Answer the B par Question 4A village has two villagers with an income of £200 each. The village decides to take contributionsto build a new commons. The commons can be of any size, and generates By utility for each of thevillagers if the total contribution is y, where B is a strictly positive real number. Contributions are alsoreal numbers, bounded between 0 and 200. If villager 1 contributes r1 and villager 2 contributes r2,then villager i's utility is 200 – Xi + B (x1 + x2).(a)What are the pure strategy Nash equilibria for each value of 3?The mayor, an LSE trained economist who only values the total utility of the villagers, decides(b)that she will only build the commons if total contributions exceed 80. That is, if r1 + r2 < 80,then citizen i gets utility of 200 – xi, and if xi +r2 > 80, she gets 200 – Xi +B (x1 + x2). Whatis the logic behind the mayor's change? For what values of B would you expect an improvementfrom the change? Explain and justify your answers with game theoretic reasoning.

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Question 4 A village has two villagers with an income of £200 each. The village decides to take contributions to build a new commons. The commons can be of any size, and generates By utility for each of the villagers if the total contribution is y, where is a strictly positive real number. Contributions are also real numbers, bounded between 0 and 200. If villager 1 contributes ₁ and villager 2 contributes x2, then villager i's utility is 200 - x + B(x₁+x₂). (a) What are the pure strategy Nash equilibria for each value of 3? (b) The mayor, an LSE trained economist who only values the total utility of the villagers, decides that she will only build the commons if total contributions exceed 80. That is, if x₁ + x2 < 80, then citizen i gets utility of 200-x, and if x1 + x2 ≥ 80, she gets 200-xi+B (x1+x2). What is the logic behind the mayor's change? For what values of 3 would you expect an improvement from the change? Explain and justify your answers with game theoretic reasoning.

Question 4 A village has two villagers with an income of £200 each. The village decides to take contributions to build a new commons. The commons can be of any size, and generates By utility for each of the villagers if the total contribution is y, where is a strictly positive real number. Contributions are also real numbers, bounded between 0 and 200. If villager 1 contributes ₁ and villager 2 contributes x2, then villager i's utility is 200 - x + B(x₁+x₂). (a) What are the pure strategy Nash equilibria for each value of 3? (b) The mayor, an LSE trained economist who only values the total utility of the villagers, decides that she will only build the commons if total contributions exceed 80. That is, if x₁ + x2 < 80, then citizen i gets utility of 200-x, and if x1 + x2 ≥ 80, she gets 200-xi+B (x1+x2). What is the logic behind the mayor's change? For what values of 3 would you expect an improvement from the change? Explain and justify your answers with game theoretic reasoning.

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter3: Preferences And Utility

Section: Chapter Questions

Problem 3.9P

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