3. Consider a risk-averse individual with utility function VW where W denotes we

Question

3. Consider a risk-averse individual with utility function VW where W denotes wealth, owning a lottery ticket with prizes dependent on the tossing of a fair coin (50% chances to fall on either side) and promising 4 or 64 if head or tail, respectively. Suppose he has no other wealth (i) What is the minimum price he wl be willing to sell the ticket for? (ii) Suppose that in addition to owning the first lottery ticket he can now purchase the ticket for another lottery associated to exactly the same coin tossing but promising to pay 30 and -30 if head or tail, respectively Assuming he can borrow the necessary amount at an interest rate of 1, how much he be willing to pay for this ticket? (iii) Suppose now that he can sold the first ticket for a prices equal or higher than the certainty equivalence. How much will he be willing to pay, if any, for the second ticket?

Explanation / Answer

(i) Expected utility from the ticket = 0.5 * squareroot(4) + 0.5 * squareroot(64) = 0.5*2 + 0.5*8 = 5

Since U = squareroot(W)

W = U2

Therefore, the certainty equivalent of the lottery = W(certainty) = (5)2 = 25

This is the certain value equivalent to the expected utility of the lottery. So, the minimum amount he will be willing to sell the ticket at is 25.

ii) Expected utility from the other ticket = squareroot(30) - squareroot(30) [negative value of 30]

= 0

Therefore the certainty equivalent of this lottery is also 0.

So, he will not buy the lottery if he can borrow money at 1% rate of interest to buy the lottery.

iii) even if he can sell the first lottery at a price above its certainty equivalent, the person will not buy the other lottery since his expected utility from the first lottery is higher and he is risk averse. He will rather keep the first lottery than sell it to purchase the other lottery.

Related Questions

Navigate

• Browse (All)
• Browse 3
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.