What is the pareto efficient size for the town skating rink


Problem

Just north of the town of Muskrat, Ontario, is the town of Brass Monkey, population 700. 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, Y) = X_i - 121/Y, where X_i 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 $7 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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Microeconomics: What is the pareto efficient size for the town skating rink
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