Gavin Jones’s friend is planning to invest $1 million in a rock concert to be held 1 year from now. The friend figures that he will obtain $2.8 million revenue from his $1 million investment—unless it rains. If it rains, he will lose his entire investment. There is a 50% chance that it will rain the day of the concert. Gavin suggests that he buy rain insurance. He can buy one unit of insurance for $0.50, and this unit pays $1 if it rains and nothing if it does not. He may purchase as many units as he wishes, up to $2.8 million. (a) What is the expected rate of return on his investment if he buys u units of insurance? (The cost of insurance is in addition to his $1 million investment.) (b) What number of units will minimize the variance of his return? What is this minimum value? And what is the corresponding expected rate of them? [Hint: Before calculating a general expression for variance, think about a simple answer.]

Gavin Jones’s friend is planning to invest $1 million in a rock concert to be held 1 year from now. The friend figures that he will obtain $2.8 million revenue from his $1 million investment—unless it rains. If it rains, he will lose his entire investment. There is a 50% chance that it will rain the day of the concert. Gavin suggests that he buy rain insurance. He can buy one unit of insurance for $0.50, and this unit pays $1 if it rains and nothing if it does not. He may purchase as many units as he wishes, up to $2.8 million. (a) What is the expected rate of return on his investment if he buys u units of insurance? (The cost of insurance is in addition to his $1 million investment.) (b) What number of units will minimize the variance of his return? What is this minimum value? And what is the corresponding expected rate of them? [Hint: Before calculating a general expression for variance, think about a simple answer.]

Managerial Economics: A Problem Solving Approach

5th Edition

ISBN:9781337106665

Author:Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor

Publisher:Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor

Chapter17: Making Decisions With Uncertainty

Section: Chapter Questions

Problem 17.1IP

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