Suppose that your current wealth is $3000 and you have logarithmic utility. You are offered an investment that costs $750 today. The investment will either pay off $1500 with probability p, or nothing with probability 1 – p. (a) Should I invest if p = 0.5? (b) What is the minimum value of p that would induce me to invest? Please round your answer to two decimal places. p = (c) Now suppose that I have power utility with a>1. Will your answer to (b) increase or decrease?

A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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Suppose that your current wealth is $3000 and you have logarithmic utility. You are offered an investment that costs $750 today. The investment will
either pay off $1500 with probability p, or nothing with probability 1 – p.
(a) Should I invest if p = 0.5?
(b) What is the minimum value of p that would induce me to invest? Please round your answer to two decimal places.
p =
(c) Now suppose that I have power utility with a>1. Will your answer to (b) increase or decrease?
Transcribed Image Text:Suppose that your current wealth is $3000 and you have logarithmic utility. You are offered an investment that costs $750 today. The investment will either pay off $1500 with probability p, or nothing with probability 1 – p. (a) Should I invest if p = 0.5? (b) What is the minimum value of p that would induce me to invest? Please round your answer to two decimal places. p = (c) Now suppose that I have power utility with a>1. Will your answer to (b) increase or decrease?
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