<p>Not a big fan of solving homework questions, but here is a hint:</p>

<p>Suppose you are selling the lottery for price $P$. Then your wealth would be $Y'=10+P$. You are looking for the minimum price $P$ such that 
$$U(10+P)  \geq \pi U(10+10)+(1-\pi)U(10+5).$$</p>

CC BY-SA 3.0
2017-01-16T17:27:52.003Z
I see so we are essentially solving for $P$ in the equation $$\sqrt{10+P} = \pi \sqrt{20} + (1-\pi)\sqrt{15}$$?
Wolfy
CC BY-SA 3.0
2017-01-16T00:27:47.933Z
2017-01-16T00:27:47.933Z
Bayesian
<blockquote>
  <p>Say you have the expected utility index $U(Y ) = \sqrt{Y}$ and an initial
  wealth $Y = 10$. Consider the lottery with a payoff of $10$ with probability $\pi\in (0,1)$ and a payoff of $5$ with probability $1-\pi$ Note: Derive general expressions in $\pi$ and then use $\pi = 0.5$ to get specific answers.</p>
  
  <p>If you own this lottery, what is the minimum price and maximum price you would be willing to sell it for?</p>
</blockquote>

<p>I am not sure how to proceed any suggestions are greatly appreciated</p>

<utility><financial-economics>
Finding the minimum and maxium price given utility index
Wolfy
# Finding the minimum and maxium price given utility index

(Asked by: username_0 on 2017-01-15)

> Say you have the expected utility index $U(Y ) = \sqrt{Y}$ and an initial
> wealth $Y = 10$. Consider the lottery with a payoff of $10$ with probability $\pi\in (0,1)$ and a payoff of $5$ with probability $1-\pi$ Note: Derive general expressions in $\pi$ and then use $\pi = 0.5$ to get specific answers.
>
> If you own this lottery, what is the minimum price and maximum price you would be willing to sell it for?

I am not sure how to proceed any suggestions are greatly appreciated

**Tags:** utility, financial-economics

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## 1 answers

### Answer by username_1 on 2017-01-16. Score: 1 | Accepted answer

Not a big fan of solving homework questions, but here is a hint:

Suppose you are selling the lottery for price $P$. Then your wealth would be $Y'=10+P$. You are looking for the minimum price $P$ such that
$$U(10+P) \geq \pi U(10+10)+(1-\pi)U(10+5).$$

> **Comments:**
> **username_0**: I see so we are essentially solving for $P$ in the equation $$\sqrt{10+P} = \pi \sqrt{20} + (1-\pi)\sqrt{15}$$?  

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