Max is thinking of starting a pinball palace near a large Melbourne university. His utility is given by u(W) = 1 - (5,000/W), where W is his wealth. Max's total wealth is $15,000. With probability p = 0.7 the palace will succeed and Max's wealth will grow from $15,000 to $x. With probability 1 - p the palace will be a failure and he’ll lose $10,000, so that his wealth will be just $5,000. What is the smallest value of x that would be sufficient to make Max want to invest in the pinball palace rather than have a wealth of $15,000 with certainty?

Max is thinking of starting a pinball palace near a large Melbourne university. His utility is given by u(W) = 1 - (5,000/W), where W is his wealth. Max's total wealth is $15,000. With probability p = 0.7 the palace will succeed and Max's wealth will grow from $15,000 to $x. With probability 1 - p the palace will be a failure and he’ll lose $10,000, so that his wealth will be just $5,000. What is the smallest value of x that would be sufficient to make Max want to invest in the pinball palace rather than have a wealth of $15,000 with certainty?

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter7: Uncertainty

Section: Chapter Questions

Problem 7.3P

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Max Pentridge is thinking of starting a pinball palace near a large Melbourne university. His utility is given by u(W) = 1 - (5,000/W), where W is his wealth. Max's total wealth is $10,000. With probability p = 0.9 the palace will succeed and Max's wealth will grow from $10,000 to $x. With probability 1 - p the palace will be a failure and he’ll lose $5,000, so that his wealth will be just $5,000. What is the smallest value of x that would be sufficient to make Max want to invest in the pinball palace rather than have a wealth of $10,000 with certainty? ____ (Please round your final answer to the whole dollar, if necessary)
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