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Microeconomics, Microeconomics

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Five identical people live in a small town and can earn a living either by having cattle $100 or by becoming a singer. If one person competes their expected payment is 210, if two compete then it is 340, 3 people = 450, 4 people = 500, 5 =550. The expected payoff for one contestant is 210, for two it''s 170, for 3 it''s 150, for 4 it''s 125, and for 5 it''s 110. How many villagers will compete to become a singer? What will be the total income of the villagers? What is the socially optimal number of villagers to enter the competition? How much would village income be if only the optimal number entered?

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