Assume that you have a von Neumann-Morgenstern utility function over lotteries that give you and amount x if Event 1 happens and y if Event 1 does not happen: U(x, y) = p √x + (1-p) √y. (a) If p=0.5, calculate the utility of a lottery that gives you $10,000 if Event 1 happens and $100 if Event 1 does not happen. In addition, calculate the expected income of the lottery. (b) If you were sure to receive $4,900, what would your utility be? (Hint: If you receive $4,900 with certainty, then you receive $4,900 in both events.) (c) Calculate the certainty equivalent (CE) of receiving $10,000 if Event 1 happens and $100 if Event 1 does not happen. Draw a graph to explain your derivation. What is your risk premium?

Assume that you have a von Neumann-Morgenstern utility function over lotteries that give you and amount x if Event 1 happens and y if Event 1 does not happen: U(x, y) = p √x + (1-p) √y. (a) If p=0.5, calculate the utility of a lottery that gives you $10,000 if Event 1 happens and $100 if Event 1 does not happen. In addition, calculate the expected income of the lottery. (b) If you were sure to receive $4,900, what would your utility be? (Hint: If you receive $4,900 with certainty, then you receive $4,900 in both events.) (c) Calculate the certainty equivalent (CE) of receiving $10,000 if Event 1 happens and $100 if Event 1 does not happen. Draw a graph to explain your derivation. What is your risk premium?

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter7: Uncertainty

Section: Chapter Questions

Problem 7.7P

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