2. Consider a town with two people, Bill and Ted. Bill's demand for tennis courts is given by Q 30-5P and Ted's demand for tennis courts is given as Q = 12 - 2P. The marginal cost of providing tennis courts is constant at $3. a. Suppose the tennis courts are a private good. Derive the market demand curve (social marginal benefit curve) and find the equilibrium quantity. (30 - 5P) + (12 - 2P) = 3 42 - 7P = 3 -7P = -39 P = approximately 5.57 Insert P into Bill or Ted's equation: Bill: Q 30-5(5.57) = approximately 2.15 optimal quantity of tennis courts Ted: 12 - 2(5.57) .86 optimal quantity of tennis courts b. Suppose the tennis courts are a public good. Derive the social marginal benefit curve and find the optimal quantity of the public good. = = =

2. Consider a town with two people, Bill and Ted. Bill's demand for tennis courts is given by Q 30-5P and Ted's demand for tennis courts is given as Q = 12 - 2P. The marginal cost of providing tennis courts is constant at $3. a. Suppose the tennis courts are a private good. Derive the market demand curve (social marginal benefit curve) and find the equilibrium quantity. (30 - 5P) + (12 - 2P) = 3 42 - 7P = 3 -7P = -39 P = approximately 5.57 Insert P into Bill or Ted's equation: Bill: Q 30-5(5.57) = approximately 2.15 optimal quantity of tennis courts Ted: 12 - 2(5.57) .86 optimal quantity of tennis courts b. Suppose the tennis courts are a public good. Derive the social marginal benefit curve and find the optimal quantity of the public good. = = =

Microeconomics A Contemporary Intro

10th Edition

ISBN:9781285635101

Author:MCEACHERN

Publisher:MCEACHERN

Chapter17: Externalities And The Environment

Section: Chapter Questions

Problem 10PAE

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Just north of the town of Muskrat, Ontario, is the town of Brass Monkey, population 6900. Brass Monkey, like Muskrat, has a single public good, the town skating rink, and a single private good, Labatt Ale. Everyone's utility function is U i = X i - 81 Y where x; is the number of bottles of ale consumed by i and Y is the size of the skating rink in square meters. The price of ale is $1 per bottle. The cost of the skating rink to the city is $6 per square meter. Everyone has an income of at least $5,000. What is the Pareto efficient size for the town skating rink?
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