Risk attitude towards monetary gains or losses x

[axokappa06]

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Suppose that a decision maker’s risk attitude toward monetary gains or losses x given by the utility function u(x)=(10,000+X)^(1/2)[/FONT][FONT=&quot] . Suppose that a decision maker has been given a lottery ticket for free. Suppose that the lottery winning is $500,000, and the chance of winning is one in a thousand. What is the minimum price that the decision maker would be willing to sell the ticket for?

I was able to follow along with the other post ([/FONT]https://www.freemathhelp.com/forum/...risk-attitude-toward-monetary-gains-or-losses[FONT=&quot]) but I am having issues solving for what we should sell the ticket for. [/FONT]

 

[JeffM]

Suppose that a decision maker’s risk attitude toward monetary gains or losses x given by the utility function u(x)=(10,000+X)^(1/2) . Suppose that a decision maker has been given a lottery ticket for free. Suppose that the lottery winning is $500,000, and the chance of winning is one in a thousand. What is the minimum price that the decision maker would be willing to sell the ticket for?

I was able to follow along with the other post (https://www.freemathhelp.com/forum/...risk-attitude-toward-monetary-gains-or-losses) but I am having issues solving for what we should sell the ticket for.

The previous question asked whether someone with a specific utility function relative to risk should buy the ticket.

You are now asking the way more complicated question of what is the RIGHT price at which someone should sell such a ticket. Going back to Aristotle, the ethical answer under commutative justice is the market price, provided that neither the seller nor buyer can materially affect the price. Distributive justice has no answer for buyers and sellers who can affect the market price. Moreover, sellers who can affect the price in an otherwise competitive market need information on the distribution of utility functions among potential punters.