of the MB curve gets steeper, the difference between the strategic equilibrium and the socially optimal quantity increases. Agrec or disagree. How do the formulas help you answer the question? In words briefly explain the economics of this result.

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a Arnold would maximize 1 MB A q A Cq A Y A q B q A q A q B q A Cqa FOC d 1dq A 0 ie Y A q B 2 q A q ... View the full answer