Econ HW - Expected Value

[tabako]

Dice: EV = 1(1/6) + 2(1/6) + 3(1/6) + 4(1/6) + 5(1/6) + 6(1/6) = 3.5

If you sell the ticket for price P, you now have (100 + P) dollars. Your utility is now (100 + P)^2.

If you keep the ticket, 25% of the time you hit for $10 and now have $110. 75% of the time you stay at $100.

Your utility here is: (.25)(110)^2 + (.75)(100)^2

You are willing to sell the ticket if your utility from selling is >= to the expected utility from holding on to the ticket. The least you will sell it for is when the two are exactly the same. So solve:

(100 + P)^2 = (.25)(110)^2 + (.75)(100)^2
10000 + 200P + P*P = 10525
P^2 + 200P - 525 = 0

P = $2.59

This is slightly larger than the solution of $2.50, which makes sense if you think about it.