Answer to Question #262577 in Microeconomics for queen

Question

Natalie entered a raffle recently and never checked her tickets. She has recently learned the exact number of the other unchecked tickets. Based on this information she knows that there is a 40% chance that she has won the raffle prize of $1,600. If she does not win the raffle her wealth will be zero. Natalie has a von Neumann–Morgenstern utility such that she wants to maximize the expected value of √c, where 𝑐 is total wealth.

What is the minimum price for which Natalie would sell her raffle tickets?  

Answer 1

Here the wealth she won as a raffle prize=4900

expected utility $=\sqrt{4900}=70$

Also if she wouldn't win, the she would loose all her wealth

$\therefore EU=0$

so, expected utility $=\frac{10}{100}\times \sqrt4900=7$

And at price p, if she sells the ticket, her expected utility $=\sqrt p$

so, if she sells he that raffle ticket:-

hence, condition $\sqrt p\ge7\space \therefore p\ge49$

so minimum price =$49