Problem 6. Suppose you have to pay $2 for a ticket to enter a competition. The prize is $19 and the probability that you win is 1/3. You have an expected utility function with u(x) = log x and your current wealth is $10. (a) What is the certainty equivalent of this competition? (b) What is the risk premium? (c) Should you enter the competition?
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This function is used to calculate the utility or satisfaction that a person gets from different levels of wealth. Show more…
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Andrew D.
Suppose you have to pay $2 for a ticket to enter a competition. The prize is $19 and the probability that you win is 1/3. If you lose, you don't get back anything. You have an expected utility function with u(w) = log(w) and your current wealth is $10. Should you enter the competition? Yes or no?
Sri K.
As in the previous exercise, consider an initial wealth of 10 and the lottery X̃. Assume now that the utility is: u = { w for w ≤ 10, 1/2w + 5 for w ≥ 10. (a) Draw the utility function. Is it globally concave? (b) Compute the certainty equivalent and the risk premium attached to X̃. (c) Can you apply the Arrow–Pratt approximation? Why? (d) Consider now the lottery Ỹ defined in exercise 1.1. Compute the risk premium attached to Ỹ. Is it smaller than for X̃? Why? (e) Answer (b) and (d) above if the individual has an initial wealth of 20. How do the risk premia for X̃ and Ỹ compare?
Rashmi S.
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