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?

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Problem 3. Carol's risk preference is represented by the following expected utility formula: U(T, C₁; 1 T, C₂) = π √√ √₁+ (17) √√C₂. i) Suppose Carol is indifferent between the following two options: the first option A returns $100 with probability and $X with probability, and the second option B returns $49 for sure. Determine X. ii) Consider the following three lotteries: L₁ = (0.9, $100; 0.1, $49), L2 = (0.7, $225; 0.3, $49), and L3= (0.5, $400; 0.5, $0). What is the ranking of these lotteries for Carol? Calculate the risk premiums of these lotteries for Carol. 1
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